[Part 1 offers an overview and introduction to the sources of distortion in power amplifiers. Part 2 focuses on distortion in the audio amplifier input stage.]
The voltage-amplifier stage (or VAS) has often been regarded as the most critical part of a power-amplifier, since it not only provides all the voltage gain but also must deliver the full output voltage swing. This is in contrast to the input stage which may give substantial transconductance gain, but the output is in the form of a current. But as is common in audio design, all is not quite as it appears. A well-designed voltage amplifier stage will contribute relatively little to the overall distortion total of an amplifier, and if even the simplest steps are taken to linearise it further, its contribution sinks out of sight.
As a starting point, Figure 1 shows the distortion plot of a model amplifier with a Class-A output (15V rails, +16dBu out). The model is as described in previous articles. No special precautions have been taken to linearise the input stage or the VAS and output stage distortion is negligible.
It can be seen that the distortion is below the noise floor at low frequencies; the distortion slowly rising from about 1 kHz is coming from the voltage amplifier stage. At higher frequencies, where the VAS 6 dB/octave rise becomes combined with the 12 or 18 dB/octave rise of input stage distortion, we can see the accelerating distortion slope typical of many amplifier designs.
The main reason why the voltage amplifier stage generates relatively little distortion is because at LF, global feedback linearises the whole amplifier, while at HF the voltage amplifier stage is linearised by local negative feedback through Cdom.
Figure 1: THD plot for model amp showing distortion below noise floor at low frequency, and increasing from 2 kHz to 20 kHz. The ultimate roll-off is due to the 80 kHz measurement bandwidth.
Examining the mechanism
Isolating the voltage amplifier stage distortion for study requires the input pair to be specially linearised, or else its steeply rising distortion characteristic will swamp the VAS contribution. This is most easily done by degenerating the input stage which also reduces the open-loop gain. The reduced feedback factor mercilessly exposes voltage amplifier stage nonlinearity. This is shown in Figure 2, where the 6 dB/octave slope suggests origination in the VAS, and increases with frequency solely because the compensation is rolling-off the global feedback factor.
Confirming that this distortion is due solely to the voltage amplifier stage requires varying VAS linearity experimentally while leaving other circuit parameters unchanged. Figure 3 achieves this by varying the VAS negative rail voltage; this varies the proportion of its characteristic over which the voltage amplifier stage swings, and thus only alters the effective VAS linearity, as the important input stage conditions remain unchanged. The current-mirror must go up and down with the VAS emitter for correct operation, and so the Vce of the input devices also varies, but this has no significant effect as can be proved by the unchanged behaviour on inserting cascode stages in the input transistor collectors.
The typical topology as shown in Figure 4(a) is a classical common emitter voltage amplifier stage with a current-drive input into the base. The small-signal characteristics, which set open-loop gain and so on, can be usefully simulated by the spice model shown in Figure 5, of a VAS reduced to its conceptual essentials. G is a current source whose value is controlled by the voltage-difference between Rin and Rf2, and represents the differential transconductance input stage. F represents the voltage amplifier stage transistor, and is a current source yielding a current of beta times that sensed flowing through ammeter V which, by spice convention, is a voltage source set to 0 V.
Figure 2: The change in HF distortion resulting from varying the negative rail in the VAS test circuit. The voltage amplifier stage distortion is only revealed by degenerating the input stage with 100 Ω resistors.
Figure 3: Voltage amplifier stage distortion test circuit. Although the input pair mirror moves up and down with the VAS emitter, the only significant parameter being varied is the available voltage swing at the collector.
Figure 4: Six variations on a voltage amplifier stage: (a) conventional current source VAS, (b) conventional bootstrapped VAS, (c) increase in local NFB by adding emitter follower, (d) increase in local NFB by cascoding, (e) one method of buffering VAS collector from output stage, (f) alternative buffering arrangement uses bootstrapping resistor.
Figure 5: Conceptual spice model of differential input stage (G) and VAS (F). The current in F is beta times the current in G.
The value of beta, representing current-gain, models the relationship between VAS collector current and base current. Rc represents the total stage collector impedance, a typical real value being 22kΩ. With suitable parameter values, this simple model provides a useful demonstration of relationships between gain, dominant-pole frequency, and input stage current outlined in the first article in this series. Injecting a small signal current into the output node from an extra current source also allows the fall of impedance with frequency to be examined.
The overall voltage gain clearly depends linearly on beta, which in real transistors may vary widely. Working on the trusty engineering principle that what cannot be controlled must be made irrelevant, local shunt NFB through Cdom sets the crucial HF gain that controls Nyquist stability. The LF gain below the dominant pole frequency P1 remains variable (and therefore so does P1) but is ultimately of little importance; if there is an adequate NFB factor for overall linearisation at HF then there are unlikely to be problems at LF where gain is highest. As for the input stage, the linearity of the voltage amplifier stage is not greatly affected by transistor type, given a reasonably high beta value.