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Op Amp Applications - Summation Amplifier and Subtraction Amplifier
Introduction | Summing Amplifier | Difference Amplifier (Differential Amplifier)
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Introduction |
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Last week, you were introduced to the operational amplifier (op amp). You learned about some of the characteristics of the op amp and how it is used as a gain amplifier. We discussed the inverting and non-inverting op amp circuits. This week, you will learn how an op amp can perform simple mathematical operations such as addition or subtraction of the signals. Next week, we will further learn how an op amp can be used to perform complex mathematical operations such as differentiation and integration.
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Summing Amplifier |
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We will now begin looking at different op amp circuits that are used to perform mathematical operations. The first circuit to be considered is the summing amplifier shown in Figure 1.
Figure 1: Summing amplifier circuit using the inverting amplifier
Recall that for negative feedback circuits with the positive op amp terminal connected to ground, the negative op amp terminal is a virtual ground. so the voltage VA is applied across the resistor R1 and the voltage VB is applied across the resistor R2. The current from each voltage source will flow through the feedback resistor R3, resulting in the following output voltage.
The inverting amplifier summing circuit can be expanded, adding more signal inputs. With the proper component selection, the summing amplifier could be used to make the output voltage equal to the average value of all input voltages.
The summing amplifier can be implemented using the non-inverting amplifier, as shown in Figure 2.
Figure 2: Summing amplifier circuit using the non-inverting amplifier
When we previously analyzed the non-inverting amplifier circuit, the input signal was applied directly to the positive op amp terminal. The resistors R1 and R2 are needed so that the two voltage sources can be applied to the circuit. The output voltage will include the non-inverting amplifier voltage gain multiplied by the voltage divider effect of the resistors R1 and R2.
The addition of more voltage sources to the non-inverting summing amplifier circuit will increase the complexity of the output voltage equation.
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Difference Amplifier (Differential Amplifier) |
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Now that we understand that addition can be performed by the op amp, we will look at the circuit to perform subtraction. The circuit is known as the difference amplifier or differential amplifier. The circuit to be considered is shown in Figure 3.
Figure 3: Difference or differential amplifier circuit
Recall that, for negative feedback circuits, the positive op amp terminal voltage is equal to the negative op amp terminal voltage. Also remember that, using the ideal op amp model, the op amp input impedance is infinite, so the voltage VB is applied across the resistors R3 and R4. The voltage appearing across the resistor R1 is the difference of the input voltage VA and the negative op amp terminal voltage VN, which is the same as VP. Considering the inverting amplifier gain and the non-inverting amplifier gain, the output voltage can be calculated with the equation provided:
When R3 = R1 and R4 = R2, the equation simplifies to the following relationship:
The resistors R2 and R1 will establish the gain for the circuit. You can definitely observe that the mathematical operation of subtraction is performed by the Figure 3 amplifier circuit.
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