Series Resonant Converter

• Ivo Barbi
• Fabiana Pöttker
Chapter
Part of the Power Systems book series (POWSYS)

Abstract

This chapter presents and describes the operation of the Series Resonant Converter (SRC). After the presentation of the power converter topology, the qualitative analysis is presented, which includes the description of operation, topological states for each time interval and relevant waveforms. Closed-form solutions for the output characteristics are derived, using the state-plane trajectory analysis technique. Simplified analysis utilizing the first harmonic approximation technique is also included. Both continuous and discontinuous conduction mode are discussed and analyzed. Also included are numerical examples to illustrate the theoretical analysis, proposed exercises with solutions and numerical simulations.

Nomenclature

Vi

Input DC voltage

V1

Half of the DC input voltage

Vo

Output DC voltage

Po

Nominal output power

Po min

Minimum output power

Co

Output filter capacitor

Ro

Ro min

q, qco, qc1

Static gain

D

Duty cycle

fs

Switching frequency (Hz)

ωs

fs min

Minimum switching frequency (Hz)

fs max

Maximum switching frequency (Hz)

Ts

Switching period

fo

Resonant frequency (Hz)

ωo

μo

Frequency ratio (fs/fo)

ρ

Frequency ratio

td

T

Transformer

n

Transformer turns ratio

N1 and N2

Transformer windings

$${{{\text{V}}_{\text{o}}^{{\prime }} }}$$

Output DC voltage referred to the transformer primary side

io

Output current

$${{{\text{I}}_{\text{o}}^{{\prime }} }}$$

Output current referred to the transformer primary side

$${{{\text{I}}_{\text{o}}^{{\prime }} }}$$$$\left( {\overline{{{\text{I}}_{\text{o}}^{{\prime }} }} } \right)$$

Average output current referred to the transformer primary side and its normalized value in CCM

$$\left( {\overline{{{\text{I}}_{{{\text{o}}\,{ \hbox{max} }}}^{{\prime }} }} } \right)$$

Maximum normalized average output current referred to the transformer primary in CCM

$$\left( {\overline{{{\text{I}}_{{{\text{o}}\,{ \hbox{min} }}}^{{\prime }} }} } \right)$$

Minimum normalized average output current referred to the transformer primary in CCM

$${{{\text{I}}_{{{\text{o}}\,{\text{D}}}}^{{\prime }} }}$$$$\left( {\overline{{{\text{I}}_{{{\text{o}}\,{\text{D}}}}^{{\prime }} }} } \right)$$

Average output current in DCM referred to the transformer primary side and its normalized value

$${{{\text{I}}_{\text{o}}^{{\prime }} }}$$SC

Short circuit average output current

S1, S2, S3 and S4

Switches

D1, D2, D3 and D4

Diodes

vg1 and vg2

Switches gate signals

Lr

Resonant inductor (may include the transformer leakage inductance)

Cr

Resonant capacitor

vCr$$\left( {\overline{{{\text{v}}_{\text{Cr}} }} } \right)$$

Resonant capacitor voltage

VCo

Resonant capacitor peak voltage

VC1

Resonant capacitor voltage at the end of time interval 1 and three

iLr$$\left( {\overline{{{\text{i}}_{\text{Lr}} }} } \right)$$

Resonant inductor current and its normalized value

ILr$$\left( {\overline{{{\text{I}}_{\text{Lr}} }} } \right)$$

Inductor peak current and its normalized value, commutation

IL

Fundamental inductor peak current

I1$$\left( {\overline{{{\text{I}}_{ 1} }} } \right)$$

Inductor current at the end of the first and third step of operation and its normalized value in CCM

Ip1 and Ip2$$\left( {\overline{{{\text{I}}_{\text{p1}} }} \;\;{\text{and}}\;\;\overline{{{\text{I}}_{\text{p2}} }} } \right)$$

Inductor peak current and its normalized value in DCM

vab

Full bridge ac voltage, between points “a” and “b”

vcb

Inductor voltage, between points “c” and “b”

vab1

Fundamental ac voltage, between points “a” and “b”

vcb1

Fundamental inductor voltage, between points “c” and “b”

vac

Voltage at the ac side of the rectifier, between points “a” and “c”

vS1, vS2

Voltage across switches

iS1, iS2

Current in the switches

∆t1

Time interval one (t1-t0)

∆t2

Time interval two (t2-t1)

∆t3

Time interval three (t3-t2)

∆t4

Time interval four (t4-t3)

∆t5

Time interval five (t5-t4)

∆t6

Time interval six (t6-t5)

A1 and A2

Area

xLr, xCR and x

Reactance

Q

Capacitor charge

z

Characteristic impedance

R1, R2

ϕr, ϕo, β, θ

State plane angles

References

1. 1.
Schwarz, F.C.: An improved method of resonant current pulse modulation for power converters. IEEE Trans. Ind. Electron. Control Instrum. IECI-23(2), 133–141 (1976)Google Scholar
2. 2.
Schwarz, F.C., Klaassens, B.J.: A 95-percent efficient 1-kW DC converter with an internal frequency of 50 kHz. IEEE Trans. Ind. Electron. Control Instrum. IECI-24(4), 326–333 (1978)Google Scholar
3. 3.
Witulski, A.F., Erickson, R.W.: Steady-state analysis of the series resonant converter. IEEE Trans. Aerosp. Electron. Syst. AES-21(6), 791–799 (1985) Google Scholar