Common-Mode Distortion

The following diagram shows two ways of applying overall negative feedback. Most, but not all, power amplifiers use one of these two methods.

In both cases if there is a high open-loop gain the closed-loop signal between the + and - inputs is small, perhaps just one or two millivolts for a 1V low frequency input signal, but one important difference is that in A the + input is earthed, so one input is at zero and the other at a small signal level. In B however there is the full 1V input signal at the + input, and almost the same signal at the - input. It is only the difference between these signals which is required to determine the output of the amplifier, but the relatively large 'common mode' voltage may also affect the output. The degree to which this unwanted signal is rejected is called the 'common-mode rejection ratio'. If a signal Vc is applied to both + and - input there will generally be some output voltage Vo, and the ratio Vo / Vc will be a function of frequency. The output voltage will certainly not be a perfect undistorted copy of Vc with just a different amplitude, it will include harmonic distortion, and intermodulation also if Vc includes more than a single frequency sine-wave.

There are many different input stage designs used in power amplifiers, and each will have its own particular response to common-mode voltage, but here just a single bipolar junction transistor (bjt) input stage will be considered to determine the requirements for minimising distortion from this source. Although differential stages can in principle cancel much of the common-mode effect this can usually only be done accurately if the signal source impedance is known, which is not the case for a general purpose power amplifier. Before resorting to more complex input stages to reduce the problem it seems worthwhile investigating simple stages and measuring examples to see what level of distortion is produced.

A simplified input and second stage are shown next, and in this circuit the pnp transistor base and emitter have the full input signal as a common-mode voltage, while the collector voltage is almost constant. The question is what effect the common mode signal, (approximately Vs) has on the base current and the base-emitter voltage of the input transistor.

What we are concerned with is generally referred to as the 'Early Effect' which is a result of the base-collector voltage changing the depletion width at the base-collector junction, which changes the effective base width. Some accounts mention only the resulting change in current gain, which affects the base current for a fixed emitter current. e.g. 'Distortion in Low-Noise Amplifiers' by Eric F. Taylor in Wireless World Aug 1977 p28-32, the voltage across the base resistor was measured, which detects only the base current changes and the collector-base capacitance (Ccb) effect. The base current distortion signal was found to be reduced by increasing the collector-emitter voltage and reducing the collector current. This account was primarily concerned with RIAA pre-amps where the inductive cartridge source can make the distortion current a problem.
Looking at the account in 'Transistor Physics' by Nichols and Vernon, pub. Chapman & Hall 1973, p247, Fig 8.3c shows Vbe as a function of emitter current for different values of Vce, from which we can conclude that at a constant collector current the base-emitter voltage is a function of Vce. Reducing the signal source impedance will do nothing to reduce this.

There are therefore three different effects, which require different measurements. The effect of current gain variations can be reduced simply by reducing the signal source impedance. There is a small internal 'base spreading' resistance in series with any transistor base, but this should be small for low noise transistors used for input stages, so direct measurement of base to emitter voltage may only include a small current gain effect. The increase in error voltage at high frequencies will indicate the Ccb capacitance effect.

Selection of transistor types may be important, but data sheets do not always give all the necessary information to make the best selection, so a simple circuit was assembled to carry out tests on a few typical devices (i.e. whatever I had available at the time). Only pnp transistors were used, partly because I am working on a design with a pnp input stage. It is reasonably certain that the conclusions should be equally applicable to npn devices. In the test circuit a signal is applied to the collector and the effect on Vbe and base current measured. This is easier than applying the signal to both base and emitter with constant collector voltage and trying to extract the error voltage, but the result is equivalent because all we have really done is redefine the earth level.

A signal generator with 600R source resistance applies 1V rms to the collector. The base-collector voltage is about 11V, and emitter current about 1.1mA, but this can be set to different values by changing the 10k emitter resistor. The emitter signal voltage is amplified by the op-amp and observed on an oscilloscope. The output is proportional to the base-emitter a.c. signal voltage plus the voltage across the 1k base resistance resulting from the base current. Shorting this 1k resistor gives the Vbe contribution alone, so the levels of both effects can be determined. Frequencies of 2kHz and 20kHz were used in the tests, there being little difference to the 2kHz figures at lower frequencies.

