28
R. W. Erickson Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder
R. W. Erickson Department of Electrical, Computer, and Energy Engineering
University of Colorado, Boulder
ECEN4797/5797 Introduction to Power Electronics
ECEE Department, University of Colorado, Boulder
Another Compensator Design Example
+
L
iL(t)
+ +
C
Iout
R
Power stage parameters
• Switching frequency: fs = 1MHz
– Vg
_
vo
_
V
C
Dead-time control
+
_
+PWM Compensator
fs = 1 MHz
errorduty-cyclecommand
R
• Vref = 1.8 V
• Iout = 0 to 5 A
• Vg = 5 V
• L = 1 PH
• RL = 30 m:Gc(s)1/VM
ECEN5797
Vref
• C = 200 PF
• Resr = 0.8 m:
• VM = 1 V
• H = 1
Point-of-Load Synchronous Buck Regulator
c( )M
Buck Averaged Small-Signal Model
L
+
Vg d iL
Resr
RL
1� sdvsG o
vd ˆˆ
)(
+–
C
R v
–
vg+– D vg
Io d
D iL2
11
)(
¸̧¹
·¨̈©
§��
oo
esrgvd
ssQ
VsG
ZZ
Z
kHz 112
1
CLfo S dB1451G
Pair of poles: Low-frequency gain (including PWM gain):
ECEN5797
MHz 12
1
esresr CR
fS
2 CLS
dB 2.73.2/o
�
Lesrloss RR
CLQ 5/
! CL
RQload
dB 2.73.2|| o��
loadloss
loadlossloadloss QQ
QQQQQ
dB145o M
vdo VG
ESR zero:
ECEN4797/5797 Introduction to Power Electronics
ECEE Department, University of Colorado, Boulder
Another Compensator Design Example
+
L
iL(t)
+ +
C
Iout
R
Power stage parameters
• Switching frequency: fs = 1MHz
– Vg
_
vo
_
V
C
Dead-time control
+
_
+PWM Compensator
fs = 1 MHz
errorduty-cyclecommand
R
• Vref = 1.8 V
• Iout = 0 to 5 A
• Vg = 5 V
• L = 1 PH
• RL = 30 m:Gc(s)1/VM
ECEN5797
Vref
• C = 200 PF
• Resr = 0.8 m:
• VM = 1 V
• H = 1
Point-of-Load Synchronous Buck Regulator
c( )M
Buck Averaged Small-Signal Model
L
+
Vg d iL
Resr
RL
1� sdvsG o
vd ˆˆ
)(
+–
C
R v
–
vg+– D vg
Io d
D iL2
11
)(
¸̧¹
·¨̈©
§��
oo
esrgvd
ssQ
VsG
ZZ
Z
kHz 112
1
CLfo S dB1451G
Pair of poles: Low-frequency gain (including PWM gain):
ECEN5797
MHz 12
1
esresr CR
fS
2 CLS
dB 2.73.2/o
�
Lesrloss RR
CLQ 5/
! CL
RQload
dB 2.73.2|| o��
loadloss
loadlossloadloss QQ
QQQQQ
dB145o M
vdo VG
ESR zero:
ECEN4797/5797 Introduction to Power Electronics
ECEE Department, University of Colorado, Boulder
Uncompensated loop gain Tu
+–
L
iL(t)
+
Vg
+
voC
Iout
Rg
_ _
Vref
Dead-time control
+
_
+PWM Compensator
fs = 1 MHz
errorduty-cyclecommand
Gc(s) = 1
Hsense = 1 (in this example)
1/VM
Gvd(s)
ECEN5797
Tu(s) = Hsense(1/VM)Gvd(s)
Plot magnitude and phase responses of Tu(s) to plan how to design Gc(s)
Magnitude and phase Bode plots of Tu
40dB
60dB
80dB
Tu(s) = Hsense(1/VM)Gvd(s)
0dB
20dB
-20dB
0o
oQ f2/110�
kHz11 of
dB145)/1( o senseMvdouo HVGT
dB/dec40�
dB2.73.2 o Q
t t f
2
¸̧¹
·¨̈©
§
c
ouo f
fT
ECEN5797
100 KHz10 KHz1 KHz100 Hz10 Hz 1 MHz
-90o
-180o
MHz1 esrf
esrf10/1o
Q f2/110�
dB/dec20�
target fc
ECEN4797/5797 Introduction to Power Electronics
ECEE Department, University of Colorado, Boulder
Magnitude and phase Bode plots of Tu
0
50
[db]
