Distortion In Power Amplifiers.

Updated: 9 Oct 2001


The distortion produced by a typical solid-state Class-B power amplifier is shown to consist of eight mechanisms, all of which may co- exist and whose distortion products overlap to give a complex result. Methods for isolating each mechanism for study, and minimising its contribution, are given. If the avoidable distortions are designed out, Class-B amplifiers of unusually low distortion (Below 0.0005% at 1kHz, 0.003% at 10 kHz) may be designed as a matter of routine, and without significant extra cost. Such amplifiers define a distortion benchmark, and I have named them "Blameless" amplifiers.

  • C O N T E N T S
  • 0: Introduction.
  • 1: The Generic Amplifier Configuration.
  • 2: The Eight Distortions.
  • 3: Three Non-existent Distortions.
  • 4: Techniques for Amplifier Investigation.
  • 5: The Distortion Mechanisms.
  • 6: The Concept of the Blameless Amplifier.
  • 7: Conclusions.
  • References.
  • Back to Home Page Back to The Amplifier Department.

    Much more detail on distortion and other matters
    can be found in the book I finally got round to writing:

    The Audio Power Amplifier Design Handbook

    Considering the economic importance of audio power amplifiers, surprisingly little reliable information has been published on their design. Distortion in particular has been neglected, although it is the most variable feature of amplifier performance. You may have two units placed side, one giving 2% THD and the other 0.0005% at full power, and both claiming to provide the ultimate audio experience.
    I investigated the origins of distortion in the period 1992-94, and determined that power amplifier distortion, traditionally a difficult and mysterious thing to grapple with, was the amalgamation of eight basic mechanisms, superimposed and sometimes partially cancelling, giving a complex result. I evolved ways of measuring and minimising each distortion mechanism separately, and the result is a design methodology for making Class-B or Class-A amplifiers with distortion performance so good that two or three years ago it would have been regarded as impossible. 0.0008% at 1 kHz and 0.003% at 10 kHz are easily obtained. The methodology gives reliable and repeatable results with moderate amounts of negative feedback; increases in complexity and cost are insignificant.

    Fig 1a shows the generic Lin power amplifier circuit, with the now universal differential input stage, representing something like 98% of the amplifiers ever built. It is the obvious starting point for amplifier investigation. [1] Fig 3 shows its distortion plot; there are two distortion regimes. Below 1 kHz THD is low at 0.002% but not zero, the noise floor being 0.0006% approx. Above 1 kHz, THD quadruples with each octave and reaches 0.5% before 20 kHz.
    The basic topology is a transconductance amplifier (voltage- difference input, current output) driving a transimpedance (current-to- voltage converter) Voltage Amplifier Stage, followed by a unity-gain power buffer. The voltage at the VAS transistor base is typically only a couple of millivolts, and is of little interest in itself; it is the current passed from the input stage to the VAS that counts. This topology has many advantages, including simple compensation. [2]

    Top | Contents | Section 3

    The distortion mechanisms of a generic power amplifier fall into eight basic categories. Distortion 3 is that generated by the output stage, subdivided into three different mechanisms 3a, 3b, 3c that are unrelated in their physical origin. Similarly, Distortion 8 normally only occurs in the capacitor at the bottom the feedback arm; however, in AC-coupled designs the output capacitor may contribute significant distortion.
    This classification assumes no clipping, overload, slew-limiting, or parasitic oscillation.

    TABLE 1.
    1 Input stage (balanced) 3rd-order 18dB/oct Inherent
    Input stage (unbalanced) 2nd-order 12dB/oct Inherent
    2 Voltage Amplifier Stage 2nd-order 6dB/oct Inherent
    3a Output stage LSN (4 Ohm) 3rd-order 6dB/oct Inherent
    3b Output stage crossover Complex 6dB/oct Inherent
    3c Output stage switchoff Complex Variable Inherent
    4 Non-linear VAS loading Complex Flat Inherent
    5 Decouple return in groundEven Flat Topological
    6 Rail induction Even 6dB/oct Topological
    7 Wrong feedback point Even Flat Topological
    8 Capacitor non-linearity Odd 12dB/oct Inherent

    Section 1 | Contents | Section 4

    3. THREE NON-EXISTENT DISTORTIONS. Audio engineering suffers from misinformation, disinformation, and downright lying more than most fields of endeavour. Here are three distortions which either do not exist in detectable quantities or are based on misunderstandings:

    3.1 Distortion From The Supply Rails
    This is often cited as a serious source of degradation. The only likely manifestations are Distortion 5 and 6, described below. Providing these two mechanisms have been suppressed (which is straightforward) and the amplifier has sufficient power-supply rejection to keep hum and ripple below the noise floor, then there should be no other way in which the power supply can degrade linearity.

    3.2 Input-Stage Common-Mode Distortion.
    This does not appear to exist at detectable levels in normal amplifier circuitry. It is however true that if an amplifier is operated at a low closed-loop (C/L) gain such as 1 or 2 times, so there is a large Common-Mode (CM) voltage on the input stage, distortion at HF is unexpectedly high, despite the much increased negative-feedback factor. This distortion is mainly second-harmonic. The immediate cause is the increased CM voltage on the input devices, but the exact mechanism is at present unclear. [3] Table 2 shows distortion increasing as C/L gain is reduced, with output kept constant at 10 V rms. It appears THD is proportional to CM voltage squared for gain changes.

    TABLE 2.
    Closed-Loop Gain 15 kHz THDCM voltage15 kHz THD
    (meas)V rms(calc)
    1.00 x.0112%10.00.00871% *
    1.22 x.00602%8.20.00585%
    1.47 x.00404%6.81.00404% (Ref)
    2.00 x.00220%5.00.00218%
    Thus the THD at 1.47 times gain (.00404%) when scaled down for a realistic C/L gain of 23, is reduced by a factor of (23/1.47)2 = 245, giving a negligible 0.000017% at 15 kHz.

    3.3 Thermal Distortion.
    Thermal distortion is sometimes described as that caused by cyclic temperature changes at signal frequency, modulating device parameters. This is a real problem in ICs, with input and output devices in close thermal proximity, but in a discrete-component power amplifier there is no such coupling, and no such distortion.
    Thermal distortion would be expected to appear as a rise in second or third harmonic distortion at very low frequencies, and the largest effects would be in Class-B output stages where dissipation varies greatly over a cycle. The effect is wholly absent.
    This is probably because drivers and output devices have large junctions with high thermal inertia. An MJE340 driver transistor has a chip area four times that of a TL072, so parameters like Vbe presumably cannot change much even at 10 Hz. The global NFB factor is also highest at LF. Using my design methodology an amplifier can be straightforwardly designed to produce less than 0.0006% THD at 10Hz (150W/8-Ohm) without considering thermal distortion; this suggests that it is not a problem.
    THD plots rising at low frequencies are common, but I have always found the LF rise could be eliminated by correcting either defective decoupling (Distortion 5) or increasing the feedback capacitor. (Distortion 8)
    As a further argument, consider the distortion residual of an underbiased Class-B amplifier, using a CFP output so that quiescent bias depends on the driver temperatures alone. When sinewave power is delivered to a load, the crossover spikes (generated by the underbiasing) on the THD residual slowly reduce in height over a couple of minutes as the drivers warm up. The height of these spikes gives a continuous indication of driver temperature, and the slow variations indicate thermal time-constants of tens of seconds, and a negligible response at 10Hz.

