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Ideal op-amp properties; inverting gain

Short answer

Ideal op-amp: infinite open-loop gain, infinite input resistance, zero output resistance, infinite bandwidth. Inverting amplifier: Vin through R1 to inverting input, Rf feedback, non-inverting terminal grounded. Virtual ground gives V- = 0. Current: Vin/R1 = -Vo/Rf => Av = Vo/Vin = -Rf/R1.

Mention any four properties of an ideal OP amp. Derive the expression of voltage gain of an inverting amplifier using OP amp.

Four properties of an ideal op-amp

  1. Infinite open-loop voltage gain.
  2. Infinite input resistance, so no current flows into the inputs.
  3. Zero output resistance.
  4. Infinite bandwidth, infinite CMRR and zero offset voltage.
          +Vcc
      |\   |
 V- o-| \  |
      |  >--o Vo
 V+ o-| /
      |/   |
          -Vcc

Voltage gain of an inverting amplifier

               +-----[ Rf ]-----+
               |                |
               |     |\         |
 Vin o--[ R1 ]-+-----|- \       |
                     |   >------+----o Vo
               +-----|+ /
               |     |/
              GND

The input Vin is applied through R1 to the inverting input; the feedback resistor Rf connects the output to the inverting input; the non-inverting input is grounded.

Derivation (ideal op-amp)

  • Virtual short: V− = V+ = 0, so the inverting node is at virtual ground.
  • No current enters the op-amp, so the input current I1 = (Vin − 0)/R1 flows entirely through Rf.
  • KCL at the inverting node: (Vin − 0)/R1 = (0 − Vo)/Rf

Av = Vo/Vin = −Rf/R1

The minus sign shows that the output is 180° out of phase with the input. The input resistance equals R1. Example: R1 = 10 kΩ, Rf = 100 kΩ gives Av = −10.

✓ Answer checked by Claude Opus 5.5 (high effort)

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