Chapter XIII differentiator circuit and the differential operational

A differentiator: an output voltage proportional to the rate of change of the input voltage waveform.

Circuit diagram:

Is the voltage across the capacitor C

and so 

If the selected sufficiently small R and C, that

then 

V is the equation of 

This equation is the mathematical expression of the differentiator;

Second, the differential operation circuit

Inverting input of differential operation circuit 

It is seen by the virtual short V + = V- = 0;

and so 

then

Third, the square wave excitation input and output of the differential circuit relationship

Generating a sharp pulse signal

Fourth, the unwanted capacitive coupling case

1, the square wave capacitively coupled into the signal circuit:

FIG useful signal is a sine wave, square wave capacitively coupled into the burr resulting signal that lacks resistive load signal path. Or reducing the source resistance of the signal path;

2, oscilloscope probe disconnected:

This case is a square wave input, but a point in the circuit is disconnected, usually oscilloscope probe is disconnected, the input resistance of a small capacitance C interrupted oscilloscope combined to form a differentiating circuit.