Analog Circuits
Analog Circuits tests op-amp configurations, feedback, filters, oscillators and power stages. Questions usually combine an ideal-op-amp calculation with a non-ideal limit such as slew rate, bandwidth or output swing.
Core rules
- Ideal op-amp with negative feedback: infinite gain, infinite input impedance, zero output impedance; virtual short V+ = V− and zero input current.
- Inverting gain = −Rf/Rin; non-inverting gain = 1 + Rf/R1; differential and instrumentation configurations build on these.
- Integrator: Vo = −(1/RC)∫Vi dt; differentiator: Vo = −RC dVi/dt. Practical versions add a resistor or capacitor to limit noise and stability problems.
- Barkhausen criterion for oscillation: loop gain magnitude 1 and phase 0° or 360° at the oscillation frequency.
- Slew rate limits large-signal high-frequency operation: SR = 2πfVp; full-power bandwidth f = SR/(2πVp).
- Gain–bandwidth product: closed-loop bandwidth ≈ GBW/Acl for a compensated op-amp.
Worked example
A non-inverting amplifier uses Rf = 47 kΩ and R1 = 10 kΩ, with ±12 V supplies and Vi = 0.2 V. Acl = 1 + 47/10 = 5.7. Ideal output = 1.14 V. Check slew rate: if the op-amp has SR = 0.5 V/µs and the signal is 1.14 V peak at 100 kHz, required SR = 2π×10^5×1.14 ≈ 0.72 V/µs, so the output slews. The gain calculation is correct, but the amplifier is slew-limited at that frequency.
Traps
- Applying the virtual short when there is no negative feedback.
- Forgetting output saturation at the rails.
- Confusing GBW with the closed-loop bandwidth at high gain.
- Ignoring input bias current in high-impedance circuits.
- Using an ideal integrator at DC, where offset charges the capacitor.