# Op-Amps: Part II

Negative Feedback.

Useful for all critical applications!

We stated in Part I that op-amps have an extremely large gain (on the order of 100,000), and that you can trade some of this gain for precision and stability. The way you do this is with negative feedback – feeding some of the output signal (Vo) back to the negative input pin (Vi-). A schematic representation of this is shown in Figure 1. A line connects the output back to the input, and an input signal is placed at the non-inverting pin (Vi+).

Figure 1: Op-Amp buffer with negative feedback.

This is the simplest form of negative feedback, as there are no resistors involved, and is called a buffer, or unity gain amplifier, for reasons which will be seen shortly. To understand what this negative feedback does, imagine that a small deviation occurs at the input, such that Vi+ is greater than Vi-. Due to the very large gain of the op-amp, this will cause a very large positive output value. Since this output value is connected to the inverting pin, Vi- would become greater than Vi+, and the output would begin to swing negative. If it were to pull the output down too far, Vi+ would again become larger than Vi-, and the whole scenario would repeat itself. So the negative feedback always works to bring Vi+ and Vi- closer together. This is such a powerful concept for op-amps, it has been codified as law!

Op-Amp RULE #1: If there is negative feedback, Vi+ = Vi-.

To get an idea of how close together these two inputs must be, take a standard powersupply voltage of 5V and divide it by your op-amp gain. This gives an input difference of 5V/100,000 = .05mV! Any greater separation than that, and the op-amp will try to go beyond its powersupply, which it can not do. Therefore, for all practical purposes, if your op-amp has negative feedback, you can assume that the two input pins are at the same voltage (Vi+ = Vi-). And, for our buffer configuration shown above, this means the output must always equal the input, since Vo = Vi- = Vi+.

This is why it is called a “unity gain amplifier”, it has a gain of exactly 1. That may not seem very useful, but remember that this gain is no longer frequency or component dependent, so you will always get an identical copy at the output. This output is also being driven by the op-amp, which can source more current than the input signal. So, if you have a microphone, for example, and you want to listen to the signal on a pair of headphones, you wouldn’t hear much if you just connected one to the other. But, with the op-amp in between, you would get a faithful representation on the headphones. This is why it is sometimes called a “buffer”, since it buffers the input source.

To see exactly how small the error between the input and output is, recall that the governing equation for an op-amp is Vo = A*[(Vi+) - (Vi-)]. In this case, since Vo is connected to Vi-, they both have the same value (Vi- = Vo), and can be substituted for each other in the equation. This gives:

Vo = Vi- = A*[(Vi+) - (Vi-)] = A*(Vi+) – A*(Vi-)
-> (Vi-) + A*(Vi-) = (1 + A)*(Vi-) = A*(Vi+)
=> Vi+ = [(1 + A)/(A)]*(Vi-) = [1 + (1/A)]*(Vi-)

There is only a difference of 1/A between Vi+ and Vi-. So the larger the op-amp’s internal gain (A) is, the lower and lower this error will be. This large gain reduces the op-amp’s error, and ensures that it behaves as an ideal circuit element. And don’t worry if the math looks like ancient Egyptian hieroglyphs, the math is not the important part. What is important, is that op-amps are very up-tight, and always try to obey the rules! And if there is negative feedback, they will do whatever they have to, to make Vi+ = Vi-.

This is very handy to keep in mind when debugging an op-amp circuit. First check if the op-amp is getting power to its powersupply pins (Vs+ and Vs-), and then check if there is the same voltage at its input pins (Vi+ and Vi-). If Vi+ does not equal V-, then there is something wrong with that op-amp.

In the next section, we will introduce Op-Amp Rule #2, and show how we can use both rules to find the gain of more complicated op-amp circuits.