ARMSTRONG`S PHASE MODULATOR
Contents
1. Figure 1 DSBSC carrier The signals described by both eqn 2 and eqn 3 are shown in phasor form in Figure 1 a and b above The amplitude spectrum is also shown it is the same for both cases a and b Each diagram shows the signals for the case m 1 That is to say the amplitude of each side frequency component is half that of the carrier In the phasor diagram the side frequencies are rotating in opposite directions so their resultant stays in the same direction co linear with the carrier for a and in phase quadrature for b Both eqn 2 and eqn 3 can be modelled by the arrangement of Figure 2 below Armstrong s phase modulator a2 107 message x DsBsc_ 9 Armstrong s sine wave signal G 100 kHz carrier sine wave adjust phase Figure 2 Armstrong s phase modulator phase deviation 108 a2 Having defined Armstrong s signal it is now time to examine its potential for producing PM But first we have been using the symbol m for the ratio of DSBSC to carrier amplitude because our starting point was an amplitude modulated signal and m has been traditionally the symbol for depth of amplitude modulation The amplitude modulation was converted to quadrature modulation We will acknowledge this in the work to follow by making the change from m to Ag Thus Ad m see eeees 4 Analysis shows see the Appendix to this experiment that the carrier of Armstrong s2. T11 model an envelope detector using the RECTIFIER in the UTILITIES module and the 3kHz LPF in the HEADPHONE AMPLIFIER module Connect Armstrong s signal to the input of the envelope detector Listen to the filter output the envelope with headphones Set the PHASE SHIFTER as far off the quadrature condition as possible and concentrate your mind on the fundamental Slowly vary the phase You will hear the fundamental amplitude reduce to zero while the second harmonic of the message appears Notice how sensitive is the point at which the fundamental disappears This is the quadrature condition Note that you have been able to detect the presence of a low finally zero amplitude tone in the presence of a much stronger one This was only possible because the low amplitude term was a sub harmonic of the higher amplitude term The opposite is extremely difficult This is a phenomenon of psycho acoustics practical applications Remember Armstrong s modulator generates phase or frequency modulation by an indirect method It does not disturb the frequency stability of the carrier source as happens in the case of modulators using the direct method eg the VCO But to keep the distortion to acceptable limits Armstrong s modulator is capable of small phase deviations only see the Appendix to this experiment This is insufficient for typical communications applications The deviation can be increased by additional processing namely by
3. Q1 by writing eqn 3 in the general form of a t cos ot t obtain approximate expressions for both a t and t as functions of m or the equivalent Ad Q2 can a conventional phase meter be used to set the DSBSC and carrier in quadrature Explain Q3 a 4 volt peak to peak DSBSC is added to a 5 volt peak to peak carrier in phase quadrature Calculate a the peak to peak and the trough to trough amplitudes of the resultant signal b the phase deviation of the carrier after amplitude limiting Q4 suppose the phasing in an Armstrong modulator is adjusted by equating adjacent envelope maxima Obtain an approximate expression for the phase error a from the ideal quadrature as a function of a small error in this amplitude adjustment Q5 if there is an error in the phasing of an Armstrong modulator the output could be written as yt E cosat E cosut sin at Obtain an approximate expression for the phase deviation following amplitude limiting for small a the phase error from quadrature Q6 the phasing in an Armstrong modulator is adjusted by listening for the null of the message in the envelope the psycho acoustic method If during this adjustment the fundamental amplitude is reduced to 40 dB below the amplitude of the second harmonic of the message what would be the resulting phase error 116 a2 Armstrong s phase modulator APPENDIX Analysis of Armstrong s signal If we define Armstrong s signal