    Section 2 | Contents | Section 5

    4.1 Open-Loop Gain and Its Measurement.
    The closed-loop distortion performance of an amplifier is the product of open-loop linearity and the negative-feedback factor. For fixed closed-loop gain, the NFB factor is set by the open-loop gain and its variations with frequency.

         The open-loop (O/L) gain has two regimes; flat below the lowest pole
    frequency P1, (LF) and falling at 6dB/octave above it. (HF)
    LF gain is:    LF gain= gm*beta*Rc      	Eqn 1
    HF gain is:    HF gain= gm/(w*Cdom)          	Eqn 2
    Pole freq is:  P1= 1/(Cdom*beta*Rc)          	Eqn 3
    gm is input stage transconductance.  Beta is VAS current gain.
    Rc is VAS collector impedance        w= 2*pi*freq
    A typical circuit modification- eg changing the value of R2 in Fig 1a- changes open-loop gain as well as linearity and it is essential to know if an observed change is due to improved O/L linearity, or simply increased O/L gain. Hence the need for a quick and convenient method of measuring O/L gain. Standard methods for op-amp open-loop gain involve breaking feedback-loops and manipulating closed-loop (C/L) gains, procedures that are unlikely to succeed with the average power-amplifier.

    Fig 1

    For the generic amplifier in Fig 1, open-loop gain is the output voltage divided by the differential voltage at the inputs. If the C/L frequency response is flat, a plot of open-loop gain versus frequency is obtained by measuring the error-voltage between the inputs, and referring it to the output level. This gives an upside-down plot rising at HF rather than falling, as the amplifier requires more error-voltage for the same output as frequency increases. Fig 2 shows O/L gain of the amplifier in Fig 1.

    Fig 2

    Given testgear with high CMRR balanced inputs, the method is simple; buffer the amplifier's differential inputs from cable capacitance with TL072 voltage-followers, which place negligible loading on the circuit, and measure the level with respect to the output. The testgear CMRR defines the maximum open-loop gain measurable; an Audio Precision System-1 works very well here.
    A calibration plot (lower trace in Fig 2) is produced by feeding the two buffer inputs from the same signal; this also rises at 6dB/octave, due to testgear input assymmetries, and must be at least 10dB below the amplifier error signal for accuracy. The curve flattens out at LF, and may rise, due to imbalance of the testgear input-blocking capacitors; this makes determination of the lowest pole P1 difficult, but P1 is not a vital parameter in itself.

    Fig 3

    4.2 Model Amplifiers.
    A linear small-signal section is the obvious starting point for a low-distortion amplifier; Distortions 1 and 2 can easily dominate amplifier performance and need to be studied without the complications of a Class-B output stage. The circuit is reduced to a "model" amplifier consisting of input stage and VAS only, plus a very linear Class A emitter-follower as output stage to drive the feedback network; there is no external loading.
    "Model" here means reduced currents rather than voltages. The model amplifier should be capable of giving a full power-amp voltage swing, as input-pair distortion depends on absolute output level, and not the proportion of the rail voltage traversed. Model amplifiers without slow output stages can give misleadingly optimistic results for HF stability. A high NFB-factor stable in a model amplifier can easily be unstable when a real output stage is added. The value of Cdom should be that anticipated for the complete amplifier.
    A typical THD plot from a model amp as in Fig 1 rises with a steepening slope, as the initial rise at 6dB/octave from the VAS is contributed to, and then dominated by, the 12dB/octave rise in distortion from an unbalanced input stage. (see 5.1.2)

    4.3 SPICE simulation.
    This is a powerful technique; I use PSpice. SPICE gives insight into the open-loop linearity of both input and output stages, but applying it to the VAS is problematical as BJT Early Effect is implemented as a linear approximation. This seems unlikely to give accurate results for a stage with a large signal on its collector.

    Section 3 | Contents | Section 6


    5.1 DISTORTION 1. Input Pair Non-linearity
    The input differential pair implements one of the few forms of distortion cancellation that is truly reliable- the transconductance of the input pair are determined by transistor physics rather than matching of variable parameters such as beta. The logarithmic relation between Ic and Vbe is proverbially accurate over eight or nine decades of collector current.
    The prime motivation for using a differential pair as the input stage of an amplifier is its low DC offset. Apart from cancellation of the Vbe voltages, it has the extra advantage that the standing current does not flow through the feedback network. A second powerful reason, which seems less well-known, is that linearity is far superior to single-transistor input stages.

    The output current is related to the differential input voltage Vin by:
        Iout= Ie.tanh(-Vin/2Vt)      Eqn 4
        (where Vt is the usual "thermal voltage" of about 26mV at 25 degC,
    and Ie the tail current)
    Transconductance (gm) is maximal at Vin=0, when the two collector currents are equal, and this maximum is proportional to the tail current Ie. [4] Device beta does not figure in the equation, and linearity of the input pair is not significantly affected by transistor type. The transconductance plot in Fig 4 shows the linearising effect of local feedback (emitter degeneration) on the voltage-in/current-out law; it plots transconductance against input voltage and demonstrates how emitter degeneration reduces peak transconductance, flattening the curve over a wider input range. Emitter degeneration markedly improves input stage linearity, but the overall amplifier NFB factor is reduced, for the vital HF closed-loop gain is determined solely by input-stage transconductance and the value of the dominant-pole capacitor. (Eqn 2)

    Fig 4

    FETs seem a poor idea for the input stage. The basic gm is so low compared with BJTs that there is little scope for linearisation by adding source resistors for local degeneration, so an FET input stage will be very non-linear compared with a BJTs degenerated down to the same transconductance: see 5.1.3.

    Fig 5

    Curve A in Fig 5 shows the distortion plot for a model amplifier, (5 Vrms output) designed so all distortion is negligible apart from that from the input stage; with a class A output this simply means ensuring that the VAS is properly linearised. Note the vanishingly low LF distortion. For R2 =10K, distortion is below the .001% noise floor until it emerges at 1 kHz, rising steeply at 12 dB/octave. This rapid increase is due to the input stage signal current doubling every octave, to feed Cdom; therefore the associated second harmonic distortion doubles with each octave increase. Simultaneously the overall NFB available to linearise this distortion falls at 6dB/octave, and the combined effect is an quadrupling or 12 dB/octave rise.
    If the input stage is properly balanced, only third harmonic is generated, which quadruples rather than doubling as amplitude doubles, resulting in a 18 dB/octave slope; however this only appears much further up the frequency range, and the total distortion produced is much less. If the VAS or output stage generates distortion it rises at only 6dB/octave, and looks quite different.

