# In a previous blog I mentioned how the lossy transmission line model included in some versions of SPICE won’t properly simulate pulses. There’s been a lot of interest in this since that posting went live, especially with regards to finding the conductance loss and in using lossy TLINES in the free or reduced cost SPICE simulators.

Some SPICE based circuit simulators include the LTRA (Lossy TRAnsmission line) model (the “O” element). It simulates TLINE behavior (including loss) for one signal conductor at one frequency. That’s why it works well for single frequency waves (such as low distortion sine waves), but it doesn’t properly calculate losses for pulses, which are made of many frequencies (harmonics). And, since the “O” line only models one signal, it can’t be used to determine crosstalk or to simulate differential pairs.

With these caveats in mind, here’s how to calculate the parameters for a 50 ohm, 5-mil wide, half-ounce thick stripline on FR4. Some of you may recognize the raw data as coming from problem 7.12 of “Understanding Signal Integrity”.

The model requires we know the trace length (LEN), along with its capacitance (C), inductance (L), resistance (R), and conductance (G) all determined at the frequency of interest. The resistance models signal loss of the conductor metal, and the conductance models the dielectric loss. Both of these get larger as frequency increases, but the model uses the same values for all frequencies.

We’ll use 350MHz (the same frequency used in problem 7.12). R, L and C are found at that frequency with a field solver, or by using the graphs or formulas in the book, to be (per inch length):

C = 3.5p

L=8.7n

R=0.7

We recall from the text that R is the AC resistance of the trace and its return path at 350MHz. It’s not the DC value.

All we need to do now is to calculate G to complete the model. As I show in the text and in problem 7.11, this is easily done once we know the capacitance and the circuit boards loss tangent (which we’ll take to be 0.02 for FR4).

G = 6.28 x f x C x LT = 6.28 x 350MHz x 3.5pF x 0.02 = 154uS/inch

The loss is given in Siemens per unit length (using the same units as for the capacitance). For a 15 inch long line at 350MHz the final model becomes:

.MODEL LOSSY50SL LTRA

+C=3.5p

+L=8.7n

+R=0.7

+G=154u

+LEN=15

As I show in the book, these need to be scaled when using the “W” line model. But that’s for another post.

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