4. signal is undergoing phase modulation The peak phase deviation is proportional to the ratio of DSBSC to CARRIER peak amplitudes at the ADDER output but it is not a linear relationship The peak phase deviation AQ is given by Ag arctan pees radians 5 CARRIER ts Remember that the amplitude of the DSBSC is directly proportional to that of the message so the message amplitude will determine the amount of phase variation For small arguments arctan arg arg Thus to minimize distortion at the receiver the ratio of DSBSC to carrier must be kept small A receiver to demodulate a phase modulated signal is sensitive to these phase deviations To keep the received signal distortion to acceptable limits the peak phase deviation at Armstrong s modulator should be restricted to a fraction of a radian according to distortion requirements as per Figure 3 The analysis of distortion is discussed in the Appendix to this experiment Armstrong s phase modulator Ao ratio DSBSC to carrier amplitude Figure 3 distortion from Armstrong s modulator practical realization of Armstrong s modulator The principle of Armstrong s method of phase modulation or his frequency modulator with the added integrator as described earlier is used in commercial practice But the circuitry employed to generate this signal is often not as straightforward as the arrangement of Figure 2 It is not always possible to isolate and so measure s
5. as Armstrong s signal cos t Ad sinutsinot tt A l and then write this in the general form of a narrowband modulated signal we have Armstrong s signal a t cos at O t nn A2 where Ja g sin ur a t UN a a a Bc s sn A3 g t arctan A d sinut tts A4 where Ad DSBSC carrier 2 tts A 5 The expressions for both a t and o t can be expanded into infinite series For small values of Ad say Ad lt 0 5 they approximate to A 5 A aa RT T L approx at 14 P 4 LO inau A6 3 3 approx o t Ao a eos ut F cos 3 ut ee A7 Equation A 6 confirms that to a first approximation the Armstrong envelope is sinusoidal and of twice the message frequency There will be higher order even harmonics of the message but as you will have observed in the psycho acoustic test earlier no component at message frequency Equation A 7 shows that the phase modulation is proportional to Ad as wanted but that there is odd harmonic distortion in the received message The need to keep the distortion to an acceptable value puts an upper limit on the size of Ao Figure 3 shown previously graphs the expected signal to distortion ratio to a better approximation Remember that eqn A 7 gives the distortion from an ideal demodulator it gives no clue as to the spectrum of the Armstrong signal the amplitude limiter From your work on angle modulated signals you will appreciate that the signal y t cosa OD
6. frequency multipliers The frequency multiplier has been discussed in this Volume entitled Analysis of the FM spectrum You can learn about them in the experiment entitled FM deviation multiplication this Volume Refer also to the Appendix to this experiment spectral components In later experiments you will be measuring the spectral components of wideband FM signals In this experiment all we have is Armstrong s signal which after amplitude limiting has relatively few components of any significance But they are there and you can find them Armstrong s phase modulator A2 113 So now you will model the WAVE ANALYSER which was introduced in the experiment entitled Spectral analysis the WAVE ANALYSER this Volume and look for them Table A 1 in the appendix to this experiment shows you what to expect Notice it will be possible to find only three possibly five components including the carrier with any confidence the simple WAVE ANALYSER you will be using has its limitations but confirming their amplitude ratios as predicted is a satisfying exercise Remember there are only three components at the output of Armstrong s modulator as modelled by you already To create the FM sidebands Armstrong s signal must first be 1 amplitude limited to produce a narrowband FM signal NBFM and then 2 frequency multiplied to generate a wideband FM signal WBFM You will take step 1 in this experiment and then step 2 in
7. ARMSTRONG S PHASE MODULATOR PREPARATION zerena e a team RSS 106 FM generation sonirn nenene aea i ana 106 Armstrong s modulator ised hase adeiaceech eecnsdbdec die edecens 107 THEORY xssdci Aes dine eee ene Reale Ae E Reet has 107 Ph ASE Ce Vidi OMssicc sacaeetasdccta shaeeegeandedtes deterdoated vate tedeahactees 108 practical realization of Armstrong s modulator e 109 EXPERIMEN Tonni onn a a ne wads R 110 p te hint UP cissadiiensareonsce i Garson awa 110 model adjustnient 5 2 3 cccsdsatscinestuioesucetecs ntestedeatncan cheeses uiadactine 110 Armstrong s phase adjustment cceecccscessseceteeeeeeeeeeeeaeees 112 phase adjustment using the envelope c ssssssssssssssesssssssssesessesssseeeeeeeee 112 phase adjustment using psycho acoustics ssssssssssseessecesseeeesesseee 112 practical applications 5a sssedie ce atest ausreisscn dame aea 113 Spectral components sis c cadscetscteccieiacy tein dactstteacascadeeriece es 113 TUTORIAL QUES TIONS kanae A E 116 APPENDIX neiuna aa a an wah teense 117 Analysis of Armstrong s signal sssessessessesseesressessrssresseese 117 th camiplitude limier nereg e ier aT EEEE EEEE 117 Armstrong s spectrum after amplitude limiting c ssssssssseseeeeeeeee 118 Armstrong s phase modulator Vol A2 ch 12 rev 1 1 105 ARMSTRONG S PHASE MODULATOR ACHIEVEMENTS modelling Armstrong s modulator quadrature phase adjustment deviation
