FTYP EQUA 10  ! Sonnet Equation File

EQN Real(gamma)
EQS USER
EQD Real part of gamma = alpha
EQH 
Procedure:
1) Z11 and Z21 are used to find "A" parameter in the ABCD matrix.
2) "A" also equals cosh(gamma*l). Given "A", solve for gamma*1, 
using arccosh(A).
3) Display only the Real part which is alpha.
----------
Notes: 
The unit is Nepers per length "l". 1 Neper = 8.6859 dB
"l" is the length of the model (not per meter). 
This value can be scaled to Nepers per meter and should agree
with the N-Coupled Line Model value for gamma.
This equation only works for a 2-port transmission line model.
This equation only works with a single TEM/QTEM mode
This equation only works for a line length < 0.25 wavelength
END EQH 
AXISLABEL "alpha(Np)"
ARGS 2
ARG 1 ! begin arg 1 definition
NAME An
ANN A-parameter numerator
RES Z 11
END ARG ! end of arg 1 definition
ARG 2 ! begin arg 2 definition
NAME Ad
ANN A-parameter denominator
RES Z 21
END ARG ! end of arg 2 definition
BODY 
real(ln((An/Ad)+sqrt((An/Ad)^2-1)))
END BODY 
END EQN

EQN Imag(gamma)
EQS USER
EQD Imaginary part of gamma = Beta
EQH 
Procedure:
1) Z11 and Z21 are used to find "A" quantity in the ABCD matrix.
2) "A" also equals cosh(gamma*l). Given "A", solve for gamma*1, 
using arccosh(A).
3) Display only the Imaginary part which is Beta.
----------
Notes: 
The unit is radians per length "l" 
"l" is the length of the model (not per meter). 
This value can be scaled to radians per meter and should agree
with the N-Coupled Line Model value for Gamma.
This equation only works for a 2-port transmission line model
This equation only works with a single TEM/QTEM mode
This equation only works for a line length < 0.25 wavelength
END EQH 
AXISLABEL "Beta(rad)"
ARGS 2
ARG 1 ! begin arg 1 definition
NAME An
ANN A-parameter numerator
RES Z 11
END ARG ! end of arg 1 definition
ARG 2 ! begin arg 2 definition
NAME Ad
ANN A-parameter denominator
RES Z 21
END ARG ! end of arg 2 definition
BODY 
imag(ln((An/Ad)+sqrt((An/Ad)^2-1)))
END BODY 
END EQN