## Saturday, January 23, 2021

### Audio Amplifier Feedback - Transient Intermodulation Distortion (TIM)

Now that I covered the linearity of the input stage, it is a good time to talk about TIM - Transient Intermodulation Distortion.

In 1970, Matti Otala published a paper called "Transient Distortion in Transistorized Audio Power Amplifiers". He argued that under certain conditions, fast signal transients create a specific type of distortion, which he called Transient Intermodulation Distortion (TIM).

In the paper, Otala considered a simple model amplifier with an RC compensation network providing a dominant pole:

Otala fed this model amplifier with a fast voltage step and observed something like this:
Here, the green is the step at the input $V_2$, blue is the slower output step, scaled down by the feedback network $\beta$, and red is $V_3$, the difference between the input and scaled output which is fed to the input stage $A_1$.

When $V_2$ grows faster (has a higher slew rate $SR=dV/dt$) then the compensation RC network can reproduce, $V_3$ overshoots its steady state level, as the red trace shows. Depending on the difference in slew rates at the input and at the output, the overshoot can be large.

Otala recognized that the overshoot at the input of the first stage may lead to the first stage clipping and thus to distortion - the effect he called Transient Intermodulation Distortion, or TIM.

I demonstrated in the previous post that a difference amplifier typically used as an input stage can easily be overloaded by relatively small signals, and that is becomes nonlinear and start distorting long before it clips. This is one of the mechanisms that potentially can give rise to TIM.

I have been arguing in my first post on audio amplifier feedback that the the difference signal seen by the input stage can be effectively reduced by increasing the loop gain. Indeed, the higher the loop gain is, the smaller both the overshoot and the steady state value of $V_3$ are, and the faster the overshoot settles to the steady state value:

The price of faster settling and smaller overshoot with higher loop gains, however, is the larger current though the RC network, all of which must be provided by the first stage $A_1$:

The extra current required by the compensation network may also lead to the first stage overload, but at the output rather than at the input. This is another mechanism that can potentially generate TIM.

The conclusions should have been that, in order to minimize TIM:

• The slew rate at an amplifier's input should be limited (by, for example, a low pass filter) to what the amplifier can reproduce at the output; and
• The first stage $A_1$ should be designed to both handle the difference input signals and drive the compensation network with low distortion; the now-standard approach (see my previous post) is to degenerate the input differential pair with emitter resistors and increase its tail current.

Otala came to the first conclusion, but not the second. Instead of designing a more robust and linear input stage, he set out to avoid both the overshoot at the input and the need to drive the compensation network at the output of $A_1$ by increasing the amplifier's slew rate, refusing to apply the dominant pole compensation and reducing the loop gain in the global feedback loop.

Importantly, Otala came up with the idea that there is an optimal level of feedback (loop gain), above which TIM would become the dominant distortion mechanism. The theme has become popular and led to the concept that it is the slew rate, and not the loop gain, that determines an amplifier's distortion. It still reverberates around the audio community in the form of amplifiers with "moderate feedback" and slew rates of 3kV per microsecond.

There is nothing wrong with high slew rate amplifiers. For a typical three stage Miller compensated amplifier, the slew rate can be an indication of how far the first stage of the amplifier is from clipping, and therefore how linear it is. It can also be an indication of the amplifier's bandwidth and hence of the loop gain in the audio range of frequencies.

Moderate feedback, on the other hand, is a problem. As I posted earlier, moderate feedback provides only moderate suppression of distortion and makes the input stage work harder and distort more. Conversely, high gain in the global feedback loop reduces the difference input signal for the input stage and thus reduces TIM. There is no need to choose between high loop gain and low TIM; one can - and should - have both.