AMPLIFIER OVERLOAD
Contents
1. Al For this experiment you will need a WAVE ANALYSER We suggest you use the model examined in the experiment entitled Spectrum analysis the WAVE ANALYSER For the non linear amplifier you will use the COMPARATOR within the UTILITIES module Please refer to the TIMS User Manual The COMPARATOR has an analog YELLOW output socket which you will use and in this application it is called aCLIPPER The CLIPPER has a non linear input output characteristic That is it will overload with input signal amplitudes comparable with the TIMS ANALOG REFERENCE LEVEL of 4volts peak to peak The overload characteristic can be varied by means of two on board DIP switches For the present application you will use the soft clipping characteristic this is set with SWI switched to ON ON and SW2 switched to OFF OFF The REF input socket used for the COMPARATOR is not used for CLIPPER applications From now on the CLIPPER will be referred to as the DUT namely the device under test For the purpose of the experiment you could consider it to be an amplifier in an audio system where it is required to amplify speech signals Thus it is a wideband device Amplifier overload You should base your experimental set up on the block diagram of Figure 5 to OSCILLOSCOPE test signal and WAVE ANALYSER Figure 5 test setup The WAVE ANALYSER model is shown in Figure 6 SPECTRUM UTILITIES l2. UNKNOWN control sine VARIABLE FREQUENCY COUNTER 538 Figure 6 the WAVE ANALYSER model single tone testing measurement of THD TI set the DIP switches on the DUT to the low gain soft limiting position before inserting the module into the TIMS SYSTEM UNIT This is the device under test DUT Include the patchings to the SCOPE SELECTOR inputs T2 patch up the model as in Figure 7 below Amplifier overload Al 53 ext trig CH1 B CH1 A CH2 A roving lead DEVICE UNDER UTILITIES C BUFFER AMPLIFIERS _ to WAVE ANALYSER REF COMPARATOR RECTIFIER DIODE LPF MASTER SIGHALS RC LPF 100kHz sin 100kHz cos 100kHz TTL SINGLE TONE TEST SIGNAL Figure 7 the single tone test model The ADDER in cascade with BUFFER 2 will be used later in the two tone test set up BUFFER 2 will be used for test signal amplitude control The other BUFFER 1 is used for polarity reversal and level adjustment of the oscilloscope display of the input test signal T3 set the gain of the ADDER to about 2 and that of BUFFER 2 to about unity T4 use the ext trig from a constant amplitude version of the test source as shown to trigger the oscilloscope Set the sweep speed to show one or two periods of the test signal T5 switch to CHI A and CH2 A Set both channels to the same gain say Y volt cm You are
3. looking at both the input and output signals of the DUT T6 use the oscilloscope shift controls to superimpose the two traces Use BUFFER 1 to equalize their amplitudes T7 notice that BUFFER 2 varies the amplitude of both traces so they stay superimposed at low input amplitudes before distortion sets in Adjust the gain of BUFFER 2 until the output signal indicates the onset of moderate distortion that is when its shape is obviously different from the input waveform which is also being displayed on the oscilloscope A ratio of about 5 6 for the distorted and undistorted peak to peak amplitudes gives a measurable amount of distortion You have duplicated Figure 2 Record the amplitude of the signal at the input to the DUT 54 Al Amplifier overload You are now set up moderate overload of the DUT You are ready to measure the distortion components T8 without disturbing the arrangement already patched up model a WAVE ANALYSER For example use the one examined in the experiment entitled Spectrum analysis the WAVE ANALYSER This is shown in Figure 6 T9 use the WAVE ANALYSER to search for and record the presence of all significant components at the output of the DUT for the conditions of the previous Task Theory suggests that these will be at 2 084 kHz set by the nominal 2 kHz test signal from the MASTER SIGNALS module and its odd multiples odd because of the approximate cubic shape of the transfer function of th
4. tone signal is stationary on the screen showing one or two periods of the envelope Note that this display will show up any imperfection in the equality of the amplitudes of the two tones or could have been used to set them equal in the first place T18 switch to CHI A and CH2 A Set both these oscilloscope channels to the same gain You are now observing the input and output of the DUT Adjust the gain of BUFFER 2 so that the output CH2 A is not distorted that is the same waveform as CH1 A T19 use the oscilloscope shift controls to overlay the two waveforms Adjust the gain of BUFFER 1 until they are of exactly the same amplitude and so appear as a single trace on the screen T20 now slowly increase the gain of BUFFER 2 Both traces will get larger but remain overlaid until the signal level into the DUT exceeds its linear operating range and the output begins to show distortion The two waveforms will no longer be identical and the difference should be clearly visible T21 familiarize yourself with the overloading process by covering the full gain range of BUFFER 2 Then set the gain to the point where distortion of the DUT output waveform is moderate A ratio of output to input signal amplitudes of about 5 6 is suggested as a start This is the condition under which you will be making some distortion measurements Record the input amplitude to the DUT sketch the input and output waveforms Remember the DUT has a c
5. too little not too much One of the aims of an analog transmission system such as an audio amplifier or a long distance telephone circuit is to present at the output a faithful reproduction of the signal at the input Analog systems will always introduce some signal degradation however defined but it is the aim of the analog design engineer to keep the amount of degradation to a minimum As you are probably already aware if signal levels within a system rise too high then the circuitry will overload it is no longer operating in a linear manner As will be seen later in this experiment extra unwanted distortion components will be generated These distortion or noise components are signal level dependent In this case the noise components arise due to the presence of the signal itself Conversely if signal levels within a system fall too low then the internal circuit noise which is independent of signal level will eventually swamp the small wanted output The background noise of the TIMS system is held below about 10 mV peak this is a fairly loose statement since this level is dependent upon the bandwidth over which the noise is measured and the model being examined at the time A general statement would be to say that TIMS endeavours to maintain a SNR of better than 40 dB for all models Thus analog circuit design includes the need to maintain signal levels at a level not to high and not too low to avoid
6. where H is the amplitude of the output signal on the same frequency as the input test signal and the Hj are the amplitudes of the 2nd and higher harmonics or unwanted terms 1 0 input volts Figure 3 THD versus input amplitude for the response of eqn 2 For the example above where the input amplitude V was 1 volt peak this evaluates to a THD of 27 48 dB Figure 3 shows the THD plotted for input amplitudes in the range 0 to 1 volts Having decided on an acceptable THD for this amplifier say 40 dB the user can now specify a maximum input level 4 volt from Figure 3 measurement of THD Amplifier overload There are instruments available which measure THD directly They supply their own test input signal to the device under test measure the total AC power output subtract the power due to the wanted signal and present the THD expressed in decibels Al 47 You will make your own measurements with TIMS by modelling a WAVE ANALYSER 2 measuring the amplitudes of the individual output components and then applying the THD formula Note that this THD is specific to the actual input signal amplitude used for the measurement There is no subsequent simple step to enable 1 prediction of the THD for another input signal amplitude 2 determination of the non linear characteristic of the amplifier This is because of the non linear relationship between the input signal amplitude and the corresponding output TH
7. AMPLIFIER OVERLOAD PREPARATION au ae en 44 not too little not too much ae a 44 amplifier DAS eenen naden 45 deal amplifier Bananen neee E E 45 real amplifiers nanne E A E 45 karmonie distorlion ua 46 calculation of harmonic distortion components nano eneen 46 definition of harmonic distortion THD nanne enen eneeneen 47 measurement of THD as scious ses accesso scavehe isco SE iE 47 narrow band systems na pcadveasacdasaileds 48 measurement of a narrow band system u eesseesseesensseesneesneennn nennen nen 48 the two tone testsional ae een 49 Shortcuts ann anne 49 signal to distortion ratio SDR annae enee onee nnersnenseenseerneenenn 50 OL Io 2ER RR E e E E T E E EE 50 TORE ee 51 two tone test signal generation nnn anne nenn 51 the two tone seen as a DSBSC nennen venvenen wensen 51 EXPERIMENT ireen 32 EXDEFIMENIAl SELF ID ann 52 sigle TONE TESTO aten E n an 53 measurement of THD encanar n 53 WO One Te a E a ee 55 measurement of SDR oeer am en eeen 55 CONCIUSIONS e near 58 TUTORIAL QUESTIONS a2 58 APPENDIX Ga ai Era 59 some USelulexpansionsa al 59 Amplifier overload Vol A2 ch 6 rev 1 1 43 AMPLIFIER OVERLOAD ACHIEVEMENTS an introduction to the definition and measurement of distortion in wideband and narrowband systems PREREOUISITES completion of the experiment entitled Spectrum analysis the WAVE ANALYSER in this Volume EXTRA MODULES SPECTRUM UTILITIES PREPARATION not
8. D narrow band systems The previous discussion requires some modification if the system being examined is narrow band 3 There are many circuits in an analog communications system which are narrowband Since many communications signals themselves are narrow band A narrowband system is one which has had its frequency response intentionally restricted This generally simplifies the circuit design and eliminates out of band noise To simplify the discussion suppose there is a bandpass filter at the system output so that only frequencies over a narrow range either side of the measurement frequency u rad s will pass to the output Let the non linearities be in the circuitry preceding the filter If this were the case for the example already discussed the output waveform would show no sign of distortion but instead be a pure sinewave No distortion would be visible on an oscilloscope connected to the output because the distorting third harmonic signal would not reach the output An instrument for measuring THD with a single tone input would register no distortion at all Is the system linear or not It is definitely non linear This can be demonstrated by observing that the relationship between input amplitude and output amplitude is not linear Using the methods so far employed this does not show up as waveform distortion and would not be revealed by a spectrum analysis of the output measurement of a narrow band system T
9. bic term has given rise to two new components one on the same frequency as the input signal and the other on its third harmonic After combining like harmonic terms the last equation can be rewritten as Vo g4 V 3 4 g3 V3 cosut 1 4 g3 V3 cos3ut eee 7 Notice that at the output 1 the amplitude of the wanted term cosut is no longer simply g times the input amplitude as suggested by eqn 1 2 there is an extra unwanted term on the third harmonic of the input The original signal has been distorted This can be observed in the time domain using an oscilloscope For the example under discussion the output for an input of amplitude V 1 volt is shown in Figure 2 undistorted reference actual output Figure 2 the output voltage waveform of eqn 7 for an input amplitude of V 1 volt 46 A1 Amplifier overload definition of harmonic distortion THD Notice that the analysis has been performed so as to describe the output in terms of harmonic components of the input The fundamental or first harmonic is the wanted term and all higher harmonic terms in this example there is only one are unwanted The wanted and unwanted harmonic terms can be compared and some measure defined to describe the amount of harmonic distortion The comparison is usually made on a power basis described as the total harmonic distortion or THD and defined as IH THD 10 log lt dB IH j 2
10. e DUT T10 from your measurements of the previous Task calculate the amount of harmonic distortion THD under the above conditions T11 now reduce the level of the input signal to the DUT by say 50 using the gain control of BUFFER 2 T12 measure the amplitude of the largest unwanted component the third harmonic of the input You should have observed that whereas the amplitude of the input was reduced by 50 that of the largest unwanted component fell by more than this This is a phenomenon of non linear distortion Now try a two tone test looking for intermodulation products as well as harmonics You will work on the same amplifier DUT as before two tone testing measurement of SDR Amplifier overload If you built the model of Figure 7 then you are almost ready The new test set up is illustrated in Figure 8 below The ADDER combines the two signals in equal proportions The tones should be of comparable frequency say within 10 or less of each other BUFFER 2 at the ADDER output is used as a joint level control As before BUFFER 1 enables the before and after signals displayed on CHI A and CH2 A respectively to be matched in amplitude Al 55 T13 patch up the model of Figure 8 below Include the patchings to the SCOPE SELECTOR inputs T14 the two tones are the nominal 2 kHz message from the MASTER SIGNALS module and a second from an AUDIO OSCILLATOR Set the seco
11. ent manner Recognising it as a form of DSBSC makes this an easy matter ENVELOPE DETECTOR ext trig TWO TONE TEST SIGNAL Figure 4 two tone test signal generation the two tone seen as a DSBSC Recall that a two tone test signal has been defined earlier as in eqn 9 The spectrum of this signal is identical with that of a DSBSC defined as DSBSC 2 V cosut cos t en 21 V cos Wt cos wt en To force the signal of eqn 21 to match that of eqn 9 it is necessary that OWSA O Amplifier overload 4 although it can be dependent on the presence of an input generator the output impedance of which can influence the system noise Al 51 DEU Wen From these two equations the DSBSC frequencies are weke rads en N u w 2 rad s vorne 26 To display a DSBSC stationary on the screen a triggering signal is required that is related to its envelope The envelope of the DSBSC of eqn 21 is a full wave rectified version of cosut but there is no signal at this frequency eqn 25 if the two tone signal is made by the addition of two tones as per eqn 9 The appropriate triggering signal can be generated with an envelope detector acting on the two tone signal Remember this is a rectifier followed by lowpass filter which will pass a few harmonics ideally the first only of the difference frequency of eqn 25 but not the sum frequency eqn 26 experimental set up 52
12. er is said to have a small signal gain of 10 Input signal amplitudes in the range say volt would be considered small signals for this amplifier A typical amplifier characteristic is likely to flatten off and become parallel to the Fig 1 typical characteristic horizontal axis whereas this characteristic as defined by eqn 2 below will approach and finally cross the input axis for larger input amplitudes So this approximation to an amplifier characteristic should be used for input amplitudes restricted to the range 0 to say 1 volts Its actual input output relationship is given by Ve 2 where v and v are the input and output voltages respectively and B L 3 4 g a en Note that the range of the so called linear part of the characteristic is not obvious from a cursory examination of eqn 2 alone We shall later obtain a method of defining an acceptable operating input signal range harmonic distortion calculation of harmonic distortion components Intuition tells us that an amplifier with the input output characteristic of Figure 1 will introduce distortion but what sort of distortion This can be checked analytically by nominating a test input signal and then determining the corresponding output Let the test signal be a single tone v where Vi Vecosut eee 5 Substituting this into eqn 2 and expanding gives Vo 84 V cosut g V3 3 4 cosut 1 4 cos3ut een Notice that the cu
13. harmonics of each of these signals as well as intermodulation products Intermodulation products IPs arise from the products of two or more signals and fall on frequencies which are the sums and differences of multiples of their harmonics The measure of distortion can no longer be called THD since the sum and difference frequencies are present in addition to the harmonic terms so the term signal to distortion ratio or SDR is used It is evaluated using the same principle as THD namely w SDR 10 log o BB 18 LU jel where the amplitude of the n wanted terms is W and of the m unwanted terms is U These are the terms which actually reach the output In a narrow band system many others will be generated which will not reach the output two tone example 50 Al We will now apply eqn 18 to calculate the SDR for the characteristic of Figure 1 The input signal is defined by eqn 9 with V 0 5 volts This makes the peak amplitude of the two tone signal equal to 1 volt which is comparable with the amplitude used earlier for the single tone testing First we will include all unwanted components in the calculation making this a wideband result wideband SDR 27 01dB 2 rer 19 For the narrowband case the terms to be neglected in this example are those on the third harmonics of u and u and the intermodulation products on the sum frequencies The result is then narrowband SDR 30 25dB een 20 Remembe
14. he single tone test signal we have been using so far is inappropriate for the measurement of THD in a narrow band system What is needed is a more demanding test signal which will reveal the non linearity and which is more representative of the signals to be found in most systems The non linearity is 48 Al 2 see the experiment entitled Spectrum Analysis the Wave Analyser or model a spectrum analyser using the TIMS320 module 3 wideband and narrowband signals are defined in the chapter entitled Introduction to Modelling with TIMS Amplifier overload revealed by the transmission of two signals simultaneously namely the two tone test signal the two tone test signal The two tone test signal consists of two equal amplitude sinusoids of comparable frequency Thus v t V cost cosut where say 4 SU en Let us use this as the input to the non linear amplifier previously examined with a single tone input The amplitudes of the various output terms from trigonometrical expansion of v t when substituted into eqn 2 are shown below cos u t gt 81 V 3 4 g3 VS 3 2 g3 V3 en 10 cos u t gt g1 V 3 4 83 VS 8 2 g3 V3 een 11 cos 3p t gt Ve 12 cos 3Hp t gt 1 483 ttn 13 cos 2Wj H t gt 8 483 V3 tetas 14 cos H 24 t gt GV 15 cos 2Wj W t gt AV 16 cos 2H t gt 3 4 g83 V3 17 short cuts Amplifier overload The calculation of these amplitude coefficient
