Jawaharlal Nehru Technological University Hyderabad B.Tech II PULSE AND DIGITAL CIRCUITS Previous Question Paper (August/September - 2022 - R15)

When a step input of magnitude V is applied to a high-pass RC circuit, the output voltage v_o(t) is determined by the charging characteristics of the capacitor. The circuit acts as a differentiator for small time constants (RC << t) and as an integrator for large time constants (RC >> t).

The output voltage is given by the expression:

Key characteristics of the response include:

• At t = 0⁺, the capacitor acts as a short circuit, and the entire input voltage V appears across the resistor.
• As time progresses, the capacitor charges towards the input voltage V, causing the output voltage to decay exponentially towards zero with a time constant τ = RC.
• The rate of decay is inversely proportional to the product of resistance and capacitance. A larger RC value results in a slower decay, making the output closer to the original step input.

A compensated attenuator is a circuit used to provide a constant attenuation factor over a wide frequency range by minimizing the effects of stray capacitance. It consists of a voltage divider network with an added parallel capacitor to compensate for the input capacitance of the following stage.

The circuit consists of two resistors R₁ and R₂ in series, with capacitor C₁ in parallel with R₁ and C₂ in parallel with R₂. The output is taken across the R₂C₂ combination.

To achieve frequency-independent attenuation, the time constants of the two branches must be equal:

When this condition is met, the capacitive reactance ratio matches the resistive ratio, ensuring that the attenuation factor remains constant regardless of the frequency of the input signal. This prevents signal distortion that would otherwise occur due to the frequency-dependent impedance of stray capacitances.