Difference Amplifier Equation Example and Simple Circuit Design

Difference amplifier is used to amplify the difference between the inputs. Along with the circuit design, we will also learn the difference amplifier equation here.

After learning what is operational amplifier, we will also learn:

  1. Ideal op amp
  2. Summing amplifier
  3. Difference amplifier
  4. Cascaded op amp circuits
  5. Digital to analog converter

Difference Amplifier Equation

Difference (or differential) amplifiers are used in various applications where there is a need to amplify the difference between two input signals. They are first cousins of the instrumentation amplifier, the most useful and popular amplifier.

A difference amplifier is a device that amplifies the difference between two inputs but rejects any signals common to the two inputs.

Consider the op amp circuit shown in Figure.(1).

difference amplifier equation
Figure 1. The difference amplifier

Keep in mind that zero currents enter the op amp terminals. Applying KCL to node a,

difference amplifier equation

Applying KCL to node b,

difference amplifier equation

But va = vb. Substituting Equation.(2) into Equation.(1) yields

difference amplifier equation

Since a difference amplifier must reject a signal common to the two inputs, the amplifier must have the property that
vo = 0 when v1 = v2.

This property exists when

difference amplifier equation

Thus, when the op amp circuit is a difference amplifier, Equation.(3) becomes

difference amplifier equation

If R2 = R1 and R3 = R4, the difference amplifier becomes a subtractor, with the output

difference amplifier equation

Difference Amplifier Examples

1. Design an op amp circuit with inputs v1 and v2 such that
vo = −5v1 + 3v2.

The circuit requires that

difference amplifier equation

This circuit can be realized in two ways.

Design 1If we desire to use only one op amp, we can use the op amp circuit of Figure.(1). Comparing Equation. (1.1) with Equation.(3), we see

difference amplifier equation


difference amplifier equation

If we choose R1 = 10 k Ω and R3 = 20 k Ω, then R2 = 50 k Ω and R4 = 20 kΩ.

Design 2If we desire to use more than one op amp, we may cascade an inverting amplifier and a two-input inverting summer, as shown in Figure.(2).

difference amplifier equation
Figure 2

For the summer,

difference amplifier equation

and for the inverter,

difference amplifier equation

Combining Equations.(1.4) and (1.5) gives

difference amplifier equation

which is the desired result. In Figure.(2), we may select R1 = 10 kΩ and R3 = 20 kΩ or R1 = R3 = 10 kΩ.


2. An instrumentation amplifier shown in Figure.(3) is an amplifier of low-level signals used in process control or measurement applications and commercially available in single-package units.

difference amplifier equation
Figure 3

Show that

difference amplifier equation

We recognize that the amplifier A3 in Figure.(3) is a difference amplifier. Thus, from Equation.(5),

difference amplifier equation

Since the op amps A1 and A2 draw no current, current i flows through the three resistors as though they were in series. Hence,

difference amplifier equation


difference amplifier equation

and va = v1, vb = v2. Therefore,

difference amplifier equation

Inserting Equations.(2.2) and (2.3) into (2.1) gives

difference amplifier equation

as required.

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