Lumped Model for microstrip-lines
I′m searching for a lumped microstrip-line model.
I have searched ieee, but haven′t found anything useful.
Appreciate any help.
Hello,
When you know the physical length, Zo and effective relative epsilon, you can make a good guess
Inductance/m = 3.33E-9*Zo*sqrt(eff.rel.eps) [H/m]
Capacitance/m = 3.333E-9* sqrt(eff.rel.eps) / Zo [F/m]
Z0 and relative epsilon you can derive from graphs or stripline formulas. When effective relative epsilon is not given, you can derive it from the propagation speed
Propagation speed = 3E8/sqrt(eff.rel.eps) [m/s]
Z0 = characteristic impedance of microstrip [Ohm]
Remember that the effective relative epsilon is mostly less than that of the substrate material (as field lines partly go to air).
When you divide your stripline in sections less then 0.125lambda electrical length (for the highest frequency), you can make PI or T sections based on the inductance/m and capacitance/m formulas.
The problem is that you don't model loss in this way. If you really require losses, you can add attenuator sections.
To see whether you model is reasonable, you might put your LC model into a spice (or other simulator) and compare it with the microstrip results. When you want to do simulation in pspice, the lossy transmission line model (O) gives in my situation many times better results than the lossless transmission line (T).
You probably know that because of the fringe effect a non-terminated microstrip (or transition from very wide to narrow strip) is electrically somewhat longer. If this is of importance (and you don't have formulas for it), come back to us.