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1. Total Noise 1E 07 120 5E 08 Dark Noise 115 3E 08 2E 08 1E 08 l l l l l L 110 1E 03 2E 03 5E 03 1E 04 2E 04 5E 041E 05 2E 05 5E 05 1E 06 Frequency Hz 1 Hz Noise V 1 Hz CNR 3E 07 E3dB 2 5E 07 2 106 2E 07 1 5E 07 lt a Total Noise 1 106 1E 07 5E 08 Dark Noise 0E 00 0 OE 00 5E 04 1E 05 1 5E 05 2E 05 2 5E 05 Frequency Hz Figure 18 7 Noise performance of the transimpedance amplifier of Figure 18 3 showing the dominance of dark noise i e additive circuit noise at high frequency At right the same data plotted on linear scales This shows the true character of the evamp problem 18 4 TRANSIMPEDANCE AMPLIFIERS 699 18 4 3 Choosing the Right Op Amp In order that the op amp not dominate the noise choose it by the following rules worst case specifications apply l iNamp lt 0 5intn We ve chosen Ry so as to lose no more than 1 dB to Johnson noise so don t mess it up by choosing an amp whose current noise is as big or bigger than R s 2 Namp lt 0 Se yin Similarly we don t want the amplifier s voltage noise to dominate under any circumstances 3 namp lt 0 5inun 27 f_3aap Ca Cin This ensures that the rising noise current due to Namp doesn t begin to dominate anywhere in the band we care about Cin is included explicitly here as a memory jogger it always has to be added in
2. 4 fr gt 2 a fec The amplifier has to be fast enough to raise the bandwidth sufficiently 5 fr lt 10 a fec Going too fast is asking for trouble The size of the noise peak will be so large that extensive filtering will be needed to get rid of it and the circuit may even oscillate 6 If finding an amp that satisfies Rules 1 4 runs into money either spend it or use a circuit hack to get round it Don t economize here 7 It is not always necessary to use a unity gain stable amplifier because of the C4 R gain peak but watch the frequency compensation extra carefully if you don t Using a decent part which has guaranteed specifications for noise and gain bandwidth usually pays for itself many times over by the relaxation this permits in the specs of the optical system Use worst case design here and leave a safety margin especially on Namp The log log plots are deceiving if vamp dominates only near the high end that is as bad as dominating over the whole band because there s a lot more high end than there is low end Table 18 3 lists some good op amps for use in photodiode front ends The exact circumstances in which each is superior are somewhat complicated try the low voltage noise ones with bright light and the low current noise ones at low light Remember that op amp input capacitance has the same effect as photodiode capacitance so that the musclebound FET units with the high Cin are not as universally usef
3. 18 22 OL T j2nBkTCa elc eae Similarly the total input referred noise current is o 2eUc B la 2 el kT 27 f Ca 18 23 we ve ignored the distinction between 6 and 6 1 that circuit instructors so often insist on and have assumed that the small and large signal betas are the same that is l c g Ic Ip At low frequency the 1 Hz SNR is 1 Ic B Ia times worse than the shot noise so we need to limit Ic lt eB for some e which we do by pulling 1 e times with a current sink in a feedback loop making e a convenient optimization parameter To stay within 1 dB of the shot noise lt 0 25 The noise doesn t start to rise until the two terms in 18 23 become comparable that is at fx elav peU e vpe e 18 24 2zkT Ca For 0 13 0 5 dB above shot noise 1000 I4 2 A and Ca 100 pF fy 1 49 MHz which is slightly better than the bootstrapped cascode result as expected This method takes a fair amount more engineering than the cascode TIA because there s the whole current feedback loop to design including getting its transient response temperature compensation output drive and supply rejection right but there s another quarter turn of the crank to be had if you really need it 18 4 13 Choosing Transistors The cascode and its variants can provide a huge performance gain but only if the devices and operating parameters are appropriately chosen Fortunately there
4. Be exhorted you really can predict the noise floor accurately to accept a noisy front end is one of the stupidest and most expensive mistakes you can make in designing sensitive optical instruments Measure it and make sure you can explain every half decibel Don t Use 50 amp Unless You re Driven to It Amplifiers with 50 Q inputs are all over the place but they shouldn t be in your front end unless there s a reactive matching network in front of them or your photocurrent is at least 1 mA Long haul fiber optic communications people use a lot of 50 amp amplifiers but they struggle for every fraction of a decibel so that lets them off the hook Provide a DC Output It is very useful to provide a DC output from a detector for setup alignment and troubleshooting If there s too much gain to allow straight DC coupling without railing an amplifier somewhere make the DC gain lower or send the DC to an auxiliary output just don t get rid of it altogether or you ll wish you hadn t Use Feedback Tee Networks We re accustomed to ignoring the noise of the second and subsequent stages of an amplifier chain and this is fine as long as the front end has high enough gain A transimpedance amplifier has a noise gain of 1 for noise other than Namp and capacitance limits how big we can make Ry so the second stage noise can easily dominate if we re not careful Use a quiet amplifier for the second stage or put a tee
5. 1E 01 VG 2 000 18 02 L CE 1 000 1E 02 1E 03 1E 04 1E 05 1E 06 1E 07 1E 08 Frequency Hz Figure 18 5 Performance of the transimpedance amplifier 18 4 TRANSIMPEDANCE AMPLIFIERS 697 Cf Rf i Nth i Ns i Namp ug s S Namp Figure 18 6 Simplified noise model of the transimpedance amplifier All noise sources except Namp are treated exactly as the photocurrent and shot noise so that only eNamp changes the SNR The only noise source that is treated differently is the amplifier s voltage noise yamp Because the amplifier amplifies only differential signals i e those in which its inputs move in opposite directions the model noise source can be put in either input lead Here we put it in the noninverting lead which simplifies the analysis clearly vamp will be multiplied by the noninverting gain of the amplifier AycL which is therefore the noise gain of the stage See Section 13 1 Taking Zf as the complex impedance of the feedback element Ry in parallel with Cf Avot AvoL 1 joCaZ r sap 18 11 For frequencies well within the loop bandwidth the resulting equivalent noise current is approximately in 2z f Cp enamp 18 12 This gain begins to rise at the RC corner frequency of Cg and Ry just where the signal rolloff would have begun if we were using a simple load resistor approach in fact the SNR as a function of frequency is identical to that of the same amplifier connected as a buf
6. Cr _ gt i 2x Rr fr fre which gives a phase margin of between 45 and 60 depending on how fast the amplifier is An alternative is to put a small resistor R in series with the photodiode where R is 18 8 1 Ra 18 9 21 Cay fr fre a In complex variables language these additions put a zero into the transfer function see Section 15 4 3 The exact value of R or Cy that gives the optimal trade off of peaking versus bandwidth for your application depends on what you are most interested in so take these values as starting points Beware of device to device variations in Cg and GBW if you re making more than one or two copies If you crank Cy down to the 696 FRONT ENDS absolute lowest tolerable value in your lab prototype Murphy s law dictates that the next 100 photodiodes will be at the upper spec limit for capacitance and all 100 circuits will oscillate merrily It is axiomatic that all prototypes contain at least one perfect component which works beautifully but is totally unrepresentative of normal production units Although the approximation 18 6 f_3 ap fcL 2 is good enough for early design purposes it is worthwhile to carefully plot the frequency response of the transimpedance because it hasn t the same shape as the closed loop gain With the approximate expression 18 3 for the op amp s gain the transimpedance is given by AvoLZf Zm P L 1 Avon j2z f Ca Z
7. 14 1 for more none of the circuits in this chapter will work properly without quiet bias supplies Even more insidiously noise can come in via the power supply leads of your op amps Op amps have power supply rejection PSR ratios of 60 dB or more near DC but it rolls off at higher frequencies Linear voltage regulators can exhibit nasty noise peaks their outputs look like small value inductors in series with very small resistors so with a big bypass cap you can produce huge noise peaks at the resulting resonant frequency Putting a few ohms resistance in series with the regulator s output pin before the first bypass will kill the Q of the resonance and make the supply noise much better behaved at the price of slightly degraded DC regulation If your front end has a noise peak in the 1 100 kHz range that you can t understand try this trick 18 4 12 Beyond Transimpedance Amps Cascode Noninverting Buffer If the Cin of your op amp is still a serious inconvenience you can eliminate the tran simpedance amplifier in favor of a simple load resistor following the cascode transistor 18 4 TRANSIMPEDANCE AMPLIFIERS 711 with a low capacitance buffer following Second stage noise need not be a limitation even though the buffer has a gain of 1 because the buffer s output impedance is low the next stage can be a low vy bipolar amplifier such as an LT1028 A good voltage follower e g a bootstrapped emitter follower see Section 18
8. 18 10 where Zp is the complex impedance of the parallel combination of Rf and Cf Figure 18 5 shows the performance of the transimpedance amplifier with frequency compensation by Cf 6 3 pF as calculated from 18 8 The transimpedance bandwidth is only about half fo and it rolls off very steeply approximately 18 dB octave equivalent to 3 poles Also shown are the open loop gain and the closed loop noninverting gain which we will encounter in the next section 18 4 2 Noise in the Transimpedance Amp Confusion reigns supreme in discussions of noise in transimpedance amps Let s try to boil it down to something reasonably memorable Figure 18 6 shows a simple but adequate noise model of a transimpedance amp plus a photodiode It is visually obvious that all the current sources are treated identically I4 inshot inm and I amp appear in parallel The Johnson noise iyi of Ry really appears across Ry of course but because the impedance of the op amp output is very low the other end of the noise current source is at ground for noise purposes The signal current thus appears in parallel with the current noise sources just as in the simple load resistor case so the rolloff in the frequency response will once again not degrade the signal to current noise ratio Gain V V Transimpedance ohms 1E 05 100 000 1E 04 L 50 000 1E 03 30 000 E 20 000 1E 02 F 10 000 1E 01 F J 5 000 1E 00 E 3 000
9. 3099 1991 732 FRONT ENDS is AC coupled to the thresholding circuit It s a simple and elegant idea which is why they sell tens of millions of them The problem with this for our purposes is that it s very noisy far too noisy for an imaging sensor The leak resistor reduces the signal level and adds a lot of Johnson noise the discrete MOSFET isn t too quiet at low frequencies and the thermal drift is bad enough to make your neigbor s porch light come on whenever there s a gust of wind The good news is that the pyroelectric pixel itself is quite a good capacitor so we can use a charge dispensing readout reminiscent of a CCD The reason this is a good idea is that you can let the pixel integrate itself for a whole frame time then dump all the collected charge in one pulse right when you want to measure it This has exactly the same nice SNR consequences as the pulsed measurements of Section 13 8 10 Integrated pyroelectrics e g those from Irisys usually stack the pyro on top of a CMOS readout chip which makes all the decisions for you A built up circuit has to do its own charge dispensing The Footprints sensor s multiplexer uses diode switches made from ordinary display LEDs Ordinary display LEDs have extraordinarily low leakage One snag is that being differentiators pyroelectrics produce a bipolar current and diodes conduct only in one direction The basic idea is to put the switch LEDs under an opaque white cover
10. 4 8 can have an input capacitance of less than 0 25 pF along with a 1 Hz noise of 5 nV Hz so Cin is not inescapable Another insidious problem shows up when we let the collector of Q swing the Early effect A transistor has a collector current that depends somewhat on its collector emitter voltage Vcr so that its output impedance has a large but finite value For small variations of Ver this effect is approximately linear increasing Vcg increases the collector current If we plot Ic versus Vcg and extrapolate linearly to the point where Ic 0 the intercept is the Early voltage Vgany This voltage is normally in the thousands of volts for general purpose transistors so it is of little concern For RF devices and those with very high 6 Vearly is much smaller as low as 40 V and so the Early effect is a significant source of gain error and nonlinearity in common emitter amplifiers It is less troublesome in the common base configuration but do look carefully for nonlinearity at large signal swings and take the transistor s collector impedance into account Example 18 2 Current Mode Amplifier One of the biggest problems we ve run into in TIA design is that the resistors are so very noisy compared with the active devices It s worth trying to build a front end without resistive feedback by basically stuffing the photocurrent into the base of a BJT with sub Poissonian current feedback This is more or less what the bootstrap and
11. AvoL f Aval Ta mf 18 7 where Hm is the gain of the feedback network usually a voltage divider For fre quencies where the loop gain Ay HpAvor gt 1 this simplifies to 1 Hp Looking at the denominator clearly what happens when Ay 1 will have a great effect on the closed loop behavior If the loop gain has a phase of 180 when it crosses unity mag nitude the denominator will go to zero and the closed loop gain will be infinite which means that the circuit will oscillate fiercely near there this is a sufficient but not neces sary condition for oscillation On the other hand if the phase is 90 then there will be a well behaved RC type corner there The difference between the actual open loop phase and 180 is called the phase margin In practice as long as the worst case phase margin is greater than 45 or so the closed loop response will not exhibit undesirable peaking and the time domain step response will not overshoot too much From 18 7 we can show that an amplifier whose phase margin is 90 that is a single RC rolloff has a closed loop 3 dB corner frequency fc at exactly the open loop unity gain crossover whereas one with 45 margin has its corner at an open loop gain of only 0 52 In order to achieve a 45 phase margin we need to stop the rolloff of the feedback network at a frequency about equal to the closed loop corner We can do this by putting a capacitor Cy across Rf where 1
