• 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 I_in and the current in the feedback resistor is I_f
• If V₋ = 0 V (Earth potential) then the equations for the currents are:

• The input resistance R_in of the op-amp is very high, so virtually no current enters or leaves the inverting input. This means:

I_f  = − I_in

• Or:

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

• The voltage gain for inverting amplifiers is given by:

• Where:
  • A = gain
  • V_out = output voltage (V)
  • V_in = input voltage (V)
  • R_f = feedback resistance (Ω)
  • R_in = input resistance (Ω)
• The voltage gain for non-inverting amplifiers is given by:

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

Worked example: Calculating resistance

Step 1:            Voltage gain equation for non-inverting amplifier

Step 2:            Rearrange for resistance R

Step 3:            Substitute in values

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

 A = 45