# Series Resonant Converter

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## 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.

## Keywords

Series Resonant Converter (SRC) Discontinuous Conduction Mode (DCM) State-plane Trajectory Resonant Capacitor Voltage Continuous Conduction Mode (CCM)## Nomenclature

- V
_{i} Input DC voltage

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

- V
_{o} Output DC voltage

- P
_{o} Nominal output power

- P
_{o min} Minimum output power

- C
_{o} Output filter capacitor

- R
_{o} Output load resistor

- R
_{o min} Minimum output load resistor

- q, q
_{co}, q_{c1} Static gain

- D
Duty cycle

- f
_{s} Switching frequency (Hz)

- ω
_{s} Switching frequency (rad/s)

- f
_{s min} Minimum switching frequency (Hz)

- f
_{s max} Maximum switching frequency (Hz)

- T
_{s} Switching period

- f
_{o} Resonant frequency (Hz)

- ω
_{o} Resonant frequency (rad/s)

- μ
_{o} Frequency ratio (f

_{s}/f_{o})- ρ
Frequency ratio

- t
_{d} Dead time

- T
Transformer

- n
Transformer turns ratio

- N
_{1}and N_{2} Transformer windings

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

- i
_{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 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

- S
_{1}, S_{2}, S_{3}and S_{4} Switches

- D
_{1}, D_{2}, D_{3}and D_{4} Diodes

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

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

- C
_{r} Resonant capacitor

- v
_{Cr}\( \left( {\overline{{{\text{v}}_{\text{Cr}} }} } \right) \) Resonant capacitor voltage

- V
_{Co} Resonant capacitor peak voltage

- V
_{C1} Resonant capacitor voltage at the end of time interval 1 and three

- i
_{Lr}\( \left( {\overline{{{\text{i}}_{\text{Lr}} }} } \right) \) Resonant inductor current and its normalized value

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

- I
_{L} Fundamental inductor peak current

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

- I
_{p1}and I_{p2}\( \left( {\overline{{{\text{I}}_{\text{p1}} }} \;\;{\text{and}}\;\;\overline{{{\text{I}}_{\text{p2}} }} } \right) \) Inductor peak current and its normalized value in DCM

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

- v
_{cb} Inductor voltage, between points “c” and “b”

- v
_{ab1} Fundamental ac voltage, between points “a” and “b”

- v
_{cb1} Fundamental inductor voltage, between points “c” and “b”

- v
_{ac} Voltage at the ac side of the rectifier, between points “a” and “c”

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

- i
_{S1}, i_{S2} Current in the switches

- ∆t
_{1} Time interval one (t

_{1}-t_{0})- ∆t
_{2} Time interval two (t

_{2}-t_{1})- ∆t
_{3} Time interval three (t

_{3}-t_{2})- ∆t
_{4} Time interval four (t

_{4}-t_{3})- ∆t
_{5} Time interval five (t

_{5}-t_{4})- ∆t
_{6} Time interval six (t

_{6}-t_{5})- A
_{1}and A_{2} Area

- x
_{Lr}, x_{CR}and x Reactance

- Q
Capacitor charge

- z
Characteristic impedance

- R
_{1}, R_{2} State plane radius

- ϕ
_{r}, ϕ_{o}, β, θ State plane angles

## References

- 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.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.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