12. SNR increase in a Johnson noise limited system One problem with the T coil is that Rz and the output are different nodes Using an active device such as a transistor with voltage feedback instead of a barefoot resistor will get you the noise temperature of the transistor instead of the resistor while keeping the noise resistance constant Aside Refrigerators In case you re still worried about how a 300 K amp can have a 35 K noise temperature sit down with a cold drink and consider the ice cubes in your glass they were made in a 300 K ambient too o L4 M Lo M EQUALS Figure 18 17 The constant resistance T coil gives a 2 8x bandwidth improvement over a plain RC with constant load resistance Carl Battjes Who Wakes the Bugler in Jim Williams ed The Art and Science of Analog Circuit Design Butterworth Heinemann Woburn MA 1995 18 6 ADVANCED PHOTODIODEFRONTENDS 721 18 6 ADVANCED PHOTODIODE FRONT ENDS 18 6 1 Linear Combinations Optical measurements are frequently based on sums and differences of the photocurrents in two or more detectors Examples are position sensitive detectors such as quadrant cells as well as autofocusing in CD players phase detection by Schlieren or Nomarski techniques and polarimetry Doing this at DC is easy almost any way you think of will work even digital tech niques Section 17 2 5 When the measurement must be done at some speed however the effects
13. Section 3 6 or in a fiber receiver an optical preamplifier such as an EDFA These devices have serious drawbacks and should not be used frivolously With an APD running at a gain M you can reduce the load resistor by a factor of M without reducing the SNR compared with M 1 see Section 3 6 3 The general rule that more photocurrent allows smaller resistors and smaller pho todiodes run at higher bias have lower capacitance gets you most of the way there most of the time Nonetheless there is one specialized VHF UHF technique that is worth mentioning because it is easily understood and implemented LC networks see Section 14 3 10 18 5 1 Series Peaking The simplest case of such a network is series peaking which is nothing more than putting an inductor between the photodiode and the load resistor as shown in Figure 18 15 The peaking coil L provides positive reactance X at high frequencies which partially cancels the negative capacitive reactance of Cg The cancellation is far from perfect because the magnitude of Xz rises with frequency while Xc s falls Nonetheless a network like this can provide a useful bandwidth increase without an SNR penalty worth worrying about The ideal photocurrent sees a load impedance including Cu of R k fo ma A 18 25 l wo i w J a oQ D 0000 40 D Cy R i Viis T Vbias V a b Figure 18 15 Adding an inductor to a phot
14. component in the circuit has limits on each of its parameters beyond which the circuit will not function well enough In a landscape full of highly multidimensional cliffs we re almost bound to be near one of them Simulation will help find it and tell us how far to move in what direction to be equidistant between cliffs This is called centering and it will save you lots of headaches Beware though that there are cliffs lurking in the simulation itself models and model parameters are all lies Some of them are just more useful than others Make sure that you check the centering experimentally by changing the values and seeing where trouble develops RF Amplifiers Noise Figures Depend on Source Reactance Every RF device has an optimum source impedance where its noise figure is best This is generally not the matched condition Amplifiers therefore have noise performance that depends on the impedance mismatch at their inputs which is a matter of critical concern in high frequency front ends Make sure that your amplifier is a type that works well with horribly reactive input impedances and that it is cannot oscillate for any value of source impedance i e it must be unconditionally stable Robert A Pease Troubleshooting Analog Circuits Butterworth Heinemann Woburn MA 1991
15. find circuit hacks to get around the rolloff without messing up the SNR too badly Load Impedance ohms 1 Hz CNR dB 1E 06 140 3E 05 130 ada e RA A 2E 05 120 1E 05 l E 110 5E 04 E L 100 2E 04 90 1E 04 E l 5E 03 F 80 2E 03 70 1E 03 la 60 1E 02 1E 03 1E 04 1E 05 1E 06 1E 07 1E 08 Frequency Hz Figure 18 2 Frequency response and narrowband CNR of the photodiode load resistor combina tion of Figure 18 1 with Rz 1 MQ and Cu 100 pF Why is it OK to move the bottom of Cy and ig to ground 692 FRONT ENDS TABLE 18 2 Noise Degradation Due to the Johnson Noise of a 300 K Resistor la R V inth tshot ASNR Ia R V inth Nshot ASNR dB 5 1 0 1 0 04 0 14 0 6 1 3 1 3 0 2 0 17 0 10 0 7 1 7 0 57 0 3 0 4 0 080 0 8 2 1 0 32 0 4 0 6 0 063 0 9 2 6 0 20 0 5 1 0 0 051 1 0 3 0 18 2 2 Reducing the Load Resistance After reverse biasing the first thing everyone thinks of is reducing the load resis tance because that reduces the RC product and speeds things up This does reduce the signal to noise ratio because unlike the previous case the resistor s noise current goes up as its value is reduced There is nothing much lost by reducing the resistance while shot noise still dominates when the shot noise current is larger than the Johnson noise current The shot noise ceases to dominate when the two become equal that is when the DC voltage drop acro
16. g a resistor many times bigger than rg all the noise current has to go through rg and none at all winds up in the collector current the real emitter lead does jiggle up and down slightly though It may be more comforting to talk about the Th venin model where the shot noise is converted to an emitter base voltage by dividing by the transconductance so that the voltage noise is y 2el 2 enta E kr 18 16 8m elc to which must be added the Johnson noise of the extrinsic base resistance Rg usually 40 100 2 They are added in RMS of course Figure 18 9 Simplified noise model of a bipolar junction transistor BJT Don t try to calculate this noise contribution by applying the Johnson noise formula to rg it s 3 dB lower than that and the physics is completely different 18 4 TRANSIMPEDANCE AMPLIFIERS 703 Whichever way you prefer if the photodiode impedance is infinite the transistor does not contribute noise to the collector current Referring back to Figure 18 8 we see that our diode really has capacitance so the finite impedance of Cg makes inc split between Ca and rg by the ratio of their admittances remember we re dealing with RMS averages of noise here so only the magnitude matters A couple of lines of algebra then give the Q contribution to the noise C C ivo Vo Y Jeler 4 18 17 V 1 Care JV 1 Careg you can instantly see this if you use the Th venin e
17. inconveniently small Don t get carried away though since this forces one end of Cp to be essentially ground Cy then loads the summing junction Once it gets up to 2 pF or so don t go any further or you ll make the instability worse rather than better consider what would happen if you replaced a 1 pF Cy with a 1 10 capacitive divider and a 10 nF C f Don t Put Photodiodes on Cables Optical systems are often large and operate under stiff constraints on weight cost and complexity It is therefore tempting to allow the light to come out anywhere it wants and put the photodiode there This is reasonable as far as it goes you can put the front end amplifier there too Unfortunately people often just hang the bare photodiode on an RG 58 cable and connect an amplifier 50 Q you guessed it to the other end This is a ticket to perdition That cable will pick up signals from everywhere including ground FM radio lightning you name it When unmatched it will exhibit huge capacitances 100 pF m at low frequencies and poorly controlled transmission resonances and phase delays at higher frequencies If there s a DC voltage on it as there usually will be with photodiodes cable vibrations produce capacitance changes that show up as signal The list goes on and on Especially when you re trying to do differential measurements and especially with noise cancelers keep the amplifier and the photodiode together Put Capacitance Multiplier
18. of circuit strays become large enough to cause serious problems For example consider trying to measure an extinction of 107 on top of a rapidly fluctuating background A typical example is a current tuned diode laser whose output power varies rapidly with tuning A common way to do this measurement is to send a fraction of the laser beam into one detector and the rest through the sample chamber to a second detector If the frequency band of interest is DC 1 MHz then to maintain an accuracy of 1074 in the face of an order unity fluctuation due to scanning requires that the circuitry following the two detectors be matched to 0 01 in amplitude and 1074 radian in phase at 1 MHz These requirements push the state of the art if separate amplifiers are used especially because you can get 107 radian of phase shift across a 10 kQ feedback resistor by having an extra 0 0016 pF of stray capacitance on one versus the other at 1 MHz This book being what it is of course there is a circuit hack for it just wire the photodiodes in series With the outer ends of the diodes bypassed solidly to ground the diodes are actually in parallel for AC and noise purposes There is no opportunity for the strays to differ you have one amplifier one summing node one ground and one cable Differences in diode capacitance are of no consequence because the two capacitances are in parallel and so both diodes see both capacitances This trick works well with discrete d
19. optimistic by 20 dB or even more Sometimes the Cj value is in the model but not in the data sheet which is another issue Always calculate the noise analytically it isn t especially difficult and compare with the SPICE model and with the prototype Linear Technology has a very well regarded free SPICE program LTSpice that you can download Generally when an op amp macromodel simulation does something uninituitive such as driving its output beyond the supplies it s very likely to be wrong Also note that SPICE models will have the typical data sheet characteristics which isn t enough to base a design on 18 4 11 Power Supply Noise All through this chapter we ve been doing our noise calculations assuming that the photodiode bias voltages have been noiseless While this is quite doable it won t happen by accident The author always uses capacitance multipliers to make these bias supplies and usually runs the front end amplifiers from them too unless there s a good reason not to Any jumping around of the supplies will be transferred directly into the photocurrent via the photodiode capacitance the noise current will be INsup VysupoCa 18 21 making it just as important an effect as amplifier noise 100 uV of wideband supply noise is just as serious as 100 uV of amplifier noise Since this is a purely AC effect capacitance multipliers are a better match than voltage regulators here Have a look at Example
20. points at which Rin has fallen to times its peak value We 1 1 1 1 le ee lt 1 1 75 Q gt 1 2 18 30 This simple exact form is valid only for Q gt 1 2 Example 18 4 Peaking a Baseband Network In the previous example we used a network with R 12 Q L 100 nH Cy 10 pF This resulted in a peak Rin of about 825 Q What if we needed to go from DC to 160 MHz Such a network will obviously not have high Q and so its input resistance will be of the same order as R rather than being multiplied by a high value of Q In a pure RC circuit a bandwidth of 160 MHz allows a maximum of 100 Q for R With a maximally flat Q 0 414 network the 3 dB corner is 2 times higher than that set by the RC so that we can use a 140 Q load and get a 1 5 dB improvement in the SNR for the same bandwidth the improvement will be greater near f because of the resonance as above This value of Q gives the maximum bandwidth improvement for a fixed C and R This does not give us the tremendous bandwidth improvements we saw in the transimpedance amplifier section but then that was low frequency and this is VHF Remember that it s hard to get decent low frequency high value inductors so that you can forget peaking a high impedance low frequency network 18 5 3 Matching Networks and Bode s Theorem People working in the 100 MHz to several GHz range often find themselves limited by the capacitance even of an InGaAs APD which is usually
21. possible In fact it is often possible to build this capacitance right into the board layout for example by putting a ring of copper around the inverting input connected to the output pin it may need to be AC coupled to avoid leakage SPICE won t be much help in making the board layout right even if you have a trustworthy model of how your cascode transistor behaves at 5 wA of collector current which you probably haven t Make sure you follow Pease s Principle bang on it Stick a square wave through a big resistor into the summing junction then into the input looking for overshoot you have to put a small resistor in series with the input first of course If the overshoot is more than 20 of the step height Cy is probably too small Finally bang on the output with a square wave through a low value resistor Do this at various frequencies too sometimes it looks different Center Your Design Component variations are one of the major causes of manu facturing yield problems in analog electronic systems You can t possibly build enough prototypes to take in the whole range of all components so use simulation Most flavors of SPICE can do Monte Carlo sampling of the normal variation in each component or you can write your own code to do it with a compiler a spreadsheet or a scratchpad program such as MathCad GNU Octave or Matlab Pick component values that lead to acceptable performance over all the cases Every last
22. re firmly in the Johnson noise limit with a CNR of 126 dB in 1 Hz On the other hand if we put in an inductor of 99 nH and work straight into a 50 Q load then from 18 27 Rin 197 Q That s 3 dB better but still far from shot noise limited Decreasing R to 12 2 perhaps by using a 2 1 RF transformer 4 1 in impedance see Section 14 3 14 between the amplifier and inductor improves Rin to 825 Q which would notionally drop 25 mV The impedance at DC is only 12 Q but for noise purposes it s the DC value of Jz times the AC value of Rin that matters The Q of this network is 8 3 which is reasonable The FWHM of R is wo Q or about 19 MHz which is equal to that of the equivalent 825 2 10 pF lowpass as we expect see Chapter 15 If the amplifier has a noise temperature of 75 K then its noise power is only a quarter that of a room temperature resistor thus Z4 Rin only needs to be 13 mV for the shot noise to begin to dominate Thus such an amplifier plus a simple series inductor and a 2 1 transformer will get us to the edge of the shot noise limit A slightly more complicated network can do better for example a z network or a tapped tank circuit but this is a good place to begin 18 5 2 Broader Band Networks There are two other common uses for reactive elements in photodiode amplifiers extend ing the bandwidth of a baseband detector and a wideband application say an octave well away from DC A slightly more complicated networ
23. smaller than in the unbiased case It grows linearly with w so although the bandwidth is increased by Ic2 I the SNR is down 3 dB at about o Ic2 Ia re2C4 just as in the biased cascode case Bootstrapping basically replaces the rg of cascode device Q with the rg2 of fol lower Q2 which gives an improvement of Ic2 Ic times in bandwidth By essentially eliminating the capacitive loading on Qj it also eliminates the effects of Q s voltage noise This trick is reminiscent of the old joke about the cowboy who after he fell into a well pulled himself up by his bootstraps Bootstrapping suffers the same multiplication of the voltage noise of the follower that we saw in the transimpedance amplifier However here the RC product is not R Cg but rg Ca a factor of 8 smaller and the follower s vy is usually smaller as well so this is not nearly as great a problem as it is with the transimpedance amplifier We wouldn t be doing this if current errors weren t important so we ll use a superbeta MPSA18 with c2 290 A The largish Cep of this device appears in parallel with C4 so it hardly matters the Cop forms a voltage divider with Cg but since it s 50 times smaller it doesn t matter much either The 7 yA flowing through Rbias makes the cascode a bit faster and the offset voltage and drift are canceled by the matching resistor and the Vee of Q3 All this together improves the CNR to 1 dB above the shot noise limit in
24. sometimes all inductors you can get within 0 5 dB of the absolute physical limit for bandwidth with a given Rin so that it isn t worth doing anything more complicated This works by transforming the 50 Q input impedance of your amplifier into some much larger effective load impedance on the diode Figure 18 16 shows a 10 pF detector matched over a 110 220 MHz band with an effective load of 1 2 k Q using this trick which makes it shot noise limited from 50 yA up with a quiet amplifier You may not need as large a load impedance as you think because good RF amplifiers have a noise temperature much below 300 K some are lower than 50 K The Miteq catalog has some with NFs below 0 5 dB at 1 GHz which is pretty impressive a noise temperature of 36 K The nice thing about this is that a lossless matching network transforms this low noise resistance into the equivalent of a cryogenically cooled resistive load so you can be shot noise limited at much lower 7 Rz values 2kTy e for this amplifier is not 50 mV but 6 mV which is good for an 8x bandwidth improvement over a 300 K load at the same SNR 18 5 4 T Coils One excellent place to go to learn about building amazingly fast baseband networks is a Tektronix oscilloscope service manual from the 1960s or 1970s when discrete circuitry iy 280 nH 100 nH mes saa esa Out a U U Ly L gt R gt L c e Rs Cy 50 Q 10 pF 12 pF Vias 1200 Q 0 e
25. to the signal power that it can deliver to a sufficiently high impedance load There will be some resistance R in series with Cg and even if there weren t loss in L would prevent the output impedance from going to 0 Nevertheless in principle this is a very lucky break it means we can potentially open a shot noise limited window in the middle of a wall of Johnson noise The Hz Johnson noise power is wu Zout and the 1 Hz shot noise power is 2e i Rin so the 1 Hz CNR is 2 CNR Hz N o 18 29 2eidcRin 4kT x 1 D2 x Q2 Of course we haven t done anything about the amplifier s intrinsic noise except to short out its input Some amplifiers work well with shorted inputs but some don t None of them has zero noise with a shorted input unfortunately You have to ask your amplifier supplier or do your own simulations and measurements if you re designing your own Nonetheless the resonant enhancement in Rin is often enough to get you to the shot noise If R is not a real resistor but instead the input resistance of an RF amplifier the appropriate value of T to use is not the ambient temperature but the noise temperature of the amplifier It may not be immediately obvious from 18 29 that things have improved but they have For narrowband applications that require high frequency operation e g 18 5 HOW TO GO FASTER 717 heterodyne systems using acousto optic modulators choosing L to resonate Cg and
26. 00 L ng noL ZHMA Asuaq eoads abeyon 727 Jpd ueo srou 1 lg9uecoywAA u eondoonoo y d11u L661 sqqoH ur axe spejop peuonIppe Augu pue WIeIseIP mono OY pueq seq MOT AIOA OY o UMOP Y Sr asiou ML e ur jurod ep 14311 uo J0q ay o 3urpuodsanoo yr 6 7 ye Aouanbary snsiaa srou q 3u rmo ojoud eu8rs snsI a stou ZH3 0I V 8 rom ra Aros oy SIY srou SY DIURISISIL seq 25 OF Y 101 SUIMO Y Pugo OSIOU J9SP DY JO UOISIOA Jop ISe y Jo Indjno orner So dy JO SION TTI IMZ a 2H Aouanbaly ool 06 08 OL 09 os oy ol oz ol 0 S OL ae ZH AU Es ool isu q Ieno ds SION 0001 Sirti PO sasa A A s ee ee F a te ee ee s rn ld 0005 uueH ATAGKO BAYOOOT 19345 E3MOJ ZHA AUEOTEO G BAV d EB2 BA4V UrPTOOE G e8A ZHAO 66 XV ZHAT X PEPPY SION pajenojeo pasean e yw juarin9ojoyd eulis L s0 c o 10 S0 0 c0 0 L0 0 AW 001 QA ib 001 qi 002 2 ZH AU SION ZHAO L 728 L661 sqqoH Wor nbruuo snorA id Aue o JoLIodns 1 ns i e row JO gp 04 Aq p ss iddns sr astou saneorydnynyy uonerodo ewou paxoo qun weaq uosuedwos wy 19m0 juaImoojoyd owes y 3uronpoxd 1usr use j Aq pooe dar weaq uosureduioo ovy taddn 19 99ue9 srou A uo onu y Jo SOUBULIOJII uone npourlur ISION q yu Og pue yu 1 gp 1 1 ym stou 2ANIPpe Jo
27. 5 4 5t 0 9t 4 5t 0 01t 0 0025 0 0001 0 0007t 0 0013t 0 0013t 0 6 0 6 3 3 1 6 1 5 1 5t 3 5t lt 2 3t 1 6t 0 4t 1 5t 2 4t 0 5 vy 10 kHz iy 10 kHz Cin nV Hz pA Hz pF 3t Tt 1 5t 2t 2 6t 1 7t 2t 2t 1 8t St 3 2t 1 4t 2 5t 2 2t 3t 2t 1 4t 1 5t 12t Cin Un typ 36 32 22 18 12 12 4 8t 3 9 6 3 8 8t 2t 7 5 12 6 3 1 4 54 Remarks Cheap good OPA637 decomp version Good in low light expensive Good at low Ig 5 V Ay gt 10 but fast and quiet Unity gain compensated 657 Good for Ig gt 5 pA Ay gt 5 Ay gt 40 35 uA Ip 5 V Good for low Rp diodes e g InAs 3600 V us slewing Poor data sheet Drives unlimited Cz 6V poor datasheet LM4562 dual LME49740 quad Quad OP270 dual 12V 12V amazing part Dual largish Cin Mostly 15 V devices due to their much greater dynamic range Unless noted devices can use 15 V supplies and are unity gain stable capacitance times the noise at its emitter contributes a 1 Hz current noise 2 inc f 20 fCagkT elp 18 14 which is 0 05 pA at 1 MHz rising 20 dB decade With a total summing junction capac itance of 190 pF including C4 Rule 3 shows that even a nice FET like this one is 16 dB too noisy for our application A pair of BF862s would be a little closer but still at least 12 dB too noisy The biggest benefit of this approach is the
28. BFG25A X or BFT25A but consider using a superbeta transistor 6 1000 like an MPSA18 Darlingtons can have huge betas but they re fairly noisy and so they often make disappointing bootstraps From 18 16 the voltage noise of the driver stage is high and the transconductance of the output stage is also high leading to lots of noise current unless the driver stage is run at a pretty high current itself A single superbeta transistor perhaps with its own collector bootstrapped is usually a better choice when base current shot noise is a limiting factor Homemade Darlingtons can be better you can make a good one from two BFG25A Xs At low currents you can make the bootstrap a fast JFET e g a BF862 That gets rid of the base current problem at the expense of lower transconductance and higher voltage noise Resistor Rg sources its full Johnson noise current into the summing junction so that the net Johnson noise is that of the parallel combination of Rf and Rg For convenience we could simply put a 75 kQ metal film resistor in parallel with Di assuming that Vbias 15 V The improvement is enough to meet our design bandwidth but the noise is degraded by 3 dB and we have to raise the positive supply enough that the voltage drop across Rf doesn t saturate the op amp This is a viable solution if we can make Vbias bigger perhaps 45 V so that Rg can grow and its Johnson noise current thereby shrink as a by product Cg will sh
29. Figure 18 16 Wideband matching network THendrik W Bode Network Analysis and Feedback Amplifier Design Van Nostrand New York 1945 Section 16 3 Bode s book is well worth reading if you can find a copy 720 FRONT ENDS dominated The constant resistance T coil of Figure 18 17 is a gem you ll find there and also in Jim Williams s books The amazing thing about it is that the diode sees a constant load resistance of Rz and the 10 90 rise time is exactly the same as if only the diode capacitance were loading it no current is wasted in the resistor while charging the capacitor 2 8x faster than the RC alone For a pure capacitance at Ca the design is symmetrical L Lo L The design equations are 1 k Lr R Ca Cy Cy T LCa b MENS d 18 32 1 1 k Vet so 2V1 k where M is the mutual inductance Lr 2L 2M is the end to end inductance and is the damping factor 5 1 2Q Don t confuse this with an ordinary T network the mutual inductance is key to its operation Example 18 5 Constant Resistance T Coil Getting 30 MHz of bandwidth with a 10 pF photodiode requires a 530 2 load resistor Using a T coil we can run 1 5 kQ with a 10 90 rise time of 11 ns and a 3 dB bandwidth of DC 30 MHz with no overshoot Q 0 707 The component values are L 8 44 uH M 2 81 uH Cp 1 25 pF This represents a 10 dB signal power increase and since the Johnson noise power is independent of R a 10 dB
30. ING ACROSS Ca Once we have carefully chosen Rz and reverse biased the photodiode the circuit will probably still be too slow as we ve seen It s time to change the circuit topology and see if that works well enough We may observe that the source of the poor bandwidth of the load resistor approach is that the full signal swing appears across Cy If we make both ends of the photodiode work at constant voltage then there will be no swing across Ca and hence no capacitive current see Section 15 3 Making the swing small requires making the load impedance small How can we do that without degrading the noise 18 4 TRANSIMPEDANCE AMPLIFIERS 693 18 4 TRANSIMPEDANCE AMPLIFIERS One way to do it is to make the detector work into a virtual ground as shown in Figure 18 3 Although the inverting input of A draws no current feedback forces the voltage there to be close to zero at all times The way this works is that A senses the voltage across C4 and wiggles the other end of Ry to zero it out Provided A has high open loop gain AyoL the swing across Cy is greatly reduced and the bandwidth greatly improved The amplifier input adds a significant amount 2 20 pF of its own capacitance Cin Which must be added to Cy Because this circuit is so important in applications it s worth spending a little time analyzing its bandwidth and noise The voltage gain of A is not infinite so that the swing is not exactly zero to produce an output voltag
31. MUS CHAPTER 18 Front Ends Life is like a sewer What you get out of it depends on what you put into it Tom Lehrer 18 1 INTRODUCTION In Chapter 3 we dealt with optical detectors and their uses from the output of the optical system to the detector leads Now it s time to discuss the electronic front end a ticklish place between the detector leads and the signal processing system The front end s job is faithfully turning the detector output into a buffered filtered electronic replica Like maintaining sewers this is not glamorous work but failure is very noticeable Bad front ends are too noisy too slow or both The two are not unrelated it s easy to make the front end fast if you are prepared to sacrifice signal to noise ratio or if you have lots of light People tend to give up much too soon it really is possible to do fast measurements at the shot noise limit at low light intensities with ordinary components This is most of what this chapter is about It has some pretty heavily technical stuff in it so don t worry too much if it doesn t stick when you read through it if you make the same struggle for SNR yourself it will become clearer very quickly A basic front end is just a transimpedance amplifier current to voltage converter More advanced ones perform linear and nonlinear combinations of the signals from more than one detector as in differential measurements and these operations must be very accurate S
32. UONLT IIULD QP 0 lt SurAous UOISIDA enu I JjjIip DY JO oupuriojrod UONE SDURI SION V SUOMBLIBA JAY9DJURI ISIOU nJ Sn OML Z 8T IMZ q e 28S 40 ST LS zH BGT an zH AAT gu 29 9 244 00 DS NyudS zH 00 0S u31N39 180 09 0 o gi A indio Bo1 ye abeyon 4 L b T T T 06 z SOOT eT Ve TTT AREA IEA EARL E eter Tae aaa us Q 09 N o 70S Q AER AAA AAA AAA 0t 3 amp nt torn umum og 2 ie uee SUENO re Doo teeter J g PONVI MIEP r u Jois Z ap 07 M31189 uo JpjaqueD 4 0 1J l11e9 0 paulnjas a u SZ EB aiii 7HY 00 0S OWI Te YNN 729 730 FRONT ENDS technique if you look closely you may be able to see that the sideband noise has even been returned to the carrier as we d hope 18 6 7 Applications Just about any laser based measurement that s limited by laser intensity noise can benefit Anyone building a laser based measurement system would do well to investigate because the simplification of the optical and signal processing systems is usually enormous life really is easier at baseband and you can have that convenience along with shot noise limited performance even in unattended measurements It saves a lot of AO cells and wasted photons in heterodyne and FM measurements The author and many others have used this device to greatly simplify a number of ultrasensitive measu
33. ancing noise sources it would be worth beginning by reviewing the discussion of noise sources and calculations in Section 13 6 2 Table 18 1 summarizes the major sources of electronic noise encountered in front end design 18 1 2 Sanity Checking Since the first edition of this book was published the author has been receiving a certain number of e mails from people with detection problems which are welcome One com mon feature that has emerged is that specifications for optical instruments are often set by people who are ahem not expert in optical measurements One of the most common is to insist on wide bandwidth with high SNR at low light levels for example 50 MHz at 20 pA of photocurrent which cannot be done for reasons having nothing to do with circuit design Accordingly here are a few representative rules of thumb for frequently asked questions 1 If you have N photons s your SNR will drop to O dB at a bandwidth B N 2 Hz This is an inescapable limit based on counting statistics Your maximum achievable SNR is N 2B so since 20 pA is 1 24 x 10 electrons s counting statistics limit the SNR to 1 24 0 9 dB in 50 MHz 2 Using a few high precision parts doesn t get you a precise measurement You can measure a photocurrent very accurately but accurate measurements of light inten sity are very hard and 24 bit A D converters don t help It isn t that photodiodes aren t good transducers there are none better but