Uncompensated loop gain, Tu = Gvd*Hsense*(1/VM) Exact magnitude and phase responses (MATLAB)
103
104
105
106
-100
-50
0
magnitude
Target cross-over frequencyfc = fs/10 = 100 kHz
ECEN5797
103
104
105
106
-200
-100
0
frequency [Hz]
phase [
deg]
No phase margin: a lead (PD) compensator is required
Lead (PD) compensator design
om 53 MT
kHz 100 cf1. Choose:
kHz 33
kHz 003
2. Compute:
3. Find Gco to position the crossover frequency:
ECEN5797
12
¸̧¹
·¨̈©
§
z
pco
c
ouo f
fG
ff
T dB 1545.512
o ¸̧¹
·¨̈©
§
p
z
o
c
uoco f
fff
TG
Magnitude of Tu at fc
Magnitude of Gc at fc
ECEN4797/5797 Introduction to Power Electronics
ECEE Department, University of Colorado, Boulder
Uncompensated loop gain Tu
+–
L
iL(t)
+
Vg
+
voC
Iout
Rg
_ _
Vref
Dead-time control
+
_
+PWM Compensator
fs = 1 MHz
errorduty-cyclecommand
Gc(s) = 1
Hsense = 1 (in this example)
1/VM
Gvd(s)
ECEN5797
Tu(s) = Hsense(1/VM)Gvd(s)
Plot magnitude and phase responses of Tu(s) to plan how to design Gc(s)
Magnitude and phase Bode plots of Tu
40dB
60dB
80dB
Tu(s) = Hsense(1/VM)Gvd(s)
0dB
20dB
-20dB
0o
oQ f2/110�
kHz11 of
dB145)/1( o senseMvdouo HVGT
dB/dec40�
dB2.73.2 o Q
t t f
2
¸̧¹
·¨̈©
§
c
ouo f
fT
ECEN5797
100 KHz10 KHz1 KHz100 Hz10 Hz 1 MHz
-90o
-180o
MHz1 esrf
esrf10/1o
Q f2/110�
dB/dec20�
target fc
ECEN4797/5797 Introduction to Power Electronics
ECEE Department, University of Colorado, Boulder
Magnitude and phase Bode plots of Tu
0
50
[db]
Uncompensated loop gain, Tu = Gvd*Hsense*(1/VM) Exact magnitude and phase responses (MATLAB)
103
104
105
106
-100
-50
0
magnitude
Target cross-over frequencyfc = fs/10 = 100 kHz
ECEN5797
103
104
105
106
-200
-100
0
frequency [Hz]
phase [
deg]
No phase margin: a lead (PD) compensator is required
Lead (PD) compensator design
om 53 MT
kHz 100 cf1. Choose:
kHz 33
kHz 003
2. Compute:
3. Find Gco to position the crossover frequency:
ECEN5797
12
¸̧¹
·¨̈©
§
z
pco
c
ouo f
fG
ff
T dB 1545.512
o ¸̧¹
·¨̈©
§
p
z
o
c
uoco f
fff
TG
Magnitude of Tu at fc
Magnitude of Gc at fc
ECEN4797/5797 Introduction to Power Electronics
ECEE Department, University of Colorado, Boulder
Lead (PD) compensator summary
¸·
¨§
¸·
¨§
¸̧¹
·¨̈©
§�
1
1)( z
cocss
s
GsGZ
dB 1545.5 o coG
kHz 33 zf
¸¸¹
·¨¨©
§�¸
¸¹
·¨¨©
§�
2111
pp
ssZZ
kHz3001 pf
kHz 100 cf (=1/10 of fs)
High-frequency gain of the lead compensator: Gco fp1/fz = 49 (34 dB)
Lead compensator
HF pole
ECEN5797
MHz 12 pf (= fesr = fs in this example)Added high-frequency pole:
Practical implementation would require an op-amp with a gain bandwidth product of at least 49*fp2 = 49 MHz
Loop gain with lead (PD) compensator
40dB
60dB
80dB
¸·
¨§�¸
·¨§�
¸̧¹
·¨̈©
§�
1
1
1
1)( z
cocss
s
GsGZ
kHz10 zf
0dB
20dB
40dB
-20dB
0o
kHz300 pf
dB7.297.28 o couoGT
kHz33 zf
kHz 100 cf
¸¸¹
¨¨©�¸
¸¹
¨¨©�
2111
pp ZZ
ECEN5797100 KHz10 KHz1 KHz100 Hz10 Hz 1 MHz
