System and method for LLC converter design

1. A method for designing an inductance-inductance-capacitance (LLC) power converter, the method comprising:

receiving, by a processor, power converter design parameters of the LLC power converter, wherein the LLC power converter comprises a switching bridge coupled to a primary winding of a transformer, a resonant inductor and a resonant capacitor coupled in series between the switching bridge and the primary winding of the transformer, and a secondary side circuit coupled to a secondary winding of the transformer, the power converter design parameters comprising:

a minimum DC input voltage V min and a maximum DC input voltage V max to be received by the switching bridge,

a minimum switching frequency f min and a maximum switching frequency f max of the switching bridge, and

a target output voltage V o and a target output power P o to be output by the secondary side circuit;

calculating, by the processor, a first power converter configuration comprising:

a calculated magnetizing inductance L mc of the primary winding equal to R e tan(φ)(2πf min ) −1 , wherein φ is a load angle complement equal to asin(V min V max −1 ), and R e is an equivalent reflected load resistance of the power converter,

a calculated resonant inductance L rc of the resonant inductor equal to L mc cos 2 (φ)(f max 2 f min −2 −1) −1 , and

a calculated resonant capacitance C rc of the resonant capacitor equal to L rc −1 (2πf max ) −2 ;

writing, by the processor, the first power converter configuration to a non-transitory computer readable medium;

determining layout component values based on the first power configuration; and

physically implementing the LLC power converter using the layout component values.

2. The method of claim 1 , wherein

the power converter design parameters further comprise a switching factor s that is equal to 2 when the switching bridge has a half-bridge configuration and that is equal to 1 when the switching bridge has a full-bridge configuration; and

the first power converter configuration further comprises a calculated turns ratio n c of the primary winding relative to the secondary winding of the transformer comprised in the power converter,

wherein n c is not less than 0.99V max (sV o ) −1 and is not greater than V max (sV o ) −1 ; and the equivalent reflected load resistance R e equals 8π −2 n c 2 V o 2 P o −1 .

3. The method of claim 1 , further comprising graphically displaying the first power converter configuration at a user terminal.

4. The method of claim 3 , wherein

the receiving the power converter design parameters comprises:

receiving a first set of cells in a spreadsheet, wherein values of the first set of cells comprise the power converter design parameters; and

the graphically displaying the first power converter configuration comprises:

displaying a second set of cells in the spreadsheet, wherein values of the second set of cells comprise the first power converter configuration.

5. The method of claim 1 , wherein the non-transitory computer readable medium is a file.

6. The method of claim 5 , further comprising:

receiving, by the processor, a list of available components; and

determining the layout component values comprises selecting, by the processor, layout component values in accordance with the list of available components and the first power converter configuration, the layout component values comprising:

an actual turns ratio n a of the transformer greater than c 1 n c and less than c 2 n c , wherein c 1 is not less than 0.75 and c 2 is not greater than 1.25,

an actual magnetizing inductance L m _ a of the primary winding of the transformer greater than c 1 L m _ c and less than c 2 L m _ c ;

an actual resonant inductance L r _ a of the resonant inductor greater than c 1 L r _ c and less than c 2 L r _ c ; and

an actual resonant capacitance C r _ a of the resonant capacitor greater than c 1 C r _ c and less than c 2 C r _ c .

7. The method of claim 6 , wherein the selecting the layout component values comprises at least one of:

selecting layout components from the list of available components such that the layout component values are closest to component values in the first power converter configuration; and

selecting layout components from the list of available components such that the layout component values jointly maximize a figure of merit in accordance with the first power converter configuration.

8. A power converter design system comprising a non-transitory computer-readable medium storing programming, wherein the programming comprises instructions to:

receive power converter design parameters of an inductance-inductance-capacitance (LLC) power converter, wherein the LLC power converter comprises a switching bridge coupled to a primary winding of a transformer, a resonant inductor and a resonant capacitor coupled in series between the switching bridge and the primary winding of the transformer, and a secondary side circuit coupled to a secondary winding of the transformer, the power converter design parameters comprising:

a minimum DC input voltage V min and a maximum DC input voltage V max to be received by the switching bridge,

a minimum switching frequency f min and a maximum switching frequency f max of the switching bridge, and

a target output voltage V o and a target output power P o to be output by the secondary side circuit; calculate a first power converter configuration comprising:

a calculated magnetizing inductance L mc of the primary winding equal to R e tan(φ)(2πf min ) −1 , wherein φ is a load angle complement equal to asin(V min V max −1 ), and R e is an equivalent reflected load resistance of the power converter,

a calculated resonant inductance L rc of the resonant inductor equal to L mc cos 2 (φ)(f max 2 f min −2 −1) −1 , and

a calculated resonant capacitance C rc of the resonant capacitor equal to L rc −1 (2πf max ) −2 ;

write the first power converter configuration to a non-transitory computer readable medium;

determine layout component values based on the first power configuration; and physically implement the LLC power converter using the layout component values.