34. and illuminate them all with a processor throttled LED so as to produce a well behaved bias current of a picoamp or two Figure 18 24 shows the multiplexer design Each time one of the column strobe logic lines goes low six pixels are read out at once and digitized in succession which takes about 300 js out of a frame time of 200 ms The RC time Multiplexer Output Amp Dd Bias LED Strobes x CS00 o l N B Polarity Reversed Figure 18 24 Current dispensing multiplexer for 16 pixels of a 96 pixel pyroelectric sensor each of the column strobes at left dumps one pixel into each of six charge sensitive amplifiers with resistive resets The duty cycle of the pulsed charge measurement is less than 0 2 For many more details see Section 13 11 16 and the papers referenced there Example 17 1 and Section 14 6 1 18 7 OTHER TYPES OF FRONT END 733 constant of the amplifier is 5 ms Because we don t get to dispense every single electron as a CCD does both the dispensing and reset operations have kT C noise so correlated double sampling doesn t actually help much here Example 17 1 explains some signal processing tricks needed to fix up the transfer function but when it s done a 96 pixel sensor costing 10 including the lens can give quite competitive sensitivity 0 13 K NEAT with room for probably 10x further improvement 18 7 3 IR Photodiode Front Ends Near infr
35. and we don t need all of its bandwidth Performance will be nearly identical to the LF357 circuit If the photocurrent can go much higher than that e g 500 yA we really need the extra 10 dB dynamic range we get from 15 V supplies In that case we can either use a compound amplifier for example that BF862 differential pair we looked at earlier running into a 15 V op amp or an external fixed gain buffer inside the feedback loop The external JFET pair is more easily frequency compensated e g with a lead lag network around the op amp but the fixed gain booster doesn t mess up the nice input accuracy of the OPA656 Alternatively we can give up about dB of SNR and use the 15 V OPA627 Its other specs are excellent for the purpose but its input capacitance is 8 pF so it will oscillate with a 300 kQRy and when we increase Cf to compensate it becomes too slow Thus we have to use Rf 80 kQ which costs us 0 7 dB in SNR at all frequencies A bipolar op amp such as an OP37 will have lower ey and Cin but its 1 Hz iy is 0 6 pA which is comparable to the 0 8 pA shot noise and so costs us 2 dB SNR in the present instance though it ll be superior at higher I Note that these problems have nothing to do with photodiode capacitance which has already been fixed by the bootstrapped cascode the problem here is amplifier Cin that is the op amp tripping over its own big feet In general technological change has made TIA design easier in som
36. are a few rules of thumb to help with this The main one is to always start with an NXP BFG25A X or BFT25A as the cascode device and use something else only when driven to it These parts are the same small geometry NPN RF transistor die in different packages and are about as near to magic as you can get in an SOT 143 surface mount package or an SOT 23 for the BFT25A Lest you think that this is mere infatuation here are the highlights lc max 6 5 mA best below 2 mA fr 5 GHz at Ic 1 mA highly linear 6 of about 100 very good for an RF device and gt 50 for Ic down to the nanoamps Cop 0 2 pF at 1 V collector The author favors the G over the T for historical reasons it has the same pinout as the late lamented MRF9331 and because its feedback capacitance is a bit lower 18 4 TRANSIMPEDANCE AMPLIFIERS 713 to base Vearly 50 V price 0 30 If these specifications don t excite you you haven t spent enough Saturday nights designing front end amplifiers This device is a near universal choice for the cascode transistor in an unbiased con figuration since a minimum of 30 means that the base current is 30 times less than the collector current and hence its shot noise power is also 30 times less The collector current comes from a photodiode and hence has full shot noise so the noise power goes up by about 3 0 12 dB in the worst case which is a small price to pay for an 8x bandwidth increase Anyway we can rec
37. ared photodiodes InGaAs and germanium work more or less the same way as silicon ones because their shunt impedance is high so that they are current sources to a reasonable approximation The main addition is that they have significant amounts of dark current which exhibits full shot noise Provided that the photocurrent is large enough to dominate the dark current this is not a limitation The dark current is a strong function of the bias voltage so with dim light it may be necessary to run these devices at much lower reverse bias This means higher capacitance Mid and far IR photodiodes are a considerably more difficult problem The Jud son InAs detector discussed in Example 3 2 had a shunt resistance of 100 Q even at 40 C dropping to 10 Q at room temperature you can t reverse bias that by very much Detectors with such low shunt resistances are limited by their own Johnson noise except at extremely high illumination levels The task of the front end designer is to make the best of this because improving the detector is usually expensive impracti cal or impossible Cryogenically cooled far IR detectors are frequently limited by the shot noise of the thermal background photons which is also not susceptible to circuit improvements Generally it is difficult to make amplifiers whose noise is significantly say 15 dB below the Johnson noise of such a low value resistor The problem is usually voltage noise rather than current noi
38. at low collector currents a 2N3904 running at 10 mA Ic is a 350 MHz transistor but at 0 1 mA it s about a 35 MHz transistor and it gets correspondingly slower as the collector current declines Remember that it s the AC value of that matters for passing signal so unless your transistor has fr gt 200 MHz that nice 6 of 200 at DC won t be there at 1 MHz Table 18 4 is a comparison chart of several transistors that are good for these jobs The current gain at the operating frequency needs to be at least 20 for the unbiased case and correspondingly more with bias For single devices whose betas go as 1 f fr needs to be about 20x the operating frequency Darlingtons can hold up longer This is often a problem for run of the mill small signal transistors The trouble is that they are relatively large geometry devices often able to handle currents of 200 mA or more In photodiode front ends we are running them way down on the low current end of their operating ranges and they are not optimal there The BFG25A X s virtues stem mainly from its small die size Most transistor data sheets don t guarantee fr values except at a single operating condition 10 V collector emitter and a few milliamps Ic A rule of thumb is that well below the fr peak fr goes as Jc but that within a factor of 10 or so below the peak the dependence is more like Tc These rules allow extrapolation of published curves to very small collector currents TThere a
39. by 40 dB up to 8 10 MHz or so as shown in Figure 18 21 It will reliably reach the shot noise even with very noisy lasers Figure 18 21 shows it getting to within 0 2 dB of the shot noise with a total of 13 mW of 532 nm DPY laser Q and Q gt were matched Motorola MRF904 RF transistors Di and D gt were Hamamatsu S 1722 photodiodes The signal beam was 5 6 mW Jsig 1 77 mA and the comparison beam was 7 2 mW Komp 2 3 mA 726 FRONT ENDS Rf 1st D1 q Vbias signal Beam isi 1722 01 MPSA64 Qs 5 11k 1 4 OP 470 Linear 1 OutPut Q4 6 f ls s 1 4 OP 470 signal Beam gt la 3 1722 01 sig2 Vbias Log Ratio Comparison Output icomp Vbias Beam 81722 01 Figure 18 20 The differential noise canceler adds a second cascoded photodiode Since most of the negative photocurrent bypasses the differential pair the nonideal behavior of the BJTs at high currents is eliminated This circuit can achieve 1 Hz measurement SNRs of 160 dB or more even with lasers 70 dB noisier than that light which is a tough test 154 dB dynamic range in 1 Hz The differential model of Figure 18 20 can do 160 dB The noise at the log ratio output is given by E Mus N ey Vos 18 34 e log sig b Vol exp kT gt 18 34 sig which is just the total photocurrent shot noise times dViog dJsig the 1 Hz SNR at the linear and log ratio outputs is ideal
40. cascode do by connecting at AC the PD between the base and emitter In the bootstrapped cascode the cascode protects us from the ev Ca noise peak and the bootstrap reduces the load impedance seen by the photocurrent If we can combine the two functions in one device we might be able to reduce the noise by 3 dB One possible way to do this is shown in Figure 18 14 Don t try building it as shown there s a lot of stuff missing Input transistor Q s 1 Hz input current noise is the shot noise of the base current 2eI B and neglecting Rp noise its voltage noise is 2eIc gm kT 2 elc a T Seq la gt i o gt Ko out Y P 8V Figure 18 14 Current mode photodiode amplifier has slightly better performance than the boot strapped cascode TIA at the expense of extra engineering This is a conceptual schematic only the analysis considers only the first stage that is Q1 712 FRONT ENDS Since the base and collector shot noise are essentially independent vy and iy are uncor related as usual The input resistance is that of the BE junction rin kT eIg assuming it obeys the diode equation The open loop bandwidth and input referred noise are approximately those of the input transistor We ll ignore the Miller effect since in a real design we d get rid of it with a cascode so the current gain is set by 6 and the parallel combination of Cg and Tin B Ao
41. citance Cin of the op amp which limits how fast we can go just the way Ca did before Switching to a slightly faster op amp such as an LF357 and using Cf 0 5 pF overcomes Cj and gets us to a 1 1 MHz 3 dB bandwidth for the whole circuit The net bias current now has 10 times less than full shot noise so 18 18 predicts that the SNR will be down 3 dB at only 330 kHz which is not good enough We could just as easily use gq 200 A so that the shot noise corner will be at 1 3 MHz but this starts to get us into trouble Let s look at why 704 FRONT ENDS 18 4 7 Noise Considerations Generating that very quiet much less than full shot noise current is easy a metal film resistor Rg to a well filtered supply is all that is required provided that the resistor drops a large enough voltage If we make Rg drop N times kT e the noise power due to iypias Will be reduced by a factor of N In our example with Ig 200 yA and Ig 2 pA if Re lg 2 5 V the shot noise power from the bias current will be reduced to 107 times the photocurrent shot noise power a negligible addition The real limitations come from base current shot noise and Johnson noise in Rg The base current Ig has full shot noise which limits the bias current noise to at least 1 PBo times full shot noise current That fp is the DC current gain which is what s relevant even at high frequency since it s the DC value of Is that sets the shot noise level Start out with a
42. cts together with a garden variety cascoded transimpedance amp we can make an electronically balanced subtracter so the grad student can adjust a pot controlling A Vgg instead of an optical attenuator We can go a bit further too by noticing that the student can be replaced by an op amp since the criterion for perfect adjustment is so simple zero volts means zero excess noise We ve arrived at the laser noise canceler a version of which is shown in Figure 18 19 It has two outputs The normal transimpedance output has its DC value nulled of course so it puts out a highpass filtered version of the signal photocurrent minus its noise The servo signal from A2 is a lowpass filtered ratiometric output which depends only on the ratio of the signal and comparison photocurrents minus both the background noise and the noise intermodulation From the Ebers Moll equation it s easy to show that o Vbias Rs D A Signal Beam qn 5 11k S1722 01 A 1 4 OP 470 Linear _ tput MPSA 64 y 1 rae Q 3 A 3 V 1k A T 1 4 OP 470 Log Ratio L D2 Output V omparison gt ico p Beam 54722 01 V icomp Vo signal 1 V bias Figure 18 19 Laser noise canceler single ended version BJT pair Q1 Q2 splits the reference photocurrent so as to null the total DC Noise and signal are treated the same way so the noise cancels at all frequencies From Hobbs 1997 Canceling th
43. d not be confused with the real metal film resistor Rg Thus our 2 uA photocurrent sees a resistance of 12 5 kQ so that the RC bandwidth increases by a factor of 8 immediately to about 130 kHz What is more the collector circuit has a shunt capacitance set only by the output capacitance Cop of the transistor and Cin of the op amp which can be chosen to be much less than C4 so that we can raise Ry if we choose without losing bandwidth or suffering from serious ewamp multiplication Aside re Auto scaling An interesting feature of the nonlinearity of rg is that it automatically adjusts to an increase in photocurrent by reducing the RC product In Section 18 2 2 we chose a value of Ry proportional to 1 17 that s just what Q does while maintaining the 8x bandwidth improvement On the other hand we can no longer improve the bandwidth by simply using a faster amplifier and besides the bandwidth of the circuit depends on J Sure the limitations of the transimpedance stage are less of a worry but if we can t get the fre fr bandwidth improvement have we really gained anything The answer is yes First remember that the RC rolloff moves 8 times higher in frequency which by itself often makes the bandwidth adequate Second we are not powerless to improve the bandwidth further in Ry Output O Figure 18 8 Using a common base amplifier greatly reduces the effects of Ca and significantly improves the SNR as well Exte
44. e V A requires an input voltage V W AvoL AvoL rolls off at high frequency which limits the bandwidth improvement Prepackaged op amps have their open loop frequency responses carefully tailored to make them easy to use which in practice means that they roll off like 1 f 6 dB per octave with a nearly constant 90 phase shift from a low frequency all the way to their unity gain crossover at fr The uppermost curve of Figure 18 4 shows the response of an LF356 105 dB DC gain 4 MHz fr which is of this character The advantage of this is that any closed loop gain will result in a stable and well behaved circuit that settles quickly This approach is called dominant pole compensation its drawback is wasted bandwidth at high closed loop gain which does not greatly concern us here Mathematically Ayo is approximately Apc A _ lt gt o e y gt gt yoc s L NOE IET a eG 18 3 The exact values of the DC gain Apc and the dominant pole frequency faom are not well controlled from unit to unit Their product known as the gain bandwidth product GBW is approximately equal to the unity gain crossover frequency fr and is a well controlled parameter The other term in the denominator which is a pole at frequency f2 represents the effects of limited bandwidth in other stages of the amplifier In amplifiers intended for use at unity gain f2 is always higher than fr but not by much a factor of 1 2 to 4 thus con
