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).

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

Applying KCL to node b,

But v_a = v_b. Substituting Equation.(2) into Equation.(1) yields

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

This property exists when

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

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

Read also : what is ohm law

Difference Amplifier Examples

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

Solution:
The circuit requires that

This circuit can be realized in two ways.

Design 1 – If 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

Also,

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

Design 2 – If 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).

For the summer,

and for the inverter,

Combining Equations.(1.4) and (1.5) gives

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.

Show that

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

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

But

and v_a = v₁, v_b = v₂. Therefore,

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

as required.