Soft Commutation Isolated DC-DC Converters pp 115-139 | Cite as

# Series Resonant Converter Operating Above the Resonant Frequency

## 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.

## Nomenclature

- V
_{i} Input DC voltage

- V
_{o} Output DC voltage

- P
_{o} Output power

- C
_{o} Output filter capacitor

- R
_{o} Output load resistor

- q and q
_{Co} Static gain

- f
_{s} Switching frequency [Hz]

- ω
_{s} Switching frequency [rad/s]

- 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

- z
Characteristic impedance

- 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 and its normalized value

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

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

- C
_{1}, C_{2}, C_{3}and C_{4} Capacitors

- C
_{r} Resonant capacitor

- v
_{Cr} Resonant capacitor voltage

- V
_{Co} Resonant capacitor peak voltage

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

- Q
Resonant capacitor charge

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

- i
_{Lr} Resonant inductor current

- I
_{Lr} Inductor fundamental peak current

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

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

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

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

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

_{1}and S_{2}- v
_{g1}and v_{g2} Switches drive signals

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

_{1}and S_{2}- i
_{C1}and i_{C2} Capacitors current

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

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

- γ, β, θ
State plane angles

- ∆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 (t

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

_{4}–t_{3})