So let's look at that third amplifier challenge problem -- design a non-inverting amplifier with a gain of exactly 1. Now, we could have done it with two inverting amplifiers, but there's a better way.
We calculate gain for a non-inverting amplifier with the following formula:
Gain = 1 + (R2/R1)
So, if we make R2 zero, and R1 infinity, we'll have an amp with a gain of exactly 1. How can we do this? The circuit is surprisingly simple.
Here, R2 is a plain wire, which has effectively zero resistance. We can think of R1 as an infinite resistor -- we don't have any connection to ground at all.
This arrangement is called an Op-Amp Follower, or Buffer. The buffer has an output that exactly mirrors the input (assuming it's within range of the voltage rails), so it looks kind of useless at first.
However, the buffer is an extremely useful circuit, since it helps to solve many impedance issues. The input impedance of the op-amp buffer is very high: close to infinity. And the output impedance is very low: just a few ohms.
This means we can use buffers to help chain together sub-circuits in stages without worrying about impedance problems. The buffer gives benefits similar to those of the emitter follower we looked at with transistors, but tends to work more ideally.