# Half Bridge Capacitor Voltage-Clamped Series Resonant Converter

## Abstract

In this chapter, a topological variation of the series resonant converter, the half bridge capacitor voltage clamped series resonant converter, is studied. 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 static gain output characteristics are derived, using the state-plane trajectory analysis technique. In subsequent sections of the chapter, numerical example and numerical simulation are provided to illustrate the theoretical analysis. At the end of the chapter, proposed exercises with answers are included.

## Nomenclature

- V
_{i} Input DC voltage

- V
_{o} Output DC voltage

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

- P
_{o} Output power

- P
_{o min} Minimum output power

- P
_{o max} Maximum output power

- C
_{o} Output filter capacitor

- R
_{o} Output load resistor

- µ
_{o} Normalized switching frequency

- q
Static gain

- D
Duty cycle

- f
_{s} Switching frequency

- f
_{s max} Maximum switching frequency

- f
_{s min} Minimum switching frequency

- T
_{s} Switching period

- t
_{d} Dead time

- T
Transformer

- n
Transformer turns ratio

- N
_{1}and N_{2} Transformer primary and secondary winding turns

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

- \( \text{i}_{\text{o}} \)
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

- S
_{1}and S_{2} Switches

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

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

- C
_{r} Resonant capacitor

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

- i
_{Lr} Resonant inductor current

- I
_{Lr}\( \left( {\overline{{{\text{I}}_{\text{Lr}} }} } \right) \) Resonant inductor peak current and its normalized value, commutation current for S

_{1}and S_{3}- ω
_{o} Resonant frequency

- z
Characteristic impedance

- z
_{1}and z_{2} State plane impedance

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

- v
_{ab} Full bridge ac voltage, between points “a” and “b”

- v
_{S1}and v_{S2} Voltage across switch S

_{1}and S_{2}- i
_{S1}and i_{S2} Current in the switch S

_{1}and S_{2}- ∆t
_{1} Time interval of the first step of operation in (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 in (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 in (t

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

_{6}−t_{5})- I
_{S RMS}\( \left( {\overline{{{\text{I}}_{{{\text{S}}\,{\text{RMS}}}} }} } \right) \) Switches S

_{1}and S_{2}RMS currents and its normalized value- I
_{DC}\( \left( {\overline{{{\text{I}}_{\text{DC}} }} } \right) \) Diodes D

_{C1}and D_{C2}average currents and its normalized value

## Reference

- 1.Agrawal, J.P., Lee, C.Q.: Capacitor voltage clamped series resonant power supply with improved cross regulation. In: IEEE IAS Annual Meeting, pp. 1141–1146 (1989)Google Scholar