Patent ID: 8725441

Claim:
A method of setting capacitance values for a matching network having a pi configuration, comprising steps: using a controller circuit coupled to said matching network, computing a target susceptance b ant — shunt,tgt of an antenna side shunt of said matching network, said antenna side shunt including an antenna side variable capacitor, using the formula: b 3 - out , target = 1 x 2 - ( 1 2 ⁢ x 2 2 ) 2 - ( g antenna - 1 2 ⁢ x 2 2 ) 2 if ⁢ ⁢ 0 < g antenna < 1 x 2 2 ⁢ ⁢ or b 3 - out , target = 1 x 2 ⁢ ⁢ if ⁢ ⁢ g antenna > 1 x 2 2 , and b ant ⁢ ⁢ shunt , target = b 3 - out , target - b antenna ; where: g antenna and b antenna are a conductance and susceptance, respectively, of an antenna coupled to said matching network at said antenna side shunt, and x 2 is a reactance of a series element of said matching network between said antenna side shunt and a circuit side shunt of said matching network; using said controller circuit, identifying a tuned susceptance of said antenna side shunt from a list of possible susceptance values of said antenna side shunt corresponding to possible capacitance values of said antenna side variable capacitor such that said tuned susceptance of said antenna side shunt is closest to said target susceptance of said antenna side shunt; using said controller circuit, identifying a capacitance value of said antenna side variable capacitor which corresponds to said tuned susceptance of said antenna side shunt; using said controller circuit, computing a tuned susceptance value b 2-out,tune at a reference plane in said matching network between said series element and said circuit side shunt, using the formula: b 2 - out , tune = Im ⁡ ( g antenna + j ⁡ ( b antenna + b ant ⁢ ⁢ shunt , tune ) 1 + j ⁢ ⁢ x 2 ⁡ ( g antenna + j ⁡ ( b antenna + b ant ⁢ ⁢ shunt , tune ) ) ) ; using said controller circuit, computing a target susceptance b ckt — shunt,tgt of said circuit side shunt, using the formula: b ckt — shunt,t arg et =−b 2-out,tune ; using said controller circuit, identifying a tuned susceptance of said circuit side shunt from a list of possible susceptance values of said circuit side shunt corresponding to possible capacitance values of a circuit side variable capacitor of said circuit side shunt, such that said tuned susceptance of said circuit side shunt is closest to said target susceptance of said circuit side shunt; using said controller circuit, identifying a tuned capacitance value of said circuit side variable capacitor which corresponds to said tuned susceptance of said circuit side shunt; and using said controller circuit, setting said circuit side variable capacitor to said tuned capacitance value.