8. a later experiment The amplitude limiting is performed by the CLIPPER in the UTILITIES module 3 with gain set to hard limit refer to the TIMS User Manual Although for the experiment there is no need to add a filter following the amplitude limiter it won t change the spectral components in the region of 100 kHz in practice this would be done and so in the block diagram of Figure 6 below this is shown If you have a 100 kHz CHANNEL FILTERS module you should use it in this position amplitude 100kHz limiter BPF Armstrong s signal mK 100kHz carrier gt cee NBFM to WAVE ANALYSER Figure 6 Armstrong s NBFM signal T12 set up for equal amplitudes of DSBSC and carrier into the ADDER of the modulator B 1 and confirm you have the quadrature condition A message frequency of about 1 kHz will be convenient for spectral measurements Although a ratio of DSBSC to carrier of unity will result in significant distortion at the output from a demodulator refer Figure 3 one can still predict the amplitude spectrum and confirm it by measurement 114 a2 3 version V2 or later Armstrong s phase modulator T13 at the output of your Armstrong modulator add the AMPLITUDE LIMITER the CLIPPER in the UTILITIES module and filter in the 100 kHz CHANNEL FILTERS module as shown in block diagram form in Figure 6 T14 model a WAVE ANALYSER and connect it to the filter output There is no need to calibra
9. calibration introduction to the amplitude limiter PREREQUISITES earlier modulation experiments an understanding of the contents of the Chapter entitled Analysis of the FM spectrum in this Volume EXTRA MODULES SPECTRUM UTILITIES 100 kHz CHANNEL FILTERS optional PREPARATION FM generation As its name implies an FM signal carries its information in its frequency variations Thus the message must vary the frequency of the carrier Spectrum space being at a premium radio communication channels need to be conserved and users must keep to their allocated slots to avoid mutual interference There is a conflict with FM the carrier must be maintained at its designated centre frequency with close tolerance yet it must also be moved modulated by the message A well know source of FM signals is a voltage controlled oscillator VCO These are available cheaply as integrated circuits It is a simple matter to vary their frequency over a wide frequency range but their frequency stability is quite unsatisfactory for today s communication systems Refer to the experiment entitled Introduction to FM using a VCO in this Volume Armstrong s modulation scheme overcomes the problem 2 It does not change the frequency of the source from which the carrier is derived yet achieves the objective by an indirect method It forms the subject of this experiment 106 a2 l Armstrong s system is well described by D L Jaffe Arms
10. ctrum is a tiresome exercise But when finished one has an analytic expression for the spectrum for small B An alternative is to use a fast Fourier transform and evaluate the spectrum for specific values of B This has been done and Table A 1 below lists the amplitude spectrum for B 0 5 and B 1 Component amplitude amplitude amplitude B 0 B 0 5 B 1 otip 0 000 0 381 Ot2u 0 000 0 026 0 072 ot4u 0 000 0 001 0 009 mtS5u 0 000 0 000 0 004 mt6u 0 000 0 000 0 001 Table A 1 0 000 0 006 0 031 Armstrong s phase modulator What would happen if this signal for B 1 was processed by a frequency multiplier The deviation would be increased What would be the new spectrum The analytic derivation of the new spectrum is decidedly non trivial 4 The easy way to find the answer is to generate it and then measure it Although not specifically suggested there will be an opportunity for this in the experiment entitled FM deviation multiplication in this Volume 4 remember this is Armstrong s signal involving the arctan function Derivation of the spectrum of a pure FM signal with B 1 is relatively straight forward see Analysis of the FM Spectrum Armstrong s phase modulator A2 119 120 a2 Armstrong s phase modulator
