ENVELOPE RECOVERY
Contents
1. the rectifier output which is rectifier output s t AM eesesoeoosoesoeeeeee A2 Note that the AM is centred on and s t is a string of terms on the ODD harmonics of Remembering also that the product of two sinewaves gives sum and difference terms then we conclude that the 1st harmonic in s t gives a term near DC and another centred at 2 Al 81 the 3rd harmonic in s t gives a term at 2 and 4 the Sth harmonic in s t gives a term at 4 and 6 and so on We define the AM signal as AM A 1 m t cost i Cs ttt tt ttt tte ee A3 where for the depth of modulation to be less than 100 m t lt 1 From the rectified output we are only interested in any term near DC this is the one we can hear In more detail term near DC 1 2 4 m A m t ttre A4 which is an exact although scaled copy of the message m t The other terms are copies of the original AM but on all even multiples of the carrier and of decreasing amplitudes They are easily removed with a lowpass filter The nearest unwanted term is a scaled version of the original AM on a carrier frequency 2 rad s For the case where the carrier frequency is very much higher than the highest message frequency that is when gt gt u an inequality which is generally satisfied the lowpass filter can be fairly simple Should the carrier frequency not satisfy this inequality we can still see that the message will be recovered2. would this affect the performance of an envelope detector as a demodulator 80 Al Envelope recovery APPENDIX A analysis of the ideal detector Envelope recovery The aim of the rectifier is to take the absolute value of the signal being rectified That is to multiply it by 1 when it is positive and 1 when negative An analysis of the ideal envelope detector is not a trivial exercise except in special cases Such a special case is when the input signal is an envelope modulated signal with m lt 1 In this case we can make the following assumption not proved here but verified by practical measurement and observations namely the zero crossings of an AM signal for m lt 1 are uniform and spaced at half the period of the carrier If this is the case then the action of an ideal rectifier on such a signal is equivalent to multiplying it by a square wave s t as per Figure 1A It is important to ensure that the phases of the AM and s t are matched correctly in the analysis in the practical circuit this is done automatically product of s t and the AM signal Figure 1A the function s t and its operation upon an AM signal The Fourier series expansion of s t as illustrated is given by s t 4 7 1 cosot 1 3 cos3 t 1 S cosS t Jo vu a Thus s t contains terms in all odd harmonics of the carrier frequency The input to the lowpass filter will be
3. ENVELOPE RECOVERY PREPARATION sccsncantessazasteatanrextasieedansdanannesaaeedinatandepiacusctanphntoussinets 72 PHS CHV CLOG ereiten nr tt Sy tata pac tata E E 72 the diode detectors rnein eaan ORT aa RT AESAAT 72 the ideal envelope detector ci csakennies setectowiakanansannweskiaits 73 thedeal rect Perse 3 is 5 c csstgssarfiehzetsaessinbeeesiaa sea bie ieee etm 73 envelope bandwidth scecic seccdescaescsesteeceledcticies de eteceoeceeseees E 73 DSBSC envelopes steed ie ei Slit do a on We ee ER 74 EXPERIMEN T cenen hannes Seid a aiii i 75 theideal MOE t ccsksiocssis hacteal sti shedoctass sedis sias 75 AM envelopes nr nt an n A RA A 75 DSBS envelopes ne a ae e a E a EE N EE 77 speech as the message M lt Lo eeceeseeesceecceseceseceseceecaeecaeeeseeeneenseeaes 78 speech as the message M gt Loi eeeeseeseesseeecceseceeceseeeeeceecseeeseeeeeeneeeaes 78 the diode detectors csiewecistocecetisancaledbarsnscncessnvseiitaivecteceiees 79 TUTORIAL QUESTIONS ci2 82 8 Ghee eit eats i ete 80 APPENDIX A iesesstetading Aeacets adsaind a Mia Sans Diadead Rea wees tao aes 81 analysis of the ideal detector sissscc ocssccysadeteeed satecasestacavapecsecestias 81 practical modification cevccccsice ehesieesss coveceee sie E eevee E R 82 Envelope recovery Vol Al ch 6 rev 1 1 71 ENVELOPE RECOVERY ACHIEVEMENTS The ideal envelope detector is defined and then modelled It is shown to perform well in all cases exami
4. UNDISTORTED so long as the carrier frequency is at least twice the highest message frequency and a filter with a steeper transition band is used practical modification 82 Al In practice it is easier to make a halfwave than a fullwave rectifier This means that the expression for s t will contain a DC term and the magnitudes of the other terms will be halved The effect of this DC term in s t is to create an extra term in the output namely a scaled copy of the input signal This is an extra unwanted term centred on w rad s and in fact the lowest frequency unwanted term The lowest frequency unwanted term in the fullwave rectified output is centred on 2 rad s This has put an extra demand upon the lowpass filter This is not significant when gt gt y but will become so for lower carrier frequencies present only with halfwave rectifier j Ni ahs om 0 20 40 60 frequency wanted unwanted Figure 2A rectifier output spectrum approximate scale Envelope recovery
