JNTU B.Tech II PULSE AND DIGITAL CIRCUITS Previous Question Paper (May - 2019 - R13)

A ringing circuit, also known as a resonant circuit or oscillator, is an electrical circuit that produces a continuous oscillation at a specific frequency when excited by a transient input. It typically consists of an inductor (L) and a capacitor (C) or a resonant cavity. The energy oscillates back and forth between the inductor's magnetic field and the capacitor's electric field.

Applications include:

• Radio frequency (RF) oscillators in transmitters and receivers.
• Timing circuits and clock generators in digital systems.
• Filters for selecting specific frequencies.
• Signal generation for testing and measurement.
• In switching power supplies for generating switching waveforms.

A high-pass RC network acts as a differentiator when the time constant RC is much smaller than the period of the input signal (RC << T). In this condition, the voltage across the capacitor, Vc, is approximately equal to the input voltage, Vi, because the capacitor has little time to charge or discharge significantly.

The voltage across the resistor, Vr, is given by Vr = Vi - Vc. Since Vc is nearly constant, the change in Vc is small. Thus, Vr is proportional to the rate of change of Vi.

The output voltage Vo is taken across the capacitor. If the output is taken across the resistor, then Vo = Vr = Vi - Vc. For the differentiator condition (RC << T), the capacitor voltage Vc(t) ≈ Vi(t - Δt) where Δt is a very small time. Therefore, Vc(t) ≈ Vi(t) - RC * dVi(t)/dt. If the output is taken across the resistor, Vo(t) = Vr(t) = Vi(t) - Vc(t). For a perfect differentiator, the output voltage is proportional to the derivative of the input voltage.

In a practical high-pass RC circuit, if the output is taken across the capacitor (Vo = Vc), and RC << T, then the current i(t) = C * d(Vi(t))/dt. The output voltage Vo(t) = i(t) * R = RC * d(Vi(t))/dt. Thus, the output voltage is proportional to the derivative of the input voltage.