Series Resonant Converter Operating Above the Resonant Frequency

• 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) operating above the resonant frequency. 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. Solved problem is used to illustrate the theoretical analysis, along with numerical simulation. Proposed problems with answers are included at the end of the chapter.

Keywords

Series Resonant Converter (SRC) State-plane Trajectory Relevant Waveforms Commutation Capacitors Soft Commutation
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Nomenclature

Vi

Input DC voltage

Vo

Output DC voltage

Po

Output power

Co

Output filter capacitor

Ro

q and qCo

Static gain

fs

Switching frequency [Hz]

ωs

fs max

Maximum switching frequency

fs min

Minimum switching frequency

Ts

Switching period

fo

Resonant frequency [Hz]

ωo

μo

Frequency ratio

z

Characteristic impedance

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 and its normalized value

S1, S2, S3 and S4

Switches

D1, D2, D3 and D4

Diodes

C1, C2, C3 and C4

Capacitors

Cr

Resonant capacitor

vCr

Resonant capacitor voltage

VCo

Resonant capacitor peak voltage

VC1

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

Q

Resonant capacitor charge

Lr

Resonant inductor (may include the transformer leakage inductance)

iLr

Resonant inductor current

ILr

Inductor fundamental peak current

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

Inductor current at the end of the first and fourth step of operation and its normalized value

vab

AC voltage, between points “a” and “b”

vcb

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

vab1

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

vcb1

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

vS1 and vS2

Voltage across switches S1 and S2

vg1 and vg2

Switches drive signals

iS1 and iS2

Current in the switches S1 and S2

iC1 and iC2

Capacitors current

xLr, xCR and x

Reactance

R1, R2

γ, β, θ

State plane angles

∆t1

Time interval of the first step of operation in (t1–t0)

∆t2

Time interval of the second step of operation (t2–t1)

∆t3

Time interval of the third step of operation (t3–t2)

∆t4

Time interval of the fourth step of operation (t4–t3)