POWER AMPLIFIER DISTORTION


     On the site www.vkaudiotest.co.uk. I've already represented my VK-5 amplifier which can not boast of a huge power but has exemplary linearity. It delivers a 50W power into a 4ohm load with less than 0,001% THD in the whole 20Hz-20kHz audio range. It's well known that distortion and linearity are the major issues in power amplifier design and I think it should be the main target for a serious design to maintain distortion of this amplifier just below the 0.001% level. Numerous publications tell that this can be achieved by traditional methods, without resorting to complicated or exotic circuitry.
     In this article I will try to show how the standard amplifier topology can be step-by-step improved to a circuit configuration with the record characteristics. One may ask how these characteristics will be measured, given that the interactive simulation method has a 0.001% limit of measuring distortion and Fourier analysis doesn't always give exact distortion characteristics of the amplifier just after its turning on, when it isn't still properly settled.
     To solve this problem, I've developed the unprecedented in its reliability and accuracy method of measuring distortion with the help of my virtual VK-2 distortion meter which can successfully exist in parallel with its real counterpart. This instrument performs the fully transparent interactive distortion measurements of fantastic sensitivity - below -170dB (0.0000003%) within 20Hz-20kHz, the automatic process of -175dB suppression of the fundamental frequency taking less than 3sec.
     On the virtual oscilloscope screen you can see the extracted "live" distortion harmonics of an amplifier or oscillator whose circuit is entered to the simulation program which contains already the VK-2 distortion meter circuit. Amplified by +80dB the exact RMS sum of these harmonics is measured confidently by an ordinary AC millivoltmeter because it is free of any swamping noise and any added distortion being unavoidable in real distortion or spectrum analysis.
     The Multisim oscillator and the VK-2 virtual meter don't create distortion and noise by definition, this trick allows to investigate the linearity just of the device under test with the help of the classic, most right method - by removing the fundamental frequency from the analyzed signal. In principle, the used automatic notch filter can provide infinite suppression of the fundamental, all depends on its performance, in the VK-2 device this performance is brought to the ultimate.
     The accuracy of measuring the residual distortion harmonics can be easily verified by applying their calibrated amounts, say -120dB, to the meter's input, along with a 1V signal of the fundamental frequency, and analyzing its output, this accuracy being better than 0.5dB at all audio frequencies.
     And at last you can comfortably watch the whole process of the notch filter 3sec tuning in detail because the simulation is running in a slow time scale and usually takes 5-30min. Every nuance of extracting distortion harmonics from the set 1V RMS input signal is seen on the oscilloscope screen and saved in a file.

Fig.1. Typical power amplifier 100W-4ohm.

     I would like to begin my research with the typical power amplifier circuit shown in Fig.1, it is capable of delivering a 100W power into a 4ohm load, the necessary for that supply voltages being +45,-45V. This power is quite sufficient for domestic purposes, it is still reachable with a single pair of output power transistors, and the specified supply voltages still don't put serious limitations on the choice of small-signal transistors. The 4ohm loading allows to clearly determine the amplifier real driving capability and its potential of doing that with minimum distortion.
     Naturally, driving the 8ohm load will be an easier job for an amplifier and the produced distortion always will be lower. The amplifier all transistors are of widely used types, their chosen operation conditions conform to the well-known recommendations of getting minimum distortion and good circuit stability.
     The typical amplifier circuit contains an input differential pair of 2N5087 transistors (Q1, Q2) fed from a current source on Q3 and loaded by a current mirror on BC546B transistors (Q5, Q6). The second, voltage amplifying stage, is a cascode arrangement of transistors Q9, Q17 (2N5550) fed from a current source on Q10 (2N5400). It also includes the biasing network for the output stage, in the form of Vbe multiplier (Q38, R71, R72).
     The amplifier output stage doesn't provide voltage gain, its function is to buffer the output of the voltage amplifying stage from the low-impedance 4ohm load and to produce a considerable current gain to drive this load at the required 100W power. Several configurations of the output transistor triples in each half of the circuit are chosen for comparison of their influence on total amplifier linearity while the input and second amplifier stages and also the used transistor types keeping the same.
     The output stage of Fig.1 is most popular in audio, it consists of two triple emitter followers - transistors Q18, Q35, Q33 at its top and Q19, Q36, Q34 at its bottom parts, these triples transport to the output node correspondingly positive and negative halves of the amplified sinusoid. In all considered further power amplifiers I use the output transistors' current limiter (Q20, Q21) and set the quiescent value of this current within 200-250mA, when the input signal is absent.
     The main characteristics of the typical power amplifier are obtained with the help of Multisim AC analysis, its open-loop gain and closed-loop gain are represented in Fig.2.



Fig.2. AC analysis of the typical power amplifier.

     The above characteristics were obtained without the input RC-filter (C2 was removed), this low-pass filter deliberately limits the amplifier bandwidth to prevent external RF-signals from interfering in the amplifier operation.
     The overall negative feedback is applied via resistors R13, R14, the closed-loop gain in the audio range being therefore

                                                    K = (R13 + R14)/R13 = (0.3+10)/0.3 =34.3=+31dB.
     At frequencies 1kHz and 16kHz we have the amplifier open-loop gain correspondingly +100dB and +75dB (see Fig.2) and the amount of the used negative feedback (NFB) being correspondingly 100-31=69dB and 75-31=44dB. Just this feedback brings the amplifier closed-loop distortion to the desirable 0.001% and lower.
     At high audio frequencies, particularly at 16kHz, this aim is harder to achieve because the feedback factor (44dB) is reduced due to the action of capacitor C5 ensuring the circuit HF stability and because the effect of alternate switching the output n-p-n and p-n-p transistors from one state to another becomes here more notable. This so-called switch-off distortion is the main drawback of the output stage push-pull operation, it depends on the stage topology and the set quiescent current through output transistors, this current determines the region where both transistors are conducting.
     Just the use of my virtual VK-2 distortion meter allows to see this distortion on the oscilloscope screen and to correctly set the circuit quiescent conditions. The test scheme of measuring the power amplifier closed-loop distortion is depicted in Fig.3.



Fig.3. VK-2 distortion measurement of the typical power amplifier-1 at 1kHz.

     The typical amplifier circuit of Fig.1, call it number 1, is simulated along with the VK-2 distortion meter circuit which is represented in Fig.3 as the active rejection filter block and output amplifier. The power amplifier is fed from the Multisim 10 non-distorting generator, its output voltage (20V producing 100W) is normalized by R139, R150 and the obtained 1V signal is applied to the input of the rejection filter. The filter consists of an input twin-T notch network, a high-performance discrete amplifier (K=100), a 100kHz low-pass filter and at last the system of fine automatic tuning of the rejection filter, its Q-factor is chosen Q=2 and it carries out more than -170dB suppression of the fundamental frequency within 20Hz-20kHz. The following then output amplifier (K=100) brings the total gain of the residuals to +80dB for measuring them by an ordinary RMS voltmeter, observing on the virtual oscilloscope screen and using them in the filter tuning.
     The whole process of measuring distortion at 1kHz takes 2.63sec, its result appears at the main VK-2 meter output, the measured distortion is shown on the screen and registered by an AC millivoltmeter, its RMS value being in this case 17mV/10000=1.7μV or 0.00017% (-115.5dB) relative to the 1V input. As can be seen in Fig.3, this distortion is mainly the third harmonic (3kHz).
     The similar procedure was conducted and for a 16kHz test frequency, the obtained in 1.25sec RMS value of extracted distortion is 164mV/10000=16.4μV or 0.00164% (-95.7dB) relative to the 1V input, it appears to be the third harmonic too (48kHz, see Fig.4).


Fig.4. VK-2 distortion measurement of the typical power amplifier-1 at 16kHz.

     Note that the shown on the screen distortion curves are free of any narrow spikes on them at the moments of the input sinusoid zero-crossing, this tells about the optimally biased output transistors by proper adjustment of resistor R121. The described measurement method is transparent and very accurate, the above distortion figures are absolutely reliable and they are close to the results of Fourier analysis performed by Multisim distortion analyzer, compare its reading -95.3dB with the VK-2 meter measurement result in dB at 16kHz.
     The next to investigate is the typical power amplifier-2 circuit placed into the above test scheme instead of the power amplifier-1 and shown in Fig.5.


Fig.5. VK-2 distortion measurement of the typical power amplifier-2 at 1kHz.

     Its output stage transistor triples contain the first, pre-driver transistors Q8, Q36 configured as common-emitter voltage amplifiers loaded by cascaded connections Q37, Q34 and Q35, Q33. Each triple behaves as a high-gain amplifier with the 100% applied local feedback, this provides lower distortion and lower output impedance but makes the circuit prone to local oscillation and therefore requires careful choice of components.
     The circuit has also the advantage of better thermal stability of the quiescent current through the output transistors. This is because the biasing network Q38, R121, R122 controls the base-emitter potentials of only two pre-driver transistors Q8, Q36 which don’t experience notable heating, always have the temperature close to the temperature of Vbe multiplier Q38 and being less influenced by the changing power dissipation of the output transistors.
     Calculation of the current-sensing output resistors R99, R101 is fairly straightforward, given that the maximum output voltage of this 100W amplifier is 20x1.41=28V. Being applied to a 4ohm load, it creates a 7A maximum current flowing also through the above resistors and producing voltage drop across them. This voltage drop must be less than 0.6V to keep the current protection transistors Q39, Q40 in the reliable turned-off state thus ensuring the amplifier normal operation. If we take the maximum current limit of 10A, the resistors R99, R101 value should be 0.6/10=0.056ohm, further rise of the output transistors’ current will be prevented by turning on the transistors Q39 and Q40.
     The procedure of measuring distortion of this amplifier is just the same as in the previous typical power amplifier-1. At first, the simulation is running at 1kHz, this frequency is set by the Multisim generator, the corresponding setting of the 1kHz fundamental frequency range should be made and in the twin-T network of the VK-2 rejection filter. The distortion measurement at 1kHz takes 2.15sec, the amplified by +80dB output reading is 15.7mV RMS, so the input signal distortion equals 15.7mV/10000=1.57μV or 0.000157% (-116.1dB) relative to the normalized 1V input. It is the clearly seen third harmonic (3kHz).


Fig.6. VK-2 distortion measurement of the typical power amplifier-2 at 16kHz.

     The distortion measurement at 16kHz is carried out in 1.55sec, it yields the output reading of 110mV RMS and distortion of the input signal is 110mV/10000=11μV or 0.0011% (-99.2dB) relative to its normalized 1V value. This distortion is again the clearly seen third harmonic (48kHz). The distortion analyzer connected to the power amplifier-2 output gives practically the same result (-99.6dB). This confirms an excellent accuracy of the conducted measurements.
     The following typical power amplifier-3 features another configuration of its output transistor triples which slightly differs from the triples of the previous amplifier and gives some food for thoughts and comparisons of the obtained distortion characteristics. This output stage can be considered as two complementary-feedback-pairs (Q39, Q36 and Q40, Q35) loaded by output emitter followers Q33, Q34 (see Fig.7). Again, the high voltage gain inside the local feedback closed loop promises low distortion, but here the base-emitter potentials of the output transistors participate in setting the quiescent current through them, this current becomes therefore more dependable on dissipated power and temperature of Q33, Q34.


Fig.7. VK-2 distortion measurement of the typical power amplifier-3 at 1kHz.

     The amplifier simulation at 1kHz takes 2.39sec but its result is somewhat unexpected. The VK-2 distortion meter main output shows 28mV RMS reading (see Fig.7) that means 28mV/10000=2.8μV of the input signal distortion or 0.00028% (-111.0dB) relative to its normalized 1V value. This distortion is notably higher than -116dB of the previous amplifiers although it is measured in most auspicious conditions – 1kHz frequency and the amplifier optimal 209mA quiescent current. If this current were, for example, 107mA (R121=326ohm) the measured distortion would be even higher – 32mV/10000=3.2μV=0.00032% or -110dB (see lower screenshot in Fig.7). This example demonstrates how the VK-2 distortion meter discerns the optimally biased and underbiased power amplifiers – the emerging spikes on distortion curves indicate that the set quiescent current through the output transistors is insufficient.


Fig.8. VK-2 distortion measurement of the typical power amplifier-3 at 16kHz.

     Divergence in distortion measurement results of the tested so far power amplifiers is smaller at 16kHz, the scheme of testing the typical power amplifier-3 at this frequency is depicted in Fig.8. After 1.98sec from the start of simulation a 140mV RMS measurement result appears at the distortion meter output, this means 140mV/10000=14μV of input signal distortion or 0.0014% (-97.1dB) relative to its 1V value, this figure is close to the virtual distortion analyzer reading (-97.6dB).
There are many combinations in connecting transistors into the output stage triples, the chosen modes of their operation being usually common-emitter or common-collector. Three of them have been already described in this article, I also explored some other combinations by placing them into the typical power amplifier circuit and hoping to find the one which could easily overcome a 0.001% distortion barrier even at highest audio frequencies, all that at a 100W power driving 4ohm load.
     Finally, such output stage configuration has been found, although something similar functions already in my VK-5 power amplifier during the last 15 years. Circuit diagram of the typical 100W power amplifier-4 with this output stage is represented in Fig.9.


Fig.9. VK-2 distortion measurement of the typical power amplifier-4 at 1kHz.

     The internal structure of each output triple includes a pre-driver emitter-follower (Q8 and Q37) feeding a complementary-feedback-pair of driver (Q35, Q36) and output (Q34, Q33) transistors. This connection constitutes a high-gain amplifier with the 100% local feedback, this feedback is a major mechanism of reducing the output stage distortion. This configuration features satisfactory quiescent current stability, it always remains high-frequency stable too.
     The amplifier 2.19sec simulation at 1kHz yields the 15.4mV reading of the distortion meter’s output measurement probe, dividing this figure by 10000 defines the input signal distortion of 1.54μV or 0.000154% (-116.2dB) relative to the signal 1V value. This distortion is mainly the third harmonic of the fundamental 1kHz frequency (see Fig.9).
     A surprising result is obtained when measuring distortion at 16kHz, the scheme of this test is depicted in Fig.10. Simulation here takes 1,87sec and the distortion meter output reading is 53mV that corresponds to the input signal distortion of 53mV/10000=5.3μV or 0.00053% (-105.6dB) relative to the 1V input. This distortion is twice lower than in any other output configuration, it is definitely the third harmonic (48kHz) without any hint at switch-off problems, the quiescent current being set here at 173mA. This output topology may be recommended for use in power amplifiers when getting low distortion is the main target.


Fig.10. VK-2 distortion measurement of the typical power amplifier-4 at 16kHz.

     I began to reduce the power amplifier distortion by choosing most perfect configuration of its output stage and finding its most optimal working conditions. The next step is to improve the interaction between the output stage and the amplifier preceding stage being a major contributor to the circuit voltage gain. It is desirable to keep this gain as high as possible for setting the unchanged amplifier closed-loop gain and for implementing very deep overall negative feedback. Just this properly used feedback can reduce distortion to the lowest, even record levels, given that other mechanisms of achieving better linearity are already acting.
     A simple method of increasing the open-loop gain is inserting an emitter follower between the output and voltage-amplifying (VAS) stages, the latter gets additional buffering from the low-impedance 4ohm load and that linearizes its transfer characteristic. The amplifier with this topology is shown in Fig.11.

Fig.11. VK-5K power amplifier 100W-4ohm.

     It represents a modernized version of my 50W VK-5 power amplifier, its output overload protection circuit differs from that of the typical power amplifier-4 - the current-sensing resistors R99, R101 are placed between the emitters of output transistors and power supply rails while their collectors become electrically connected and the transistors can be mounted on a common heatsink. The maximum allowable current through the output MJ21293-MJ21194 devices is 10A, its quiescent value in the absence of input signal is set as earlier between 200mA and 250mA.



Fig.12. AC analysis of the VK-5K power amplifier.

     The Multisim AC analysis (see Fig.12) discovers the VK-5K amplifier’s increased by 5dB open-loop gain in comparison with that of its typical counterparts, now it equals +110dB at 1kHz and +80dB at 20kHz, the closed-loop gain remaining the same +31dB. The VK-5K amplifier output stage has additional elements C3, R122 and C4, R123 that perform high-frequency correction of its characteristic and ensure the amplifier closed-loop stability.


Fig.13. VK-2 distortion measurement of the VK-5K power amplifier at 1kHz.

     The VK-5K power amplifier circuit imported to the VK-2 distortion measurement scheme is shown in Fig.13. Simulation of the combined circuit usually continues until the minimum settled readings of the output voltage measurement probe and the connected dB-meter are obtained. In the case of VK-5K amplifier this procedure at the fundamental frequency of 1kHz takes 2.85sec, its output result is 2.8mV RMS that corresponds to the input signal distortion of 2.8mV/10000=280nV or 0.000028% (-131dB) relative to the 1V input. It’s the lowest distortion figure registered so far, this is explained by the improved linearity of the VAS stage rather than by the increased feedback factor.


Fig.14. VK-2 distortion measurement of the VK-5K power amplifier at 16kHz.

     More humble distortion data is obtained when testing the amplifier at 16kHz, because the feedback factor here can not be made more than 45dB for reasons of guaranteeing the circuit HF stability. The carried out in 1.21sec measurement yields a 21mV RMS output reading which corresponds to the input signal distortion of 21mV/10000=2.1μV or 0.00021% (-113.6dB) relative to the 1V input (see Fig.14). And although the distortion curve looks quite nicely, the distortion value isn’t quite satisfactory for me and that prompted me to continue the amplifier modernization.


Fig.15. VK-2 distortion measurement of the VK-5L power amplifier at 16kHz.

