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Module 10.2 Stability Circle of Transistor
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Freq :   Radius :


Simultaneous conjugate match conditions

Γ(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)^**