Some Useful Operational Amplifier Circuits
Unity Gain Buffer Amplifier
Summing Amplifier
Integrator
And, don't forget the original op-amp circuit
The Inverting Amplifier
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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 non-inverting 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 op-amp.
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:

• Vout = Vin
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, Vin, and that copy, Vout, 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 op-amp.
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.
• (V1 - V- )/R1 + (V2 - V- )/R2 + (Vout - V- )/R0 = 0
• Since V- is assumed to be zero, we get:
• V1 / R1 + V2 / R2 + Vout / R0 = 0
• or
• Vout / R0 = - V1 / R1 - V2 / R2
• or
• Vout = - (V1 / R1 + V2 / R2 )R0
• or
• Vout = - (V1R0 / R1 + V2R0 / R2 )
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 op-amp.
Then, we have - after we write KCL:
• C(dVout/dt) + V1/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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