    Fig 6

    5.1.1 Input stage distortion in isolation.
    For serious research we need to measure input-stage non-linearity open-loop and in isolation. This is simply done with the test circuit of Fig 6. The current-to-voltage conversion op-amp uses shunt feedback to generate an AC virtual-earth at the input-pair output, and uses a third -30V rail to allow the i/p pair collectors to work at a realistic DC voltage just above the V- rail; the 10K feedback resistor may be scaled to prevent op-amp clipping. Input DC balance is set by the 10K pot; the THD residual diminishes as balance is approached, until the second- harmonic is nulled, leaving almost pure third harmonic.

    5.1.2 Input stage balance.
    Exact DC balance of the input differential pair is essential for minimum distortion. It seems almost unknown that even minor deviations from equality of collector current (Ic) in the input devices seriously upset the 2nd-harmonic cancellation, by moving the operating point from A to say, B, in Fig 4. The gm is both less and changing faster at B, so imbalance reduces open-loop gain as well as increasing distortion. The effect of small amounts of Ic imbalance is shown in Fig 7 & Table 3; with an input of -45dBu an Ic imbalance of only 2% seriously worsens linearity, THD increasing from 0.10% to 0.16%, while for 10% imbalance this deteriorates to 0.55%. Ic balance needs an accuracy of 1% or better for lowest distortion at HF, where the input pair works hardest. Imbalance in either direction gives similar results.
    Fig 7

    TABLE 3  (Key to Fig 7)
                   Curve No.      Ic Imbalance
                        1                0%
                        2              0.5%
                        3              2.2%
                        4              3.6%
                        5              5.4%
                        6              6.9%
                        7              8.5%
                        8               10%
         Imbalance defined as deviation of Ic (per device) from that value
    which gives equal Ic in the pair.
    Fig 8

    This explains the complex distortion changes that accompany the apparently simple experiment of altering the value of R2. We might design an input stage as in Fig 8a, where R1 has been selected as 1K by uninspired guesswork and R2 made high at 10K in a plausible but misguided attempt to maximise O/L gain by minimising TR2 collector loading. R3 is also 10K to give the stage a notional "balance"; unhappily this is a visual rather than electrical balance. The asymmetry is shown in the resulting collector currents; this design generates a lot of avoidable second harmonic distortion, displayed in the 10K curve of Fig 5.
    Recognising the crucial importance of Ic balance, the circuit can be rethought as Fig 8b. If the collector currents are to be equal, R2 must be twice R1, as both have about 0.6V across them. The dramatic effect of this simple change is shown in the 2K2 curve of Fig 5; the improvement is accentuated as O/L gain has also increased by some 7 dB, though this has only a minor effect on the closed-loop linearity compared with the improved input stage balance. R3 has been removed as it contributes nothing to input balance.
    The input pair can be approximately balanced by the correct values for R1 and R2, but we remain at the mercy of several circuit tolerances. The current-mirror configuration in Fig 8c forces the two collector currents very close to equality when global NFB is applied, giving excellent cancellation of the second harmonic; the great improvement is seen in the current-mirror curve of Fig 5. A simple mirror has well- known Ib errors but they are not large enough to affect distortion.
    The hyperbolic-tangent law also holds for the mirrored pair, [5] but the output current swing is twice as great for the same input voltage. This doubled output is at the same distortion as a perfectly-balanced non-mirror input, as linearity depends on the input voltage, which has not changed. Putting a current-mirror in a well-balanced input stage therefore increases the total O/L gain by at least 6dB, and possibly by up to 15dB if the stage was previously poorly balanced; the compensation by Cdom must allow for this.
    Another happy consequence is that slew-rate is roughly doubled, as the input stage can now source and sink current into Cdom without wasting some in resistive collector load R2. If Cdom is 100pF, the slew-rate of Fig 9a is about 2.8V/usec up and down, while 9b gives 5.6V/usec. The unbalanced pair at Fig 8a displays further vices by giving 0.7V/usec positive-going and 5V/usec negative-going.

    Fig 9

    A discrete current-mirror needs its own emitter-degeneration for accuracy. A voltage-drop across the mirror emitter-resistors of 60mV is enough to make the effect of Vbe tolerances negligible; without degeneration there is significant variation in HF THD with different transistor specimens.
    To summarise, the advantages of a mirrored input stage are that second-harmonic distortion is eliminated, and maximum slew-rate is doubled.

    5.1.3 Improving input-stage linearity.
    Even if the input pair has a current-mirror, HF distortion can still be excessive; once it emerges from the noise floor it octuples with each doubling of frequency, and so it is well worth postponing the evil day until as far as possible up the frequency range. Input stage transconductance increases with Ic, so it is possible to raise gm by increasing the tail-current, and then reduce it back to its previous value (otherwise Cdom must be increased to maintain stability) by applying local NFB in the form of emitter-degeneration. This greatly improves input linearity, despite its rather unsettling flavour of something-for-nothing. Input transistor non-linearity can be regarded as an internal non-linear emitter resistance re, and we have reduced the value of this (by increasing Ic) and then replaced the missing part with a linear external resistor Re.

    For a single device, the value of the internal re is approximated by:
            re= 25/Ic Ohms   (Ic in mA)          Eqn 5
    The original input stage in Fig 1 has a per-device Ic of 600uA, giving a differential (ie, mirrored) gm of 23 mA/V and re= 41.6 Ohm. The improved version in Fig 9b has Ic= 1.35mA and so re= 18.6 Ohm; emitter degeneration resistors of 22 Ohm are added to reduce gm back to its original value, as 18.6 + 22 is approx 41.6 Ohm. The THD measured by the circuit of Fig 6 for a -40dBu input voltage falls from 0.32% to 0.032%, an extremely valuable linearisation which translates into an HF distortion reduction of about 5 times for a complete Class-B amplifier; the full advantage is rarely gained. The remaining distortion is still visually pure third-harmonic if the input pair is balanced. The reduction of re is limited by the need for practical values of tail current. As a further benefit, increasing the tail current also increases slew rate.

    5.2 DISTORTION 2
    The Voltage-Amplifier Stage (or VAS) is often regarded as a critical part of a power-amplifier. It provides all the voltage gain and simultaneously the full output voltage swing. However, as is not uncommon in audio, all is not quite as it appears. A well-designed VAS stage contributes relatively little to the total distortion of an amplifier; if even the simplest steps are taken to linearise it further, its contribution disappears. This is because the action of Miller dominant-pole compensation in this stage is rather elegant. It is not simply a matter of finding the most vulnerable transistor and setting it in treacle. As frequency rises and Cdom takes effect, negative feedback is no longer applied globally around the whole amplifier, which would include the higher poles, but instead is smoothly transferred to a purely local role in linearising the VAS. Since this stage is effectively a single transistor, a large amount of local NFB can be applied to it without stability problems.

    VAS distortion arises from the fact that the transfer characteristic of a common-emitter amplifier is curved, being a portion of an exponential. [6] This generates predominantly second-harmonic distortion, which in a closed-loop amplifier will increase at 6dB/octave with frequency. VAS distortion does not worsen for more powerful amplifiers because the stage traverses a constant proportion of its characteristic as the supply-rails are increased. This is not true of the input stage; increasing output swing increases the demands on the transconductance amp as the current to drive Cdom increases.