11. eparately the amplitudes of the DSBSC and the CARRIER So it is not possible to calculate the phase deviation in such a simple straight forward manner Amplitude limiters are also incorporated in the circuitry These intentionally remove the envelope which otherwise could be used as a basis for measurement In these cases other methods must be used to set up and calibrate the phase deviation of the modulator These include for example the use of a calibrated demodulator There is also the method of Bessel zeros This is an elegant and exact method and is examined in the experiment entitled FM and Bessel zeros in this Volume Armstrong s phase modulator a2 109 patching up In this experiment you will learn how to set up Armstrong s modulator for a specified phase deviation and a unique method of phase adjustment Armstrong s generator in block diagram form in Figure 2 is shown modelled in Figure 4 below CH1 A TUS loscittaror ext trig CH2 A MASTER ADOH sin 100K cas 00K TTL sample TTL message sin Figure 4 the model for Armstrong s modulator TI patch up the model in Figure 4 You will notice it is exactly the same arrangement as was used for modelling AM The major difference for the present application will be the magnitude of the phase angle a zero degrees for AM but 90 for Armstrong T2 choose a message frequency of about 1 kHz from the AUDIO OSCILLATOR model adjustme
12. ith the fundamental frequency being twice that of the message from which the DSBSC was derived Each of these two findings suggests a different method of phase adjustment phase adjustment using the envelope T10 trim the front panel control of the PHASE SHIFTER until adjacent peaks of 112 a2 the envelope are of equal amplitude To improve accuracy you can increase the sensitivity of the oscilloscope to display the peaks only Equating heights of adjacent envelope peaks with the aid of an oscilloscope is an acceptable method of achieving the quadrature condition For communication purposes the message distortion as observed at the receiver due to any such phase error will be found to be negligible compared with the inherent distortion introduced by an ideal Armstrong modulator Armstrong s phase modulator phase adjustment using psycho acoustics There is another fascinating method of phase adjustment first pointed out to the author by M O Felix The envelope of Armstrong s signal is recovered using an envelope detector and is monitored with a pair of headphones For the in phase condition this would be a pure tone at message frequency As the phase is rotated towards the wanted 90 degrees difference it is very easy to detect by ear when the fundamental component disappears at u rad s and initially of large amplitude leaving the component at 2u rad s initially small but now large This is the quadrature condition
13. nt T3 check that the oscilloscope has triggered correctly using the external trigger facility connected to the message source Set the sweep speed so that it is displaying two or three periods of the message on CH1 A at the top of the screen Now pay attention to the setting up of the modulator The signal levels into the ADDER are at TIMS ANALOG REFERENCE LEVEL but their relative magnitudes and phases will need to be adjusted at the ADDER output To do this 110 a2 Armstrong s phase modulator T4 rotate both g and G fully anti clockwise T5 rotate g clockwise Watch the trace on CH2 A A DSBSC will appear Increase its amplitude to about 3 volts peak to peak Adjust the trace so its peaks just touch grid lines exactly a whole number of centimetres apart This is for experimental convenience it will be matched by a similar adjustment below T6 remove the patching cord from input g of the ADDER T7 rotate G clockwise The CARRIER will appear as a band across the screen Increase its amplitude until its peaks touch the same grid lines as did the peaks of the DSBSC the time base is too slow to give a hint of the fine detail of the CARRIER in any case the synchronization is not suitable T8 replace the patch cord to g of the ADDER At the ADDER output there is now a DSBSC and a CARRIER each of exactly the same peak to peak amplitude but of unknown relative phase Observe the envelope of this signal CH2 A and compare i
14. te it you are interested in relative amplitudes T15 set the phase deviation to zero by removing the DSBSC from the ADDER of the modulator Observe and sketch the waveform of the signals into and out of the channel filter Find the 100 kHz carrier component with the WAVE ANALYSER This the unmodulated carrier is your reference For convenience adjust the sensitivity of the SPECTRUM UTILITIES module so the meter reads full scale T16 replace the DSBSC to the ADDER of the modulator The carrier amplitude should drop to 84 of the previous reading if you leave the meter switch on HOLD nothing will happen This amplitude change is displayed in Table A 1 of the appendix to this experiment T17 search for the first pair of sidebands They should be at amplitudes of 38 of the unmodulated carrier T18 there are further sideband pairs but they are rather small and will take care to find T19 you could repeat the spectral measurements for B 0 5 which are also listed in Table A 1 T20 you were advised to look at the signal from the filter when there was no modulation Do this again Synchronize to the signal itself and display ten or twenty periods Then add the modulation You will see the right hand end of the now modulated sinewave move in and out the oscillating spring analogy confirming the presence of frequency modulation there is no change to the amplitude Armstrong s phase modulator A2 115 TUTORIAL QUESTIONS