-90o
-180o
om 53 M
ECEN4797/5797 Introduction to Power Electronics
ECEE Department, University of Colorado, Boulder
Lead (PD) compensator summary
¸·
¨§
¸·
¨§
¸̧¹
·¨̈©
§�
1
1)( z
cocss
s
GsGZ
dB 1545.5 o coG
kHz 33 zf
¸¸¹
·¨¨©
§�¸
¸¹
·¨¨©
§�
2111
pp
ssZZ
kHz3001 pf
kHz 100 cf (=1/10 of fs)
High-frequency gain of the lead compensator: Gco fp1/fz = 49 (34 dB)
Lead compensator
HF pole
ECEN5797
MHz 12 pf (= fesr = fs in this example)Added high-frequency pole:
Practical implementation would require an op-amp with a gain bandwidth product of at least 49*fp2 = 49 MHz
Loop gain with lead (PD) compensator
40dB
60dB
80dB
¸·
¨§�¸
·¨§�
¸̧¹
·¨̈©
§�
1
1
1
1)( z
cocss
s
GsGZ
kHz10 zf
0dB
20dB
40dB
-20dB
0o
kHz300 pf
dB7.297.28 o couoGT
kHz33 zf
kHz 100 cf
¸¸¹
¨¨©�¸
¸¹
¨¨©�
2111
pp ZZ
ECEN5797100 KHz10 KHz1 KHz100 Hz10 Hz 1 MHz
-90o
-180o
om 53 M
ECEN4797/5797 Introduction to Power Electronics
ECEE Department, University of Colorado, Boulder
Add lag (PI) compensator
Integrator at low frequencies
ECEN5797
Choose 10fL < fc so that phase margin stays approximately the same: fL = 8 kHz
Keep the same cross-over frequency: dB 1545.5 o f cmcoc GGG
Adding PI Compensator
40dB
60dB
80dB
0dB
20dB
-20dB
0o
kHz8 Lf
Lf10
kHz 100 cf
ECEN5797
100 KHz10 KHz1 KHz100 Hz10 Hz 1 MHz
-90o
-180o
Lf 10/1
Lf
om 53 M
PI compensator phase
ECEN4797/5797 Introduction to Power Electronics
ECEE Department, University of Colorado, Boulder
Add lag (PI) compensator
Integrator at low frequencies
ECEN5797
Choose 10fL < fc so that phase margin stays approximately the same: fL = 8 kHz
Keep the same cross-over frequency: dB 1545.5 o f cmcoc GGG
Adding PI Compensator
40dB
60dB
80dB
0dB
20dB
-20dB
0o
kHz8 Lf
Lf10
kHz 100 cf
ECEN5797
100 KHz10 KHz1 KHz100 Hz10 Hz 1 MHz
-90o
-180o
Lf 10/1
Lf
om 53 M
PI compensator phase
ECEN4797/5797 Introduction to Power Electronics
ECEE Department, University of Colorado, Boulder
Complete analog PID compensator: summary
dB 1545.5 o cmG
kHz 33 zf
kHz 3001 pf
MHz 12 pf
kHz 8 Lf
ECEN5797
kHz 100 cf
53om M
(=1/10 of fs)Crossover frequency:
Phase margin:
Magnitude and phase Bode plots of T
40dB
60dB
80dB
0dB
20dB
40dB
-20dB
0o
kHz 100 cf
Phase of uncompensated Tu
ECEN5797100 KHz10 KHz1 KHz100 Hz10 Hz 1 MHz
-90o
-180o
om 53 M
Phase of compensated T
ECEN4797/5797 Introduction to Power Electronics
ECEE Department, University of Colorado, Boulder
Complete analog PID compensator: summary
dB 1545.5 o cmG
kHz 33 zf
kHz 3001 pf
MHz 12 pf
kHz 8 Lf
ECEN5797
kHz 100 cf
53om M
(=1/10 of fs)Crossover frequency:
Phase margin:
Magnitude and phase Bode plots of T
40dB
60dB
80dB
0dB
20dB
40dB
-20dB
0o
kHz 100 cf
Phase of uncompensated Tu
ECEN5797100 KHz10 KHz1 KHz100 Hz10 Hz 1 MHz
-90o
-180o
om 53 M
Phase of compensated T
ECEN4797/5797 Introduction to Power Electronics