    5.2.1 Measuring VAS distortion in isolation.
    Isolating the VAS distortion for study requires the input pair to be specially linearised, to prevent its steeply-rising distortion characteristic from swamping the VAS contribution. This is done by heavily degenerating the input stage; this also reduces open-loop gain, and the reduced global NFB factor exposes VAS non-linearity. See Fig 10, where the 6dB/octave slopes suggest an origin in the VAS. Distortion increases with frequency as Cdom rolls-off the global NFB factor.
    To confirm that this distortion is due solely to the VAS, it is necessary to find a method for experimentally varying VAS linearity while leaving all other circuit parameters unchanged. In a model amplifier this can be done simply by varying the V- voltage; this varies the proportion of its characteristic over which the VAS swings, and thus only alters the effective VAS linearity, as input stage operation is not significantly affected. (Fig 10) The Vce of the input devices varies, but this has negligible effect.
    Fig 10

    5.2.2 VAS configurations.
    Various kinds of VAS are shown in Fig 11. It is important that the local open-loop gain of the VAS (that inside the local feedback loop closed by Cdom) be high, to linearise the VAS. Therefore a simple resistive collector load is unusable. Increasing the value of a resistive load to increase voltage gain decreases the VAS transistor Ic, reducing its gm and getting you back where you started.
    Local loop gain is enhanced by using an active load to increase the VAS collector impedance and thus increase the raw voltage gain; either bootstrapping or a current-source do this effectively, though the current source is the usual choice. Both active-load techniques have another important role; ensuring that the VAS can source enough current to drive the upper half of the output stage. If the VAS collector load was just a resistor to V+, this capability would be lacking.

    Fig 11

    The popular current source VAS is shown in Fig 11a. This works well, though the collector impedance and hence gain is limited by Early Effect and output stage loading. It is often stated that this topology provides current-drive to the output stage; this is not really true. Once the local NFB loop has been closed by adding Cdom the impedance at the VAS output falls at 6dB/octave for frequencies above P1. With typical values the impedance is only a few kohm at 10kHz, and this hardly qualifies as current-drive.
    Fig 11b shows the bootstrapped equivalent. One drawback is that the increase in voltage gain is determined by the exact gain of the output stage, which is below unity and varies with loading. A more dependable form of bootstrapping is available if the amplifier incorporates a unity-gain buffer between the VAS collector and the output stage; this is shown in Fig 11f, where R is the VAS collector load, defining VAS collector current by establishing the Vbe of the buffer transistor across itself. This voltage is constant, so R is bootstrapped and appears to the VAS collector as a constant-current source. A VAS current of 3mA is sufficient, compared with 6mA for the buffer stage.

    5.2.3 VAS enhancements.
    The VAS distortion in Fig 10 shows the need for further improvement over that given by local NFB through Cdom, if our small-signal stages are to be distortion-free. The virtuous approach might be to try to straighten out the curved VAS characteristic, but in practice the simplest method is to increase the amount of local negative feedback around the VAS through Cdom. Equation 1 shows that LF O/L gain (also the gain before Cdom is connected) is the product of input stage transconductance, TR4 beta and the collector impedance Rc. The last two factors represent the VAS gain and the local NFB can be augmented by increasing either. So long as Cdom remains the same, the global feedback factor at HF is unchanged and so stability is not affected. The effective beta of the VAS can be substantially increased by adding an emitter-follower. (Fig 11c) Adding an extra stage requires thought, for if additional phase-shift is introduced, the global loop stability will suffer. Here the extra stage is inside the Cdom Miller- loop and so there is little likelihood of trouble from this. The function of such an emitter-follower is sometimes described as "buffering the input stage from the VAS" but this is quite wrong; its true function is VAS linearisation by enhancing local NFB through Cdom.
    Alternatively the VAS collector impedance can be further increased to get more local gain. This can be done with a cascode configuration- (see Fig 11d) but this technique is only useful when the VAS is not loaded by a seriously non-linear impedance... such as the input of a Class-B output stage. See section 5.4. The non-linear loading renders cascoding largely cosmetic unless a Class-A stage buffers the VAS collector from the output stage, as in Fig 11e.
    When a VAS-buffer is added, the drop in distortion is dramatic, as it is for the beta-enhancement method. The gain increase is ultimately limited by Early effect in the cascode and current-source transistors, and more seriously by the loading effect of the next stage, but it is of the order of 10 times and gives a useful effect. Fig 12 plots the distortion of a model amplifier with 100 Ohm input pair degeneration resistors, showing the extra distortion from a simple VAS. However, the beta-enhanced version has the THD submerged in the noise floor for most of the audio band, being well below 0.001%. I think this justifies my contention that input-stage and VAS distortions need not be problems; we have all but eliminated Distortions 1 and 2 from the list of eight.

    Fig 12

    The beta-enhancing emitter-follower is slightly simpler than the buffered-cascode, but the cost difference is tiny. When wrestling with these kind of financial decisions it is as well to remember that the small-signal section of an amplifier usually represents less than 1% of the total cost, including mains transformer and heatsinks.
    Although the two VAS-linearising approaches look very different, the basic strategy of increased local feedback through Cdom is the same. Either method linearises the VAS into invisibility.

    5.3 DISTORTION 3.
    The almost universal choice in semiconductor power amplifiers is a unity-gain output stage, specifically a voltage-follower. The most common output stages are shown in Fig 13; two versions of the double- emitter-follower, (EF) the Complementary Feedback Pair (CFP), and a source-follower FET output.

    Fig 13

    The use of power FETs in output stages is often advocated. However, after much investigation, I have found the conclusion inescapable that FETs suffer not only from poor basic linearity, due to low gm, but also a crossover region that is inherently more jagged than BJTs. It is not possible to explore this in detail here, but see [7],[8]

    A fundamental factor in determining output-stage distortion is the Class of operation. Apart from its inherent inefficiency, Class-A is ideal, having no crossover or switchoff distortion. Distortions 4, 5, 6 and 7 are direct results of Class-B operation and also disappear from a Class-A design. Distortion 1 (input-stage), Distortion 2 (VAS), and Distortion 3a (output-stage large-signal non-linearity) remain, however. Of those Class-A designs which have been published or reviewed, it is notable that the distortion produced is still significant. This need not be so; see [9] for a Blameless amplifier biased into Class A, giving THD below 0.002%, 10 Hz-20 kHz.
    It is not generally appreciated that moving into Class-AB, by increasing the quiescent current, does NOT simply trade efficiency for linearity. If the output power is above the level at which Class-A operation can be sustained, THD increases as the bias advances into AB operation. This is due to so-called "gm-doubling" (ie the voltage-gain increase caused by both devices conducting simultaneously in the centre of the output-voltage range, in the Class-A region) putting edges into the distortion residual that generate high-order harmonics much as under-biasing does. This vital fact is little known, presumably because gm-doubling distortion is at a relatively low level and is obscured in most amplifiers by other distortions.

