# Big loop gain vs. big bandwidth

If one was looking for an audio amplifier of high quality, with very low distortion, which one of these two options would be better?

• Large loop gain (i.e. $af$) but small open loop bandwidth
• Small loop gain but large open loop bandwidth

I think that the first option would be the best one, because a large loop gain would mean that the bandwidth of the final circuit (namely, the closed loop bandwidth) would be increased by a factor of $(1+af)$, so the bandwidth would not be a problem. But also, distortion would decrease by the same factor, so, as I see it, the first option guarantees a large bandwidth and a decrease in distortion, while the second one only offers a large bandwidth.

However, this is a very general reasoning. I don't really know where that decrease in distortion comes from: does it depend on the position of the open loop poles? Does it depend on anything as well as on the loop gain?

So the specific question would be: which one of the two options would you choose for a very low distortion audio amplifier, and why?

If you want a amp with low distortion, look at the distortion numbers. It shouldn't matter to you how that is achieved under the hood, only that it is.

There are all kinds of ways to trade off parameters in a audio amplifier. Taking one or two parameters in isolation doesn't mean anything. Look at the result, not the method.

That said, simply using large open loop gain, then global feedback to fix everything, isn't how it's generally done. The problem is that such a system tends to suffer from TIM (transient intermodulation distortion). The better systems tend to use some local feedback in each stage, with the overall open loop gain not wildly above the desired closed loop gain. Then moderate application of negative feedback keeps the closed loop gain predictable and the frequency response flat.

Again though, measure results, not how they were achieved. There is more than one way to design good audio amplifiers.

• Thanks for the answer. However, the scope of my question was another one: if you should choose between the two options, which one would it be? I'm trying to understand how distortion is modified by feedback and how strong can its impact be, without forgetting that bandwidth is also an important parameter for the amplifier. – Tendero Nov 27 '16 at 16:29
• @Tendero, Olin has expressed the opinion that the better systems do not use your first option due to TIM (which implies that he would not use that option) and I think he has answered the question well. Read Olin's answer on this post too : electronics.stackexchange.com/questions/156643/… – Matthew Nov 27 '16 at 22:26

Why pick the option (2) small loop gain but large open loop bandwidth.

Consider one major source of distortion in an opamp: the input differential pair. As frequency increases, we'd like to keep that distortion constant, but the way we keep distortion constant is to keep [Vin+ - VIn-] a constant.

Examine an opamp with open loop gain being flat out to 20Khz (or 50KHz, if you want). The voltage on the virtual-ground [Vin+ - Vin-] remains constant, thus all frequencies experience the same distortion.

On the other hand, an opamp with enormous DC gain, rolling off at 10Hz, will very precisely control the Virtual-ground at 10Hz, less well at 100Hz, even less well at 1,000Hz and so forth. Example: Assume UGBW is 1MHz, DC gain is 100,000x and you want a closed-loop gain of 10, with 10 voltsPeakPeak output.

At 10Hz, [Vin+ - Vin-] is 10voltPP/ 100,000*0.1 = 10v/10,000 = 1milliVolt

At 100Hz, vin_differential is 10vpp/1,000 = 10milliVolts, and bipolars are rather nonlinear with 10mV inputs.

At 1,000Hz, vin_diff is 100milliVolts, and current thru that diffpair has over 10:1 imbalance from side to side; indeed the diffpair is close to hard clipping.

At 10,000Hz vin_diff is 1,000milliVolts and the diffpair is hard-clipping.

## As we've shown, the high-gain-low-bandwidth opamp has enormous variation of distortion with frequency.

The other option "low-gain-high-bandwidth" has moderate distortion at all frequencies.