ECEE Department, University of Colorado, Boulder
0
50Loop Gain
[db]
Verification: exact loop gain magnitude and phase responses (MATLAB)
kHz 105 cf
3 4 5 6-100
-50
mag
nitu
de
-100
-50
0
deg]
om 6.51 M
ECEN5797
103
104
105
106
-250
-200
-150
frequency [Hz]
phas
e [ m 6.5M
Analog PID compensator implementation
R2C2
C3
C4 R4
+
_
Vrefoutputvoltagesense
R1
2
vccontrolvoltage
¸̧·
¨̈§�¸
·¨§ � 11 L sZ
Design equations (approximate)
1
2
RR
Gcm 222
1CR
fL S
ECEN5797
¸¸¹
·¨¨©
§�¸
¸¹
·¨¨©
§�
¸̧¹
¨̈©�¸
¹¨©�
2111
11)(
pp
z
L
cmcss
sGsG
ZZ
Z1
� � 44121
CRRf z �
S 441 2
1CR
f p S
322 2
1CR
f p S
ECEN4797/5797 Introduction to Power Electronics
ECEE Department, University of Colorado, Boulder
0
50Loop Gain
[db]
Verification: exact loop gain magnitude and phase responses (MATLAB)
kHz 105 cf
3 4 5 6-100
-50
mag
nitu
de
-100
-50
0
deg]
om 6.51 M
ECEN5797
103
104
105
106
-250
-200
-150
frequency [Hz]
phas
e [ m 6.5M
Analog PID compensator implementation
R2C2
C3
C4 R4
+
_
Vrefoutputvoltagesense
R1
2
vccontrolvoltage
¸̧·
¨̈§�¸
·¨§ � 11 L sZ
Design equations (approximate)
1
2
RR
Gcm 222
1CR
fL S
ECEN5797
¸¸¹
·¨¨©
§�¸
¸¹
·¨¨©
§�
¸̧¹
¨̈©�¸
¹¨©�
2111
11)(
pp
z
L
cmcss
sGsG
ZZ
Z1
� � 44121
CRRf z �
S 441 2
1CR
f p S
322 2
1CR
f p S
ECEN4797/5797 Introduction to Power Electronics
ECEE Department, University of Colorado, Boulder
Verification of closed-loop responses
Closed-loop reference-to-output response
Closed-loop output impedance
and step-load transient response
ECEN5797
and step-load transient response
Construction of closed-loop T/(1+T) response
40dB
60dB
80dB
Closed-loop reference-to-output response v/vref = T/(1+T)
0dB
20dB
-20dB
-40dB
||v/vref||
Closed-loop BW | fc
ECEN5797
100 KHz10 KHz1 KHz100 Hz10 Hz 1 MHz
-60dB
-80dB
ECEN4797/5797 Introduction to Power Electronics
ECEE Department, University of Colorado, Boulder
Verification of closed-loop responses
Closed-loop reference-to-output response
Closed-loop output impedance
and step-load transient response
ECEN5797
and step-load transient response
Construction of closed-loop T/(1+T) response
40dB
60dB
80dB
Closed-loop reference-to-output response v/vref = T/(1+T)
0dB
20dB
-20dB
-40dB
||v/vref||
Closed-loop BW | fc
ECEN5797
100 KHz10 KHz1 KHz100 Hz10 Hz 1 MHz
-60dB
-80dB
ECEN4797/5797 Introduction to Power Electronics
ECEE Department, University of Colorado, Boulder
Closed-loop reference-to-output response
50
Reference-to-output response
-50
0
T/(
1+
T)
[db]
||v/vref||
ECEN5797
103
104
105
106
-100
Small-signal step-reference response
1.78
1.8
1.82
vo(t)10 mV step
(1.79 V to 1.8 V) in vref
4.8 5 5.2 5.4 5.6 5.8 6 6.2 6.4 6.6 6.8
x 10-4
4.8 5 5.2 5.4 5.6 5.8 6 6.2 6.4 6.6 6.8
x 10-4
0
5iL(t)
ECEN5797
x 10
4.8 5 5.2 5.4 5.6 5.8 6 6.2 6.4 6.6 6.8
x 10-4
0
0.5
d(t)
20 Ps/div
