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Op-amp properties and summing amplifier

Short answer

Ideal op-amp: infinite gain, infinite input resistance, zero output resistance, infinite bandwidth. Two-stage design: first inverting summer for V2, V3 with Rf1=30kΩ, R2=15kΩ, R3=10kΩ gives Vo1 = -(2V2+3V3). Second inverting summer with inputs V1 and Vo1, equal resistors 10kΩ gives Vo = -(V1+Vo1) = -V1+2V2+3V3.

State any four properties of an ideal op-amp. Design a summing amplifier using Op-Amp to get the output voltage V0 = -V1 + 2V2 + 3V3.

Four properties of an ideal op-amp

  1. Infinite open-loop voltage gain.
  2. Infinite input resistance (no input current).
  3. Zero output resistance.
  4. Infinite bandwidth, infinite CMRR and zero offset voltage.

Design for V0 = −V1 + 2V2 + 3V3

A single inverting summer gives all inputs the same (negative) sign. Here V1 has a negative sign while V2 and V3 have positive signs, so two stages are used.

Stage 1: inverting summer for V2 and V3

V01 = −(Rf1/R2 V2 + Rf1/R3 V3) = −(2V2 + 3V3)

Choose Rf1 = 30 kΩ: R2 = 30k/2 = 15 kΩ, R3 = 30k/3 = 10 kΩ.

 V2 o--[ 15k ]--+
                |
 V3 o--[ 10k ]--+-----[ 30k ]----+
                |                |
                |     |\         |
                +-----|- \       |
                      |   >------+----o V01
                +-----|+ /
                |     |/
               GND

Stage 2: inverting summer for V1 and V01

V0 = −(Rf2/R4 V1 + Rf2/R5 V01), with both gains equal to 1: Rf2 = R4 = R5 = 10 kΩ.

V0 = −(V1 + V01) = −V1 + (2V2 + 3V3) = −V1 + 2V2 + 3V3 ✓

 V01 o--[ 10k ]--+
                 |
 V1  o--[ 10k ]--+-----[ 10k ]----+
                 |                |
                 |     |\         |
                 +-----|- \       |
                       |   >------+----o V0
                 +-----|+ /
                 |     |/
                GND

Answer: Stage 1: Rf1 = 30 kΩ, R2 = 15 kΩ, R3 = 10 kΩ. Stage 2: R4 = R5 = Rf2 = 10 kΩ.

✓ Answer checked by Claude Opus 5.5 (high effort)

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