Voltage to Time ADC
The output of the integrator on the voltage to time ADC, Vc, as shown
above, has the same functional form as the integrator output on the voltage
to frequency ADC, that is:
Vc = (Vcomp)t/tau
where tau = RC
Applying a reference voltage (must be negative as compared to Vin), Vcomp, charges up the capacitor, thereby increasing Vc. As Vc increases to Vin, the comparator output goes low, turning off the counter. The control line soon goes low for a brief time, sending data through the latch to the output, and shorting out the capacitor, thereby reducing Vc to zero. This takes the output of the comparator high again, and with the control line also already having gone high, the counter has been reset, and begins counting the clock pulses again.
The equation for Vc above, with t = T and Vc = Vin gives
Vin = (Vcomp)T/tau
Thus the analog input voltage is proportional to the time T during which the
clock pulses come out of the AND gate. This time T is in turn proportional
to the number of clock pulses as recorded by the counter.