Derivation of Gain of Inverting Amplifiers
- The virtual Earth approximation is:
- An op-amp has a very large open-loop voltage gain
- V+ is at earth potential (0 V)
- If the amplifier is not to saturate, V− input must be almost at earth potential too
- In an inverting amplifier circuit, the current in the input resistor is Iin and the current in the feedback resistor is If
- If V− = 0 V (Earth potential) then the equations for the currents are:
- The input resistance Rin of the op-amp is very high, so virtually no current enters or leaves the inverting input. This means:
If = − Iin
- Or:
Voltage Gain of Inverting and Non-inverting Amplifiers
- The voltage gain for inverting amplifiers is given by:
- Where:
- A = gain
- Vout = output voltage (V)
- Vin = input voltage (V)
- Rf = feedback resistance (Ω)
- Rin = input resistance (Ω)
- The voltage gain for non-inverting amplifiers is given by:
- Where:
- Rf = feedback resistance (resistance of resistor connected to the amplifier)
- R = additional resistor
- Both resistors form a potential divider