Analog Circuit Design

Inverting amplifier — Vin drives Rin into the summing node; Rf from output back to the node holds it near the + input (virtual ground), producing Vout = −(Rf/Rin)·Vin with inverted polarity.

Non-inverting amplifier — Vin feeds the + input directly (very high input impedance); the Rf/Rin divider sets the gain 1 + Rf/Rin with the same polarity as the input.

Comparator with hysteresis — R1 feeds a little of the output back into the + node, while R2 pulls it to Vref. That feedback splits the trip point into VT+ and VT− and rejects noise at the threshold.

3-op-amp instrumentation amplifier — Two input amplifiers each add R1 with a common Rg between them giving gain 1 + 2R1/Rg, while a difference stage cancels the common-mode levels of the two inputs.

Difference amplifier (subtractor) — V1 drives the − input through Rin while V2 reaches the + input scaled by R2; with R1=Rf and R2=Rin the output becomes (Rf/Rin)(V2 − V1), subtracting common-mode voltages.

Unity-gain buffer — The output is wired straight back to the − input, forcing Vout to track Vin exactly (A = 1) with near-infinite input impedance to isolate the source from the load.

Open-loop vs closed-loop response — Open-loop gain rolls off at −20 dB/decade and reaches unity at the gain–bandwidth product GBW. A closed-loop gain Acl holds its flat value only until f = GBW / Acl, where the response starts rolling off.

Slew-rate limiting waveform — If the required slope 2πf·Vp exceeds the op-amp slew rate, the output cannot follow the sine and its edges flatten into straight, limited slopes — a triangular limit that distorts before the −3 dB bandwidth is reached.

Op-amp noise sources — The amplifier has a series voltage-noise source En at the + input and current-noise sources In at each input. Source and feedback resistors add thermal noise 4kTR. Each density is multiplied by √BW and the noise gain to get output RMS noise.

Offset & bias sources — An input-referred offset voltage Vos and bias currents Ib leaving each input are the DC error sources. The output offset equals the input errors times the noise/DC gain; matching the two input impedances cancels the bias-current term.

Driving a capacitive load — A large capacitance at the op-amp output introduces a pole inside the feedback loop that erodes phase margin and can cause ringing or oscillation. Inserting a small series resistor Ri isolates the capacitor from the loop.