45. e noise intermodulation means that e g in spectroscopy both the baseline and the peak heights are independent of laser intensity and intensity noise 18 6 ADVANCED PHOTODIODE FRONT ENDS 725 A VBE is O AVgg In Ez 1 18 33 e Lig BJT differential pairs are unique among active devices in that A Vgg depends only on the ratio of the collector currents not on their magnitudes This relation holds over several decades of collector current and is why the fluctuations split exactly as the DC which as we saw is the key BJT property for cancellation to work Thus measuring A Vgg allows us to make measurements of relative attenuation even with order unity fluctuations of laser power a key virtue for spectroscopy for instance A cardinal fact here is that the cancellation itself comes from circuit balance not from the feedback the feedback just establishes the conditions for the cancellation to be exact Thus the cancellation operates at all frequencies completely independent of the feedback bandwidth What that means is that we can make shot noise limited measurements of optical power at baseband even with very noisy lasers This has very beneficial consequences for measurements because it makes the bright field quieter than the dark field 18 6 4 Using Noise Cancelers Noise cancelers are simple to use as we saw in Section 10 8 6 you take a sample of your laser beam with some etalon fringe free beamsplitter like a Wollas
46. e ways and harder in others Remember that the distance between the two curves is total noise Johnson noise not shot noise Johnson noise 18 4 TRANSIMPEDANCE AMPLIFIERS 709 TABLE 18 4 Suggested Transistors for Cascode Transimpedance Amp and Bootstrap Service Manu Fr Olc Olc Re Cob Device facturer MHz mA mA 2 pF V Remarks NPN BFG25A X P 5000t 1 50 0 5 0 2t 1 Excellent device BFT25A P 5000t 1 50 0 5 0 3t 1 Easier to get BFG505X P 9000t 5 60 5 0 2 6 Higher power good 6 linearity BF240 P 600t 1 65 1 It 1 MAT 04 AD 300t 1 175 01 1 0 6 17t 0 Quad good linearity low Rg MPSA14 2N6426 Many 125 10 10k 10 0 3t 14t 0 Good Darlington MMBTA14 SMT MPSA18 M 160t 1 1000t 0 5 10 3101 Super 6 good for bootstraps MPSH20 M 400 4 25 4 1200 UPA103 NEC 9000 40 5t Quint good linearity poor Ry 2N2484 M 60 05 200 0 5 605 Very well specified 2N3904 All 300 10 100 1 5t E 0 05 Ubiquitous manufacturers differ well spec d PNP BFT92 P 5000t 14 20 14 0 7t MAT 03 AD 40t 1 90 0 1 0 75 30t 5 Dual accurate slow MPSA 64 Many 125 10 10k 10 0 6t 15t 0 Darlington MSC2404 M 450 1 65 1 1 6 JFET BF862 P 715t 10 35 10 10 1 9 0 8 nV Hz typical 2SK369 T 50 10 40 10 50 80 0 7 nV HJFET NE3509 N 18G 10 80 10 0 04t 0 3t Ty 35 K 2 GHz RDSon 6 Q Ca 0 4 pF These are mostly through hole devices for easier prototyping but surface mount equivalents exist The JFETs are most useful as bootstrap
47. em this can add that 40 to the cost of the optics or stretch the measurement time by 26 These factors of 1 26 multiply so that if the loss is more than 1 dB life gets a lot worse fast This is an absolute inescapable information theoretic limit and cannot be got round by any postprocessing whatever Put lots of effort into getting your detector subsystem really right you ll be grateful later when the measurement is fast and the data are good Even if you are building a spy Satellite or solar telescope where photons are not the problem make the detector subsystem right anyway It s good for the soul builds your expertise and anyway you re liable to reuse it another time Dynamic Range Is Precious Many measurements must operate over a wide range of optical powers It is obnoxious to be forced to choose between railing your amplifier on the peaks or having the troughs disappear into the noise Don t use 3 V or 5 V supplies in high dynamic range applications You re throwing away as much as 20 dB of dynamic range compared with a 15 V system After the dynamic range has been reduced for example by filtering out the DC background this is usually much less of a problem so the amount of circuitry requiring 15 V is usually small This makes it feasible to power the front end of a mostly 5 V system with a small DC to DC converter You can use charge pump voltage converters such as the ICL7660 and its descendants or a small switchi
48. etting etalon fringes and spontaneous emission in the polarization orthogonal to the laser light These can usually be fixed easily enough but finding them does require some care and thought There isn t space here to go into all of its ins and outs but if laser intensity noise is a problem for you check the referenced articles Because of all the fine points a noise canceler will show you it takes a little while to get up to speed with it the average seems to be about 2 weeks but the investment pays off over and over Learning to spot those etalon fringes vignetted beams and coherence fluctuations will make all your systems work better whether they have noise cancelers TP C D Hobbs Reaching the shot noise limit for 10 Optics and Photonics News April 1991 and Ultra sensitive laser measurements without tears Appl Opt 36 4 903 920 February 1 1997 K L Haller and P C D Hobbs Tunable diode laser spectroscopy with a novel all electronic noise canceller SPIE Proc 1435 1991 Available at http electrooptical net www canceller iodine pdf Available as the Nirvana detector from New Focus Inc 18 7 OTHER TYPES OF FRONT END 731 or not One key piece of advice there are lots of things that appear to be common mode but aren t for example etalon fringes in two different polarizations 18 7 OTHER TYPES OF FRONT END 18 7 1 Really Low Level Photodiode Amplifiers We ve spent almost all of our time in thi
49. evices but unfortunately split detectors usually come with all the anodes or all the cathodes wired together so that this is not possible For high frequency split cell applications transformer coupling with the DC bias applied to a center tap is a good solution It is possible to use the series connection with cascoding either use a biased cascode so that the net DC photocurrent can be positive or negative without reverse biasing the transistor or use a separate cascode for each diode one will be NPN and the other PNP with their collectors connected together and with a big capacitor between their emitters so that the diodes are connected together at AC There are two difficulties with this basic approach One is that there are slight differ ences between diodes that do matter Besides shunt resistance photodiodes have a small series resistance often 50 100 Q for fast devices much more for lateral effect cells which forms an RC transmission line with the shunt capacitance Cy If the two diodes have slightly different series resistances there will be a slight phase shift between the currents they produce given identical illumination Unlike 1 femtofarad circuit strays this is easily trimmed out and will stay trimmed Figure 18 18 shows how to wire the detectors plus one version of the R balancing tweak using a loaded pot Section 14 2 4 It could use a 10 pot but these are unreliable The circuit also has a conveniently nonlinear ad
50. fer following a photodiode and load resistor which is reassuringly reasonable All we ve done is to tailor the frequency response by using feedback to jiggle the far end of Ry this shouldn t get us something for nothing The addition of Cf or R doesn t fundamentally change this but it causes the input referred noise to level off at the frequency of the feedback zero If the op amp s voltage noise is very low or if we are not trying to get a huge bandwidth improvement through the fr fec mechanism this rising noise con tribution will not limit us If we are relying heavily on this mechanism though the noise may increase catastrophically it will begin to dominate all other noise sources at approximately 3 where P AKT 2ela amp 18 13 f Ry 20 Namp Ca 698 FRONT ENDS We can see this nefarious gotcha in action in Figure 18 7 which is a plot of the noise power spectral density of our LF356 circuit The voltage noise is unimportant at low frequency but rises to dominate the entire noise budget The log log plot is a bit deceiving plotting the noise power versus frequency on linear scales as in Figure 18 7 gives a more visceral feel for the problem It only gets worse when we try to go faster One reason for the confusion is that most of us have a persistent idea that noise spectra are flat or nearly so which is often true but not here 1 Hz Noise 1 Hz CNR dB 1E 06 130 5E 07 L 3E 07 125 2E 07
51. justment which allows 6x finer control in the middle of the range Use a one turn cermet pot and metal film resistors s porp Y Jo SIDUBISISOI SOLOS JUDIOYIP APYSI S 107 739109 o 19M e Surpniour uoNoeNqns LINIE 194814 JOJ PINO Y YFU W SUOISIAIP JO uonoenqns sn ULO Jey ut s s WRdG OM DLIQUIS Y Y Je spoul ur UOIssaiddns stou umr q oAL gI SI IMZ sedy 1ndinO ssajasion lt 10 99 8q yeubis d 1 t Josseiddns SION 1019919 HI Sdualajay sl dl d AY Jose wa s s pesando Joni ds wesg 722 18 6 ADVANCED PHOTODIODE FRONT ENDS 723 Circuit problems can be kept at bay but the second difficulty is more fundamental how to keep the two photocurrents exactly equal Can we really make the two beams identical to 1 part in 10 over all scanning conditions with different sample absorptions etalon fringes dust and so on This is a nontrivial requirement It would be convenient to have an automatic way of maintaining the adjustment 18 6 2 Analog Dividers One possibility is to divide one current by the other rather than subtracting them You do this by converting each photocurrent separately to a voltage and then applying the two voltages to an analog divider IC which returns a voltage indicating the ratio between the two applied voltages Due to circuit strays and divider errors this idea is not adequate for the demandi
52. k e g a m or T network can match a 50 Q RF amplifier input to weird source impedances Resonating away the capacitance of the photodiode works well but only at one frequency whereas for these applications we need a decent bandwidth as well as a high operating frequency tSee for example Terman or The Radio Amateur s Handbook 718 FRONT ENDS Just putting a Judiciously chosen inductance L in parallel with Di with appropriate biasing and DC blocking so as not to short it out moves the low frequency RC bandwidth to the resonant frequency of L and Cy fo 1 2z LC4 This happens approximately symmetrically for example a 40 MHz lowpass network becomes a bandpass of 40 MHz full width This assumes that the load resistance remains in parallel with Di as well and that the Q is large enough that the low frequency response has rolled off a long way before hitting DC If you don t mind building your own RF amplifiers this can be a good technique a dual gate GaAs FET follower can do a good job of buffering such a circuit without loading it down unduly The circuit of Figure 18 15 has response all the way to DC Although we used it in a relatively high Q application earlier it is also useful at Os of around 1 for improving baseband networks It could in principle be used with transimpedance amps as well You may want to try it out Don t expect good performance from inductors larger than 50 uH From 18 27 we can calculate the
53. l power to the rms noise which is really a carrier to noise ratio CNR since what we think of as the signal will usually be much smaller than the DC The SNR is what we care about so we ll use that for rhetorical purposes 18 2 1 The Simplest Front End A Resistor Say we need with a detector subsystem whose 3 dB bandwidth is 1 MHz a photocurrent of 2 uA from a silicon photodiode whose capacitance is 600 pF at zero bias Given a detector whose output is a current the easiest way to form a voltage from it is to shove it into a resistor say 1 MQ as shown in Figure 18 1 While this circuit generates an output voltage V R with admirable linearity at least until we forward bias the PD too far problems arise as soon as we ask about AC performance Since the full signal swing appears across the detector capacitance C4 the output rolls off starting at 1 18 1 27 Rr Ca frc which is 265 Hz at zero bias This is a mere factor of 3800 slower than our 1 MHz design point As we saw in Section 3 4 5 most visible and NIR detectors can be operated at reverse bias which will reduce Cg by as much as 7 10 times while increasing the leakage current slightly This is nearly always an excellent trade contrary to what you ll often read elsewhere This diode s data sheet says that its leakage current is about 0 5 nA at room temperature for a 12 V reverse bias and that this bias will reduce Cy by a factor of 6 to 100 pF That gets u
54. lower 0 25 pF each will get us to beyond 200 MHz VHF design is actually quite a bit harder than this since all our analyses have been based on RC circuits alone Above 200 MHz everything has enough inductance to worry about and stray capacitance is generally the limiting factor Aside Optical Communications In optical communications and especially in the emerging area of short range optical interconnection on chip chip to chip and module to module it is frequently necessary to go a great deal faster than this 20 GHz or faster This is generally done with extremely small photodiodes made from compound semiconductors such as InP or InGaAs closely integrated with IC One design meeting this description has gone faster than 200 MHz shot noise limited above 50 A Ig with a 5 pF photodiode 18 5 HOW TO GO FASTER 715 preamplifiers designed for the specific application Instrument builders aren t that rich usually but if you can piggyback on this technology consider doing so Of course due to widespread reliance on erbium doped fiber amplifiers EDFAs most telecom detector modules aren t all that quiet There are situations where it is frankly impossible to reach the shot noise in the required bandwidth with the available light and ordinary photodiodes Long distance fiber optic communication is a good example In situations like that you may be forced to use avalanche photodiodes or photomultipliers which we discussed in
55. ly the same Figure 18 22 shows the depen dence of the log ratio output noise on sig compared to the shot noise solid line and the shot noise corrected for the Johnson noise of a 40 Q base resistance rg The base resistance contribution can be reduced by paralleling transistors if necessary The log output s noise is also flat with frequency Figure 18 22 also shows the noise PSD of the highest photocurrent data point where Li 931 A t s flat way down into the low audio and its lt 10 Hz behavior is dominated by temperature swings in Q and O 18 6 6 Multiplicative Noise Rejection Because of the ratiometric property of A Vgg the noise canceler s log ratio output is the best thing going for multiplicative noise It can cancel both additive noise and the noise intermodulation down to the shot noise level most of the time Figure 18 23 shows at least 70 dB suppression of noise intermodulation which is much better than any competing roJ q se s oen wWoyoq pue do aouRrWOJ1ed ZHI 01 oq q estou Joys aaoge gp p O 100p srou e SUIMOYS UO SUILIQ yoq ven WOO p yoolq Weaq uOsteduos e dol e mdjno eun 94 J2 JOOY srou etun n J9 9DULI ISIOU orsegq IZ ST AMZA a 995 G8 5 15 244 BA T an 2H 00 T1 gx ZHW 0 BI dOLS ZH 005 Luvs e ZHx Aouanbes4 00L 0 ban T Gin qu 226 18 u0L u
