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Frequency Response

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Switched Inductor Power IC Design

Abstract

This chapter uses insight to explain how switched-inductor power supplies react and respond across frequency to dynamic fluctuations. It explains the guiding principles that govern two-port models to ultimately show how switched inductors reduce to simple current- and voltage-sourced networks. The material also shows how couple, shunt, and bypass capacitors and inductors respond individually and collectively with and without current- and voltage-limiting resistances. With this insight, deriving the frequency response of loaded bucks, boosts, and buck–boosts in continuous and discontinuous conduction is more insightful and easier to comprehend and apply. Along the way, this chapter introduces and explains capacitor and inductor poles, in- and out-of-phase left- and right-half-plane zeros, reversal poles and zeros, transitional LC frequency, LC quality and gain, peaking and damping effects, and other relevant concepts that help describe switched LC networks. Illustrative figures, equations, examples, and SPICE simulations complement discussions throughout.

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Abbreviations

CCM:

Continuous-conduction mode

CMOS:

Complementary metal–oxide–semiconductor

DCM:

Discontinuous-conduction mode

LED:

Light-emitting diode

SL:

Switched inductor

RSS:

Root sum of squares

A0:

Zero-/low-frequency gain

AGI:

Input transconductance

AGO:

Output transconductance

AHF:

High-frequency gain

AII:

Input current gain

AIO:

Output current gain

AN:

Norton gain

AT:

Thévenin gain

AVI:

Input voltage gain

AVO:

Output voltage gain

AZI:

Input transimpedance

AZO:

Output transimpedance

CB:

Bypass capacitor

CC:

Couple capacitor

CO:

Output capacitor

CS:

Shunt capacitor

dD:

Drain duty cycle

dO:

Output duty cycle

dE:

Energize duty cycle

dE':

Energize command

ΔiL:

CCM current ripple

fLC:

Transitional LC (resonant) frequency

fO:

Operating frequency

fSW:

Switching frequency

CG:

Gate capacitance

i:

Imaginary unit

iDO:

Duty-cycled current

iIN:

Input current

iL:

Inductor current

iN:

Norton current

iO:

Output current

is:

Small-signal current source

LC:

Couple inductor

LDO:

Duty-cycled inductance

LS:

Shunt inductor

LX:

Switched (transfer) inductor

pC:

Capacitor pole

pL:

Inductor pole

pLC:

LC double pole

pSW:

Switching pole

pX:

Reversal pole

QLC:

LC peak quality

RC:

Couple resistor/capacitor resistance

RDO:

Duty-cycled resistance

RI:

Current-limit resistor

RIN:

Input resistance

RL:

Inductor resistance

RLD:

Load resistance

RLD':

Equivalent load resistance

RN:

Norton resistance

RO:

Output resistance

RP:

Parallel resistance

RS:

Series resistance

RT:

Thévenin resistance

RV:

Voltage-limit resistor

sA:

Analog signal

sC:

Control signal

sI:

Input signal

sO:

Output signal

tC:

Conduction time

tD:

Drain time

tE:

Energize time

tO:

Output conduction time

tSW:

Switching period

vD:

Drain voltage

vE:

Energize voltage

vIN:

Input voltage/input

vL:

Inductor voltage

vO:

Output voltage/output

vs:

Small-signal voltage source

vT:

Thévenin voltage

ωO:

Angular frequency

zC:

Capacitor zero

zDO:

Duty-cycled zero

ZDO:

Duty-cycled impedance

zL:

Inductor zero

zX:

Reversal zero

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Rincón-Mora, G.A. (2023). Frequency Response. In: Switched Inductor Power IC Design. Springer, Cham. https://doi.org/10.1007/978-3-030-95899-2_5

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  • DOI: https://doi.org/10.1007/978-3-030-95899-2_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-95898-5

  • Online ISBN: 978-3-030-95899-2

  • eBook Packages: EngineeringEngineering (R0)

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