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Ideal op-amp properties; non-inverting gain

Short answer

Ideal op‑amp properties: infinite open‑loop gain, infinite input resistance, zero output resistance, infinite bandwidth. For the non‑inverting amplifier, virtual short gives V– = Vin = Vo R1/(R1+Rf), so voltage gain Av = Vo/Vin = 1 + Rf/R1.

Mention any four properties of ideal Op-amp. Derive the expression of voltage gain of non-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 input terminals.
  3. Zero output resistance.
  4. Infinite bandwidth and infinite CMRR (also zero offset voltage).
          +Vcc
      |\   |
 V- o-| \  |
      |  >--o Vo
 V+ o-| /
      |/   |
          -Vcc

Voltage gain of the non-inverting amplifier

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

R1 is connected from the inverting input to ground and Rf from the output to the inverting input (negative feedback). The input Vin is applied directly to the non-inverting terminal.

Derivation (ideal op-amp)

  • No current enters the op-amp inputs.
  • Virtual short: V− = V+ = Vin.
  • The voltage at the inverting node is set by the divider R1, Rf: V− = Vo × R1/(R1 + Rf).

Equating V− = Vin:

Vin = Vo R1/(R1 + Rf)

Av = Vo/Vin = 1 + Rf/R1

The gain is positive (the output is in phase with the input) and always at least 1. For Rf = 0 or R1 = ∞ (open), the circuit becomes a unity gain buffer (voltage follower), Av = 1.

✓ Answer checked by Claude Opus 5.5 (high effort)

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