Some
Useful Operational Amplifier Circuits
Unity Gain Buffer
Amplifier
Summing Amplifier
Integrator
And, don't forget the original opamp
circuit
The Inverting Amplifier
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Amplifiers  Useful Circuits
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Operational amplifiers are useful devices that can be used for numerous
types of operations on signals. In this lesson you will examine a
number of operational amplifier circuits that are useful in many situations.
To predict the behavior of remember these facts about how operational amplifiers
perform when they operate out of saturation.

The input difference,
(V_{+}  V_{ }) is small enough that we can consider the
value to be approximately zero. This is due to large gain of the
amplifier  the infinite gain assumption. We
assume that the input voltage difference is zero.

Since we will treat the
input difference as zero, and assume input resistance (the resistance between
the noninverting and inverting inputs) is infinte, then the current flowing
through both of the inputs of the amplifier will also be so small that
it is negligible. We assume that no
current enters the input terminals of the opamp.
As we encounter different circuits we will use
these assumptions to predict circuit behavior.
The
Unity Gain Buffer Amplifier
If the difference between V_{+} and V_{ }is negligibly
small so that V_{+} = V_{ }we must have:
This
circuit is often used when a voltage source with a high internal impedance
is used, and you want to draw more current than the source can deliver.
The solution is to use this circuit to make a copy of the original voltage,
V_{in}, and that copy, V_{out}, appears at the output of
an operational amplifier that can often deliver more current without lowering
the output voltage because the internal resistance of the operational amplifier
is lower than the internal resistance of the original source.
The
Summing Amplifier
For this circuit, the analysis is very similar to that of the inverting
amplifier. If you want to review that analysis, click
here. We start with the same two assumptions.

V_{+} =
V_{}We
assume that the input voltage difference is zero.

We assume that no current
enters the input terminals of the opamp.
Here's
what happens in sequence.

The first assumption leads
us to assume that V_{} = 0. In other words, the voltage
at the inverting input becomes a virtual ground.
In practice, that point is at ground potential  zero volts.

We write KCL at
the node at the inverting input  the virtual ground point. The KCL
equation is relatively simple.

(V_{1}
 V_{ })/R_{1} + (V_{2} 
V_{ })/R_{2} + (V_{out} 
V_{ })/R_{0} = 0

Since V_{} is
assumed to be zero, we get:

V_{1} /
R_{1} + V_{2} / R_{2} + V_{out}
/ R_{0} = 0

or

V_{out}
/ R_{0} =  V_{1} / R_{1} 
V_{2} / R_{2}

or

V_{out}
=  (V_{1} / R_{1} + V_{2}
/ R_{2} )R_{0}

or

V_{out} =
 (V_{1}R_{0} / R_{1} + V_{2}R_{0}
/ R_{2} )
The result is that the output is a weighted
sum of the two inputs. If we just wanted to add the two inputs we
could choose all of gthe resistors to be equal. Of course, we get
a minus sign, but that's unavoidable.
Q1 If
you want to get rid of the minus sign, do you have any options?
Where would you use a circuit like this?

If you have two microphones
and you want to add the signals to produce one signal that is the sum of
the two  so you can hear both signals together  you can use this circuit.
In audio circles, that's called a mixer.

In a common type of control
system, signals proportional to an error signal, and the integral of the
error are added together, and this circuit is often used. That's
a PI (Proportional + Integral) controller.
We're sure that you can  and will  find many
other uses for the summing amplifier.
The
Integrator
The integrator does just what the name implies. It integrates  in
the calculus sense  the input signal to produce the output signal.
There is a scaling factor and a minus sign again, but that's pretty much
what happens.
Here's the analysis. We make the usual
assumptions:

V_{} =
0_{ }We assume that the input voltage
at the inverting input is a virtual ground.

We assume that no current
enters the input terminals of the opamp.
Then, we have  after we write KCL:

C(dV_{out}/dt)
+ V_{1}/R = 0

Then:
A
Circuit with Infinite Input Resistance/Impedance and a Gain Larger Than
1.0
This circuit is particularly useful when you need to avoid loading the
signal circuit, and you also want a gain larger than 1, and you don't want
to have to build one of those pesky inverter circuits.
In this circuit, the
two resistors form a voltage divider.
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