Operational Amplifiers and Applications
This domain tests the ideal op-amp model, negative-feedback configurations and the practical limits that appear in numerical problems.
Core concepts
- Ideal op-amp: infinite open-loop gain, infinite input impedance, zero output impedance, infinite CMRR and bandwidth.
- With negative feedback, the virtual-short rule applies: V+ ≈ V− and input current ≈ 0.
- Inverting amplifier: A_v = −R_f/R_in. Non-inverting: A_v = 1 + R_f/R_in. Voltage follower: A_v = 1, used as a buffer.
- Other circuits: summing amplifier (weighted inputs), integrator (feedback capacitor), differentiator (input capacitor), comparator (open loop, no feedback), instrumentation amplifier (three op-amps).
- Practical limits: slew rate in V/µs caps the maximum frequency for a given amplitude; gain–bandwidth product is constant, so gain 100 gives one-hundredth of the unity-gain bandwidth; input offset voltage and CMRR cause DC errors. The 741 has a typical slew rate of 0.5 V/µs.
Worked example
A non-inverting amplifier has R_f = 90 kΩ and R_in = 10 kΩ, so A_v = 1 + 9 = 10. With V_in = 0.5 V, V_out = 5 V on the ±12 V rails, so no clipping. Required slew rate for a 10 kHz, 5 V peak sine: 2π f V = 2π × 10^4 × 5 ≈ 3.14 × 10^5 V/s ≈ 0.31 V/µs, within the 741 limit.
Traps
Using the virtual short without negative feedback (comparators do not obey it); dropping the minus sign in the inverting gain; forgetting output clipping at the supply rails; swapping the integrator and differentiator component positions.