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Homework3

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EE4227 Fall 2019 NAME:_____________________________________

EE4227: Power Electronics

Homework 3 - Fall 2019

Q1. 20 pts
hidden)

A voltage divider provides 1 V output from 5 V input as shown below. The maximum output current is 1 mA.
The resistors are chosen to provide load regulation of better than 1% over the load current range of 0-1 mA.

(a) Find the values necessary for this application.
(b) What is the efficiency at full load?
Solution
hidden)

◼ Solution (a)
The desired output should drop no less than
= 1 % = 0.01 [V ]
Vout

Vout R2
=
Vin R1 +R2
R2 1
=
R1 +R2 5
R1 = 4 R2
RL = Iout max load
0.99
=
0.001
RL = 990[Ω]
The parallel combination of R2 and RL
R2 RL
R2 // RL = R2 +RL
R2 990
=
R2 +990

The voltage divider equation becomes

Rel. Date: 9/27/19 1 of 10
EE4227 Fall 2019 NAME:_____________________________________

Vout R2 //RL
=
Vin R1 +R2 //RL
R2 990
0.99 R2 +990
= R 990
5 R1 + 2
R +990
2

4010. R2
R1 = 990. +R2
[Ω]

Solving the two equations for R1 and R2 to answer (a)
R1 = 4 R2
4010. R2
R1 = 990. +R2
R1 = 50 [Ω]
R2 = 12.5 [Ω]

◼ Solution (b)
Solving for Pout at max load
Pout@max = Vout@max( Iout@max)
= 0.99 (0.001)
= 990 10-6 [W ]
Solving for Pin at max load
Pin@max = Vin@max( Iin@max)
= 5 80.20 10-3 
= 401 10-3 [W ]
Solving for Iin at max load
Vin@max
Iin@max = Req
Vin@max
= R R
R1 + R 2+RL
2 L

5
=
62.3441
= 80.20 10-3 [ A]
Solving for efficiency to answer (b)
Pout@max
Η@max =
Pin@max
990 10-6
= 100
401 10-3
= 0.2469 [%]
Mathematica Solution
hidden)

Rel. Date: 9/27/19 2 of 10
EE4227 Fall 2019 NAME:_____________________________________

Q2. 25 pts

Consider the signal below. Assume the peaks to be at ±10 V.

Initialization
hidden)

(a) 5 pts. Calculate the average value of the signal.
(b) 5 pts. Calculate the RMS value of the signal.
(c) 10 pts. Can the THD value of this signal be calculated? If so, calculate it. If not, why?
Solution
hidden)

◼ Solution (a)
Some base assumptions:
(i) The signal is periodic
(ii) The signal frequency is the wanted, or desired, frequency
There are two approaches to solving these questions. Both will result in the same answer:
(Α) BLUE - Using the original signal, Τ = 0
(Β) RED - Shifting the signal to make use of symmetry, Τ = - 18 T

Define f (t); Τ = 0
10; -0 < t < 2.5 ms
f (t ) =  
-10; 5 < t < 7.5 ms

Find average value of f (t)
1 Τ+T
< f >= ∫Τ f (t ) ⅆ t
T
1 0.0025 0.0075
=
0.01
∫0 10 ⅆ t + ∫0.005 - 10 ⅆ t
= ~0
Define f (t); Τ = - 1.25 ms
10; -1.25 < t < 1.25 ms
f (t ) =  
-10; 3.75 < t < 6.25 ms

Find average value of f (t)

Rel. Date: 9/27/19 3 of 10
EE4227 Fall 2019 NAME:_____________________________________

1 Τ+T
< f >= f (t ) ⅆ t
T ∫Τ
1 0.00125 0.00625
=...

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