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Op-amp circuits perform a wide range of analog signal processing functions. The summing amplifier linearly combines weighted inputs; the difference amplifier computes a scaled difference of two signals. Integrator and differentiator circuits place capacitors in the feedback or input path, implementing mathematical operations on signals in continuous time. Active filters combine op-amps with RC networks to achieve sharp roll-offs with gain, overcoming the passive filter limitation of attenuation-only. A comparator (op-amp without feedback) detects when a signal crosses a threshold and outputs a digital-level signal. All linear circuits are analyzed using the virtual short and virtual open rules.
Analyze each circuit type by drawing the small-signal equivalent and applying KCL at the inverting input. For active filters, derive the transfer function using impedances and compare roll-off characteristics to passive equivalents. Build and measure physical circuits to observe limitations: DC drift in integrators, slew-rate limiting in differentiators, and gain-bandwidth product effects.
From your study of op-amp fundamentals, you know the two golden rules for an ideal op-amp in negative feedback: the differential input voltage is zero (virtual short), and no current flows into the input terminals (virtual open). These two rules, combined with KCL at the inverting node, let you analyze any linear op-amp circuit by inspection. Every application in this topic is a variation on that single technique — the circuits change, but the analysis method does not.
The summing amplifier connects multiple input resistors to the inverting input. By virtual short, the inverting input sits at ground potential (virtual ground). Applying KCL: the sum of all input currents through their respective resistors must equal the current through the feedback resistor. The output is a weighted sum of the inputs with sign inversion: V_out = −R_f·(V_1/R_1 + V_2/R_2 + ...). This is the principle behind analog audio mixers — each channel contributes a weighted amount, and varying its resistor adjusts its level independently. The difference amplifier uses matched resistors at both inputs to form V_out = (R_f/R_1)·(V_2 − V_1), enabling rejection of voltages common to both inputs. The instrumentation amplifier extends this with a programmable-gain input stage to achieve very high, adjustable differential gain with excellent common-mode rejection — critical in sensor interfaces and biomedical applications.
Place a capacitor in the feedback path of an inverting amplifier and the feedback impedance becomes 1/(jωC), growing large at low frequencies. The circuit integrates: V_out(t) = −(1/RC)∫V_in dt. Place the capacitor in the input path instead and the circuit differentiates: V_out = −RC·(dV_in/dt). Integrators are workhorses in analog control loops and waveform generators; differentiators amplify high-frequency noise and are used more cautiously. Both are analyzed by replacing the capacitor with its complex impedance Z = 1/(sC) and applying the standard inverting amplifier gain formula G = −Z_f/Z_in.
Active filters add gain to the filtering function. A passive RC low-pass attenuates high frequencies but also attenuates the desired signal in the passband and loads the source. Adding an op-amp provides a controlled passband gain and isolates stages from each other. First-order active filters achieve −20 dB/decade roll-off; second-order topologies like the Sallen-Key achieve −40 dB/decade with a controlled quality factor Q that shapes the response near cutoff into Butterworth (maximally flat), Chebyshev (equiripple), or Bessel (linear phase) characteristics. The comparator is an op-amp used open-loop: without feedback, the enormous open-loop gain (105 to 106) drives the output to one supply rail or the other depending on which input is larger. This converts analog signal levels to digital logic — the interface between the analog and digital domains.