    Fig 14a

    Fig 14b

    Fig 14c

    This is demonstrated in Fig 14a,b,c showing THD residuals for under- biasing, optimal, and over-biasing of a 150W/8-Ohm amplifier at 1kHz. All non-linearities except Distortion 3 (output stage) have been eliminated. The over-biased case had its quiescent current increased until the gm-doubling edges in the residual had a 1:3 mark/space ratio, and so was in Class A about one quarter of the time. All three traces were averaged 64 times to reduce noise; the distortion in 14b is normally invisible in a 80 kHz measurement bandwidth. The RMS THD reading for Fig 14a was 0.00151%, for 14b 0.00103%, and for 14c 0.00153% Spectrum analysis of Fig 14c shows the higher harmonics to be at least 10dB greater than those for the optimal Class-B case, and comparable with 14a. In short, Class-AB offers lower distortion than Class-B below the AB threshold but more above it.
    Distortion 3a is the Large-Signal Non-linearity (LSN) that is produced by in both Class-A and B output stages, ultimately because of the large current swings in the active devices; in bipolars, but not FETs, large collector currents reduce beta, leading to drooping gain at large output excursions. It excludes crossover and switchoff phenomena. Distortion 3b is classic crossover distortion, resulting from the non-conjugate nature of the two output halves. Distortion 3c is switchoff distortion, generated by the output devices failing to turn off quickly and cleanly at high frequencies, and is strongly frequency-dependent. The contributions of 3b and 3c to Distortion 3 occur in Class-B only.

    Fig 15

    Fig 16

    Fig 17

    The linearity of the open-loop output stages in Fig 13 with typical values are shown in Figs 15,16,17. These diagrams were generated by SPICE, plotting incremental output gain against output voltage, with load resistance stepped from 16 to 2 Ohms, which I hope is the lowest impedance that feckless loudspeaker designers will throw at us. These plots have come to be known as "wingspread" diagrams, from their birdlike appearance. The power devices were Motorola MJ802 and MJ4502, which are more complementary than many so-called pairs, and minimise distracting large-signal asymmetry. The quiescent conditions are in each case set to minimise peak-to-peak gain deviations in the crossover region for 8-Ohm loading.

    The EF output stage.
    I have deliberately called this the Emitter-Follower (EF) rather than Darlington configuration, the latter implying an integrated device with driver, output, etc in one ill-conceived package. In the EF topology the input is transferred to the output via two base-emitter junctions in series, with 100% voltage feedback applied to each device separately to create cascaded emitter-followers. Fig 13a shows the most prevalent version (Type I) with driver emitter resistors R1,2 connected to the output rail. Type II uses one shared resistor Rd, and this improves HF switchoff; (Fig 13b) basic linearity is the same, see Fig 15. The crossover region width is approx 10 V, and optimal bias 2.86 V.

    .The CFP output stage.
    The other major type of bipolar complementary output is the Complementary Feedback Pair (CFP) or Sziklai Pair, seen in Fig 13c. The drivers now compare the output voltage with that at the stage input. Wrapping the outputs in a local NFB loop gives better linearity than EF versions with 100% feedback applied separately to driver and output transistors. The CFP topology is generally considered to show better thermal stability than the EF, because the Vbe of the output devices is inside the local NFB loop, and only the driver Vbe affects the quiescent conditions. The true situation is rather more complex. [10],[11],[12] The output gain plot is shown in Fig 16; Fourier analysis shows the CFP generates less than half the LSN of an emitter-follower stage. (See Table 4) It is hard to see why this topology is not more popular. The crossover region is much narrower, at about 1V. When under- biased, this appears on the distortion residual as narrower spikes than those from an emitter-follower output. Optimal bias here is 1.296V.

    TABLE 4.
    Fourier analysis of each SPICE gain plot, for 4 and 8 Ohm loading,
    yielded these THD % results for a +/-40V input:
            	Emitter          CFP            Simple 
    	        Follower              		MOSFET 
    8-Ohm THD      0.031%       	0.014%    	0.47%  
    Gain:   	0.97		0.97      	0.83   
    4-Ohm THD      0.042%       	0.030%    	0.84%  
    Gain: 		0.94       	0.94      	0.72   
    Combining one of these stages with a distortionless small-signal section, and applying 30 dB of global NFB, we might expect an amplifier with vanishingly small THD. In fact, crossover distortion remains at HF, due to the difficulty of linearising high-order distortion with feedback that reduces with frequency; Fig 18 shows the typical Blameless performance.

    Fig 18

    5.3.1 Large-Signal Nonlinearity. (Distortion 3a)
    LSN increases as load impedance decreases. In a typical output stage loaded with 8 Ohms or more, closed-loop LSN is negligible, the THD residual being almost entirely high-order crossover artifacts that are reduced less by NFB. As load impedance falls below 8 Ohms, third- harmonic appears in the residual, and soon dominates. The BJT output gain plots reveal that LSN is compressive, ie voltage gain falls with higher outputs.
    The fundamental reason for this gain-droop is the fall in output- transistor beta as Ic increases. [13] In the Emitter-Follower (EF) topology, beta falloff draws more output-base current from the driver emitter, pulling driver gain down further from unity; this is the change in gain that affects the overall transfer ratio. Output-device gain is not directly affected, as given zero source impedance, beta does not appear in the equation for emitter-follower gain. As further evidence:

    * In SPICE simulation, driving the output bases directly from zero- impedance voltage-sources (rather than drivers) abolishes the gain droop effect. The cause is in the output devices, but the effect is in the drivers.

    * The SPICE Gummel-Poon model can be altered so output device beta does not drop with Ic (increase parameter IKF) and once more gain-droop does not occur, with drivers present.

    * Measured LSN levels correlate well with the degree of beta-falloff shown in manufacturer's data sheets. This holds for many different BJTs produced over the last 30 years.

    LSN does not appear to afflict FET outputs, which have no equivalent beta-falloff mechanism. See Fig 17 where the "wings" of the FET gain plot do not turn downwards at large outputs.

    LSN may be reduced in two ways:

    * Use output devices that sustain beta well as Ic increases. The 2SC3281 and 2SA1302 transistors (Toshiba, Motorola) show much less beta-droop than average, and 4-Ohm distortion is reduced by about 1.4 times.

    * Use two or more output devices in parallel even though this is unnecessary for handling the power output. Falloff of beta depends on collector current, and if two output devices are connected in parallel, the collector current divides in two between them, and beta-droop is much reduced. Doubling devices reduces distortion by about 1.9 times.

    * These two techniques may be combined by using double sustained-beta devices. Doubled device results are shown in Fig 19; distortion at 80W/4 Ohm has halved from 0.009% to 0.0045%. 8 and 4 Ohm traces are now very close, the 4 Ohm THD being only 1.2 times higher.

