Presentation is loading. Please wait.

Presentation is loading. Please wait.

AC modeling of converters containing resonant switches

Similar presentations

Presentation on theme: "AC modeling of converters containing resonant switches"— Presentation transcript:

1 AC modeling of converters containing resonant switches
State-Space Averaging: see textbook section 7.3 Averaged Circuit Modeling and Circuit Averaging: see textbook section 7.4

2 Averaged Switch Modeling
Separate switch elements from remainder of converter Remainder of converter consists of linear circuit The converter applies signals xT to the switch network The switch network generates output signals xs We have solved for how xs depends on xT

3 Block diagram of converter
Switch network as a two-port circuit:

4 The linear time-invariant network

5 The circuit averaging step
To model the low-frequency components of the converter waveforms, average the switch output waveforms (in xs(t)) over one switching period.

6 Relating the result to previously-derived PWM converter models: a buck is a buck, regardless of the switch We can do this if we can express the average xs(t) in the form

7 PWM switch: finding Xs1 and Xs2

8 Finding µ: ZCS example where, from previous slide,

9 Derivation of the averaged system equations of the resonant switch converter
Equations of the linear network (previous Eq. 1): Substitute the averaged switch network equation: Result: Next: try to manipulate into same form as PWM state-space averaged result

10 Conventional state-space equations: PWM converter with switches in position 1
In the derivation of state-space averaging for subinterval 1: the converter equations can be written as a set of linear differential equations in the following standard form (Eq. 7.90): These equations must be equal: Solve for the relevant terms: But our Eq. 1 predicts that the circuit equations for this interval are:

11 Conventional state-space equations: PWM converter with switches in position 2
Same arguments yield the following result: and

12 Manipulation to standard state-space form
Eliminate Xs1 and Xs2 from previous equations. Result is: Collect terms, and use the identity µ + µ’ = 1: —same as PWM result, but with d  µ

13 Perturbation and Linearization
The switch conversion ratio µ is generally a fairly complex function. Must use multivariable Taylor series, evaluating slopes at the operating point:



16 Small signal model Substitute and eliminate nonlinear terms, to obtain: Same form of equations as PWM small signal model. Hence same model applies, including the canonical model of Section 7.5. The dependence of µ on converter signals constitutes built-in feedback.

17 Salient features of small-signal transfer functions, for basic converters

18 Parameters for various resonant switch networks

19 Example 1: full-wave ZCS Small-signal ac model

20 Low-frequency model

21 Example 2: Half-wave ZCS quasi-resonant buck

22 Small-signal modeling

23 Equivalent circuit model

24 Low frequency model: set tank elements to zero

25 Predicted small-signal transfer functions Half-wave ZCS buck

Download ppt "AC modeling of converters containing resonant switches"

Similar presentations

Ads by Google