In the previous chapter we have seen the configuration of an adder circuit. In this chapter we are going to study the differential amplifier or also known as subtractor amplifier. Basically, it is a small modification that we do in the addition amplifier, removing the non-inverting
input from the earth and connecting a voltage source in series with a resistor. With this, we use the
differential amplifiers whenever we have as an objective to amplify the difference between two signals.
2. The Differential Operational Amplifier
In the figure below, we see the circuit of a differential amplifier. Remember that the
currents at the input of the operational amplifier is equal to
zero. Therefore, to the node Va, we can write:
(V1 - Va) / R1 = (Va - Vo) / R2
By doing an algebraic rearrangement in the above equation, we have:
Vo = [(R2 /R1) + 1] Va - (R2/R1) V1
Figure 45-01
Now, doing the same for the node Vb, we have:
(V2 - Vb) / R3 = Vb / R4
Again, by doing an algebraic rearrangement in the above equation, we arrive at:
Vb = [R4 /(R3 + R4)] V2
But, remembering that Va = Vb and making the necessary substitutions in the equation that
defines Vo, we can calculate what will be
the output voltage of the circuit, or:
eq. 45-01
This equation shows that the first parcela,
- (R2 / R1) = - K1,
is due to the gain of the inverting input and
the second parcela, K2, is due to the gain of the non-inverting input.
Therefore, we can also write Vo as:
Vo = K1 V1 + K2 V2
Let's look at the particular case where we have:
R4 / R2 = R3 / R1
In this case, we can simplify the final equation, making it easy to understand why this type of configuration is called a
differential amplifier. See below, how the final result depends on the
difference between the input voltages, multiplied by the voltage gain to the closed loop of the circuit, represented
by R2 / R1.
eq. 45-02
One of the characteristics of the differential amplifier is to have the ability to reject
signals common to both inputs. If this happens, we have V1 = V2 and by the equation above,
the result will be Vo = 0, reaching the goal of the circuit.
