ELECTRICAL PROPERTIES OF DIELECTRICS - Advanced Signal Integrity for High-Speed Digital Design - page 290

Consequently, the classic form of the telegrapher's equations for a lossy dielectric
and a realistic conductor are
∂v(z,t)
∂z

R ac i(z, t)

+ L total ∂
∂t

=− (5-72a)

G + C ∂
∂t

v(z, t)

∂i(z,t)
∂z

=− (6-51)

REFERENCES

Balanis, Constantine, 1989, Advanced Engineering Electromagnetics , Wiley, New York.
Brillouin, L., 1960, Wave Propagation and Group Velocity , Academic Press, New York.
Djordjevic, A. R., R. M. