Fundamentals of Power Electronics 1Chapter 19: Resonant Conversion

19.4.4 Design Example

Select resonant tank elements to design a resonant inverter that meets the following requirements:

• Switching frequency fs = 100 kHz

• Input voltage Vg = 160 V

• Inverter is capable of producing a peak open circuit output voltage of 400 V

• Inverter can produce a nominal output of 150 Vrms at 25 W

Fundamentals of Power Electronics 2Chapter 19: Resonant Conversion

Preliminary calculations

The requirements imply that the inverter tank circuit have an open-circuit transfer function of:

The required short-circuit current can be found by solving the elliptical output characteristic for Isc:

hence

Use the requirements to evaluate the above:

Fundamentals of Power Electronics 3Chapter 19: Resonant Conversion

Matched load

Matched load therefore occurs at the operating point

Hence the tank should be designed such that its output impedance is

Fundamentals of Power Electronics 4Chapter 19: Resonant Conversion

Solving for the tank elements

Let’s design an LCC tank network for this example

The impedances of the series and shunt branches can be represented by the reactances

Fundamentals of Power Electronics 5Chapter 19: Resonant Conversion

Analysis in terms of Xs and Xp

The transfer function is given by the voltage divider equation:

The output impedance is given by the parallel combination:

Solve for Xs and Xp:

Fundamentals of Power Electronics 6Chapter 19: Resonant Conversion

Evaluate tank element values

The capacitance Cp should therefore be chosen as follows:

The reactance of the series branch should be

Fundamentals of Power Electronics 7Chapter 19: Resonant Conversion

DiscussionChoice of series branch elements

The series branch is comprised of two elements L and Cs, but there is only one design parameter: Xs = 733 Ω. Hence, there is an additional degree of freedom, and one of the elements can be arbitrarily chosen.

This occurs because the requirements are specified at only one operating frequency. Any choice of L and Cs, that satisfies Xs = 733 Ω will meet the requirements, but the behavior at switching frequencies other than 100 kHz will differ.

Given a choice for Cs, L must be chosen according to:

For example, Cs = 3Cp = 3.2 nF leads to L = 1.96 µH

Fundamentals of Power Electronics 8Chapter 19: Resonant Conversion

Rcrit

For the LCC tank network chosen, Rcrit is determined by the parameters of the output ellipse, i.e., by the specification of Vg, Voc, and Isc. Note that Zo is equal to jXp. One can find the following expression for Rcrit:

Since Zo0 and H are determined uniquely by the operating point requirements, then Rcrit is also. Other, more complex tank circuits may have more degrees of freedom that allow Rcrit to be independently chosen.

Evaluation of the above equation leads to Rcrit = 1466 Ω. Hence ZVS for R < 1466 Ω, and the nominal operating point with R = 900 Ω has ZVS.