5. e case of AM with m lt 1 It would be better expressed in the present instance as he carrier frequency must be very much higher than the highest frequency component expected in the envelope This is certainly NOT so here T10 repeat the previous Task but with the RECTIFIER followed by a simple RC filter This compromise arrangement will show up the shortcomings of the RC filter There is an independent RC LPF in the UTILITIES MODULE Check the TIMS User Manual regarding the time constant T11 you can examine various combinations of diode ideal rectifier RC and other lowpass filters and lower carrier frequencies use the VCO The 60 kHz LPF is a very useful filter for envelope work T12 check by observation is the RECTIFIER in the UTILITIES MODULE a halfwave or fullwave rectifier Envelope recovery Al 79 TUTORIAL QUESTIONS Q1 an analysis of the ideal envelope detector is given in the Appendix to this experiment What are the conditions for there to be no distortion components in the recovered envelope Q2 analyse the performance of a square law device as an envelope detector assuming an ideal filter may be used Are there any distortion components in the recovered envelope Q3 explain the major difference differences in performance between envelope detectors with half and fullwave rectifiers Q4 define what is meant by selective fading If an amplitude modulated signal is undergoing selective fading how
6. elope Now let us test the ideal envelope detector on a more complex envelope that of a DSBSC signal T7 remove the carrier from the AM signal by turning g fully anti clockwise thus generating DSBSC Alternatively and to save the DC level just used pull out the patch cord from the g input of the ADDER or switch the MULTIPLIER to AC Were you expecting to see the waveforms of Figure 5 What did you see Figure 5 a DSBSC signal You may not have seen the expected waveform Why not With a message frequency of 2 kHz a filter bandwidth of about 12 kHz is not wide enough You can check this assertion for example a lower the message frequency and note that the recovered envelope shape approaches more closely the expected shape b change the filter Try a 60 kHz LOWPASS FILTER Envelope recovery Al 77 T8 a lower the frequency of the AUDIO OSCILLATOR and watch the shape of the recovered envelope When you think it is a_ better approximation to expectations note the message frequency and the filter bandwidth and compare with predictions of the bandwidth of a fullwave rectified sinewave b if you want to stay with the 2 kHz message then replace the TUNEABLE LPF with a 60kHz LOWPASS FILTER Now the detector output should be a good copy of the envelope speech as the message m lt 1 Now try an AM signal with speech from a SPEECH module as the message To listen to the recovered s
7. he message and the envelope attributed directly to the absolute sign in eqn 5 Envelope recovery the diode detector It is assumed you will have referred to a text book on the subject of the diode detector This is an approximation to the ideal rectifier and lowpass filter How does it perform on these signals and their envelopes There is a DIODE DETECTOR in the UTILITIES MODULE The diode has not been linearized by an active feedback circuit and the lowpass filter is approximated by an RC network Your textbook should tell you that this is a good engineering compromise in practice provided a the depth of modulation does not approach 100 b the ratio of carrier to message frequency is large You can test these conditions with TIMS The patching arrangement is simple T9 connect the signal whose envelope you wish to recover directly to the ANALOG INPUT of the DIODE LPF in the UTILITIES MODULE and the envelope or its approximation can be examined at the ANALOG OUTPUT You should not add any additional lowpass filtering as the true diode detector uses only a single RC network for this purpose which is already included The extreme cases you could try would include a an AM signal with depth of modulation say 50 and a message of 500 Hz What happens when the message frequency is raised Is gt gt yu b a DSBSC Here the inequality gt gt u is meaningless This inequality applies to th
