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).
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).
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Solution and Explanation
Step 1: Determine the duty ratio
For a boost converter, the output voltage is related to the input voltage by:
\[ V_o = \frac{V_s}{1-\alpha} \]
\[ 40 = \frac{20}{1-\alpha} \]
\[ \alpha = 0.5 \]
Step 2: Calculate load current
\[ I_o = \frac{V_o}{R} = \frac{40}{10} = 4\ \text{A} \]
Step 3: Average inductor current
For a boost converter operating in CCM:
\[ I_L = \frac{I_o}{1-\alpha} \]
\[ I_L = \frac{4}{1-0.5} = 8\ \text{A} \]
Step 4: Inductor current ripple
The peak-to-peak inductor current ripple is:
\[ \Delta I_L = \frac{\alpha V_s}{fL} \]
\[ \Delta I_L = \frac{0.5 \times 20}{500 \times 2 \times 10^{-3}} = 10\ \text{A} \]
Step 5: Peak inductor current
\[ I_{\text{peak}} = I_L + \frac{\Delta I_L}{2} \]
\[ I_{\text{peak}} = 8 + \frac{10}{2} = 13\ \text{A} \]
Final Answer:
Peak inductor current = 13 A
Top Questions on Current
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).
A single-phase full-controlled thyristor converter bridge is used for regenerative braking of a separately excited DC motor with the following specifications:
- Rated armature voltage = 210 V
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- Armature resistance = 1 Ω
- Input to the converter bridge = 240 V at 50 Hz
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:
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