Module 10.4 Matching Network

  Mode  :     Input mode    Output mode
  
Please input the `Γ_(MS)` `Γ_(ML)` :

`Γ_(MS)` `Γ_(ML)`(mag∠phase) = ∠



  `Z_(MS)` `Z_(ML)`   =    * ( +`j` `Omega`)
  Operating Frequency`(F_{0})`   =   GHz
  Operating Frequency`(F_{0})` Range  =  0.1 GHz ~ 6GHz
  
  Shunt L   Shunt C   Series L   Series C
  Series TL   Shunt Open Stub   Shunt Short Stub
  Shunt L   Shunt C   Series L   Series C
  Series TL   Shunt Open Stub   Shunt Short Stub
匹配
*

Introduction:

Simultaneous conjugate match conditions:


The conditions required to obtain maximum transducer power gain are

`Γ_(S)` = `Γ_(MS)`= `Γ_(IN)^**`

`Γ_(L)` = `Γ_(ML)`= `Γ_(OUT)^**`

`Γ_(S)^**` = `S_(11)` `+` `(S_(21) S_(12) Γ_(L) )/(1 - S_(22) Γ_(L) )`

`Γ_(L)^**` = `S_(22) + (S_(21) S_(12) Γ_(S) )/(1- S_(11) Γ_(S) )`


Solving the above equations simultaneously, we obtain

`Γ_(MS)` = `(B_(1) ± sqrt( B_(1)^2-4|C_(1)|^2 )) / (2C_(1))`

`Γ_(ML)` = `(B_(2) +- sqrt(B_(2)^2 - 4|C_(2)|^2 ))/ (2C_(2))`


`B_(1)` = `1+|S_(11)|^2 -|S_(22)|^2 -|⧍|^2`

`B_(2)` = `1+|S_(22)|^2 -|S_(11)|^2 -|⧍|^2`

`C_(1)` = `S_(11) -⧍S_(22)^**`

`C_(2)` = `S_(22) -⧍S_(11)^**`

`Γ_(MS)` = `|Γ_(MS)|e^(jθ_(Γ_(s)))` = `(Z_(MS)-Z_(0))/(Z_(MS)+Z_(0) )`    `Γ_(ML)` = `|Γ_(ML)|e^(jθ_(Γ_(L)))` = `(Z_(ML)-Z_(0))/(Z_(ML)+Z_(0) )`

`Γ_(MS)` : Required input reflection coefficient for the simultaneous conjugate match.
`Γ_(ML)` : Required output reflection coefficient for the simultaneous conjugate match.
`Z_(MS)` : Required input Impedance for the simultaneous conjugate match
`Z_(ML)` : Required output Impedance for the simultaneous conjugate match

Simultaneous conjugate matching network design:



The impedance, `Z_(MS)`, represented by the input reflection coefficient,
`Γ_(MS)`, is the impedance seen into the input matching network.
Thus, the input matching network has to transform `Z_(0)` to the impedance `Z_(MS)`.

The impedance, `Z_(ML)`, represented by the output reflection coefficient,
`Γ_(ML)`, is the impedance seen into the output matching network.
Thus, the output matching network has to transform `Z_(0)` to the impedance `Z_(ML)`.