Operational Amplifiers: Linear Integrated Circuits

Explore open loop configuration: an op amp with no feedback amplifies the difference between inputs v1 and v2 by the open loop gain a, producing vo.

Explore the virtual short and virtual ground concepts in ideal op-amps, showing how the inverting and non-inverting inputs hold equal voltages and behave as if grounded.

Explore how negative voltage feedback in an inverting op-amp stabilizes gain, yielding a closed-loop gain of -Rf/Rin and a virtual ground at the inverting input.

Study how dc biasing a practical operational amplifier with no inputs yields a small output from input bias current and input offset current via the feedback path.

Slew rate defines the maximum rate of change of an op-amp output for ac signals, with dv/dt max = ω v_m, expressed in volts per microsecond.

Design a voltage follower using an op-amp to achieve unity gain, buffering signals for impedance matching and delay without distortion.

Design an analog inverter using an op-amp by configuring an inverting amplifier with equal input and feedback resistances, yielding a closed-loop gain of minus one and inverted output.

Explore a nonlinear op-amp application by using an output diode in a voltage follower to create a half wave rectifier that yields pulsating DC on the positive half cycle.

Explore analogue comparators in open-loop op-amps, including inverting and non-inverting types, and understand saturation bounded by plus and minus supply, producing a square output.

Build an open loop comparator with an op-amp by connecting V1 to the non-inverting input and V2 to the inverting input, biasing supplies enable plus or minus Vsat.

The zero crossing detector uses a grounded v2 and v1 at the non-inverting input; when v1>0 the output goes to plus vset, and when v1<0 it goes to minus vset.

Design a summing amplifier with a closed-loop op-amp to add multiple inputs, yielding their sum with optional phase inversion, achieved by using equal resistors for unity gain.

Implement a subtractor with an operational amplifier to produce v2 minus v1, using a voltage divider at the non-inverting input to set unit gain.

Analyze analog multiplier circuits using op-amps, log and anti-log stages to convert multiplication into addition via log properties, then recover the product with anti-log.

Explore constructing an op-amp differentiator that outputs the derivative of the input using a input capacitor and feedback path, and see how a square wave produces spikes at transitions.

Build an integrator with an op-amp by swapping the feedback resistor for a capacitor, yielding an output proportional to the input's integral and a low-pass response.

An open-loop operational amplifier saturates with a sine input, yielding a square-wave output at plus and minus supply levels, acting as an analog comparator.

Demonstrate how an op-amp with grounded inputs still yields an output from input offset and leakage currents; with a -RF/R1 gain, a 1 mV offset produces -1 V.

Apply the superposition principle to a dual-input op-amp circuit, computing the inverting contribution and the non-inverting contribution before summing to the final output of -0.5 v.

Treat the ideal op-amp as an inverting summing amplifier with the noninverting input grounded. Equal capacitances yield unit gain, producing Vout = −(V1 + V2) sin(ωd), a phase-inverted sum.

Solve a problem on operational amplifiers by recognizing a closed-loop inverting amplifier with negative feedback and identifying input and feedback resistors, applying the gain formula -Rf/Rin after a circuit redraw.