1. Analyzing the Triangular Waveform: A triangular wave consists of linear voltage ramps. It has a constant positive slope during its rising edge and a constant negative slope during its falling edge.
• Rising Edge: The slope ($m = \frac{dV}{dt}$) is a positive constant value.
• Falling Edge: The slope ($m = \frac{dV}{dt}$) is a negative constant value.
2. Effect of Differentiation: When these constant slopes are differentiated:
• The derivative of a constant positive slope results in a
constant positive voltage level.
• The derivative of a constant negative slope results in a
constant negative voltage level.
3. Resulting Output: The output switches abruptly between a fixed positive level and a fixed negative level at the peaks of the triangular wave. This geometric pattern is the definition of a
square waveform (or a rectangular waveform if the duty cycle is not 50%).
Note: If the differentiator is an inverting Op-Amp type, the output will be a square wave that is $180^\circ$ out of phase with the slopes (negative voltage for positive slope), but it remains a square waveform.