+ Post New Thread
Results 1 to 4 of 4

13th July 2018, 11:35 #1
 Join Date
 Oct 2006
 Location
 Real Homeless
 Posts
 2,108
 Helped
 583 / 583
 Points
 14,090
 Level
 28
Charateristics of {A,B ; C,D} Matrix for lossless circuit
As well known, Scattering Matrix [S] is a unitary matrix for lossless circuit.
Is there any simple relation in [F]={A,B ; C,D} Matrix for lossless circuit ?
Reciprocity is reflected to determinant(F)=1.
Here {A,B ; C,D} Matrix is called as "Fundamental Matrix", "Ketten Matrix", "Cascade Matrix" or "Chain Matrix".

Advertisment

13th July 2018, 19:25 #2
 Join Date
 Jan 2011
 Posts
 3,316
 Helped
 1179 / 1179
 Points
 20,065
 Level
 34
Re: Charateristics of {A,B ; C,D} Matrix for lossless circuit
Hmm, I like these sort of puzzles. I'll give it a shot.
If A and D are real valued and B and C are imaginary valued, then it should be lossless.
I base this on the fact that impedance parameters of a lossless network are all imaginary, and the known conversions from Z parameters to ABCD parameters.

Advertisment

14th July 2018, 02:04 #3

Advertisment

14th July 2018, 11:25 #4
 Join Date
 Jul 2018
 Posts
 1
 Helped
 0 / 0
 Points
 13
 Level
 1
Re: Charateristics of {A,B ; C,D} Matrix for lossless circuit
It is assumed that ABCDparameters are defined by the following equations:
V1 = A*V2  B*I2,
I1 = C*V2  D*I2.
Noloss condition:
0 = real(conj(V1)*I1 + conj(V2)*I2)
= real(conj(A*V2  B*I2)*(C*V2  D*I2) + conj(V2)*I2)
= real(conj(A)*C*conj(V2)*V2)
+ real(conj(B)*D*conj(I2)*I2)
+ real((1  conj(A)*D)*conj(V2)*I2)
 real(conj(B)*C*conj(I2)*V2)
= real(conj(A)*C*conj(V2)*V2)
+ real(conj(B)*D*conj(I2)*I2)
+ real((1  conj(A)*D  B*conj(C))*conj(V2)*I2).
Consequently,
real(conj(A)*C) = 0,
real(conj(B)*D) = 0,
conj(A)*D + B*conj(C) = 1.
+ Post New Thread
Please login