A standard op-amp integrator (resistor in, capacitor in feedback) integrates voltage. But many sensors — photodiodes in coulomb-counting mode, electrometers, piezoelectric force sensors, ionization chambers — produce charge or current that you want to integrate directly without converting through a resistor first. The charge integrator (also called a charge-sensitive amplifier, or CSA) is the right tool, and it's the front end of nearly every particle detector and CT scanner on Earth.

The topology is deceptively simple: invert the op-amp with a capacitor C_f in the feedback path, and tie the sensor directly to the inverting input. The output voltage is:

V_out = −Q_in / C_f

Every coulomb of charge injected at the summing junction shows up as a voltage step of 1/C_f volts. With C_f = 1 pF, a single femtocoulomb (6,240 electrons) gives you 1 mV — easily measurable. This is why CSAs dominate radiation detection: a silicon detector dumps ~3.6 eV per electron-hole pair, so a 60 keV gamma deposits ~17,000 electrons (~2.7 fC), which becomes a clean 2.7 mV pulse.

The reset problem. A pure integrator has infinite DC gain. Op-amp bias current (even 1 pA on a JFET part) charges C_f until the output saturates. Three fixes:

• Reset switch across C_f — a small JFET or analog switch closes periodically to dump accumulated charge. Used in CT and gated-integrator readout.
• Reset resistor R_f across C_f — turns the integrator into a leaky integrator with time constant τ = R_f·C_f. With R_f = 1 GΩ and C_f = 1 pF, τ = 1 ms — long enough to capture fast pulses, short enough to bleed off DC drift.
• Continuous reset via a current-mode feedback transistor (the "Krummenacher feedback" used in modern pixel detectors).

Noise rules of thumb. The Equivalent Noise Charge (ENC) of a CSA scales as ENC² ≈ a·C_det²/τ + b·C_det²·τ, where C_det is detector capacitance. Two consequences: (1) minimize C_det — keep traces short, use a low-capacitance detector. (2) There's an optimum shaping time τ; too fast and series noise dominates, too slow and parallel (leakage) noise wins. For a typical silicon detector at room temp, τ ≈ 1–3 µs is the sweet spot.

Op-amp choice: JFET or CMOS input is mandatory — bipolar bias currents (nA range) overwhelm the signal. Look for parts with input capacitance under 5 pF and en under 5 nV/√Hz. The OPA657, ADA4817, or LMP7721 are classic CSA choices.