Impedance match

Impedance match for ~Gamma~,T and ~pi~ circuits
Pi T Gamma C1 C2 R1 L1 C1 C2 R1 L1 Z0 C1 R1 L1
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))`