ECEN4797/5797 Introduction to Power Electronics
ECEE Department, University of Colorado, Boulder
Closed-loop reference-to-output response
50
Reference-to-output response
-50
0
T/(
1+
T)
[db]
||v/vref||
ECEN5797
103
104
105
106
-100
Small-signal step-reference response
1.78
1.8
1.82
vo(t)10 mV step
(1.79 V to 1.8 V) in vref
4.8 5 5.2 5.4 5.6 5.8 6 6.2 6.4 6.6 6.8
x 10-4
4.8 5 5.2 5.4 5.6 5.8 6 6.2 6.4 6.6 6.8
x 10-4
0
5iL(t)
ECEN5797
x 10
4.8 5 5.2 5.4 5.6 5.8 6 6.2 6.4 6.6 6.8
x 10-4
0
0.5
d(t)
20 Ps/div
ECEN4797/5797 Introduction to Power Electronics
ECEE Department, University of Colorado, Boulder
Small-signal step-reference response
1.78
1.8
1.82
vo(t)10 mV step
(1.79 V to 1.8 V) in vref
4.8 5 5.2 5.4 5.6 5.8 6 6.2 6.4 6.6 6.8
x 10-4
4.8 5 5.2 5.4 5.6 5.8 6 6.2 6.4 6.6 6.8
x 10-4
0
5iL(t)
1.795
1.8
1.805
1.81
Note: duty-cycle command does not
ECEN5797
x 10
4.8 5 5.2 5.4 5.6 5.8 6 6.2 6.4 6.6 6.8
x 10-4
0
0.5d(t)
20 Ps/div 4.7 4.72 4.74 4.76 4.78 4.8 4.82 4.84 4.86 4.88 4.9 4.92 4.94 4.96 4.98 5
x 10-4
1.78
1.785
1.79
2 Ps/div
command does not saturate, response
correlates very well with theory based on linear small-signal models
Output impedance
Synchronous buck open-loop output impedance
·§ 1
• L = 1 PH
• RL = 30 m:
• C = 200 PF
� �sLRsC
RsZ Lesrout �¸¹·
¨©§ � ||
1)(
ResrRL L
C
Zout
ECEN5797
• Resr = 0.8 m:
ECEN4797/5797 Introduction to Power Electronics
ECEE Department, University of Colorado, Boulder
Small-signal step-reference response
1.78
1.8
1.82
vo(t)10 mV step
(1.79 V to 1.8 V) in vref
4.8 5 5.2 5.4 5.6 5.8 6 6.2 6.4 6.6 6.8
x 10-4
4.8 5 5.2 5.4 5.6 5.8 6 6.2 6.4 6.6 6.8
x 10-4
0
5iL(t)
1.795
1.8
1.805
1.81
Note: duty-cycle command does not
ECEN5797
x 10
4.8 5 5.2 5.4 5.6 5.8 6 6.2 6.4 6.6 6.8
x 10-4
0
0.5d(t)
20 Ps/div 4.7 4.72 4.74 4.76 4.78 4.8 4.82 4.84 4.86 4.88 4.9 4.92 4.94 4.96 4.98 5
x 10-4
1.78
1.785
1.79
2 Ps/div
command does not saturate, response
correlates very well with theory based on linear small-signal models
Output impedance
Synchronous buck open-loop output impedance
·§ 1
• L = 1 PH
• RL = 30 m:
• C = 200 PF
� �sLRsC
RsZ Lesrout �¸¹·
¨©§ � ||
1)(
ResrRL L
C
Zout
ECEN5797
• Resr = 0.8 m:
ECEN4797/5797 Introduction to Power Electronics
ECEE Department, University of Colorado, Boulder
Open-loop output impedance: algebra on the graph
40dB:
60dB:
80dB:
ResrRL L
C
Zout
0dB:
20dB:
-20dB:
-40dB:
C
:�o: dB 5.30m 30LR
CZ/1 LZ
kHz 11 of
ECEN5797
100 KHz10 KHz1 KHz100 Hz10 Hz 1 MHz
-60dB:
-80dB:
-100dB:
:�o: dB 62m 8.0esrR
Construction of 1/(1+T)
40dB
60dB
80dB
0dB
20dB
40dB
-20dB
ECEN5797100 KHz10 KHz1 KHz100 Hz10 Hz 1 MHz
ECEN4797/5797 Introduction to Power Electronics
ECEE Department, University of Colorado, Boulder
Open-loop output impedance: algebra on the graph
40dB:
60dB:
80dB:
ResrRL L
C
Zout
0dB:
20dB:
-20dB:
