Circuit samples derivative of a waveform

Joaquin Garcia and Jose Carrasco, Universidad Miguel Hernandez, Elche, Spain -- EDN, 9/14/2000

Basic derivative (differentiating) circuits use a lowpass filter or an active operational-amplifier implementation. These circuits need a large-value capacitor when differentiating a slowly varying signal. Moreover, the circuits are not useful for nonperiodic waveforms. The circuit in Figure 1 offers a simple way of differentiating a waveform, even if it changes slowly or is nonperiodic. The circuit uses an AD781 sample/hold circuit and a subtracting circuit. By sampling the value of the input waveform at a given instant and then subtracting it from itself, op amp IC₂ produces a voltage proportional to the rate of change of the original waveform and to the duration of the hold time (the time the sample/hold input is held low). You can use a µC to transform the circuit's output to the derivative or use the output as is. IC₁ simplifies the subtraction operation and compensates the voltage shift of the sample/hold circuit during its sampling period. Figure 2 shows a sinusoidal voltage and its derivative at the hold instants. Note that the sign of the derivative is inverted. To optimize the circuit, you should adjust the gain of the IC₂ subtraction circuit as a function of the input frequency.