1. Lossy Transmission Lines
ECE 546
Lecture - 09
Lossy Transmission Lines
Spring 2018
Jose E. Schutt-Aine
Electrical & Computer Engineering
University of Illinois

2. Loss in Transmission Lines
Signal amplitude decreases with distance from the source.

3. Skin Effect in Lines

4. Skin Effect in Microstriper
H. A. Wheeler, "Formulas for the skin effect," Proc. IRE, vol. 30, pp ,1942

5. Skin Effect in Microstrip
Current density varies as
Note that the phase of the current density varies as a function of y
The voltage measured over a section of conductor of length D is:

6. Skin Effect in Microstrip
The skin effect impedance is
where
is the bulk resistivity of the conductor
with
 Skin effect has reactive (inductive) component

7. Lossy Transmission Line
Telegraphers Equation: Time Domain

8. Lossy Transmission Line
Telegraphers Equation: Frequency Domain

9. Lossy Transmission Line
forward wave
backward wave

10. Lossy Transmission Lineg

11. Effects of Losses Signal attenuation Dispersion
- Rise time degradation

12. RC Transmission Line R : series resistance per unit length
C : shunt capacitance per unit length
For very high w,

13. RC Transmission Line If then RT = Rl : total resistance
CT = Cl : total capacitance

14. RC Transmission Line
Logic
threshold
Logic
threshold

15. Long Cable
100m Category-5 Cable

16. Short Cable
1m Category-5 Cable

17. Resistance and velocity
Category 5 Cable
Resistance and velocity

18. Cable Loss Model Zo vro vrs Rs p fmax
Category
24-Ga
Category
SMA
Zo vro vrs Rs p fmax
(W) (m/ns) (m/ns-GHz) (W/m-GHzp) (GHz)

19. Lossy TL Simulation To simulate lossy TL with resistive loads
No closed form solution
Simplest method is to use IFFT
For multiconductor transmission lines: see: J. E. Schutt-Aine and R. Mittra, "Transient analysis of coupled lossy transmission lines with nonlinear terminations," IEEE Trans. Circuit Syst., vol. CAS-36, pp , July 1989

20. Time-Domain Simulations

21. Pulse Propagation (CAT-5)

22. Pulse Propagation (MP/CM)

23. Pulse Propagation (RG174)