56. making R small will make the denominator quadratically small R is increased by a factor of approximately Q Reasonable values of Q to use depend on the frequencies encountered but will seldom be above 10 and never above 25 One thing to remember is that the impedance trans formation is accomplished by a large current circulating around the loop This current is Q times larger than the AC photocurrent and leads to a large AC voltage across Ca It may seem strange to be increasing the swing across Cg now when we worked so hard to reduce it before The difference is that in a pure RC circuit all the current going into Ca was lost and here it isn t There are limits to this of course since at sufficiently high frequency the photodiode stops looking like a pure capacitor and its intrinsic losses become important Example 18 3 Narrowband 160 MHz Heterodyne System If we have a heterodyne system using two passes through a typical 80 MHz acousto optic modulator the pho tocurrent component we care about is in a narrow band centered on 160 MHz Using a photodiode with Cg 10 pF and Jz 30 uA we could in principle use a huge R such as 10 kQ and get a shot noise limited CNR of 140 dB in 1 Hz as in Figure 18 2 Of course the RC time constant is 100 ns so that the voltage would have rolled off by 100 times at 160 MHz which makes it a bit impractical to use If we choose R 100 Q to control the rolloff then we drop only 3 mV across it and we
57. mplifier whose 1 Hz voltage and current noises are 1 nV and 4 pA will be quite good total noise 1 dB above the detector noise with a 250 Q source but poor 8 5 dB over detector noise at 10 Q Since the increased Johnson noise makes the 10 Q detector 14 dB noisier to begin with this is really adding insult to injury A transformer can make the 10 Q detector look like 250 Q to the amplifier eliminating the additional 7 5 dB SNR loss though we re still stuck with the 14 dB Another advantage of transformer coupling with low shunt resistance detectors is that the DC voltage across the detector is held at zero because there is a wire connected all the way from one side to the other There are two main disadvantages you can t tell what the DC photocurrent is because there is no DC connection between the amplifier and the detector and there is no simple way to reduce the intrinsic RC time constant of the detector except by reducing the load resistance which seriously degrades the noise performance The first you can fix with some circuit hacks but the second you re stuck with Good transformers are available from EG amp G PARC Jensen Transformer and Mini Circuits Labs 18 8 HINTS These maxims will help keep you out of the worst potholes in front end design If you ignore any of these make sure you know why you re doing it One dB Matters A loss of 1 dB in the SNR requires 26 more signal power to overcome it In a photon limited syst
58. network in the feedback loop of the transimpedance amplifier as shown in Figure 18 25 This network increases Zm and Avc by reducing Hw without having to increase Ry and so suffer extra phase shift Of course the bandwidth will be reduced by the voltage divider ratio of the tee network as well so a faster amplifier will be needed Some people like to put two amplifiers inside the same high gain feedback loop to get extra bandwidth and eliminate the second stage noise and input errors If you do this the booster stage needs its own local feedback to ensure it runs at a fixed AC gain and must be fast enough not to mess up the overall loop stability For differential detectors it is nice but not essential to bring out both ends as well as the difference perhaps using current mirrors to bring the voltages down near ground 736 FRONT ENDS Cr Ry lt lt R AAA Re V l I O Output l O Vbias Figure 18 25 A tee network in the feedback loop of a transimpedance amp provides extra voltage gain at the expense of loop bandwidth The increased signal gain reduces the effects of second stage noise Don t reduce Rr The value of Cy is not changed by the addition of the tee network The parallel combination Rgiy R R2 must be small enough so that 1 27 Raiv Cr gt fraps Even without the resistive divider a tee network made up of small capacitors can allow the use of a somewhat larger Cf if the calculated value is
59. ng application above but may be useful in lower performance situations Its main charm is that the two photocurrents no longer have to be identical A less obvious one is that since everything is proportional to the laser power the signal gets intermodulated with the noise which can be extremely obnoxious dividers ideally fix this as well Dividers unfortunately are too noisy and slow for most uses and their accuracy is very seldom better than 0 5 18 6 3 Noise Cancelers In principle differential laser measurements should be totally insensitive to additive noise due to source fluctuations because of three perfect properties 1 With lasers it is possible to make sure that the two detectors see exactly the same beam this requires some care for example putting an efficient polarizer at the laser so that spontaneous emission in the polarization opposite to the laser beam does not get converted to uncorrelated amplitude noise in the two beams VCSELs are especially bad 2 Optical systems are very wideband 0 01 nm bandwidth in the visible is 10 GHz temporal bandwidth 3 Optical systems and photodiodes are very linear as well 4 Therefore Given two beams from the same laser hitting two photodiodes the instan taneous excess noise current is exactly proportional to the DC photocurrent This is a very powerful fact as we ll soon see Imagine taking a laser beam splitting it into two carefully without vignetting it or introduci
60. ng etalon fringes and sending one of the resulting beams the signal beam through your optical system into one photodiode and the second the comparison beam directly to a second photodiode Since everything is very wideband and linear the fluc tuations in the original beam split exactly as the carrier does The shot noise of the two beams is of course uncorrelated This means that if you adjust the beam intensities so that the DC photocurrents cancel exactly the excess noise above shot noise cancels identically at all frequencies of interest even far outside the control bandwidth Twid dling an attenuator to keep this exactly true requires a graduate student to be shipped with each instrument of course which may reduce its practicality but at least he doesn t have to adjust it very fast 724 FRONT ENDS We re rescued by another remarkable fact 1 A bipolar transistor differential pair is an extremely linear voltage controlled cur rent splitter Take two BJTs with their emitters connected together Ground the base of one and put some fixed voltage AV 60 mV S AVE 60 mV on the other Now inject some current Jj into the emitter node For a fixed value of A Vgg the ratio of the collector currents is constant over a range of several decades in emitter current and the ratio can be adjusted over a very wide range As a consequence any fluctuations in fin split in just the same ratio as the DC does Putting these five fa
61. ng regulator Use fully shielded inductors and don t omit to filter the output of these devices with a three terminal regulator or better a capacitance multiplier Bypass capacitors won t do it Watch out for inductive pickup from switching regulators and for the fuzz that any of these sorts of devices always puts on its input supply 18 8 HINTS 735 Always Plot the SNR It is depressing how many people ignore how the SNR changes with frequency In this chapter we ve seen that there are lots of counterintuitive things SNRs can do so don t omit to calculate what SNR you expect Sometimes a slower front end with a peaking filter in a subsequent stage to compensate for its rolloff can work just as well as a gold plated ultrafast front end Always Measure the Noise Floor In Section 1 7 we talked about making sure that the photon budget was met and not being satisfied with less than full theoretical performance The noise floor of the front end amplifier is one place that people never seem to expect good results and often don t even measure even though it s trivially easy a flashlight will produce a photocurrent with exactly full shot noise find out what photocurrent gives a 3 dB noise increase and you know the input referred noise This works independently of gain measurement bandwidth and so on but don t try to do it on a scope by eye use a spectrum analyzer or a filter plus an AC voltmeter see Sections 2 5 4 and 13 6 5
62. o get a good result Databooks and SPICE models tend to get out of date since many of the transistors we d like to use are old designs As the old production processes are closed down and the old part numbers reimplemented on newer processes the parameters change but the databook specifica tions stay the same It is very inconvenient to have an unannounced device change break your design For a situation like this where the parts are cheap but the consequences of a change can be painful the smart plan is to buy as many devices as you anticipate ever needing and stick them in a safe somewhere see Section 14 7 3 At the very least keep enough known good devices on hand to last you for however long it may take to change the design 18 5 HOW TO GO FASTER We had a struggle to get to 1 MHz with a 2 yA photocurrent while staying in the shot noise limit Is there any hope that we can do shot noise limited measurements at higher speed Well yes there is In our example we purposely chose a moderately high capacitance photodiode and a low light level We saw that the RC corner frequency frc from a diode capacitance Cq and a photocurrent Jy was Iqg 27 0 2 V Ca if we were to be within dB of the shot noise If we use a smaller fast photodiode with a capacitance of 10 pF and run it at a photocurrent of 100 yA with a 2 KQ Rz that corner is not at 16 kHz but at 8 MHz This is not the limit either using a biased cascode with a bootstrapped fol
63. odiode a Series peaking with coil L increases the RCq bandwidth by 1 4x in a baseband system or 2x in a narrowband AC system b Shunt peaking keeps the bandwidth at 1 27 RCa but moves the passband up to fe 1 27 LCaq More complicated networks can do better 716 FRONT ENDS where w is 27 f Dale 3 18 26 _ R2Cq R woRCa and oo LCa 2 is the resonant frequency of L and Cu alone The load impedance Zin is Rin j Xin In the absence of losses in L all the power dissipated by in the real resistive part Rin gets transferred to R The total power P dissipated by Iq is E Rin Where Rin is R Ria 1 o LCa R2C3 18 27 Computing the signal to noise ratio is a bit more subtle here The rms noise voltage at the output is the Johnson noise current iy of R times the magnitude Z of the output impedance of the whole network which is R x 1 Va D2 F Q Zout 18 28 where x w wk At frequency wo the series combination of L and C is a dead short thus the Johnson noise current yin from R generates no noise voltage whatsoever across R Nevertheless a signal power of IZ Rin is delivered to the load This one way transfer seems a bit odd not to say impossible The reason for it is that we ve assumed that the photodiode has no dissipation of its own that it is a perfect current source in parallel with an ideal capacitor Such a device is unphysical since there is no limit
64. over more than that by jacking up Ry and so reducing its Johnson noise current since R Ca no longer sets the bandwidth Life gets a bit more complicated in the biased case Here the base current is not 3 of la but 3 of Iza which can easily be comparable to Jy Since it still has full shot noise this can represent a significant noise increase In this case you can use a superbeta or Darlington for the cascode device as we did in the bootstrap example You can build the Darlington from a pair of BFG25A Xs since Ica is still small Bias the driver transistor so that its Ig is about 0 1 0 25 times Jz to keep its voltage noise down without contributing large amounts of shot noise When a fast transistor running at high collector current has a capacitive load in its emitter circuit the input impedance has a tendency to look like a negative resistance at high frequency leading sometimes to UHF oscillations if the driving impedance is too low These may be very difficult to see on an oscilloscope but will make the amplifier act very mysteriously A 100 Q resistor in the base of Q solves this problem in most cases In case you have a real embarrassment of riches and your photocurrent is too large to allow you to use the BFG25A X you can use another device of the same general type a BFG505 for example or a small signal Darlington such as an MPSA14 The problem with general purpose devices such as the 2N3904 is that their frs roll off so badly
65. quite small There are lots of differences between that regime and baseband which make front end design a challenge If you re working in a bandwidth of less than an octave you can do some reactive matching tricks that help a great deal There s an inescapable trade off between mismatch and bandwidth For the common case of a parallel RC circuit there is a Just off resonance Xz and Xc have equal and opposite slopes making the total reactance change twice as rapidly with frequency as in the lowpass prototype This reduces the 3 dB width by a factor of 2 making the total bandwidth about the same as the lowpass prototype 18 5 HOW TO GO FASTER 719 theorem of Bode that states ee 1 20 In dow lt 18 31 J IP RC Darlington and Fano later published more general versions for complex impedances but Bode s is the most useful Thus if you don t mind a return loss of 6 dB 75 efficiency set T 0 5 and you can get a BW of 2x In 4 or 4 5x the RC band width The 25 average passband loss is 1 24 dB compared to a perfectly matched resistance Considering that the average passband loss of the unaltered RC rolloff is 10 log arctan 1 1 04 dB we get a 4 5x bandwidth improvement for an additional signal loss of 0 2 dB which is a pretty good payoff Note that I must be close to 1 almost everywhere in order that the integral have a finite value The basic rule of thumb is that if you use a three element tee network
