Impedance match
Impedance match for ~Gamma~,T and ~pi~ circuits
constants:c
Parameters
frequency
f
\(Hz\)
Load impedance
`R_L`
\(\Omega\)
Target impedance
`Z_0`
\(\Omega\)
Quality factor
Q
\(\)
`Gamma` impedance match circuit
anger frequency `omega`
`omega=2 pi f`
Quality factor Q
`Q=sqrt(Z_0/R_L-1)`
Inductor `L_1`
`L_1=(Q R_L)/omega`
Capacitor `C_1`
`C_1=Q/(omega Z_0)`
T impedance match circuit
Inductor `L_1`
`L_1=(Q R_L)/omega`
Capactor `C_1`
`C_1=1/(omega Z_0 sqrt((R_L(1+Q^2))/Z_0-1))`
Capactor `C_2`
`C_2=(Q-1/(omega C_1 Z_0))/(omega R_L (1+Q^2))`
`pi` impedance match circuit
Capactor `C_2`
`C_2=Q/(omega Z_0)`
Capactor `C_1`
`C_1=1/(omega R_L)sqrt((R_L(1+Q^2))/Z_0-1)`
Inductor `L_1`
`L_1=(QZ_0+omega C_1 R_L Z_0)/(omega(1+Q^2))`