    Fig 19

    5.3.2 Crossover distortion. (Distortion 3b)
    In a field like Audio where consensus of any sort is rare, it is widely acknowledged that crossover distortion is the worst problem afflicting Class-B power amplifiers. The pernicious nature of crossover distortion is that it occurs over a small part of the transfer characteristic, and so generates high-order harmonics. Worse still, this range is around the zero-crossing, so it is present at all levels, the THD percentage potentially increasing as output level falls, threatening very poor linearity at low powers.
    I investigated crossover distortion to see if it really did increase with decreasing output level in a Blameless amplifier. One problem is that an optimally-biased Blameless amplifier has such a low level of distortion at 1 kHz (0.001% or less) that the crossover artifacts are barely visible in circuit noise, even if low-noise techniques are used. Thus the THD percentage of the noise-plus-distortion residual is bound to rise with falling output, for the noise contribution remains constant; this is the lowest line in Fig 20. To circumvent this, the amplifier was deliberately underbiased by varying amounts to generate ample crossover spikes; these upper traces also rise as level falls, but Fig 20 shows that the THD percentage increases more slowly as level falls. Both EF and CFP output stages give similar results; whatever the degree of underbias, THD increases by about 1.6 times as the output voltage is halved. In other words, reducing the output power from 25 W to 250 mW, which is pretty drastic, only increases THD % by six times, and there is no sign of it increasing uncontrollably at low levels.

    Fig 20

    Distortion versus level was also investigated at high frequencies, ie above 1 kHz where there is more THD to measure and optimal biasing can be used. Fig 21 shows THD versus level for the EF stage at a selection of frequencies; Fig 22 shows the same for the CFP. Neither shows a sudden rise in percentage THD with falling level, though it is noticeable that the EF gives a good deal less distortion at lower power levels around 1 W. This is an unexpected observation, and is probably due to the greater width of the EF crossover region.

    Fig 21

    Fig 22

    To further get the measure of the problem, Fig 23 shows how HF distortion is greatly reduced by increasing the load resistance, providing further confirmation that almost all the 8 Ohm distortion originates as crossover in the output stage.

    Fig 23

    The amount of crossover distortion produced depends crucially on optimal quiescent adjustment, so the thermal compensation used to stabilise this against changes in ambient temperature and power dissipation must be accurate. Investigation shows that the critical parameter is not quiescent current as such, but rather Vq, the quiescent voltage between the output device emitters; see Fig 13. In both EF and CFP output stages, changing Re from 0.1 to 0.47 Ohms alters the optimal Iq considerably, but the values of Vbias and Vq barely change. Thus the voltage across the transistor base-emitter junctions and Re's is what counts, not the resulting Iq.
    Selecting Re= 0R1 for maximum efficiency is probably the over-riding consideration. This has the additional benefit that if the stage is erroneously over-biased into Class AB, the resulting gm-doubling distortion will only be half as bad as if the more usual 0R22 values had been used for Re.

    5.3.3 Switchoff distortion. (Distortion 3c)
    This depends on the speed characteristics of the output devices and on the output topology. For topologies, the critical factor is whether the output stage can reverse-bias the output device base-emitter junctions to maximise the speed at which carriers are swept out, so the device is turned off quickly. The only conventional configuration that can reverse-bias the output junctions is the EF Type II, described below.
    The EF Type II configuration in Fig 13b is at first sight merely a pointless variation on Type I, but its valuable property is that the shared driver emitter-resistor Rd, with no output-rail connection, allows the drivers to reverse-bias the base-emitter junction of the output device being turned off.
    Assume that the output voltage is heading downwards through the crossover region; the current through Re1 has dropped to zero, but that through Re2 is increasing, giving a voltage-drop across it, so TR4 base is caused to go more negative to get the output to the right voltage. This negative excursion is coupled to TR3 base through Rd, and can reverse bias it by up to -0.5V at 8 Ohms, increasing to -1.6V at 4-Ohms. Speed-up capacitor Cs improves this action, preventing the charge-suckout rate being limited by the resistance of Rd. A 1 uF speedup capacitor can half the THD at 40kHz, implying cleaner switchoff.
    The EF Type I has a similar voltage drop across Re2, but the connection of R1,R2 to the output rail prevents this from reaching TR3 base; instead TR1 base is reverse-biased as the output moves negative. Charge-storage in the drivers is usually not a problem, so this does little good. Likewise, a CFP stage can only reverse-bias the driver bases, and not the outputs.
    The second influence on turnoff is the value of the driver emitter or collector resistors; the lower they are the faster the stored charge can be removed. Applying these two criteria can reduce HF distortion markedly, but of equal importance is that it minimises overlap of output conduction at HF, which if unchecked gives an inefficient and potentially destructive increase in supply current. [14]

    5.4 DISTORTION 4: VAS loading distortion.
    Distortion 4 is that which results from the loading of the Voltage Amplifier Stage (VAS) by the non-linear input impedance of the Class-B output stage. The VAS collector impedance tends to be high, rendering it vulnerable to non-linear loading unless buffered or otherwise protected.
    The VAS is routinely (though usually unknowingly) linearised by applying local negative-feedback via the dominant-pole Miller capacitor, and this is a powerful argument against any other form of compensation. If VAS distortion still adds significantly to the amplifier total, then the local open-loop gain of the VAS stage can be raised to increase the local feedback factor. The obvious method is to raise the impedance at the VAS collector, and so the gain, by cascoding. However, if this is done without buffering the VAS, the loading will render the cascoding almost completely ineffective. A VAS-buffer eliminates this problem.
    The VAS collector impedance, while high at LF compared with other circuit nodes, falls with frequency as Cdom takes effect, so Distortion 4 is usually only visible at LF. It is also often masked by the increase in output stage distortion above dominant-pole frequency P1 as the amount of global NFB reduces.

    Fig 24

    The fall in VAS impedance with frequency is demonstrated in Fig 24, obtained from a SPICE conceptual model.[15] The LF impedance is that of the VAS collector resistance, but halves with each octave above P1. By 3 kHz the impedance is down to 1Kohm, and still falling. Nevertheless, it remains high enough for the input impedance of a Class-B output stage to significantly degrade linearity, the effect being shown in Fig 25.

    Fig 25

    In [16] it was shown that as an alternative to cascoding, the VAS may be effectively linearised by adding an emitter-follower within the VAS local feedback loop, increasing the local NFB factor by raising effective beta rather than the collector impedance. As well as good VAS linearity, this establishes a much lower VAS collector impedance across the audio band, and is much more resistant to Distortion 4 than the cascode version. VAS buffering is not required, so this method has a lower component count. The only drawback is a greater tendency to parasitics near negative clipping, when used with a CFP output stage.
    Fig 26 confirms that the input impedance of an optimally-biased EF Type I output stage is highly non-linear; even with an undemanding 8-Ohm load, the impedance varies by 10:1 over the output voltage swing. The Type II EF output has a 50% higher impedance around crossover, but the variation ratio is greater. CFP output stages have a more complex variation including a steep drop to below 20 KOhm around the crossover region.

    Fig 26

    5.5 DISTORTION 5: Decoupling errors.
    Most amplifiers incorporate small electrolytics (10 - 220uF) between each rail and ground to ensure HF stability. As a result rail-voltage variations cause current to flow into the ground.
    If an unregulated power supply is used, (and there are almost overwhelming reasons for doing so) the rails have non-zero AC impedance and bear voltage variations due to amplifier load currents as well as 100Hz ripple. In Class-B, the supply-rail currents are halfwave- rectified sine pulses, and if they contaminate the signal then distortion is badly degraded. The usual route for intrusion is via decoupling grounds shared with input or feedback networks, and a separate decoupler ground back to the star point is usually a complete cure.(Note that the star-point should be defined on a short spur from the heavy connection joining the reservoirs; using B as the star point introduces hum due to the large reservoir-charging current pulses passing through it)
    Fig 27 shows the effect on an otherwise Blameless amplifier handling 60W/8-Ohm, with 220uF rail decouplers; at 1kHz distortion has increased by more than ten times, which is quite bad enough. However, at 20Hz the THD has increased 100-fold, turning a very good amplifier into a profoundly mediocre one by one misconceived connection.

