ECEN5817 Lecture 4. Transfer function H(s) ) (t) i R. (t) v R

Transcription

1 ECEN5817 Lecture 4 A resonant dc-dc converter: Transfer function H(s) ) dc source v g i s L C s i R i v s v R v R N S N T N R N F Switch network Resonant tank network Rectifier network Low-pass dc filter load network If tank responds primarily to fundamental component of switch network output voltage waveform, then harmonics can be neglected Section 19.1: modeling based on sinusoidal approximation 1

2 The sinusoidal approximation Switch output voltage spectrum Resonant tank response Tank current spectrum Tank current and output voltage are essentially f s 3f s 5f s f sinusoids at the switching frequency f s f s 3f s 5f s f Neglect harmonics of switch output voltage waveform, and model only the fundamental component Remaining ac waveforms can be found via standard phasor analysis f s 3f s 5f s f 2

3 Controlled switch network model N S i s 1 v g 2 2 v s 1 Switch network Fourier series expansion of square-wave switch network output voltage v s : The fundamental component is So model switch network output port with voltage source of value v s1 3

4 Model of switch network input port N S i s Find dc (average) component of the switch network input current 1 v g 2 2 v s 1 Switch network Fundamental component of the output current: 4

5 Switch network: equivalent circuit Switch network converts dc to ac Dc components of input port waveforms are modeled Fundamental ac components of output port waveforms are modeled Model is power conservative: predicted average input and output powers are equal 5

6 Model is power conservative Use trig identity: 6

7 Modeling the rectifier and capacitive filter networks i R i R i v R v R N R Rectifier network N F Low-pass filter network dc load Assume large output filter capacitor, having small ripple. v R is a square wave, having zero crossings in phase with tank output current i R. If i R is a sinusoid: Then v R has the following Fourier series: 7

8 Sinusoidal approximation: rectifier Again, since tank responds only to fundamental components of applied waveforms, harmonics in v R can be neglected. v R becomes 8

9 Rectifier dc output port model v R i R i R i v R Output capacitor charge balance: dc load current is equal to average rectified tank output current N R Rectifier network N F Low-pass filter network dc load Hence 9

10 Equivalent circuit of rectifier Rectifier input port: Fundamental components of current and voltage are sinusoids that are in phase Hence rectifier presents a resistive load to tank network Effective resistance R e is Rectifier equivalent circuit With a resistive load R, this becomes Loss free resistor: all power absorbed by R e is transferred to the output port 10

11 Resonant tank network Model of ac waveforms is now reduced to a linear circuit. Tank network is excited by effective sinusoidal voltage (switch network output port), and is load by effective resistive load (rectifier input port) Can solve for transfer function via conventional linear circuit analysis 11

12 Solution of tank network waveforms 12

13 Solution of converter voltage conversion ratio M = V/V g 13