CIE A Level Physics (9702) 2019-2021

Revision Notes

24.1.4 Gain of Amplifiers

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:

Derivation of Gain of Inverting Amplifiers equation 1

  • 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:

Derivation of Gain of Inverting Amplifiers equation 2

  • Hence the gain (amplification) of the inverting amplifier A is given by:

Derivation of Gain of Inverting Amplifiers equation 3

Voltage Gain of Inverting and Non-inverting Amplifiers

  • The voltage gain for inverting amplifiers is given by:

Voltage Gain of Inverting and Non-inverting Amplifiers equation 1

  • 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:

Voltage Gain of Inverting and Non-inverting Amplifiers equation 2

  • Where:
    • Rf = feedback resistance (resistance of resistor connected to the amplifier)
    • R = additional resistor
  • Both resistors form a potential divider

Worked example: Calculating resistance

Voltage_Gain_of_Inverting_and_Non-inverting_Amplifiers_Worked_example_-_Calculating_Resistance_Question, downloadable AS & A Level Physics revision notes

Step 1:            Voltage gain equation for non-inverting amplifier

Voltage Gain of Inverting and Non-inverting Amplifiers equation 2

Step 2:            Rearrange for resistance R

Voltage Gain of Inverting and Non-inverting Amplifiers Worked Example equation 2

Step 3:            Substitute in values

Rf = feedback resistance = 20 kΩ = 20 × 103 Ω

 A = 45

Voltage Gain of Inverting and Non-inverting Amplifiers Worked Example equation 3

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