Operational Amplifier as Differential Amplifier
In a differential amplifier; also known as a subtractor, both inputs are connected to a signal. If all resistors are of equal value, the output represents the difference between the two input signals.
Operational Amplifier as Differential Amplifier
Derivation of the equation for the output voltage considering that all 4 resistors R1 to R4 are of different values:
Case: VIN1 = 0 and thus Vi- = 0:
Calculation of Vi+ via voltage divider:
For the partial output voltage VOUT+ you get:
Eq. (1) in Eq. (2) results in
Case: VIN2 = 0 and therefore Vi+ = 0:
Bringing together equations (3) and (4):
If the input voltage in both inputs should be acquired in the same way:
The symmetry of the resistors must be right, i.e. the resistance ratios R1=R2 and R3=R4 must apply so that the operational amplifier, as a differential amplifier, acquires the same voltages at its inputs in the same way:
Exercise:
In the following circuit you see a differential amplifier using an OP-amp. Calculate the resistor R4.
Operational Amplifier as Differential Amplifier
I1 = VR1 = VOUT - Vin1 ⇒ VR1 = (5V - 2V) × 47 kΩ = 0,4913 V V+ = VIN1 + VR1 = 2V + 0,4913V = 2,4913V V- = V+ ⇒ V+ = 2,4913 V VR3 = VIN2 - V+ = 9V - 2,4913 V = 6,5087 V VR4 = V+ = 2,4913V I2 = VR3 = V+ ⇒ R4 = V+ × R3 = 2,4913 V × 131 kΩ = 50 kΩ
. R1 R1 + R2
. 287 kΩ
. R3 R4
VR3 6,5087 V