General Solution for the Steady-State Characteristics of the Series Resonant Converter Type k CCM Mode index k and subharmonic number 

General Solution for the Steady-State Characteristics of the Series Resonant Converter Type k CCM

Type k CCM Steady-State Solution Elliptical output characteristic with Control plane characteristic

Normalization with transformers

Type k CCM Waveforms Switch network output voltage Tank inductor current, odd k (ZCS) Tank inductor current, even k (ZVS)

Type k DCM Tank inductor current, odd k Tank inductor current, even k

Type k DCM Steady State Solution and Mode Boundaries Type k DCM, odd k Output voltage Mode boundaries and Type k DCM, even k Output current Mode boundaries and

Type k DCM Output plane Equivalent model odd k even k

CCM and DCM Boundaries

Complete SRC Characteristics Control Plane

SCR Output Characteristics Above Resonance

SRC Output Characteristics Selected Modes Below Resonance

The Parallel Resonant Converter Basic state plane analysis The discontinuous conduction mode (DCVM) Summary of converter characteristics Design methodologies

DC-DC Parallel Resonant Converter During each interval, the tank circuit reduces to

State plane trajectory

Averaging and flux linkage arguments

Averaging and flux linkage arguments

Steady-state solution

Steady state solution of state plane 1. Find expr Steady state solution of state plane 1. Find expr. for radii in subintervals 2 and 3 (Define angles ζ and ξ)

Steady state solution of state plane 2a. Find expr Steady state solution of state plane 2a. Find expr. for jL at end of subinterval 2 (ω0t = γ)

Steady state solution of state plane 2b. Find expr Steady state solution of state plane 2b. Find expr. for jL at start of subinterval 3 (ω0t = γ)

Steady state solution of state plane 2c. Equate expr Steady state solution of state plane 2c. Equate expr. for jL at end of subinterval 2 and (ω0t = γ) start of subinterval 3 (ω0t = γ)

Steady state solution of state plane 3a. Find expr Steady state solution of state plane 3a. Find expr. for mc at end of subinterval 2 (ω0t = γ)

Steady state solution of state plane 3b. Find expr Steady state solution of state plane 3b. Find expr. for mc at start of subinterval 3 (ω0t = γ)

Steady state solution of state plane 3c. Equate expr Steady state solution of state plane 3c. Equate expr. for mc at end of subinterval 2 and (ω0t = γ) start of subinterval 3 (ω0t = γ)

Steady state solution of state plane 4. Find expr Steady state solution of state plane 4. Find expr. for φ using jL and mc boundary matching conditions

Steady state solution of state plane 5 Steady state solution of state plane 5. Solve for JL1 and then M in terms of φ

Steady state solution of state plane 6 Steady state solution of state plane 6. Two possible trajectories for given M and J

Two possible trajectories for given M and J

Two possible trajectories for given M and J

CCM output plane characteristics