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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Online ISBN: 978-3-030-95899-2
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