If you have Matlab or equivalent you can do a simple model and play with
its internal G and feedback factor, the ratio of the two resistors.
Note system is given 1 V to amplify, the constant block to left.
So if you look at above I set internal K (gain) at 1, and fdbk factor at .1 (feed 10% back). You can see
that the output is not very accurate, and that the differential input to OpAmp is large. So one
becomes suspicious that low K inside OpAmp not very appealing.
Now lets set K to 100,000 (typical OpAmp these days).
Several observations
1) Now overall G of whole simulation is 10, which is 1 / fdbk factor. Also the differential input
into OpAmp is very tiny. There is a term in industry, "virtual ground", that basically says an OpAmp
with - fdbk, fdbk back to inv input, results in that inv input virtually at same V with non inv input. If non
inv input was connected to ground then the inv input would also be close to ground. So if we connect
a summer like this -
So the virtual ground allows one to sum inputs without one input affecting the
other. Above the current of any input is set just by the input V and its R, the
other inputs do not affect each other. Then each input current is summed with
the others and flows thru fdbk R to produce a summed output.
Note no appreciable current flows into / out of the opamp inputs. In high performance
systems there is some, and causes errors, but for this discussion its essentially zero.
You can play with OpAmp internal K and the fdbk factor and observe that with
high K you get predictable output. Note G thru whole system is 1 / fdbk factor.
So for a fdbk factor of .1 overall system G = 10.
Also notice now with large K the G thru the whole system is suspiciously only a f(fdbk factor).
Its no longer a f(K) of the actual amplifier. fdbk factor is the ratio of the R's. So G is as
accurate as just the R's, or very close to it.
Early in electronics amps where cascades of one stage transistor amps, and transistor
K (for transistors gain normally called beta or alpha) varied all over the map. And to get
high G thru system you had to cascade many stages. Temperature performance due to
component changes and supply voltage variations caused significant performance vari-
ations. So designs had, compared to today, low performance and stability.
- feedback improves systems, original paper by Black at Bell Labs.
Positive fdbk is also used to achieve other characteristics in opamp circuits, thats a topic for another day.
Lastly this whole discussion is DC performance, AC is a whole other topic and also
quite interesting.
Regards, Dana.