The Ideal Current Controller The ideal current controller causes the average inductor current to follow the control input: Large-signal and small-signal.

The Ideal Current ControllerThe ideal current controller causes the average inductor current to follow the control input:

Large-signal and small-signal averaged switch models, buck example:

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

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

hfs

s

sT

sTc

L

sssT

e

esi

si s

s

ωπωααα

α

+=

−++

≈−

−−

=−

−

1

1

)/(111

11 1

1)(ˆ)(ˆ

)/(1

)/(1

πω

πω

s

ssT

s

s

e s

+

−≈−

ππαα 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

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

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

'==

LTDD

F sg

1/A 1.01

2

1

21

=−+

=s

a

m TMMMF

Example (cont.)

kHz 2.81

2

1==

LCfo π

1==LC

RQ

47.047.01

1==

+

+= Q

LVRCFRVF

QQgm

gm

ckHz 3.1851 ==+= ogm

oc fRVF

ff

kHz 4.81 =≈ ccp fQf

kHz 39/2 =≈= cchfp Qfff

Duty-cycle control

Peak current-mode control (CPM)

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

ωπωααα

α

+=

−++

≈−

−−

=−

−

1

1

)/(111

11 1

1)(ˆ)(ˆ

)/(1

)/(1

πω

πω

s

ssT

s

s

e s

+

−≈−

kHz 32221

1

1

1

2

==+−

=+−

=πππα

α ss

a

shf

ff

mm

DD

ff

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

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

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