Module 10.2 Stability Circle of Transistor
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Freq
(GHz) 		MagS11
(Magnitude) 		AngS11
(Phase Angle) 		MagS21
(Magnitude) 		AngS21
(Phase Angle) 		MagS12
(Magnitude) 		AngS12
(Phase Angle) 		MagS22
(Magnitude) 		AngS22
(Phase Angle)

Freq :   Radius :


Simultaneous conjugate match conditions

`Γ_(MS)`(Magnitude, Phase Angle) =

`Γ_(ML)`(Magnitude, Phase Angle) =

Make a common Sparameter.s2p file.
Step 1 : the Sparameter.s2p template file from example.
Step 2 : Open the Sparameter.s2p with a text editor.
Step 3 : Replace the value of the Freq., Mag., and Ang. with your device Sparameter
Step 4 : Save the file and exit.
Step 5 : Browse and submit your new Sparameter.s2p file.

  
 
Introduction:

   Stability circle is used to determine the stability of the two-port network:

Output stability circle

`Γ_L` values for `|Γ_(IN)|` = 1


`|Γ_(IN)|` = `|S_(11)+(S_(21) S_(12) Γ_(L))/(1-S_(22) Γ_(L))|` = 1

`|Γ_(L) - (S_(22)-∆S_(11)^**)^**/(|S_(22)|^2-|∆|^2 )|` = `|(S_(12) S_(21))/(|S_(22) |^2-|∆|^2 )|`

`r_(L)` = `|(S_(12) S_(21))/(|S_(22) |^2-|∆|^2 )|` (radius)

`C_(L)`= `(S_22-∆S_(11)^**)^**/(|S_(22) |^2-|∆|^2 )` (center)

`∆` = `S_(11) S_(22)-S_(12) S_(21)` = `det [S]`

 

Input stability circle

`Γ_s` values for `|Γ_(OUT)|` = 1


`|Γ_(OUT)|` = `|S_(22) + (S_(21) S_(12) Γ_(S))/(1- S_(11) Γ_(S) )|` = 1

`|Γ_(S) - (S_(11)-∆S_(22)^**)^**/(|S_11 |^2-|∆|^2 )|` = `|(S_(12) S_(21))/(|S_(11) |^2-|∆|^2 )|`

`r_s` = `| (S_(12) S_(21)) / (|S_(11) |^2-|∆|^2 ) |` (radius)

`C_(S)`= `(S_(11)-∆S_(22)^**)^** / (|S_(11) |^2 - |∆|^2 )` (center)

`∆` = `S_(11) S_(22) - S_(12) S_(21)` = `det [S]`





 



`r_(L)` = The radius of the output stability circle

`c_(L)` = The center of the output stability circle.

 `r_(S)` = The center of the input stability circle.

`c_(S)` = The center of the input stability circle.

 `Γ_(L)` = The reflection coefficient of the output.

`Γ_(S)` = The reflection coefficient of the input.

   Simultaneous conjugate match conditions.
      The conditions required to obtain maximum transducer power gain:
`Γ_S` = `Γ_(IN)^**`     `Γ_L` = `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))`

`Γ_(ML)` = The simultaneous conjugate match of the output.

`Γ_(MS)` = The simultaneous conjugate match of the input.

 `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)^**`