JNTU B.Tech II PULSE AND DIGITAL CIRCUITS Previous Question Paper (November/December - 2020 - R13)

A high pass RC circuit acts as a differentiator when the time constant (τ = RC) is much smaller than the pulse width (t_p). The output waveform depends significantly on the ratio of the time constant to the input pulse duration.

1. Response to a Step Input:

When a step voltage of magnitude V is applied, the capacitor charges exponentially. The output voltage is given by v_o(t) = V * e^-t/τ.

• If τ >> t_p (Large time constant): The capacitor charges very slowly, so the output voltage remains nearly constant at V, appearing as a slightly tilted flat top.
• If τ << t_p (Small time constant): The capacitor charges rapidly, resulting in a sharp spike at the leading edge that decays quickly to zero.
• If τ ≈ t_p: The output shows a noticeable exponential decay during the pulse duration.

2. Response to a Square Wave Input:

A square wave is a sequence of positive and negative steps. The output is a series of pulses corresponding to the transitions of the input square wave.

• Large Time Constant (τ >> T/2): The output waveform closely resembles the input square wave but with a slight tilt (sag) on the top and bottom portions due to the slow charging/discharging of the capacitor.
• Small Time Constant (τ << T/2): The output consists of a series of positive and negative spikes. The positive spike occurs at the rising edge of the input, and the negative spike occurs at the falling edge. The output returns to zero quickly between transitions.
• Medium Time Constant (τ ≈ T/2): The output exhibits significant exponential decay, resulting in a rounded, distorted waveform that does not reach the full amplitude of the input square wave.

In summary, the high pass circuit preserves the transitions of the signal while attenuating the low-frequency components, with the degree of distortion determined by the relationship between the time constant and the signal period.