-40dB:
C
:�o: dB 5.30m 30LR
CZ/1 LZ
kHz 11 of
ECEN5797
100 KHz10 KHz1 KHz100 Hz10 Hz 1 MHz
-60dB:
-80dB:
-100dB:
:�o: dB 62m 8.0esrR
Construction of 1/(1+T)
40dB
60dB
80dB
0dB
20dB
40dB
-20dB
ECEN5797100 KHz10 KHz1 KHz100 Hz10 Hz 1 MHz
ECEN4797/5797 Introduction to Power Electronics
ECEE Department, University of Colorado, Boulder
Construction of closed-loop output impedance
40dB:
60dB:
80dB:
TZ
Z outCLout �
1,
0dB:
20dB:
40dB:
-20dB:
-40dB:
ECEN5797100 KHz10 KHz1 KHz100 Hz10 Hz 1 MHz
-60dB:
-80dB:
-100dB:
Closed-loop output impedance Zout,CL
40dB:
60dB:
80dB:
TZ
Z outCLout �
1,
0dB:
20dB:
-20dB:
-40dB: 8 m:, -42 dB:
ECEN5797
100 KHz10 KHz1 KHz100 Hz10 Hz 1 MHz
-60dB:
-80dB:
-100dB: |||| ,CLoutZ
ECEN4797/5797 Introduction to Power Electronics
ECEE Department, University of Colorado, Boulder
Construction of closed-loop output impedance
40dB:
60dB:
80dB:
TZ
Z outCLout �
1,
0dB:
20dB:
40dB:
-20dB:
-40dB:
ECEN5797100 KHz10 KHz1 KHz100 Hz10 Hz 1 MHz
-60dB:
-80dB:
-100dB:
Closed-loop output impedance Zout,CL
40dB:
60dB:
80dB:
TZ
Z outCLout �
1,
0dB:
20dB:
-20dB:
-40dB: 8 m:, -42 dB:
ECEN5797
100 KHz10 KHz1 KHz100 Hz10 Hz 1 MHz
-60dB:
-80dB:
-100dB: |||| ,CLoutZ
ECEN4797/5797 Introduction to Power Electronics
ECEE Department, University of Colorado, Boulder
50Output impedance
Verification: closed-loop output impedance
-50
0
tput
impe
danc
e [d
bOhm
]
l d l
|||| outZopen-loop
ECEN5797
103
104
105
106
-100
Ou closed-loop
|||| ,CLoutZ
Step-load transient responses
1 78
1.8
1.82
vo(t)2.5-5 A step-load
transient
4.8 5 5.2 5.4 5.6 5.8 6 6.2 6.4 6.6 6.8
x 10-4
1.78
4.8 5 5.2 5.4 5.6 5.8 6 6.2 6.4 6.6 6.8
x 10-4
0
5iL(t)
ECEN5797
x 10
4.8 5 5.2 5.4 5.6 5.8 6 6.2 6.4 6.6 6.8
x 10-4
0
0.5
d(t)
20 Ps/div
ECEN4797/5797 Introduction to Power Electronics
ECEE Department, University of Colorado, Boulder
50Output impedance
Verification: closed-loop output impedance
-50
0
tput
impe
danc
e [d
bOhm
]
l d l
|||| outZopen-loop
ECEN5797
103
104
105
106
-100
Ou closed-loop
|||| ,CLoutZ
Step-load transient responses
1 78
1.8
1.82
vo(t)2.5-5 A step-load
transient
4.8 5 5.2 5.4 5.6 5.8 6 6.2 6.4 6.6 6.8
x 10-4
1.78
4.8 5 5.2 5.4 5.6 5.8 6 6.2 6.4 6.6 6.8
x 10-4
0
5iL(t)
ECEN5797
x 10
4.8 5 5.2 5.4 5.6 5.8 6 6.2 6.4 6.6 6.8
x 10-4
0
0.5
d(t)
20 Ps/div
ECEN4797/5797 Introduction to Power Electronics
ECEE Department, University of Colorado, Boulder
Step-load transient responses
1.78
1.8
1.82
vo(t)2.5-5 A step-load
transient
4.8 5 5.2 5.4 5.6 5.8 6 6.2 6.4 6.6 6.8
x 10-4
4.8 5 5.2 5.4 5.6 5.8 6 6.2 6.4 6.6 6.8
x 10-4
0
5iL(t)
1.795
1.8
1.805
1.81
ECEN5797
4.8 5 5.2 5.4 5.6 5.8 6 6.2 6.4 6.6 6.8
x 10-4
0
0.5
d(t)
20 Ps/div 4.7 4.72 4.74 4.76 4.78 4.8 4.82 4.84 4.86 4.88 4.9 4.92 4.94 4.96 4.98 5
x 10-4
1.78
1.785
1.79
'v | 15 mV|10 Ps settling
time
2 Ps/div