     A slightly better amplifier performance at highest audio frequencies is achieved by altering its input differential stage. The input n-p-n transistors are employed here in the cascode connection with the following p-n-p transistors, this configuration is loaded then by a current mirror , the rest of circuitry remaining unchanged. This so-called VK-5L power amplifier is depicted in Fig.15, the simulation data of running the amplifier at 16kHz is represented there too.
     The VK-2 distortion meter obtained output of 18mV RMS means that the input signal distortion is 18mV/10000=1.8μV or 0.00018% (-115dB) relative to the 1V input. For comparison, the tested above VK-5K power amplifier produces -113.6dB distortion at 16kHz when delivering a 100W power into 4ohm load.
     A cardinal solution of most distortion problems offers my ultimate VK-5M power amplifier (see Fig.16).

Fig.16. VK-5M power amplifier 100W-4ohm.

     Its input circuit configuration resembles that of the famous Electrocompaniet amplifiers which contain three voltage amplifying stages. In the VK-5M device, the input n-p-n transistor differential pair has simple resistive load , the signal being then amplified by the second differential pair built on p-n-p transistors and loaded by a current mirror. The subsequent, already familiar voltage amplifying stage provides a major part of the circuit voltage gain. This is good illustrated by the Multisim AC analysis of the VK-5M power amplifier with and without the overall negative feedback (see Fig.17).



Fig.17. AC analysis of the VK-5M power amplifier.

     The amplifier open-loop gain is +118dB at 1kHz and +92dB at 20kHz, the closed-loop gain remaining +31dB as in all the considered above amplifiers. The increased feedback factor gives the reason to expect a further reduction of the amplifier distortion. Of course, that requires more careful adjustment of the circuit characteristics, particularly in the high frequency region to prevent the amplifier instability there.


Fig.18. VK-2 distortion measurement of the VK-5M power amplifier at 1kHz.

     After the preliminary Multisim analysis, the amplifier circuit is entered into the VK-2 distortion measurement scheme and its first test is conducted at 1kHz frequency (see Fig.18). The obtained in 2.53sec measurement result is phenomenal indeed – 324μV RMS that corresponds to the input normalized signal distortion of 324μV/10000=32nV or 0.0000032% (-149.8B) relative to the 1V input. I would like to note that the amplifier open-loop distortion at this frequency and at this output 100W power is 0.034%, the rest is the matter of the applied deep NFB.
     At the 16kHz test frequency the distortion figure isn’t so low, the performed in 1.45sec simulation brings the VK-2 output reading of 3.92mV RMS which corresponds to 3.92mV/10000=0.39μV distortion at the VK-2 input or 0.000039% (-128.2dB) relative to the presented at this input amplifier normalized 1V signal (see Fig.19).


Fig.19. VK-2 distortion measurement of the VK-5M power amplifier at 16kHz.

     The above test is the last in this series, but my search of the most perfect power amplifier will be continued. In the pre-computer era I spent months and years for developing and testing amplifiers, that required a substantial resources of electronic components which sometimes turned to scrap metal and ashes. The present computer simulation is free of these drawbacks and it offers the fantastic possibilities for an electronics designer.
     To make the simulation more complete and informative, I use not only the Multisim virtual instruments (oscilloscopes, DC and AC voltmeters, distortion analyzer and others). There are also the measurement probes placed at most critical points of the circuit to monitor the simulation process at these points and to obtain detailed time-varying information about its main parameters (voltage, current, frequency) until stopping the simulation, the gathered measurement data and screenshots being then saved in a file.
     Of course the simulation is a miraculous process involving hundreds of electronic components, but it requires very intensive computer work and every additional component or measurement probe makes this work more difficult and hence more slow.



Fig.20. VK-2 rejection filter (16kHz setting).

     To acquaint the reader with the simulation potential of the Multisim 10 program, I would like to represent in Fig.20 the circuit diagram of the VK-2 active rejection filter. In all distortion measurement schemes it is shown as a subcircuit rectangle, but its functional capability is great indeed. In this study, extracting the power amplifier distortion within 0.0002-0.002% is too easy exercise for this device, it handles as well distortion down to 0.0000003% (-170dB), but unfortunately the amplifier of such linearity hasn’t still be found. I would be glad if somebody can submit to me the circuit of such a beast for testing purposes. The most linear amplifier I’ve ever tested features -157dB distortion.
     As for modern super-linear op amplifiers, the virtual VK-2 distortion meter is unable to directly evaluate their distortion because their simulation models simply don’t contain the corresponding data and they therefore exhibit infinite linearity. The distortion evaluation may be done correctly if entering the op amplifiers’ full circuit diagrams into the simulation program and using then the VK-2 meter. Some of the super-linear op amplifiers have been already tested in this way and the results are very interesting.
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