8. hen passes the result through a lowpass filter The output from this lowpass filter is the required envelope signal See Figure 1 Absolute envelope operator Figure 1 the ideal envelope recovery arrangement The truth of the above statement will be tested for some extreme cases in the work to follow you can then make your own conclusions as to its veracity The absolute value operation being non linear must generate some new frequency components Among them are those of the wanted envelope Presumably since the arrangement actually works the unwanted components lie above those wanted components of the envelope It is the purpose of the lowpass filter to separate the wanted from the unwanted components generated by the absolute value operation The analysis of the ideal envelope recovery circuit for the case of a general input signal is not a trivial mathematical exercise the operation being non linear So it is not easy to define beforehand where the unwanted components lie See the Appendix to this experiment for the analysis of a special case the ideal rectifier A circuit which takes an absolute value is a fullwave rectifier Note carefully that the operation of rectification is non linear The so called ideal rectifier is a precision realization of a rectifier using an operational amplifier and a diode in a negative feedback arrangement It is described in text books dealing with the applications of opera
9. l of the ideal envelope detector is shown in block diagram form in Figure 2 PRECISION RECTIFIER in gt LPF out within UTILITIES module Figure 2 modelling the ideal envelope detector with TIMS The ideal rectifier is easy to build does in fact approach the ideal for our purposes and one is available as the RECTIFIER in the TIMS UTILITIES module For purposes of comparison a diode detector in the form of DIODE LPF is also available in the same module this will be examined later The desirable characteristics of the lowpass filter will depend upon the frequency components in the envelope of the signal as already discussed We can easily check the performance of the ideal envelope detector in the laboratory by testing it on a variety of signals The actual envelope shape of each signal can be displayed by observing the modulated signal itself with the oscilloscope suitably triggered The output of the envelope detector can be displayed for comparison on the other channel AM envelope For this part of the experiment we will use the generator of Figure 3 and connect its output to the envelope detector of Figure 2 Envelope recovery Al 75 test signal 100kHz 0 Figure 3 generator for AM and DSBSC T1 plug in the TUNEABLE LPF module Set it to its widest bandwidth which is about 12 kHz front panel toggle switch to WIDE and TUNE control fully clockwise Adjust it
10. l signal in receivers It is important to note that it is possible for the bandwidth of the envelope to be much wider than that of the signal of which it is the envelope In fact except for the special case of the envelope modulated signal this is generally so An obvious example is that of the DSBSC signal derived from a single tone message DSBSC envelope The bandwidth of a DSBSC signal is twice that of the highest modulating frequency So for a single tone message of 1 kHz the DSBSC bandwidth is 2 kHz But the bandwidth of the envelope is many times this For example we know that analytically DSBSC cosutcosot ts 1 alt cosfat o 2 because U lt lt q then a t cosut tts 3 on a 4 and envelope e t a t by definition 4 22 5 So from the mathematical definition the envelope shape is that of the absolute value of cosut This has the shape of a fullwave rectified version of cosut by looking at it and from considerations of Fourier series analysis the envelope must have a wide bandwidth due to the sharp discontinuities in its shape So the lowpass filter will need to have a bandwidth wide enough to pass at least the first few odd harmonics of the 1 kHz message say a passband extending to at least 10 kHz 74 Al I see the section on Fourier series and bandwidth estimation in the chapter entitled Introduction to modelling with TIMS in this Volume Envelope recovery the ideal model The TIMS mode
11. ned The limitations of the diode detector an approximation to the ideal are examined Introduction to the HEADPHONE AMPLIFIER module PREREQUISITES completion of the experiment entitled Envelopes in this Volume PREPARATION the envelope You have been introduced to the definition of an envelope in the experiment entitled Envelopes There you were reminded that the envelope of a signal y t is that boundary within which the signal is contained when viewed in the time domain Jt is an imaginary line Although the envelope is imaginary in the sense described above it is possible to generate from y t a signal e t having the same shape as this imaginary line The circuit which does this is commonly called an envelope detector A better word for envelope detector would be envelope generator since that is what these circuits do It is the purpose of this experiment for you to model circuits which will generate these envelope signals the diode detector 72 Al The ubiquitous diode detector is the prime example of an envelope generator It is well documented in most textbooks on analog modulation It is synonymous with the term envelope demodulator in this context But remember the diode detector is an approximation to the ideal We will first examine the ideal circuit Envelope recovery the ideal envelope detector The ideal envelope detector is a circuit which takes the absolute value of its input and t