66. quivalent circuit for inc and rg In an unbiased cascode where Ic is all from photocurrent this contribution exactly cancels the rolloff of the photocurrent shot noise so that the collector current of Q has full shot noise at all frequencies Thus the 1 Hz SNR rolls off exactly as the signal does and is 3 dB down at the signal corner frequency f This is at least easy to remember On the other hand if the applied emitter current Iza has only times full shot noise power as it will in a minute the inc contribution will start to dominate the bias current noise at a somewhat lower frequency fsnr fev 18 18 which turns out to be a serious limitation Aside Q Voltage Noise If the Rg noise of the transistor is important its voltage noise has to be added in to the numerator surd of 18 17 which becomes ino J2eler2 4kT Rg 18 19 V 1 Carg BJT noise models have a good handle on the fundamental physics so BJT circuits actually follow the model 18 4 6 Externally Biased Cascode Of the two promised ways we can improve the bandwidth the simpler one is to apply a very quiet DC bias current Jgq to the emitter of Q in addition to The value of rg can be reduced considerably this way further improving frc For example if we use Iza 20 WA re drops to 1 25 KQ and fre is 1 27 MHz quite a bit better than our original 1600 Hz and enough for the circuit requirement We start running into the input capa
67. rc fr f and the loop bandwidth of the resulting transimpedance amplifier is there fore approximately fer y fre fr 18 5 which for the LF356 100 kQ2 100 pF combination is 16 kHz 4 MHz or about 250 kHz The transimpedance rolls off somewhat earlier than this since it depends on the magnitude of the impedances of the feedback elements and not merely on their ratio Calculating the transimpedance bandwidth is a straightforward exercise you put a cur rent into the summing junction and calculate how much goes through Rf and how much through C4 Without going hip deep into algebra you lose a factor of between 2 and 2 in bandwidth depending on the details of the frequency compensation scheme so for a rule of thumb we ll say that V frc fr a Fa ap Y 18 6 18 4 TRANSIMPEDANCE AMPLIFIERS 695 We ll actually get around 130 kHz transimpedance bandwidth from the LF356 circuit a factor of more than 8 improvement This is still fairly far from 1 MHz but getting a lot closer We need about 8 times more bandwidth so if we choose an amp with a bandwidth 60 or so times higher i e 250 MHz then we ought to get there Right Well sort of There are two things we ve left out of this picture One is noise and the other is frequency compensation Frequency compensation is easier so let s knock that off first 18 4 1 Frequency Compensation The equation for the closed loop noninverting gain of a feedback amplifier is
68. re much faster small BJTs available for example the 25 GHz BFG424F but they don t have the BFG25A X s beta linearity or highish Early voltage and anyway it s hard to keep something that fast from oscillating when you hang a capacitance on its emitter 714 FRONT ENDS With most devices it is impossible to rely on worst case specifications way down in the mud because there aren t any frequently not even typical ones Use the typical specs but build in a safety factor of at least 3x on fr and In the biased cascode arrangement positive or negative photocurrent is equally accept able provided that the bias is larger than the largest expected photocurrent This is convenient since no PNP transistor comparable to the BFG25A X is available In an unbiased cascode bootstrapped or not a positive photocurrent requires a PNP transistor or P channel FET These are not as good as their NPN or N channel relatives The MMBR321 is a good fast PNP 5 GHz for high currents but is not as much use for low ones as its beta falls off badly Probably the best thing to use is a small signal Darlington such as an MPSA64 which has been found to work well Darlingtons ideally should have a 1 f behavior because the driver transistor returns the output device s base current to the collector circuit until its own fr is approached The deficiencies of the cascode device are partly hidden by the bootstrap if used Some cutting and trying is necessary t
69. rements including transient extinction tunable diode laser spec troscopy and coherent lidar Spectroscopy and extinction experiments use the opti cal system of Figure 10 10 and the coherent lidar just adds an interferometer as in Example 1 12 Noise cancelers are easily constructed and are commercially available Note This circuit is much easier to mess up than to improve If you re building your own for the first time build the basic model exactly as shown with capacitance multipliers and a few bypasses on the supplies and perhaps different photodiodes e g BPW34s which have Ca 10 pF 25 V and see how it works before changing it Seemingly small changes such as switching to CMOS op amps can make a profound difference Especially resist the temptation to put the photodiodes on cables 1 inch leads at most 18 6 8 Limitations The most serious limitation of the canceler is the deviations of the transistors from ideal behavior principally the parasitic series resistances of the emitter and base Rg and Rp respectively This can be got round by using the differential model in which only a small fraction of the photocurrent has to go through the differential pair From an optical point of view the noise canceler s biggest liability is its own strength after it cancels the big ugly correlated noise it shows up all the second order warts on your beams Cancellation is hindered by anything that decorrelates the noise vign
70. rink which is a great help A simple charge pump followed by a capacitance multiplier will get you a nice quiet 24 V which is usually lots The calculated transimpedance gain and CNR of the cascoded transimpedance ampli fier appear in Figure 18 10 with and without an additional 30 uA Iza Using a higher bias current makes it worse rather than better there s a big improvement in bandwidth and mid frequency SNR but even in this best case the 1 MHz SNR is down by 6 dB due to the bias current noise so we have to go a bit further still Aside DC Offset A minor drawback to the externally biased cascode circuit is that the DC level at the output of the transimpedance amplifier is no longer zero at zero photocurrent This offset can be trimmed out but it will drift somewhat with temperature so that more circuit hackery is necessary if a highly stable DC level is needed Most of the time it isn t especially since other drift sources such as etalon fringes are normally much more serious If we can raise Vpias enough a resistor from there to the summing junction can get rid of the DC offset without adding too much Johnson noise A diode connected transistor in series with this resistor will provide first order temperature compensation Transimpedance Ohms 18 4 TRANSIMPEDANCE AMPLIFIERS 705 1 Hz CNR dB Eo ld dotan lito diles ia SEOs TUTUO ee ee 4 125 2E 05 l 1E 05 S ae F Unbiased Zm i k D 2E 04 Bia
71. rnal biasing via Rz provides even more improvement 702 FRONT ENDS fact there are two ways to fix these minor warts while gaining even more bandwidth First of all though let s look at the SNR of the cascode to see what this bandwidth improvement costs us 18 4 5 Noise in the Cascode In the simple load resistor case the signal shot noise and Johnson noise contributions rolled off together resulting in a constant SNR Here we re not quite that lucky because there is an additional noise contribution from Q which rises with frequency it is much more benign than the eyamp problem with transimpedance amplifiers however Any transistor has some noise of its own A simple noise model of a BJT is shown in Figure 18 9 which neglects only the Johnson noise of the base resistance rg nor mally only a problem when Ic 2 1 mA The active device in the model has infinite transconductance i e emitter impedance of 0 2 and no noise Noise current inp is the shot noise of the base current Ig Ic f which is inescapable while inc is the shot noise of the collector current which shows up in parallel with the small signal emitter resistance rg we ignore the difference between Jc and Ig for now and just talk about the collector current Jc If the emitter is grounded all of inpias goes from ground into the emitter and so contributes full shot noise to the collector current On the other hand if the emitter is biased by a current source e
72. s and outboard differential pairs to reduce the noise of another op amp Manufacturer codes AD Analog Devices M ON Semiconductor N NEC P NXP Semiconductor T Toshiba Aside Input Capacitance Specs Many newer op amps have two input capacitance specifications for common mode and differential signals for instance the OPA656 s are 0 7 pF common mode and 2 8 pF differential This has to do with the way their input structures work because the sources of the differential pair are connected together differential signals see the two Cg of the two input devices in series but common mode signals don t Unfortunately none of the manufactures specifies now these capacitances are measured so the safe procedure is to use the larger one or perhaps Caiff Cem 2 The OPA657 a 710 FRONT ENDS decompensated OPA656 has 4 5 pF of differential Cin surprisingly high for its 1 6 GHz GBW Gotcha SPICE Macromodels If you re doing your front end design with SPICE or another circuit simulator good luck to you with care you can do a reasonable job but be suspicious many op amp models contain inaccurate noise models or none at all An appalling number also omit the input capacitance of the op amp which as we ve seen is a vital parameter If you use simulation as a substitute for thought you ll get the performance you deserve sometimes the SNR from a correctly formulated SPICE simulation using the manufacturer s op amp models can be
73. s chapter fighting to stay at the shot noise limit but sometimes that just isn t possible For example if our 2 A photocurrent were 50 pA instead we d need a GQ load resistor to get within 3 dB of the shot noise and only physicists use resistors that large What s more in a DC measurement any significant reverse bias will corrupt the data with leakage current What we d like to do then is go to an AC measurement but that may involve choppers and so forth which are bulky expensive and unreliable If we have to do a DC measurement with no opportunity to measure the leakage current independently we re stuck with operating at exactly zero bias to make the leakage zero As we saw in Section 14 6 1 the small signal resistance of a zero biased photodiode can be quite low most are nowhere near GQ even at room temperature and all drop by half or even a bit further every 10 C This resistance appears in shunt with the photodiode It contributes Johnson noise current of course but what s more it increases the noise gain of the stage in much the same way that the photodiode capacitance does except that being a resistor it does it at all frequencies Keep the photodiode small the load resistor no larger than necessary to override the amplifier noise and consider cooling the diode Aside Heroic Efforts Some specially selected diodes can reach 1 or even 50 GQ at 20 C and really careful work can get these down to a few h
74. s on the Supplies We talked about the virtues of capacitance multipliers in Example 14 1 they have poor regulation near DC where that s OK and unsurpassed regulation at AC where it really counts because the supply rejec tion of your amplifiers is poor and your switching power supplies very noisy Front ends are an excellent place for a capacitance multiplier Always Build a Prototype and Bang on lt It is not possible to build a first class front end with nothing but SPICE and a PC board layout package This subsystem absolutely must be prototyped and the prototypes characteristics measured to within a 18 8 HINTS 737 gnat s eyebrow to make sure that you understand where all the noise is coming from If its noise performance at your expected minimum photocurrent is not within a couple of tenths of a decibel of what you expected stop and find out why A certain healthy paranoia is indicated here The other reason is that circuit strays are very important The transimpedance amp design we wound up with used an LF357 with a 300 kQ feedback resistor and a 0 8 pF feedback capacitor Without the capacitor its phase margin was negative it would have oscillated at about 1 MHz depending slightly on where the second pole fell Increasing the capacitor will seriously degrade its bandwidth Ordinary metal film W axial lead resistors have a capacitance of about 0 25 pF and surface mount ones less than that so such a small feedback capacitance is
75. s to 1600 Hz still not blazing fast We get to keep Figure 18 1 The world s simplest front end a load resistor 18 2 PHOTODIODE FRONT ENDS 691 that factor of 6 all through the design however so eventually it ll take us from 170 kHz to 1 MHz which is a bit more impressive sounding Since the noise of the bias current will be more than 30 dB below the photocurrent shot noise this seems like a good thing to do we get a factor of 6 in bandwidth for a shot noise increase of 0 004 dB which is too small even to measure See Section 3 5 2 The signal voltage V goes as ia f RL O TF 2 RLCIF 18 2 as shown in Figure 18 2 Somewhat surprisingly though the signal to noise ratio does not deteriorate at all The resistor s iy and the shot noise current are both treated exactly as the signal is The reason for this is apparent from Figure 18 1 the signal and noise sources are all connected in parallel Thus they all roll off together with increasing frequency which makes their ratios frequency independent as Figure 18 2 shows Any deterioration of the signal to noise ratio of the measurement is due to the subsequent amplifier stages It s not the poor amplifier s fault though a source whose impedance changes by a factor of 600 over the band of interest is not the best of neighbors As is usual when it s circuit constants and not laws of nature which are in the way with a bit of ingenuity we can
76. se because the Johnson noise current is so large at these resistances There are two techniques that work reasonably well transformer coupling and very quiet bipolar current amplifiers At high frequency reactive matching networks are a third 18 7 4 Transformer Coupling If the source impedance is a poor match for any available amplifier why not change it Of course the source impedance could be increased by wiring a resistor in series with it but that would be a strange way to improve the noise performance Instead an impedance transforming network is used For high frequency narrowband 1 octave or less an LC matching network is usually best The same idea can be applied at low frequency or wide bandwidth as well using a transformer A good transformer has strong mutual coupling between its windings and low losses to ohmic heating in the copper and hysteresis or eddy currents in the magnetic core material usually powdered iron or ferrite sometimes permalloy This means that nearly all of the available power from the primary is available at the secondary furthermore by the fluctuation dissipation theorem low losses mean low added thermal noise The reason this is useful is that if we wind a transformer with an N turn primary and M turn secondary winding the voltage at the secondary is K M N times the primary 734 FRONT ENDS voltage and the current is 1 K times Thus the impedance has been transformed by a factor of K2 An a
