Operational Amplifiers – Complete Theory
Page 4 – Inverting Amplifier (Derivation)
The Inverting Amplifier is one of the most commonly used operational amplifier circuits.
In this configuration, the input signal is applied to the inverting terminal through a resistor.
Circuit Components
- Input resistor → Rin
- Feedback resistor → Rf
- Operational amplifier
Virtual Ground Concept
Because of the very high gain of the op-amp:
V+ ≈ V-
If the non-inverting terminal is grounded:
V- ≈ 0
This point is called Virtual Ground.Current Through Input Resistor
I = Vin / Rin
Because input current of op-amp is approximately zero:Iin ≈ 0
So the same current flows through the feedback resistor.Output Voltage
Vout = - I Rf
Substitute current value:Vout = - (Vin / Rin) Rf
Voltage Gain
Av = Vout / Vin = - Rf / Rin
Important Properties
- Output is 180° phase shifted
- Gain controlled by resistors
- Input resistance = Rin
- Stable amplifier configuration
GATE Important Points
- Gain = −Rf / Rin
- Virtual ground concept
- Input current ≈ 0
- Output inverted signal
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