You may recall a dual-slope ADC integrates a voltage across a capacitor for a fixed period and then discharges the capacitor at a constant rate and measures the discharge time. A larger voltage charges the cap more and results in a longer discharge time and thus a larger digital value. A simple time-to-digital converter (TDC) works in almost the reverse way. It charges a capacitor for the unknown period you want to measure (t1to t2) and at the end of that charging period, you quickly measure the circuit's output voltage.
The time may come when you need to quickly design a practical circuit to measure times of a second or less. For a quick-and-dirty bench technique when you lack a counter timer, try a simple integrator. An event closes a switch, usually a field-effect transistor (FET), that lets current flow into a capacitor. The capacitor continues to charge in a linear fashion as long as the switch remains closed. Open the switch and the charging stops. Then, you can measure the voltage with a high-impedance DVM and indirectly determine the time needed to charge the capacitor to the measured voltage. Of course, you calibrate your measurements so you know the relationship between charge times and voltages. Don't grab a run-of-the-mill ceramic capacitor for an integrator circuit. You will need a high-quality metal-Teflon, polycarbonate or polystyrene capacitor with very low dielectric absorption and low leakage. And your op-amp circuit should compensate for the usual errors.
After you measure the voltage, you close another switch to discharge the capacitor and reset the integrator to 0V. Simplistic integrator circuits often lack a resistor in parallel with the capacitor, but you will need one to prevent small bias currents in the circuit from charging the capacitor.
The example above assumed you need to time one event. If you must time the period between two separate events, use a flip-flop. One event triggers the flip-flop to close the switch; the other event triggers the flip flop to open the switch. Although not shown completely here, you will need a control signal to reset the capacitor and to trigger your DVM to measure the integrator's output.
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