1 ECEN5807 CPM. 2 3 4 5 6 7 8 9 10 ECEN5807 CPM.

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High-frequency pole(from the accurate averaged model (4))

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Compare to first-order approximation of the sampled-data control-to-current model

hfs

s

sT

sTc

L

sssT

e

esi

si s

s

1

1

)/(11

1

11

1

1

)(ˆ)(ˆ

)/(1

)/(1

s

ssT

s

s

e s

s

a

shf

f

mm

DD

ff

2

221

1

1

1

Control-to-inductor current response behaves approximately as a single-pole transfer function with a high-frequency pole at

Model (4) is consistent with the sampled-data small-signal model

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DC gain of line-to-output Gvg-cpm(based on model (4))

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Example

• CPM buck converter: Vg = 10V, L = 5 H, C = 75 F, D = 0.5, V = 5 V,

I = 20 A, R = V/I = 0.25 , fs = 100 kHz

• Inductor current slopes:m1 = (Vg – V)/L = 1 A/s

m2 = V/L = 1 A/sD = 0.5: CPM controller is stable for any compensation ramp, ma/m2 > 0

Select: ma/m2 = Ma/M2 = 1, Ma = 1 A/s

A/V 25.02

'

L

TDDF sg

1/A 1.01

2

1

21

s

a

m TMMM

F

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Example (cont.)

kHz 2.81

2

1

LCfo

1L

CRQ

47.047.01

1

Q

L

VRCFR

VF

QQgm

gm

ckHz 3.1851 ogm

oc fR

VFff

kHz 4.81 ccp fQf

kHz 39/2 cchfp Qfff

Duty-cycle control

Peak current-mode control (CPM)

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Compare to first-order approximation of the high-frequency sampled-data control-to-current model

hfs

s

sT

sTc

L

sssT

e

esi

si s

s

1

1

)/(11

1

11

1

1

)(ˆ)(ˆ

)/(1

)/(1

s

ssT

s

s

e s

kHz 32221

1

1

1

2

ss

a

shf

ff

m

mDD

ff

Control-to-inductor current response behaves approximately as a single-pole transfer function with a high-frequency pole at

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2nd-order approximation in the small-signal averaged model

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2nd-order approximation in the small-signal averaged model