|A Note on "Gain"
What's this "Gain" Anyway?
When you use an operational amplifier in a circuit you often need to remember
that the operational amplifier has a very high gain. What is gain, anyway?
There's a very simple answer.
In an operational amplifier, we
have a relationship between the output voltage and the input voltages at the
input terminals of the operational amplifier.
In the case of the inverting amplifier (Which is an operational amplifier
circuit. In other words, it is a circuit which uses an op-amp and some
other circuitry.) we might use the word "gain" to describe something entirely
different. Here's an inverting amplifier with lots of variables defined.
We want to focus on the input voltage, V1
and the output voltage, Vout.
analyze this circuit, you can find that the output voltage and the input
voltage are related by this equation.
= - V1 R0 / R1
In this expression, we can
see that the input voltage is multiplied by a factor of
For the circuit, the gain is -R0/R1.
That gain might have a value of -10 or something like that.
The gain of the circuit
is always going to be smaller than the gain of the operational
The gain of the circuit is
negative. If you have a philosophical problem with the gain being
negative, remember that all that means is that this circuit (and some others,
but not all others) changes the sign of the signal that enters the circuit.
You need to distinguish between the gain of the operational amplifier (which is
large and postive) and the gain of the circuit which is much smaller and can be
negative (like it is for this circuit).
Now, if you followed all of that, you might be tempted to assume that gain has
no units. That is not always true. In the circuits above, you put in
a voltage and you get out a voltage. When you divide the output by the
input, the units go away. If you have a motor, you put in a voltage you
get out so many rpm. The gain has units of rpm/volt.
And, that's the end of this story.