Soft Commutation Isolated DC-DC Converters pp 93-113 | Cite as

# Half Bridge CVC-PWM Series Resonant Converter

## Abstract

This chapter studies a capacitor voltage clamped series resonant converter, regulated at constant frequency by pulse-width modulation (PWM-CVC-SRC). The principle of operation, topological states and relevant waveforms are described, after the presentation of the converter power stage diagram. Theoretical analysis is carried out, using the state-plane trajectory approach, which gives the static gain and output characteristics. In the subsequent sections, simplified design example and methodology are provided, along with simulation results. Proposed exercises with answers are included at the end of the chapter.

## Nomenclature

- V
_{i} DC Bus voltage

- V
_{1} Half of the DC Bus voltage

- V
_{o} Output DC voltage

- P
_{o} Output power

- P
_{o min} Minimum output power

- C
_{o} Output filter capacitor

- R
_{o} Output load resistor

- q
Static gain

- D
Duty cycle

- D
_{max} Maximum duty cycle

- D
_{min} Minimum duty cycle

- f
_{s} Switching frequency

- f
_{s max} Maximum switching frequency

- f
_{s min} Minimum switching frequency

- T
_{s} Switching period

- f
_{o} Resonant frequency [Hz]

- ω
_{o} Resonant frequency [rad/s]

- μ
_{o} Frequency ratio

- \( {\text{V}}^{\prime}_{\text{o}} \)
Output DC voltage referred to the transformer primary side

- i
_{o} Output current

- \( {\text{i}}^{\prime}_{\text{o}} \)
Output current referred to the transformer primary side

- \( {\text{i}}^{\prime}_{\text{o}} \left( {\overline{{{\text{I}}^{\prime}_{\text{o}} }} } \right) \)
Average output current referred to the transformer primary and its normalized value

- I
_{o min} Minimum average output current

- \( {\text{i}}^{\prime}_{{{\text{o}}\,\hbox{min} }} \)
S

_{2}—main switches- S
_{3}and S_{4} Auxiliary switches

- v
_{g1}, v_{g2}, v_{g3}and v_{g4} Switches gate signals

- \( \text{S}_{1} \text{and} \, \text{S}_{2}\)
main switches

- D
_{C1}and D_{C2} Clamping diodes

- C
_{r} Resonant capacitors

- L
_{r} Resonant inductor (may include the transformer leakage inductance)

- z
Characteristic impedance

- i
_{Lr} Resonant inductor current

- v
_{Cr} Resonant capacitor voltage

- \( {\text{I}}_{1} \left( {\overline{{{\text{I}}_{1} }} } \right) \)
Inductor current at the end of the first step of operation and its normalized value

- \( {\text{I}}_{2} \left( {\overline{{{\text{I}}_{2} }} } \right) \)
Resonant inductor peak current and its normalized value

- \( {\text{I}}_{3} \left( {\overline{{{\text{I}}_{3} }} } \right) \)
Inductor current at the end of the third step of operation and its normalized value

- v
_{ab} AC voltage, between points “a” and “b”

- v
_{S1}, v_{S2}, v_{S3}and v_{S4} Voltage across switches

- i
_{S1}, i_{S2}, i_{S3}and i_{S4} Switches currents

- ∆t
_{1} Time interval of the first step of operation (t

_{1}−t_{0})- ∆t
_{2} Time interval of the second step of operation (t

_{2}–t_{1})- ∆t
_{3} Time interval of the third step of operation (t

_{3}–t_{2})- ∆t
_{4} Time interval of the fourth step of operation (t

_{4}–t_{3})- ∆t
_{5} Time interval of the fifth step of operation (t

_{5}–t_{4})- ∆t
_{6} Time interval of the sixth step of operation (t

_{6}–t_{5})- ∆t
_{7} Time interval of the seventh step of operation (t

_{7}–t_{6})- ∆t
_{8} Time interval of the eighth step of operation (t

_{8}–t_{7})- ∆t
_{9} Time interval of the ninth step of operation (t

_{9}–t_{8})- ∆t
_{10} Time interval of the tenth step of operation (t

_{10}–t_{9})- ϕ, θ
_{o}, θ_{r}, θ State plane angle

- \( \overline{{{\text{r}}_{1} }} \,{\text{and}}\,\overline{{{\text{r}}_{ 2} }} \)
State plane radius

## Reference

- 1.Freitas Vieira, J.L., Barbi, I.: Constant frequency PWM capacitor voltage-clamped series resonant power supply. IEEE Trans. Power Electron.
**8**(2), 120–126 (1993)CrossRefGoogle Scholar