Degenerative Feedback and Distortion Reduction

Continuing on negative feedback, on SolderSmoke I recently asked for help in understanding why negative feedback is said to "reduce distortion." Let me know if you think I'm on the right track. Thanks to all who sent e-mails.

Following Fourier’s advice, let’s think of distortion as an additional waveform riding along with our desired signal. In the diagram we have a 5X voltage amplifier with 20 mV at the input, let’s say that it produces a complex distorted waveform that consists of our desired 100 mV sine wave, along with an ugly 10 mV distortion signal.

The feedback network takes 10 percent of both signals and feeds them back to the input (with a 180 phase shift). At the input, for the desired signal, the 10 mV of feedback meets up with 30 mV of input signal (as in TM 11-455, I’ll keep outputs the same, but increase inputs); we end up with 20mV at the input to the amplifier device. This then goes through the 5X amp and we get our 100 mV output.

But look what happens to the ugly distortion signal: It arises IN the device. When the feedback portion of this distortion gets to the input, it does NOT meet up with an input signal. It just goes back through the amp. So the feedback network takes 10% of the 10 mV distortion, introduces a 180 phase shift and sends this 1 mV waveform through the 5X amp. At the output of the amp we can think of the original 10 mV of distortion combining with what is now a 5mV out of phase signal. In this case, half of the distortion signal is canceled. We can say that compared with the no-feedback amplifier, distortion has been reduced from 10% to 5%. We can say that this circuit discriminates against distortion signals that arise inside the device. The desired signal meets up with the input signal, cancels a portion of it, but then the remaining signal goes through the amp producing the desired amplified signal. But the distortion signal has nothing to meet at the input. It just goes through the amp and then cancels a portion of distortion signal at the output. More desired signal, less distortion.

Beta Independence (an explanation from 1941)

We've been talking about why negative feedback renders irrelevant even large variations in the gain characteristics of individual tubes and transistors. As is often the case, I had to go through several technical tomes before I found a book that really answered my “how does it really work” kind of questions. Enlightenment on negative feedback came to me from the days before Pearl Harbor, from War Department Technical Manual TM-11-455 “Radio Fundamentals,” published on July 17, 1941.

Figure 1 shows an amplifier that increases the input voltage by a factor of 100. In Figure 2, 10 percent of the output voltage is fed back – out of phase – to the input. Now, when trying to understand feedback amps, you can find yourself trying to figure out how changes to the input produce changes to the output, which in turn produce changes at the input, etc. Like the amplifier you are trying to understand, you become like a dog chasing his tail! TM 11-455 elegantly breaks this cycle. It has us think this way: Assuming we maintain 100 mV at the output, with 10% fed back, how much of an input signal will we need? Well, the amplifier itself still amplifies voltage by 100. So we still need a net voltage of 1 mV at the input. So now we need a signal voltage of 11 mV to produce the 100 mV output (Figure 2). The feedback cancels 10 mV, putting 1 mV on the input. Negative feedback reduces gain.

How does negative feedback reduce the impact of variations in the gain characteristics of the individual devices? Without feedback, if we substituted our 100X amplifier for a device with a gain of only 50, our 1 mV input would produce only 50 mV out, possibly playing havoc with our overall design. We’d need an input of 2 mV -- a doubling of the input voltage -- to make up for the variation, to get our desired 100 mV output. But look at the situation with feedback (Figure 3). We still assume 100 mV at the output, and 10 percent negative feedback. But now, even though device gain has dropped from 100 to 50, we only need an increase in signal input from 11 mV to 12mV. With this feedback arrangement, if we kept the input signal level at 11mV, and then used a transistor that happened to have only HALF the voltage gain of the original device, the output voltage would drop only to around 92 mV, a drop of about 9% -- not the 50% drop we saw in the circuit without feedback. Negative feedback reduces the impact of gain variations from device to device. It makes our amplifier stages more “beta independent.” Negative feedback reduces the impact of gain variations from device to device. It makes our amplifier stages more “beta independent.” Our thanks to the War Department!