15. trong s Frequency Modulator Proc IRE Vol 26 No 4 April 1938 pp475 481 2 but introduces another it is not capable of wide frequency deviations Armstrong s phase modulator Armstrong s modulator Armstrong s modulator is basically a phase modulator it can be given a frequency modulation characteristic by an integrator inserted between the message source and the modulator For a single tone message at one frequency it is not possible to tell by what ever measurement if the integrator is present so it is an FM signal or not a PM signal Only with a change of message frequency can one then make the decision by noting the change to the spectral components for example theory You are already familiar with amplitude modulation defined as AM E 1 m sinut sinot 2220 ees 1 This expression can be expanded trigonometrically into the sum of two terms AM E sinot E m sinut sinot 4 ste 2 In eqn 2 the two terms involved with are in phase Now this relation can easily be changed so that the two are at 90 degrees or in quadrature This is done by changing one of the sinwt terms to coswt The signal then becomes what is sometimes called a quadrature modulated signal It is Armstrong s signal Thus Armstrong s signal E cos t E m sinutsin t 4 ae 3 a 0 z z E m 1 mai zs i gt a b H H frequency Phasor Form Amplitude Spectrum
16. ts A8 has the potential for many spectral components Armstrong s phase modulator A2 117 This is an angle modulated signal which is what is expected from Armstrong s modulator But Armstrong s signal as defined by eqn A 1 has only three components We know this since it is the linear sum of a DSBSC two components and a carrier one component Then where are all the spectral components suggested by eqn A 7 The signal of the form of eqn A 8 is what we want but we have one of the form of eqn A 2 The difference is the multiplying term a t We would like a t to become a constant This is the function of the amplitude limiter It is required to remove envelope variations The amplitude limiter has been discussed in the Chapter entitled Analysis of the FM spectrum Armstrong s spectrum after amplitude limiting 118 a2 Obtaining the spectrum of the amplitude limited Armstrong signal whilst taking into account the inevitable distortion involves an expansion of eqn A 8 with o t arctan B cosut ts A9 The phase function can be expanded into an odd harmonic series of u o t By cosut Bz cos3ut Bs5 cosSutt i te A 10 This expansion is then substituted in eqn A 8 Taking any more than two terms makes the expansion of eqn A 8 extremely tedious and so this means that the approximation is only valid for say the range 0 lt B lt 1 Even with two terms in t the expansion of eqn A 8 to obtain the spe
17. ts shape with that of the message CH1 A also being displayed T9 vary the phasing with the front panel control on the PHASE SHIFTER until the almost sinusoidal envelope CH2 A is of twice the frequency as that of the message CH1 A The phase adjustment is complete when alternate envelope peaks are of the same amplitude As a guide Figure 5 shows three views of Armstrong s signal all with equal amplitudes of DSBSC and carrier but with different phase errors ie errors from the required 90 phase difference between DSBSC and carrier Armstrong s phase modulator a2 111 Figure 5 Armstrong s signal with Ad 1 and phase errors of 45 deg lower 20 deg centre and zero upper Armstrong s phase adjustment An error from quadrature at the transmitter will show up as distortion of the recovered message at the receiver This will be in addition to the inherent distortion introduced by the approximation arctan arg arg The addition would be anything but linear and difficult to evaluate but easy to measure for a particular case How can the phase of the DSBSC and the added carrier be adjusted to be in exact quadrature An analysis of the envelope of Armstrong s signal is given in the Appendix to this experiment There it is shown that 1 when in phase quadrature the envelope is sinusoidal like in shape Figure 5 above with adjacent peaks of equal amplitude 2 the envelope waveform is periodic w
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