# O-device (Lossy Transmission Line) and T-device (Lossless Transmission Line) modelling issues

The O-device (Lossy Transmission Line) in LTspice does not seem to correctly model dc behavior. This is troubling and could lead to very confusing simulation results in some cases. Also the O-device does not allow its loss elements to be frequency dependent so that skin effects (which are very real and sometimes very important) may not be modeled. I think that these limitation are generic to SPICE and are not just specific to LTspice.

It is worth noting that the T-device (Lossless Transmission Line) behaves with connectivity counter to that suggested by its symbol graphic - there is no dc connection between the input pins and the output pins (this is why both ends must have a path to ground). An equivalent circuit for this device can be found the Pspice manual and looks like it would be easy to build in LTspice using b-sources to provide the controlled sources with delay.

A while ago, EE Times online? published a series of articles by Roy McCammon that developed an easy-to-follow model for a frequency dependent lossy transmission line complete based on the so-called telegrapher's method.

His final subcircuit is reproduced schematically in the article and the text version is copied below:

```.param Kft=1 ; 1 Kft = 1000 feet
.param Lcon=10n ; convergence inductance
+ C=15.72e-9 ; the value of capacitance at dc
+ Gdc=0.5n ; the value of conductance at dc
+ Rdc=52.50 ; the value of resistance at dc
+ Ldc=0.1868e-3 ; the value of inductance at dc
+ Linf=0.133e-3 ; inductance at infinite frequency
+ Ldel=(Ldc-Linf) ; inductance parameter
+ Zinf=(Linf/C)**0.5 ; characteristic impedance at infinite frequency
+ Yinf=1/Zinf ; characteristic conductance at infinite frequency
+ F2=5e6 ; the highest frequency in Hz
+ W2=6.28318*F2 ; the highest frequency in rad/sec
+ G1=23u ; the value of conductance at F1
+ G2=36u ; the value of conductance at F2
+ Rac=304.62 ; the value of resistance at F2
+ F1=3e6 ; the second highest frequency in Hz
+ A=1.6 ; inductance parameter
+ k=Log(G2/G1)/Log(F2/F1)/2 ; conductance parameter
+ WL=6.28318*161000 ; inductance parameter
+ WR=W2*(Rdc**2)/(((Rac**4)-(Rdc**4))**0.5) ; resistance parameter

.subckt single_mode_xline L1 R1
G1 N1 0 N1 0 Laplace=(((((Gdc+G2*(-(s/w2)^2)^k)+s*C)/
+ ((Rdc*(1-(s/wR)^2)^0.25)+s*(Linf+Ldel/(1+A*((-(s/wL)^2)^0.5)-
+ (s/wL)^2)^0.25)))^0.5))-Yinf
G2 0 N1 N2 0 1
G3 0 L1 N2 0 1
V1 L1 N1 0 Rser=0
H1 N4 0 V1 1
G4 N6 0 N6 0 Laplace=(((((Gdc+G2*(-(s/w2)^2)^k)+s*C)/
+ ((Rdc*(1-(s/wR)^2)^0.25)+s*(Linf+Ldel/(1+A*((-(s/wL)^2)^0.5)-
+ (s/wL)^2)^0.25)))^0.5))-Yinf
G5 0 N6 N5 0 1
G6 0 R1 N5 0 1
V2 R1 N6 0 Rser=0
H2 N3 0 V2 1
R1 N6 0 {Zinf}
R2 N1 0 {Zinf}
G7 0 N2 N3 0 Laplace= Exp(-Kft*( (((Rdc*(1-(s/wR)^2)^.25)+
+ s*(Linf+Ldel/(1+A*((-(s/wL)^2)^.5)-(s/wL)^2)^.25))*
+ (Gdc+G2*(-(s/w2)^2)^k+s*C))^.5))/(s*Lcon+1)
L1 N5 0 {Lcon} Rser=1
G8 0 N5 N4 0 Laplace= Exp(-Kft*( (((Rdc*(1-(s/wR)^2)^.25)+
+ s*(Linf+Ldel/(1+A*((-(s/wL)^2)^.5)-(s/wL)^2)^.25))*
+ (Gdc+G2*(-(s/w2)^2)^k+s*C))^.5))/(s*Lcon+1)
L2 N2 0 {Lcon} Rser=1
.ends single_mode_xline
```