9. The system of claim 8 , wherein

the power converter design parameters further comprise a switching factor s that is equal to 2 when the switching bridge has a half-bridge configuration and that is equal to 1 when the switching bridge has a full-bridge configuration; and

the first power converter configuration further comprises a calculated turns ratio n c of the primary winding relative to the secondary winding of a transformer comprised in the power converter,

wherein n c is not less than 0.99V max (sV o ) −1 and is not greater than V max (sV o ) −1 ; and the equivalent reflected load resistance R e equals 8π −2 n c 2 V o 2 P o −1 .

10. The system of claim 8 , wherein the programming further comprises instructions to graphically display the first power converter configuration at a user terminal.

11. The system of claim 10 , wherein

the instructions to receive the power converter design parameters comprise instructions to receive a first set of cells in a spreadsheet, wherein values of the first set of cells comprise the power converter design parameters; and

the instructions to graphically display the first power converter configuration comprise instructions to display a second set of cells in the spreadsheet, wherein values of the second set of cells comprise the first power converter configuration.

12. The system of claim 8 , wherein the non-transitory computer readable medium is a file.

13. The system of claim 12 , wherein the programming further comprises instructions to:

receive a list of available components; and

determine the layout component values by selecting the layout component values in accordance with the list of available components and the first power converter configuration, the layout component values comprising:

an actual turns ratio n a of the transformer greater than c 1 n c and less than c 2 n c , wherein c 1 is not less than 0.75 and c 2 is not greater than 1.25,

an actual magnetizing inductance L m of the primary winding of the transformer greater than c 1 L mc and less than c 2 L mc ;

an actual resonant inductance L r of the resonant inductor greater than c 1 L rc and less than c 2 L rc ; and

an actual resonant capacitance C r of the resonant capacitor greater than c 1 C cr and less than c 2 C rc .

14. The system of claim 13 , wherein the instructions to select the layout component values comprise at least one of:

instructions to select the layout component values from the list of available components such that the layout component values are closest to component values in the first power converter configuration; and

instructions to select the layout component values from the list of available components such that the layout component values jointly maximize a figure of merit in accordance with the first power converter configuration.

15. The system of claim 13 , wherein the programming further comprises instructions to:

apply the layout component values to the file, wherein the file is a layout representing a physical circuit for the power converter.

16. The system of claim 15 , wherein the programming further comprises instructions to synthesize the physical circuit in accordance with the layout.

17. A power conversion system comprising:

a switching bridge comprising a plurality of switches coupled to a DC power source having a minimum input voltage V min and a maximum input voltage V max ,

wherein the switching bridge is configured to switch at a frequency that is not less than a minimum frequency f min and that is not greater than a maximum frequency f max ;

a primary side circuit coupled to the switching bridge, the primary side circuit comprising a primary winding of a transformer; and

a secondary winding magnetically coupled to the primary winding through a core of the transformer, and

an output terminal coupled to the secondary winding and configured to supply an output voltage that is not greater than a maximum output voltage V o and an output power that is not greater than a maximum output power P o ;

wherein the transformer has a magnetizing inductance L m such that

L m is greater than c 1 R e (2πf min ) −1 tan(φ) and less than c 2 R e (2πf min ) −1 tan(φ), wherein

c 1 is not less than 0.75 and c 2 is not greater than 1.25,

φ is a load angle complement equal to asin(V min V max −1 ), and

R e is an equivalent reflected load resistance;

wherein the primary side circuit has a resonant inductance L r such that L r is greater than c 1 Lm(f max 2 f min −2 −1) −1 cos 2 (φ) and L r is less than c 2 L m (f max 2 f min −2 −1) −1 cos 2 (φ); and

wherein the primary side circuit has a resonant capacitance C r in series with the resonant inductance such that C r is greater than c 1 L r −1 (2πf max ) −2 and less than c 2 L r −1 (2πf max ) −2 .

18. The system of claim 17 , wherein

the switching bridge comprises two switches; and

the primary winding has a number of turns that is a multiple n times a number of turns of the secondary winding, wherein n is greater than c 1 V max (2V o ) −1 and less than c 2 V max (2V o ) −1 ; and

R e is not less than 8(πs) −2 (0.99V max ) 2 P o −1 and not greater than 8(πs) −2 V max 2 P o −1 , wherein s is a switching factor equal to 2.

19. The system of claim 17 , wherein

the switching bridge comprises four switches;

the primary winding has a number of turns that is a multiple n times a number of turns of the secondary winding, wherein n is greater than c 1 V max V o −1 and less than c 2 V max V o −1 ; and

R e is not less than 8π −2 (0.99V max ) 2 P o −1 and not greater than 8π −2 V max 2 P o −1 .