12. peech use the HEADPHONE AMPLIFIER The HEADPHONE AMPLIFIER enables you to listen to an audio signal connected to its input This may have come via an external lowpass filter or via the internal 3 kHz LOWPASS FILTER The latter is switched in and out by the front panel switch Refer to the TIMS User Manual for more information Only for the case of envelope modulation with the depth of modulation 100 or less will the speech be intelligible If you are using a separate lowpass filter switching in the 3 kHz LPF of the HEADPHONE AMPLIFIER as well should make no difference to the quality of the speech as heard in the HEADPHONES because the speech at TRUNKS has already been bandlimited to 3 kHz speech as the message m gt 1 78 Al Don t forget to listen to the recovered envelope when the depth of modulation is increased beyond 100 This will be a distorted version of the speech Distortion is usually thought of as having been caused by some circuit imperfection There is no circuit imperfection occurring here The envelope shape for all values of m including m gt 1 is as exactly as theory predicts using ideal circuitry The envelope recovery circuit you are using is close to ideal this may not be obvious when listening to speech but was confirmed earlier when recovering the wide band envelope of a DSBSC The distortion of the speech arises quite naturally from the fact that there is a non linear relationship between t
13. s passband gain to about unity To do this you can use a test signal from the AUDIO OSCILLATOR or perhaps the 2 kHz message from the MASTER SIGNALS module T2 model the generator of Figure 3 and connect its output to an ideal envelope detector modelled as per Figure 2 For the lowpass filter use the TUNEABLE LPF module Your whole system might look like that shown modelled in Figure 4 below DIODE LPF RC LPF UTILITIES TUHEABLE LPF i une COMPARATOR e C en ida C CH2 B spare O CH1 B ENVELOPE GENERATOR RECOVERY Figure 4 modulated signal generator and envelope recovery T3 set the frequency of the AUDIO OSCILLATOR to about 1 kHz This is your message T4 adjust the triggering and sweep speed of the oscilloscope to display two periods of the message CH2 A 76 Al Envelope recovery T5 adjust the generator to produce an AM signal with a depth of modulation less than 100 Don t forget to so adjust the ADDER gains that its output DC AC will not overload the MULTIPLIER that is keep the MULTIPLIER input within the bounds of the TIMS ANALOG REFERENCE LEVEL 4 volt peak to peak This signal is not symmetrical about zero volts neither excursion should exceed the 2 volt peak level T6 for the case m lt 1 observe that the output from the filter the ideal envelope detector output is the same shape as the envelope of the AM signal a sine wave DSBSC env
14. tional amplifiers to analog circuits An extension of the principle produces an ideal fullwave rectifier You will find a halfwave rectifier is generally adequate for use in an envelope recovery circuit Refer to the Appendix to this experiment for details envelope bandwidth Envelope recovery You know what a lowpass filter is but what should be its cut off frequency in this application The answer the cut off frequency of the lowpass filter should be high enough to pass all the wanted frequencies in the envelope but no more So you need to know the envelope bandwidth Al 73 In a particular case you can determine the expression for the envelope from the definition given in the experiment entitled Envelopes and the bandwidth by Fourier series analysis Alternatively you can estimate the bandwidth by inspecting its shape on an oscilloscope and then applying rules of thumb which give quick approximations An envelope will always include a constant or DC term This is inevitable from the definition of an envelope which includes the operation of taking the absolute value It is inevitable also in the output of a practical circuit by the very nature of rectification The presence of this DC term is often forgotten For the case of an AM signal modulated with music the DC term is of little interest to the listener But it is a direct measure of the strength of the carrier term and so is used as an automatic gain contro
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