    Fig 27

    5.6 DISTORTION 6: Induction from supply rails.
    Like Distortion 5, this stems directly from the Class-B nature of the output stage. The supply-rail currents are halfwave-rectified sine pulses, which can readily crosstalk into sensitive parts of the circuit by induction. This is very damaging to the distortion performance; Fig 28 shows a large extra distortion component rising at about 6dB/octave. The distortion may intrude into the input circuitry, the feedback path, or even the output cables.

    Fig 28

    This inductive effect was first publicised by Cherry [17], though the effect has been recognised by some practitioners for many years.[18] This effect, apparently unfamiliar to most designers, seems to be a widespread cause of unnecessary distortion.
    The contribution of Distortion 6 can be reduced below the noise floor. Firstly, rigorously minimise loop areas in the input and feedback circuitry, ie keep each signal line very close to its ground. Secondly, limit the ability of the supply wiring to establish magnetic fields in the first place, by minimising the area of circuit loops carrying half- wave pulses.

    5.7 DISTORTION 7: NFB Takeoff point distortion.
    There is a subtle trap in applying global NFB. Class-B output stages are awash with large halfwave-rectified currents, and if the feedback takeoff point is in slightly the wrong place, these currents contaminate the feedback signal, making it an inaccurate representation of the output voltage, and so introducing distortion; Fig 29 shows the problem.

    Fig 29

    At these current levels, all wires and PCB tracks must be treated as resistances, and it follows that point C is not at the same potential as point D whenever TR2 conducts. If feedback is taken from D, then a clean signal is established here, but the signal at output point C has a half- wave rectified sinewave added to it, due to the resistance C-D. The output will be distorted but the feedback loop does nothing about it as it does not know about the error. Fig 30 shows the practical result for an amplifier driving 100W into 8-Ohm. The resistive path C-D that did the damage was a mere 6mm length of heavy-gauge wirewound resistor lead.
    To eliminate this distortion is easy, once you are alert to the danger. Taking the NFB feed from D is not advisable as D is not a mathematical point, but has a physical extent, inside which the current distribution is unknown. Point E on the output line is much better, as half-wave currents do not flow through this arm of the circuit.

    Fig 30

    5.8 DISTORTION 8: Capacitor distortion.
    It seems to be little-known that electrolytic capacitors generate distortion when they have a significant AC voltage across them. It is even less well known that non-electrolytics show a similar effect in applications like Sallen & Key high-pass filters. This has nothing to do with Subjectivist hypotheses about mysterious non-measurable effects; this is all too real.

    Fig 31

    Electrolytic distortion usually arises in DC blocking circuitry with significant resistive loading. Fig 31 shows the distortion for a 47uF 25V capacitor driving 8 Vrms into a 680 Ohm load. The distortion is a mixture of second and third harmonic, rising rapidly as frequency falls, at something between 12 and 18 dB/octave. The great danger of this mechanism is that serious distortion begins while the response roll-off has barely begun; here THD reaches 0.01% at 20 Hz when the response is only down 0.2 dB. The voltage across the capacitor is 2.6 Volts peak, and this is a better warning of danger than the amount of roll-off. THD roughly triples as the applied voltage doubles; the factor varies with capacitor voltage rating.
    The mechanism by which capacitors generate this distortion is unclear. Dielectric absorption appears to be ruled out as this is invariably modelled by adding linear components to the basic capacitor. Reverse biasing is not the problem, for DC biasing by up to +15V shows increased, not reduced distortion. Non-polarised electrolytics show the same effect but at a much greater AC voltage, typically giving the same distortion at one-tenth the frequency of a conventional capacitor of the same value; cost and size generally rules out their use to combat this effect. The best solution is simply to increase the capacitor value until the LF distortion remains flat to 10 Hz. A small roll-off in the audio band is not a sufficient criterion.
    While the bandwidth of a system must be defined, using electrolytics in high-pass filters is never good design practice, because the tolerances are so large; it is now clear they generate distortion as well.
    Capacitor distortion in DC-coupled power amplifiers is most likely to occur in the feedback network blocking capacitor. (C2 in Fig 1) The input capacitor C1 usually feeds a high impedance, but the feedback arm must have low resistances to minimise noise and DC offset. The feedback capacitor is thus an electrolytic, and if not quite large enough the THD shows a characteristic LF rise. Such LF rises are common, but need never occur. Capacitor distortion is usually the reason, but Distortion 5 (Rail Decoupling Distortion) can also contribute. They can be distinguished because Distortion 5 typically rises by only 6 dB/octave as frequency decreases, rather than 12 - 18 dB/octave for capacitor distortion.
    The distortion generated by an AC-coupled amplifier's output capacitor is more serious, as it is not confined to low frequencies. A 6800uF output capacitor driving 40 W into an 8-Ohm load gives mid-band third-harmonic distortion at .0025%, as shown in Fig 32. This is five times more than a Blameless amplifier generates mid-band. Also, the LF THD rise is much steeper than in the small-signal case.

    Fig 32

    Section 4 | Contents | Section 7

    The basis of the design methodology is really the old clich‚ "Make the amplifier as linear as possible before applying Negative Feedback". In 5.1 and 5.2 it was demonstrated that the distortion from the small-signal stages can be made negligible compared with output-stage distortion, by balancing the input pair and adding local negative feedback to input and VAS stages. Likewise, 5.4 - 5.8 showed that Distortions 4 to 8 can be effectively eliminated by little-known but straightforward layout precautions. This leaves Distortion 3, in its three components, as the only distortion that is in any sense unavoidable, as Class-B stages free from crossover artifacts are so far beyond us. This leads to the concept of what I have called a "Blameless Amplifier", the name being chosen to emphasise that the remarkably low THD comes from the avoidance of errors rather than from fundamental advances in circuitry.
    A Blameless Amplifier gives a distortion benchmark that varies relatively little if confined to 8-Ohm loading. It forms a well-defined point of departure for more ambitious and radical amplifier designs. So far I have used it as a basis for an extremely linear Class-A design [9], a Trimodal amplifier (so-called as it operates in any of the modes A, AB and B, as required) [19], and a Load-Invariant amplifier that minimises the THD increase with sub-8 Ohm loads.[20]

    Fig 33.

    Above: Fig 33 shows the circuit of a Blameless Class-B amplifier.

    Note that Fig 33 is only slightly more complex than the standard amplifier in Fig 1. The input pair now has a current-mirror to ensure input balance, and has undergone constant-gm degeneration, running at about 3.5 times the tail current of Fig 1. The VAS is linearised by addition of beta-enhancer TR12, and the remaining topological distortions were eliminated by careful layout. Performance is shown in Fig 18.

    I am aware that the distortion figures given here are unusually low for power amplifiers, but I would emphasise they are not freak results nor dependant on component selection. The only aspect of the linearity directly affected by device characteristics is distortion below 8 Ohms, as described in 5.3.1. So far more than twenty thousand 260W/8-Ohm amplifiers based on the Blameless methodology have been built, with completely repeatable performance.

    Section 5 | Contents | References

    In this paper I have attempted a concise but complete account of power amplifier distortion. The linearity obtainable with relatively conventional circuitry is far better than one would suspect. It also shows that if power amplifier distortion is to be eradicated entirely, future work must be focused on the output stage distortions.


      Fig 1: Fig 1a is the generic/Lin power amplifier circuit, with typical component values. 1b shows the small-signal Class-A output stage that replaces TR6-9 to make a "model" amplifier.
    • Fig 2: The measured open-loop gain for Fig 1. Closed-loop gain is +27 dB, so feedback factor is easily calculated. 535b
    • Fig 3: Generic amplifier THD plot, for 8 and 4 Ohm loading. Measurement bandwidth always 80 kHz, unless stated otherwise.
    • Fig 4: Input stage transconductance against input voltage, for varying emitter degeneration resistances. Gain is lower but more constant for higher values.
    • Fig 5: Input pair distortion from model amplifier. HF distortion is reduced as pair approaches balance, and is least when current- mirror enforces balance. 279b
    • Fig 6: Test circuit for isolation of input distortion. Note the opamp works between 0V and -30V rails.
    • Fig 7: Input distortion in isolation, showing that even a small Ic imbalance seriously increases distortion. Rise in curves below -10 dBu is due to noise floor. 223b
    • Fig 8: Input stages, showing how value of R2 sets Ic balance. The third version with a degenerated current-mirror enforcing balance, gives the best results.
    • Fig 9 The constant-gm degeneration technique. Both stages have the same transconductance, but the degenerated version is ten times more linear.
    • Fig 10: VAS distortion in isolation, showing its reduction as the negative supply rail voltage is increased.
    • Fig 11: VAS configurations. 11a,b show the two standard topologies. 11c,d are two methods for increasing local NFB through Cdom. 11e,f show VAS buffering.
    • Fig 12: THD plot for a model amplifier at 15 Vrms. The middle trace shows an amplifier based on the small-signal section of Fig 33; the upper shows the extra VAS distortion without beta- enhancer TR12. The bottom trace is the distortion of the Audio Precision test system; note the step at 20 kHz. 578b
    • Fig 13: Standard Emitter-Follower, CFP, & FET source-follower output stages.
    • Fig 14: 14a: THD residual for underbiased Class-B, with spikes. 14b: Optimal-bias Class-B, showing discontinuity at crossover that cannot be removed. 14c: Class AB. Note the edges introduced by gm-doubling.
    • Fig 15: Incremental gain diagram for Emitter-Follower output stages, loading from 16 to 2 Ohms
    • Fig 16: Incremental gain diagram for CFP output stage, loading from 16 to 2 Ohms
    • Fig 17: Incremental gain diagram for FET source-follower output stage, loading 16 to 2 Ohms.
    • Fig 18 THD plot for a Blameless Class-B amplifier, 40W into 8 Ohms. Invar 1a.
    • Fig 19 Large Signal Nonlinearity reduction by using sustained-beta output devices, doubled. 20W into 8 Ohms. Invar 23a.
    • Fig 20 Crossover distortion with output stage underbiased by varying amounts. Lowest curve is for optimal biasing, and is essentially noise. #550
    • Fig 21 Crossover distortion at increasing frequencies for EF output stage. Note low-distortion area below -15 dB. (ref 25W/8 Ohm) #551b
    • Fig 22 Crossover distortion at increasing frequencies for CFP output stage. Low-distortion area is absent. #552b
    • Fig 23 Crossover distortion under light loading. 68 Ohms is sufficient to produce measurable crossover. #541a
    • Fig 24 The VAS collector impedance falls as frequency increases, due to local NFB through Cdom.
    • Fig 25 VAS loading (Distortion 4) is present below 2 kHz if no measures to deal with it are taken.
    • Fig 26 The varying input impedance of an EF output stage.
    • Fig 27: Severe effect of misconnected rail decoupling: Distortion 5.
    • Fig 28: Induction of half-wave currents: Distortion 6.
    • Fig 29: Principle of NFB takeoff-point error: Distortion 7.
    • Fig 30: The effect of NFB Takeoff-Point distortion.
    • Fig 31: Electrolytic capacitor non-linearity for small sizes, eg in NFB arm: Distortion 8.
    • Fig 32: Distortion from large electrolytic used as amplifier output capacitor: Distortion 8. #564a
    • Fig 33: Circuit of Blameless power amplifier. Circuit changes from Fig 1 are minor.


    • 1] Lin, H C "Transistor Audio Amplifier" Electronics, Sept 1956, p173
    • 2] Feucht "Handbook of Analog Circuit Design" Academic Press 1990, p256. (Pole-splitting)
    • 3] Stocchino,G Letters, Electronics World, July 1995, p597.
    • 4] Gray & Meyer "Analysis & Design of Analog Integrated Circuits." Wiley 1984, p194. (tanh law of simple pair)
    • 5] Gray & Meyer Ibid, p256. (tanh law of current-mirror pair)
    • 6] Gray & Meyer Ibid, p251 (VAS law is portion of exponential)
    • 7] Self, D "Audio Power Amplifier Design Handbook." Newnes 1996, p231. ISBN 0-7506-2788-3 (poor FET linearity)
    • 8] Self, D "FETs vs BJTs- the linearity competition." Electronics & Wireless World, May 1995 p387. (poor FET linearity)
    • 9] Self, D "Distortion In Power Amplifiers, Part 8." Electronics & Wireless World, March 1994, p225 (Class A amp)
    • 10] Self, D "Thermal dynamics of Power Amplifiers: I" Electronics World, May 1996, p410.
    • 11] Self,D "Thermal dynamics of Power Amplifiers: II" Electronics World, June 1996, p481.
    • 12] Self,D "Thermal dynamics of Power Amplifiers: II" Electronics World, Oct 1996, p754.
    • 13] Self, D "Load Invariant Audio Power" Electronics World, Jan 1997, p16 (Beta droop)
    • 14] Self, D "Distortion In Power Amplifiers: Part 5." Electronics World, Dec 1993, p1011. (HF switchoff distortion & losses)
    • 15] Self, D "Audio Power Amplifier Design Handbook." Newnes 1996, p128. ISBN 0-7506-2788-3 (VAS linearisation reduces collector impedance)
    • 16] Self, D "Distortion In Power Amplifiers: Part 3." Electronics World, Oct 1993, p820. (VAS linearisation)
    • 17] Cherry, E "A New Distortion Mechanism In Class-B amplifiers." JAES May 1981, p237. (Inductive distortion)
    • 18] Baxandall,P Private communication, 1995
    • 19] Self, D "A Trimodal Power amplifier: I" Wireless World, June 1995, p462
    • 20] Self, D "Load-Invariant Audio Power" Electronics & Wireless World, Jan 1997, p16
    Douglas Self, London, Jan 1997. Words= 9441

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