22.1 Analysis of a half-bridge dc-dc parallel resonant converter, operated above resonance. In Fig. 22.58, the elements Co, LF, and CF are large in value and have negligible switching ripple. You may assume that all elements are ideal. You may use the sinusoidal approximation as appropriate.
(a)
i(t)
L = 10 H
Vg = 160V
v(t)
(b)
Vg
f = 1/T
0
0
0.5T
Ts
Fig. 22.58 Half-bridge parallel resonant converter of Problem 22.1: (a) schematic, (b) switch voltage waveform
(a) Sketch the waveform of the current i(t). (b) Construct an equivalent circuit for this converter, similar to Fig. 22.22, which models the fundamental components of the tank waveforms and the dc components of the converter input current and output voltage. Clearly label the values and/or give expressions for all elements in your model, as appropriate. (c) Solve your model to derive an expression for the conversion ratio V/Vg = MF,Q,n. At rated (maximum) load, this converter produces I = 20 A at V = 3.3 V. (d) What is the converter switching frequency f at rated load? (e) What is the magnitude of the peak transistor current at rated load? At minimum load, the converter produces I = 2 A at V = 3.3 V. (f) What is the converter switching frequency f at minimum load? (g) What is the magnitude of the peak transistor current at minimum load? Compare with your answer from part (e). What happens to the conduction loss and efficiency at minimum load?
Transfer function H(s)
i(t)
iR1(t)
L = 888
C
VRI(1) < R.
vf = cos(t) 4Vg sin(t)
Parallel tank network
R
Fig. 22.22 Equivalent circuit for the parallel resonant converter, which models the fundamental components of the tank waveforms and the dc components of the converter input current and output voltage