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A Look At Amplifier Stability & Compensation

Elsewhere in this issue, we present the updated Ultra-LD Mk.3 Audio Power Amplifier Module. It has a new frequency compensation arrangement which helps it achieve even lower distortion than the Mk.2 version. In this article, we explain why amplifier frequency compensation is necessary and how it works.

By Nicholas Vinen

AMPLIFIER FREQUENCY compensation and stability are complicated topics about which books can be (and have been) written. These issues are important when designing or modifying audio circuitry, yet they are widely misunderstood. Here’s a brief summary of the relevant fundamentals.

Negative feedback

Stability and compensation relate to systems with negative feedback. But initially, let’s consider a power amplifier (or op amp) with its feed-

back network disconnected. We connect the inverting input to ground and apply a small signal to the non-inverting input, as shown in Fig.1(a). This is known as “open loop” operation.

Nominally, the output voltage is the difference in input voltages multiplied by the open loop gain which can be as high as one million (120dB). So a 1µV RMS input signal could result in a 1V RMS output signal.

Amplifiers operated in this mode aren’t very linear which is another way of saying that they produce a significant amount of harmonic distortion. Also, this is far too much gain for most purposes and it varies from device to device.

Closed loop operation

Click for larger image
Fig.1: (A) an op amp operated in open loop mode, with a large but ill-defined gain and poor linearity; (B) an op amp configured as a voltage follower, operated in closed-loop mode with a gain of one; (C) closed loop operation with a fixed gain of 10 (the output accuracy and bandwidth are reduced compared to unity gain).

If we feed a portion of the output signal back to the inverting input to apply negative feedback, the amplifier now operates in “closed loop” mode. The simplest method is to connect the output directly to the inverting input, as shown in Fig.1(b).

Assume for a moment that we have an “ideal” op amp. It has zero input bias current, infinite open loop gain at all frequencies, zero output impedance and no phase shift (ie, no signal delay) from input to input.

If we configure it as in Fig.1(b), whenever the input signal swings positive, the input voltage difference (“+” - “-”) becomes positive. This is amplified by a huge factor and so the op amp’s output swings towards the positive rail.

However, it stops when the output voltage equals the input signal voltage, as the input voltage difference is then zero. Similarly, if the input signal swings negative, the input voltage difference becomes negative so the output voltage decreases, tracking the input signal perfectly. Hence, this circuit is known as a “voltage follower”.

Now consider what happens with the same circuit if we use a real op amp, which has a very high but finite open loop gain, say 1,000,000 times. We then apply 0V DC to the non-inverting input followed by a step change to +1µV. Shortly after that change, the output swings positive, towards 1V (ie, 1µV x 1,000,000).

But again, this positive slewing slows and then stops before the output gets to 1V because the inverting input voltage approaches that of the non-inverting input. The differential input voltage approaches but does not reach zero. The output (and thus the inverting input) settles at around 0.999999µV.

We know this because the input voltage difference is then 0.000001µV and this, multiplied by the open loop gain, is 1µV (ie, almost exactly the output voltage). So in reality, the output tracks the input with an error factor of 1 ÷ open loop gain. Higher open loop gain means better accuracy, explaining why ideal an op amp would have infinite open loop gain.

AC signal non-linearities are also reduced by the same factor (at low frequencies), vastly improving the distortion performance compared to open loop operation. At higher frequencies, the distortion cancellation becomes much less effective for various reasons, some of which will be explained later.

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