JNTU B.Tech III PULSE AND DIGITAL CIRCUITS Previous Question Paper (March - 2021 - R13)

A low pass RC circuit acts as a filter that allows low-frequency components to pass while attenuating high-frequency components. When a square wave is applied, the output waveform depends on the time constant τ = RC relative to the pulse width T. If τ << T, the output follows the input closely. If τ >> T, the capacitor charges and discharges slowly, resulting in a triangular-like waveform with rounded edges.

The waveform exhibits exponential rise and fall times, where the slope is determined by the charging and discharging rates of the capacitor.

For an RC low pass circuit, the output voltage v_o(t) is taken across the capacitor. The input voltage v_i(t) is applied across the series combination of R and C. The circuit equation is:

Since i = C(dv_o/dt), we substitute this into the equation:

If the circuit is designed such that the time constant RC is very large compared to the duration of the input signal t, then v_o << RC(dv_o/dt). Under this condition, the term v_o can be neglected, simplifying the expression to:

Rearranging for v_o:

This expression shows that the output voltage is proportional to the integral of the input voltage, confirming that the circuit acts as an integrator when RC >> T.