A single-phase half-controlled bridge converter supplies an inductive load with ripple-free load current. The triggering angle of the converter is \( 60^\circ \). The ratio of the rms value of the fundamental component of the input current to the rms value of the total input current of the bridge is (rounded off to 3 decimal places).
In the DC–DC converter shown in the figure, the current through the inductor is continuous. The switching frequency is \(500\,\text{Hz}\).
The output voltage \(V_o\) across the load is assumed to be constant and ripple-free.
The peak value of the inductor current (in amperes) is __________ (rounded off to the nearest integer).

A single-phase full-controlled thyristor converter bridge is used for regenerative braking of a separately excited DC motor with the following specifications:
Assume that the motor is running at 600 rpm and the armature terminals are suitably reversed for regenerative braking.
If the armature current of the motor is to be maintained at the rated value, the triggering angle of the converter bridge (in degrees) should be ____________ (rounded off to two decimal places).
Motor and converter parameters:
| Parameter | Value |
|---|---|
| Rated armature voltage | 210 V |
| Rated armature current | 10 A |
| Rated speed | 1200 rpm |
| Armature resistance | 1 Ω |
| Input to converter bridge | 240 V at 50 Hz |
The armature of the DC motor is fed from the full-controlled bridge, and the field current is maintained constant.
A difference amplifier is shown in the figure. Assume the op-amp to be ideal. The CMRR (in dB) of the difference amplifier is (rounded off to 2 decimal places).
In the given circuit, the diodes are ideal. The current \( I \) through the diode \( D_1 \) in milliamperes is (rounded off to two decimal places).
Consider the stable closed-loop system shown in the figure. The magnitude and phase values of the frequency response of \( G(s) \) are given in the table below. The value of the gain \( K_I \; (>0) \) required for a 50° phase margin is __________ (rounded off to two decimal places).
Frequency response data of \( G(s) \):
| \(\omega\) (rad/s) | Magnitude (dB) | Phase (degrees) |
|---|---|---|
| 0.5 | -7 | -40 |
| 1.0 | -10 | -80 |
| 2.0 | -18 | -130 |
| 10.0 | -40 | -200 |
System diagram:

Given an open-loop transfer function \(GH = \frac{100}{s}(s+100)\) for a unity feedback system with a unit step input \(r(t)=u(t)\), determine the rise time \(t_r\).
Consider a linear time-invariant system represented by the state-space equation: \[ \dot{x} = \begin{bmatrix} a & b -a & 0 \end{bmatrix} x + \begin{bmatrix} 1 0 \end{bmatrix} u \] The closed-loop poles of the system are located at \(-2 \pm j3\). The value of the parameter \(b\) is: