1. Announcements Change in office hours for tomorrow, Thursday Feb. 21
On-campus office hours: 1:00 – 2:00, 3:00 – 4:00
Telephone office hours: 2:00 – 3:00
HW #5 due Friday, Feb. 29

2. Outline of discussion DIRECT MODELING APPROACH
How small-signal variations in the switching frequency affect the spectrum of the switch network output voltage vs1(t)
Passing the frequency-modulated voltage vs1(t) through the tank transfer function H(s) leads to amplitude modulation of the output voltage v(t)
How to recover the envelope of the output voltage and determine the small-signal control-to-output-envelope transfer function Genv(s)
PHASOR TRANSFORMATION APPROACH
Equivalent circuit modeling via the phasor transform
PSPICE simulation of Genv(s) using the phasor transform

3. Large signal phasor models of circuit elements
Express all circuit signals in phasor form and substitute into v-i equations for the circuit elements. Freqeuncy modulation is represented by imaginary resistors in inductor and capacitor models.

4. Small-signal phasor models of circuit elements
From perturbing and linearizing large signal equations/models. Split each large signal waveform into DC plus small signal and substitute into large signal equations for each circuit component:

5. Inductor equivalent circuit model

6. Inductor equivalent circuit model

7. Inductor equivalent circuit model

8. Modelling the switch network

9. One way

10. More general – model the switch network with an equivalent transformer

11. Steps

12. Steps

14. The generalized phasor transformer model

15. Power balance and current scaling for phasors defined using peak amplitudes

16. Power balance and current scaling for phasors defined using RMS amplitudes

17. Linearization of the phasor transformer model

18. Linearization of the phasor transformer model

19. Linearization of the phasor transformer model

20. Linearization of the transformer model

21. The linearized phasor transformer model Steady-state plus small-signal

22. Example: Full-bridge parallel resonant inverter 1
Example: Full-bridge parallel resonant inverter 1. Construct steady-state plus small-signal phasor model

23. Example: Full-bridge parallel resonant inverter 2
Example: Full-bridge parallel resonant inverter 2. Steady-state solution

24. Example: Full-bridge parallel resonant inverter 3
Example: Full-bridge parallel resonant inverter 3. Small-signal perturbation in output phasor

25. Example: Full-bridge parallel resonant inverter 3
Example: Full-bridge parallel resonant inverter 3. Small-signal perturbation in output phasor

26. Recovering the actual output envelope

27. Recovering the actual output envelope

28. Recovering the actual output envelope

29. Simulation using SPICE

30. SPICE inductor model

31. SPICE models

32. SPICE models

33. Example: Full-bridge parallel resonant inverter SPICE-compatible model

34. Recovering the actual output envelope in SPICE

35. Recovering the actual output envelope in SPICE