Transcript Solved Class Problems

Practice Problem
The periodic waveform shown is applied to a 100Ω resistor.
What value of α yields 50W average power to the resistor?
150V
0V

T
2
0
T
T
α is the “duty cycle”
2
2
VRMS
 VTRI
, RMS  (1   )0
2
RMS
V
 150 


3


2
2
VRMS
P
R
2

3
1
Practice Problem
iin
+
Vin
–
id
iL
L
C
iC
–
Vout
+
Iout
4a.
Assuming continuous conduction in L, and ripple free Vout and Iout , draw the “switch
V
closed” and switch open” circuits and use them to develop the out equation.
Vin
4b.
Consider the case where the converter is operating at 50kHz, Vin = 40V, Vout = 120V, P =
240W. Components L = 100µH, C = 1500µF. Carefully sketch the inductor and capacitor
currents on the graph provided.
4c.
Use the graphs to determine the inductor’s rms current, and the capacitor’s peak-to-peak
current.
4d.
Use the graphs to determine the capacitor’s peak-to-peak ripple voltage.
2
!
Practice Problem
iin
+
Vin
–
id
iL
L
iC
C
–
Vout
+
Iout
Hint #1: This is a buck-boost converter
iin
Hint #2: Pin = Pout
Pin = DVin IL = VinIin
Pout = Vout Iout
Hint #3: IC = 0
Iout = (1-D) IL
IL
Vin
DT
t
Since the input voltage is constant
only the dc component of iin
contributes to Pin
3
Practice Problem
December 16 was a brilliant solar day here in Austin. Consider a PV installation that has 60º tilt,
and 225º azimuth (i.e., facing southwest). Use the following equation,


(GH  DH )
Pincident   DH 
 cos(  incident )W / m 2 ,
zenith
cos( sun
)


and the graphs on the following page to estimate
5a.
the maximum incident solar power density on the panels (in W/m2), and
5b.
the time at which the maximum occurs.
4
Sun Zenith Angle (Top Curve), and Incident Angle on Panel (Bottom Curve), for Dec. 16
(Panel Tilt and Azim uth = 60 and 225 Degrees, Respectively)
90
85
Zenith
80
75
70
65
60
Degrees
55
50
45
40
35
30
Incident
25
20
15
10
5
0
11
11.5
12
12.5
13
13.5
14
14.5
15
15.5
16
16.5
17
Hour of Day
Global Horizontal (Top Curve), and Diffuse Horizontal (Bottom Curve), for Dec. 16
650
600
550
500
Watts Per Square Meter
450
400
350
300
GH
250
200
150
100
DH
50
5
0
11
11.5
12
12.5
13
13.5
14
Hour of Day
14.5
15
15.5
16
16.5
17