Measurements

The transistors tested so far are a 30 year old BC214B, a more recent low cost low noise type BC560B, a 120V very low noise 2SA1085, and a 250V low capacitance BF423, which has a relatively low current gain, and is not intended for low noise input stages. High voltage transistors may be expected to have low base width modulation, otherwise they would suffer from 'punch-through' at very high voltages where the base width would reduce to zero. Common mode distortion also results from modulation of the non-linear base-collector capacitance, so the BF423 is expected to show some improvement here, though the other transistors have fairly low capacitance. High frequency transistors with under 0.15pF collector-base capacitance are available, but their other characteristics, such as current gain, are generally not so good.

### RESULTS. Emitter a.c. level in microvolts rms.

From these results we can see that the greatest effects are by far at 20kHz with a 1k source impedance, which is certainly caused by the collector-base capacitances. This is relatively low for the BF423, and is highest for the 2SA1085. The only surprise is the much better 2kHz figures for the BF423, while the 2SA1085 is second best at 2kHz but worst at 20kHz. Reducing the collector current makes only a small difference, as does increasing the collector-emitter voltage and reducing the source impedance at 2kHz. This suggests that the change in current gain is not the important effect it was in the E.F Taylor article mentioned earlier, and the main effects are the capacitance and the changes in base-emitter voltage.
The worst figure of 492 uV is only -66dB relative to the 1V input, and in an amplifier will be an input error voltage not reduced by overall negative feedback. This is not as bad as it may seem for two reasons. First, for a normal music signal, the level at 20kHz will be lower than at 2kHz, typically by a factor of 10, and the error will also be smaller. Secondly, the error voltage, viewed on an oscilloscope, looks like an almost perfect sine-wave, and it is only the distortion we need to worry about. To check the distortion level the 2SA1085 was tested at 1.14mA with 1k source impedance, the harmonic distortion of the test circuit output at 2kHz is shown first, and then the intermodulation distortion for 20kHz plus 19kHz.

The only significant distortion products are the second harmonic of 2kHz at 40dB below the signal in the first picture and in the second the intermodulation at 1kHz also at -40dB. ( Or -46dB relative to the sum of the two test signal components.) The other peaks are mostly interference and noise. From this we can conclude that even for the worst case figures the common mode intermodulation distortion will be no worse than -112dB for common mode 1V rms at both 20kHz and 19kHz, and typically much less with normal music signals with reduced level at this frequency. What harmonic distortion there is is mostly just second harmonic. Using the BF423 instead of the 2SA1085 will reduce distortion for the 2kHz signal by 8dB, but second harmonic at -113dB is certainly of no importance, and the excellent noise performance of the 2SA1085 makes this a good choice. The maximum distortion will probably be around the same level as the noise, but is well masked by the high level signal, while the noise is still present with zero signal where there is no masking, so low noise is of far greater importance.

Unless the source impedance is much more than the 1k used here, or the collector-emitter voltage is much lower than 11V, or the common mode voltage much more than 1V rms, then we can conclude that although transistor type does make a clearly measurable difference the common mode distortion is low enough to be ignored, and input transistor types can be chosen for low noise. (I have no noise specification for the BF423, so I would not completely rule out its use in this application.) It should be remembered that transistors of the same type can vary significantly, and the results shown here are for only the individual samples tested.

One other consideration is the phase modulation resulting from the collector-base capacitance being changed by the common mode signal, and here the BF423 should reduce the effect by about 40% compared to the 2SA1085. Keeping the source impedance low will also reduce the effect. An initial calculation suggests that phase modulation under the operating conditions considered here is typically only +/- 0.001 degrees, so not a great cause for concern.

The test results are also relevant to other applications, for example the voltage amplifying stage transistor of a power amplifier will have the full output voltage swing, or more, at its collector and therefore the same effects can be expected, and there will be some advantage in choosing transistors with low collector-base capacitance and a high collector voltage rating. Typical examples of types I would expect to perform well are 2SC3503 (npn) and 2SA1381 (pnp), both rated at 300V and with low capacitance.

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