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Control Loops

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Switched Inductor Power IC Design

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Abstract

This chapter uses insight to show how feedback loops control switched-inductor dc–dc power supplies. It explains how pulse-width-modulated (PWM), hysteretic, and constant-time peak/valley loops switch the inductor, offset the current or voltage they control, and respond to fast input or output variations. It also illustrates how summing comparators can contract control loops and remove the loading effect that current-mode voltage loops normally exhibit. The handbook ends with compact, fast, and low-cost resistive, filtered, and voltage-mode voltage-looped (voltage-squared) bucks. Along the way, the material introduces and reviews comparators, hysteretic comparators, summing comparators, pulse-width modulators, SR flip flops, pulse generators, sub-harmonic oscillations, and slope compensation. Design notes and illustrative figures, equations, examples, and SPICE simulations complement discussions throughout.

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Abbreviations

LED :

Light-emitting diode

OCP:

Over-current protection

PWM:

Pulse-width modulator

SL:

Switched inductor

SR:

Set–reset flip flop

AE:

Error amplifier

AIE:

Current-error amplifier

AG:

Transconductance gain

AG0:

Static low/zero-frequency transconductance gain

ALG:

Loop gain

APWM:

PWM gain translation

AV0:

Static low/zero-frequency voltage gain

βFB:

Feedback translation

βIFB:

Current-feedback translation

CLDC:

Load-compensation capacitor

CPE:

Error comparator

CPHYS:

Hysteretic comparator

CPPWM:

PWM comparator

CPT:

Time-loop comparator

dD:

Drain duty cycle

dE:

Energize duty cycle

dE′:

Energize duty-cycle command

dO:

Output duty cycle

dOFF:

Off duty cycle

dON:

On duty cycle

ΔiLD:

Load-dump current

ΔvT:

Hysteresis voltage

f0dB:

Unity-gain frequency

fCLK:

Clock frequency

fI0dB:

Current loop’s unity-gain frequency

fSW:

Switching frequency

iL:

Inductor current

iLD:

Load current

iO:

Output current

KO:

Overdrive factor

LC:

Capacitor’s equivalent series inductance

LX:

Switched transfer inductor

pBW:

Bandwidth-setting pole

pC:

Capacitor pole

pHYS:

Hysteretic pole

pIBW:

Current loop’s bandwidth

pLC:

LC double pole

pLD:

Load-compensation pole

Q:

Current state

Q−1:

Previous state

\( \overline{\mathrm{Q}} \) :

Opposite/complementary state

R:

Reset flip-flop terminal

RC:

Capacitor’s equivalent series resistance

RL:

Inductor’s equivalent series resistance

RLDC:

Load-compensation resistor

S:

Set flip-flop terminal

SROFF:

Off-time flip flop

SRON:

On-time flip flop

SRPK:

Peak-current flip flop

SRVL:

Valley-current flip flop

ΣvID:

Differential sum

tCLK:

Clock period

tE:

Energize time

tLC:

LC’s resonant period

tO:

Output pulse width

tOFF:

Off time

tON:

On time

tOSC:

Oscillating period

tP:

Propagation delay

tP(BW):

Bandwidth propagation delay

tP(SR):

Slew-rate propagation delay

tR:

Response time

tSR:

SR flip flop’s propagation delay

tSW:

Switching period

τBW:

Bandwidth-setting time constant

τHYS:

Hysteretic time constant

vD:

Drain voltage

vDD:

Positive power supply

vE:

Energize voltage

vEO:

Amplified error voltage

vFB:

Feedback voltage

vHOS:

Hysteretic offset voltage

vI:

Input voltage

vID:

Differential input voltage

vIDI:

Differential current-mode input voltage

vIDV:

Differential voltage-mode input voltage

vIFB:

Current-feedback voltage

vIN:

Input/input voltage/input power supply

vIO:

Amplified current-error voltage

vIOS:

Current-loop offset

vIR:

Current-reference voltage

vL:

Inductor voltage

vLD:

Loading-effect voltage

vLOS:

Loop-offset voltage

vN:

Negative input

vO:

Output/output voltage

VOH:

Output high

VOL:

Output low

vP:

Positive input

vPOS:

Projection offset voltage

vR:

Reference voltage

vS:

Sawtooth voltage

vSOS:

Slope compensation offset voltage

vSS:

Negative power supply

vSW:

Switch-node voltage

vT(HI):

Rising trip point

vT(LO):

Falling trip point

vVOS:

Voltage-loop offset

zC:

Capacitor zero

zDO:

Duty-cycled zero

Author information

Authors and Affiliations

  1. School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA, USA

    Gabriel Alfonso Rincón-Mora

Authors
  1. Gabriel Alfonso Rincón-Mora
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© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

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Cite this chapter

Rincón-Mora, G.A. (2023). Control Loops. In: Switched Inductor Power IC Design. Springer, Cham. https://doi.org/10.1007/978-3-030-95899-2_7

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  • DOI: https://doi.org/10.1007/978-3-030-95899-2_7

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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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