Consider the following step up converter with a resistive load of value R=5 Q2. It is suppliedby a DC power source of magnitude V₁-200 V. The switching frequency is 5 kHz and theduty cycle k is first set to 0.5 and the inductance used within the circuit has a value of L=10mH. The switch is supposed to be ideal. Suppose the solutions for charging and dischargingmodes are given as below:Charging mode, Initial value IlDischarging mode, Initial value I2O+V₂oL܀+VL▷D₁ChopperLoadVo1₂ =i4₁ =VekzR11- e-(1-k)z Ri₁Vekz e-(1-k)z+1-e-(1-k)z RRCircuit Analysis:1. Analyze briefly the principle of operation of this circuit.2. Demonstrate that the ripple currents can be written as follow:VsΔΙ = .k.TLAi3. Demonstrate that the average output voltage can be written as follow:V₁ = V₁₁1=K²+ with z =Numerical Application:4. Find the average output voltage, the minimum and maximum load current values.5.Find the peak to peak load current value.6. Find the average value of load current Ia.7. Find the RMS load current Io.8. Find the value of the inductance that would reduce the current ripples to its half.T.RL

Solution of question (1) and (3): The given circuit diagram of the Boost converter is shown below.…

Consider the following step up converter with a resistive load of value R=5 2. It is supplied by a DC power source of magnitude V₁-200 V. The switching frequency is 5 kHz and the duty cycle k is first set to 0.5 and the inductance used within the circuit has a value of L=10 mH. The switch is supposed to be ideal. Suppose the solutions for charging and discharging modes are given as below: Charging mode, Initial value I1 Discharging mode, Initial value I2 + V₂ + VL it KH D₁ Chopper Load Vo Al = 2.k.T L 1₂ = 1₁ 1-k 4₁ = Vekz R Circuit Analysis: 1. Analyze briefly the principle of operation of this circuit. 2. Demonstrate that the ripple currents can be written as follow: V.kz R e-(1-k)z V₂ 1-e-(1-k)z R +- 1 Vs 1-e-(1-k)z R 3. Demonstrate that the average output voltage can be written as follow: V₁ = V₁.₁ + with z = Numerical Application: 4. Find the average output voltage, the minimum and maximum load current values. 5. Find the peak to peak load current value. 6. Find the average value of load current la. 7. Find the RMS load current Io. 8. Find the value of the inductance that would reduce the current ripples to its half. T.R L

Consider the following step up converter with a resistive load of value R=5 2. It is supplied by a DC power source of magnitude V₁-200 V. The switching frequency is 5 kHz and the duty cycle k is first set to 0.5 and the inductance used within the circuit has a value of L=10 mH. The switch is supposed to be ideal. Suppose the solutions for charging and discharging modes are given as below: Charging mode, Initial value I1 Discharging mode, Initial value I2 + V₂ + VL it KH D₁ Chopper Load Vo Al = 2.k.T L 1₂ = 1₁ 1-k 4₁ = Vekz R Circuit Analysis: 1. Analyze briefly the principle of operation of this circuit. 2. Demonstrate that the ripple currents can be written as follow: V.kz R e-(1-k)z V₂ 1-e-(1-k)z R +- 1 Vs 1-e-(1-k)z R 3. Demonstrate that the average output voltage can be written as follow: V₁ = V₁.₁ + with z = Numerical Application: 4. Find the average output voltage, the minimum and maximum load current values. 5. Find the peak to peak load current value. 6. Find the average value of load current la. 7. Find the RMS load current Io. 8. Find the value of the inductance that would reduce the current ripples to its half. T.R L

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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Question

Consider the following step up converter with a resistive load of value R=5 Q2. It is supplied
by a DC power source of magnitude V₁-200 V. The switching frequency is 5 kHz and the
duty cycle k is first set to 0.5 and the inductance used within the circuit has a value of L=10
mH. The switch is supposed to be ideal. Suppose the solutions for charging and discharging
modes are given as below:
Charging mode, Initial value Il
Discharging mode, Initial value I2
O
+
V₂
o
L
܀
+
VL
▷
D₁
Chopper
Load
Vo
1₂ =
i
4₁ =
Vekz
R
1
1- e-(1-k)z R
i₁
Vekz e-(1-k)z
+
1-e-(1-k)z R
R
Circuit Analysis:
1. Analyze briefly the principle of operation of this circuit.
2. Demonstrate that the ripple currents can be written as follow:
Vs
ΔΙ = .k.T
L
Ai
3. Demonstrate that the average output voltage can be written as follow:
V₁ = V₁₁1=K²
+ with z =
Numerical Application:
4. Find the average output voltage, the minimum and maximum load current values.
5.
Find the peak to peak load current value.
6. Find the average value of load current Ia.
7. Find the RMS load current Io.
8. Find the value of the inductance that would reduce the current ripples to its half.
T.R
L

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