15. lved Some useful expansions are cos A 1 2 1 2 cos2A cos A 3 4 cosA 1 4 cos3 A costA 3 8 1 2 0082A 1 8 cos4A cosSA 5 8 cosA 5 16 cos3A 1 16 cos5 A cos A 5 16 15 32 cos2A 3 16 cos4A 1 32 cos6 A Perhaps you can see the pattern developing It is clear that when n is odd the expansion of cosmt gives rise to all odd harmonics counting down from the nt when n is even the expansion of cosut gives rise to all even harmonics counting down from the nt Note that the count goes down to the zeroeth term which is DC After an expression has been reduced to the sum of harmonic terms those of similar frequency must be combined taking into account their relative phases Thus V cospyt V gt cospyt Vi V cospyt but V cosu t V sinut V cos u t where V V V and a tan v As an exercise develop the above expansions in terms of sin functions There must be some obvious similarities but just as importantly there must be differences Explain Further useful expansions may be found in Appendix B to this Text Al 59 60 Al Amplifier overload
16. nd tone close to the first say 1 8 kHz CH1 B CH1 A CH2 A n ext trig SIGNALS i recovery of the envelope of the two tone Ait sine signal for oscilloscope triggering 100kHz cost DUT input DUT output to WAVE i ANALYSER i i roving i gt lead DEVICE RC LPF TWO TONE GENERATOR i INSTRUMENTATION WAVE ANALYSER not shown Figure 8 two tone test setup The two tone signal necessitates new oscilloscope triggering arrangements As already explained an envelope recovery circuit is needed and this is shown modelled with a RECTIFIER in the UTILITIES module and a TUNEABLE LPF Three of the four SCOPE SELECTOR positions are shown permanently connected The fourth CH1 B can be used as a roving lead for various waveform inspections including the next task T15 adjust the two tones at the ADDER output to equal amplitudes say 2 volt peak to peak each Adjust the gain of BUFFER 2 to about unity T16 check the envelope detector output using CH1 B What is wanted is a 56 Al periodic signal at envelope frequency suitable for oscilloscope triggering Its shape is not critical Tune the filter to its lowest bandwidth set the front panel passband GAIN control to its mid range Amplifier overload T17 when satisfied with the previous Task use the output of the envelope detector to trigger the oscilloscope and check on CHI A with BUFFER 1 set to mid gain that the envelope of the two
17. oduction to the methods of measuring and describing the non linear performance of an analog circuit A problem associated with the measurement of a narrowband system has been demonstrated together with a method of overcoming it TUTORIAL QUESTIONS QI why were the two tones in the two tone test signal set relatively close in frequency to each other Q2 equation 19 suggests an alternative method of making a two tone test signal It has the particular advantage of providing a synchronizing signal from the low frequency source the two tones are automatically of equal amplitude and the whole signal can be swept across the spectrum with one control that of the high frequency oscillator What are some disadvantages of this method of generation Q3 explain qualitatively how the display of the two added tones as a DSBSC signal can be used to equalize the amplitudes of the two tones Use a phasor diagram or other method to explain the process quantitatively Q4 two businesses advertise the same amplifier one saying it is a 50 watt amplifier and the other a 60 watt amplifier There is no dishonesty How could this be 58 Al Amplifier overload APPENDIX some useful expansions Amplifier overload In analysing a non linear system in terms of sinusoidal signals as in the above work the aim is to convert expressions in terms of powers of sinusoidal signals to expressions in terms of harmonics of the fundamental frequencies invo
18. r that had a single tone been used for this narrowband system there would have been no signal dependent distortion products found at the output and the amplifier would have appeared ideal The noise output would not in fact have been zero We have been dealing with large signal operation and so have ignored the existence of random noise Amplifier overload noise In the work above we have divided the output signal into wanted and unwanted components All the unwanted components so far had magnitudes which were directly dependent upon the amplitude of the input signal Such unwanted components are referred to as signal dependent noise Also to be considered in any system is random noise or system noise This arises naturally in all circuitry and its magnitude is independent of any input signal In the work above we have made no mention of such noise This is because it has been assumed insignificant with respect to signal dependent noise This was a reasonable assumption since in a well designed system signal dependent noise only occurs for large input signal magnitudes two tone test signal generation The two tone signal can be made from any two signals of suitable frequencies a convenient pair of signals for TIMS is the nominal 2 kHz message at the MASTER SIGNALS module and an AUDIO OSCILLATOR Refer to the block diagram of Figure 4 below A lot can be learned about the two tone signal if it can be displayed in a conveni
19. s can be very tedious But one soon observes certain phenomena involved and with a narrowband system applies short cuts to avoid unnecessary work Remember that the two frequencies u and p are close together Some observations are The trigonometrical expansions can only generate terms on harmonics of the original frequencies and on sum and difference frequencies of the form n u m u and n u m u where n and m are positive integers Components with frequencies u and u will pass through the system but none of their higher harmonics Of the sum and difference frequencies n u m u and n u m m it is agreed that only those of the difference group where n and m differ by unity will pass through the system When n is odd the expansion of cosut gives rise to all odd harmonics counting down from the nt Al 49 When n is even the expansion of cosut gives rise to all even harmonics counting down from the ntt Note that the count goes down to the zeroeth term which is DC Taking these observations into account when dealing with a narrowband system the number of necessary calculations can be reduced signal to distortion ratio SDR We have seen that when the test input is a single tone the distortion components are restricted to being harmonics of this signal But with a more complex test signal other distortion products are possible As has just been seen a two tone test input gives rise to
20. these two extremes The TIMS working level or ANALOG REFERENCE LEVEL has been set at 4 volts peak to peak Modules will generally overload if this level is exceeded by say a factor of two 44 Al 1 noise is here considered to be anything that is not wanted Amplifier overload It is the purpose of this experiment to introduce you to the phenomenon of circuit overload and to offer some means of defining and measuring its effects amplifier gain ideal amplifier gain Consider an amplifier which is said to have a gain of g This is understood to mean that if v is the input signal voltage then the output v is given by Vo SEM This would be described as an ideal amplifier Its input output i o characteristic would be a straight line with a slope of g volts volt In simple terms g is a dimensionless constant More generally it can be complex and frequency dependent but such complications will be ignored in the work to follow real amplifiers Amplifier overload Unfortunately a real amplifier does not have an ideal straight line input output characteristic It is more likely to look like that of Figure 1 It is obvious to the eye that the characteristic shown in Figure 1 could not be considered straight or linear except perhaps for input signal amplitudes in the range say volt In this range the slope of the characteristic i a is 10 volts volt _ tl input volts The amplifi
21. ubic non linearity This suggests it will generate odd order harmonic and intermodulation products If the two test signals are f and f then the largest unwanted components are likely to be on frequencies 3f 3 Uff and 2f f T22 use the WAVE ANALYSER to search for and record the presence of all significant components in the output of the DUT for the conditions of the previous Task Record clearly the frequency of each component found and relate it to the frequencies of the two tone signal T23 from your measurements of the previous Task calculate the SDR using eqn 18 5 if you make it too slight the distortion components will be hard to find Amplifier overload Al 57 In the above calculation you might have included all components which you measured But suppose the output signal DUT had then been transmitted via a channel with a bandpass characteristic Then many of the distortion components would have been removed But distortion would still have been measured since those intermodulation products close to the two wanted tones would have been passed T24 re calculate the SDR assuming transmission was via a bandpass filter conclusions During the experiment you might have taken the opportunity to listen to the signals with and without distortion to gain a qualitative idea and appreciation of what level of distortion with these types of signals is detectable by ear This experiment has served as an intr
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