77. sed Zm 1E 04 Unbiased CNR i 5E 03F Biased CNR 2E 03 L Shot Noise CNR 110 1E 03 I l l 0 01 002 0 05 01 02 05 1 2 5 10 Figure 18 10 Calculated response and Frequency MHz CNR of the cascode transimpedance amplifier of Figure 18 8 at I4 2 uA with and without a 30 yA leq 18 4 8 Bootstrapping the Cascode If even small DC shifts are obnoxious or the required value of gq is so large that base current shot noise is a limitation another technique is superior bootstrapping As shown in Figure 18 11 driving the cold end of D with a follower Q gt forces the drop across Ca to be constant at least at frequencies where Xc2 is small and Xcg gt rp In order for this to be any use the bootstrap has to have much lower impedance than the cascode so make lc gt Ic analyze for noise but the results are The bootstrap circuit is a bit more complicated to nearly the same as for a biased cascode with the R Dys Qi E Output gt L A E Ca eae V Q2 Vbias Figure 18 11 Bootstrapping the unbiased cascode circuit reduces the effects of rg and has per formance similar to that of the biased cascode without the offset current due to Rg 706 FRONT ENDS same collector current Assuming c2 gt Ici the noise current from Q gt flowing to the emitter of Q via C4 is 1 UNbootstrap Y A 2elqwCarE 18 20 C2 to leading order in o This is approximately 1c2 14 1 times
78. sing to 1 dB over shot noise at 1 MHz There are no unpleasant surprises which helps us to be confident that we finally understand the circuit 18 4 9 Circuit Considerations Although the cascoding and bootstrapping tricks seem like a free lunch nevertheless like all circuit hacks they have their limitations The linearity of the transistor s gain may not be as good as that of the photodiode Normally a small amount of bias 20 wA or so will linearize the transistor well enough For the most critical applications use a highly linear transistor a Darlington or if driven to it FET FETs have no base current nonlinearity but their transconductance is low and their noise high so they don t usually work as well The BF862 is sometimes an exception 18 4 10 One Small Problem Obsolete Parts Most inconveniently National Semiconductor discontinued the 75 cent LF357 in 2004 There s no single replacement with its particular combination of virtues not even among the fancy 50 parts See Table 18 4 For the current design we need Ry gt 300 kQ to keep the SNR drop to 0 5 dB at low frequency and 1 dB at 1 MHz with a minimum of 2 uA If the maximum Jy is less than 100 uA we can get away with a 5 V amplifier in which case things are easier we can drop in a 5 OPA656 and we re done its input capacitance is about the same as the 357 s and it has lower voltage noise We can leave Cy the same since the 656 is unity gain stable
79. ss Rz is 2kT e 51 mV at room temperature and we enter the Johnson noise limit Good instrument designers grind their teeth if they re stuck in the Johnson noise regime since the data from an expensive optical system are being seriously damaged by circuit limitations In particular running a photodiode into a room temperature 50 Q load is always a mistake unless the light level is very high milliwatts in the visible There are lots of things you can do to get decent bandwidth so resist the 50 Q temptation As we ll see later it s also possible to achieve an effective temperature of the load resistance as low as 35 K at room temperature so all is not lost Remember too that the SNR versus thermal noise curve doesn t have a sharp corner Table 18 2 shows the SNR degradation due to load resistor Johnson noise as a function of the DC voltage across Rz which is a convenient way to remember it If 77R 0 2 V then nin 0 Siyshor 6 dB down and we ve already lost 1 dB in SNR Making R too big wastes both bandwidth and dynamic range so it is usually best to choose a value that drops 100 mV to 1 V Later we ll do this with transimpedance amps too For the present circuit we will assume that a 1 dB loss is acceptable so we ll shoot for a voltage drop of 0 2 V With our 2 yA photocurrent we ll need a 100 k resistor which will improve the RC bandwidth to 16 kHz a mere factor of 60 away from our goal 18 3 KEY IDEA REDUCE THE SW
80. that the problem isn t well posed The mapping of what you actually care about onto the photocurrent is just about always imprecise at the level of a percent or two due for example to etalon fringes calibration drift background light glints and so on There are honorable exceptions but not that many and no measurement whatsoever can give a clear answer to a fuzzy question 3 Physicists such as the author are often prone to oversimplifying circuit require ments It is not enough to aim at being shot noise limited or Ry limited and TT d have been less complimentary but then you couldn t show them this section when the problem comes up Miller and Friedman s book Photonics Rules of Thumb was written partly to help cure this problem Time bandwidth product issues like this show up in digital signal processing too see Section 17 5 690 FRONT ENDS stop there Filters do not cut off everything outside their passbands Not every thing has a one pole rolloff Shot noise limited SNR can be improved by getting more photocurrent There s no substitute for calculating the SNR and frequency response 18 2 PHOTODIODE FRONT ENDS This section is really an extended example of how to design a front end amplifier for a visible or near IR photodiode and how to get a factor of 4000 improvement in bandwidth over the naive approach without sacrificing SNR All the signal to noise comparisons we ll be making will be the DC signa
81. the flatband degrading to 3 dB above shot noise at 1 MHz and gets us a 3 dB bandwidth of 2 MHz The final circuit is shown in Figure 18 12 its calculated performance in Figure 18 13 a Figure 18 13 b shows the prototype s measured performance which is somewhat better than the worst case calculation The measured shot noise dark 15V C 0 25 pF 2N3904 2M re i Qs la BFG25A X a Q Q a i ig MPSA18 A L i Ca Output LF357A 15V Figure 18 12 The final circuit cascode Q plus bootstrap Q2 cope with the obese 100 pF diode and diode connected Qs cancels the Vgg drift of Q1 LT JO URS O8eIOA eIOAO ue sey dn s AL ANS p le no e3 uey Joyoq Surwous yusrmoojogd y gz UNA stou Mdo ostrou yIep wioyoq adAjoj01d y Jo mdmo q ZHN 1 gp g g ATWO UMOP SI WNO PWMP e Nm euy 94 JO IDUBUIIOJI9A T ST ANSIA q 23S AG ET LS 7HW 298 2 dOlS ZH BBE She 2H4 B AS zH 0 OT gy 14915 An 2 3E 1 e ZHIN Aouenbe4 O S Z t SO ZO HO S00 ZO0O 100 T T F T T T T T vO 3S OLA TN SELF u s ss YNO ZH L uz 031 so 3z Sel gp UNO ZH L S0 3 did S0 3S swyoO souepaduisuea y 707 708 FRONT ENDS noise ratio is 9 5 dB at low frequency dropping to 4 5 dB at 1 MHz These numbers correspond to total noise 0 5 dB over shot noise at low frequency ri
82. ton shove the more powerful of the two the comparison beam into the lower photodiode and run the other signal beam through your optical system to the signal photodiode It is a very good idea to put a good quality polarizer right at the laser because otherwise the spontaneous emission contribution doesn t split the same way as the laser light and that disturbs the cancellation The exact ratio is usually not critical a rule of thumb is to make the comparison beam 1 1x to 2x as strong as the signal beam Choosing 2x costs more laser power but sets the operating point at A Vgg 0 where the temperature drift of the baseline is zero The linear output is very convenient to use because with the comparison beam blocked it turns into an ordinary transimpedance amp which makes setup easy you can adjust the aiming by maximizing the DC and a spectrum analyzer will tell you how much cancellation you re getting The log ratio output of course rails when either beam is blocked you get log 0 or log oo There are several useful variations of the basic circuit including the differential model of Figure 18 20 and the fast ratio only model which extends the log bandwidth to several megahertz 18 6 5 Noise Canceler Performance This is a surprisingly powerful technique In a measurement whose sensitivity is limited by laser residual intensity noise RIN the noise canceler can improve the SNR by as much as 70 decibels at low frequencies and
83. tributing an additional phase shift at fr from 40 down to 15 C Ri la Dy pusu E Output E Ta Ca Vias Figure 18 3 Op amp transimpedance amplifier 694 FRONT ENDS Gain V V Phase deg 1E 05 180 1E 04 135 1E 03 1E 02 E 1E 01 1E 00 45 1E 01 F 0 1E 02 1E 02 1E 03 1E6 04 1E 05 1E 06 1E 07 1 08 Frequency Hz Figure 18 4 Frequency responses of parts of the transimpedance amplifier loop A is an LF356 op amp Ry 100 KQ Cf 6 3 pF Ca 100 pF See Section 18 4 1 for the choice of Cf When we close the feedback loop by connecting some network between the output and input of the amplifier we can predict the frequency response of the resulting circuit from the open loop responses of the amplifier and the feedback network The feedback network here is the series combination of Rf and Cg whose voltage gain is 1 18 4 1 j2nfR Ca Ha f Roughly speaking the closed loop gain of an amplifier starts to roll off at about the point where the product of the open loop gains of the amplifier and feedback network falls to 0 dB Extra phase shifts due to the other poles in the circuit can modify this somewhat as we ll see below but it s within a factor of 2 Far down on their slopes the responses of the feedback network and the amplifier are approximately jfrc f and jfr f respectively Their product is approximately f
84. uch advanced front ends allow you to make high stability measurements in bright field make simultaneous amplitude and phase measurements or reject laser noise with extremely high efficiency A good one can spectacularly improve your measurement Throughout this chapter we ll be tossing around ultraquiet voltage and current sources and most of the time we ll be behaving as though light source noise doesn t exist Don t be concerned about where we re getting these magic parts quiet voltages and currents are constructed in Section 14 6 5 and Example 14 1 and source intensity noise is largely vanquished in Section 10 8 6 Preamble to We Will All Go Together When We Go in An Evening Wasted with Tom Lehrer private label recording 1959 reissued by Reprise Records 1966 Building Electro Optical Systems Making It All Work Second Edition By Philip C D Hobbs Copyright 2009 John Wiley amp Sons Inc 688 18 1 INTRODUCTION 689 TABLE 18 1 Major Sources of Noise in Front Ends Source Type Formula Dominates When Photocurrent Shot noise inshot Cel Bright light large Rz Load resistor Johnson noise inth 4kT R 2 Dim light small R Amplifier Input current noise in as specified Ideally never Amplifier Input voltage noise vy as specified Dim light large RC or a fast noisy amp Power supply Ripple regulator noise Only by blunders 18 1 1 Noise Sources Since good front end design is largely a matter of bal
85. ul as their low noise specs would suggest This remains true even if we put them on steroids as the following example shows Example 18 1 External JFET Differential Pair It s often possible to improve the noise performance of op amp TIAs by adding a discrete JFET front end By adding a pair of 2SK369s with a voltage gain of 20 or so running at Jp 10 mA Vas 0 1 V we get 1 Hz vy 0 7 nV which is 1 0 nV for the pair combined Keeping Vps down to 6 V or so keeps the gate current below 5 pA so iy should be in the femtoamps Most of the input current noise comes in via the drain gate capacitance so we ll assume a cascode stage Getting a stage gain of 20 requires Rg 20 gm 400 Q The resulting amplifier has about 90 pF of inverting input capacitance unfortunately due to the very large die size of the JFETs With the BJT cascode the 50 pF feedback 700 FRONT ENDS TABLE 18 3 Suggested Op Amps for Front Ends Device FET LF356 OPA627 OPA129 AD795 OPA657 OPA656 Bipolar OP 27 OP 37 OPA687 LT1028 AD829 AD8397 LM6311 LM7332 LMH6624 LME49710 OP 470 AD8397 ADA4898 1 MC33078 Manu facturer MHz NS TI TI AD TI TI AD AD TI LT AD AD NS NS NS NS AD AD AD ST fr 4 20 lt 1 6t 1600 230 45 3800 50 600t 69t 80t 21t 1500t 55t 6t 33t 33t 10 12t 6 15t 11 4 8t Tt 3 8 3 8 1 1 1 1 4 5t 2 3t 15 5t 0 9t 4 7
86. undred electrons s worth of noise in millihertz bandwidths if you can wait long enough 18 7 2 Pyroelectric Front Ends Pyroelectric detectors are difficult devices to interface to since they convert a temperature change into a charge rather than a current as quantum detectors and bolometers do That means that at low frequencies the current available is proportional to the time derivative of the sensor temperature which is inconvenient Example 17 1 shows one way to solve that problem here we re concerned with keeping as much SNR as we can which means high stability and femtoamp leakage From the front end s point of view the trouble with pyroelectrics is their low signal level and very high impedance The most familiar pyroelectrics namely porch light sensors make their AC signal by using a segmented Fresnel lens that casts a dozen or so images on a split detector The two are wired in opposing parallel so when you walk up to the door twelve of you in a row cross from the half to the half generating a nice AC signal The two pyros are connected between the gate of a discrete MOSFET and ground with a 10 MQ leak resistor to keep the DC level constant The FET s drain Well electrical engineers use them once in a while but it takes a physicist to put one on a cable G Eppeldauer and J E Hardis Fourteen decade photocurrent measurements with large area silicon photodi odes at room temperature Appl Optics 30 22 3091
87. very low Cin you can get by cascoding which allows the use of much bigger feedback resistors as we ll see below 18 4 TRANSIMPEDANCE AMPLIFIERS 701 18 4 4 No Such Amp Exists Cascode Transimpedance Amplifiers In our design if we are aiming at getting to 1 MHz transimpedance bandwidth Rules 1 5 lead to an amplifier with the following characteristics Iyamp lt 0 20 pA Hz Namp lt 0 32 nV Hz 250MHz lt fr lt 1250 MHz No such amplifier exists not even with an external input stage Now what Another circuit hack of course Recall that our reason for using the transimpedance amplifier was to get rid of the voltage swing across C We can do this another way by using a common base transistor amplifier as shown in Figure 18 8 Resistor Rg will come in later ignore it for now The transistor faithfully transmits its emitter current to its collector while keeping its emitter at a roughly constant voltage This idea is used in common emitter transistor amplifier design to eliminate severe bandwidth limitations due to collector base feed back capacitance the Miller effect The resulting amplifier configuration resembles a two layer cake and is called a cascode The cascode idea works here as well In the Ebers Moll transistor model the small signal resistance rz of the transistor s emitter circuit is kT T g elc 18 15 where kT e is 25 mV at room temperature rg is intrinsic to the transistor and shoul

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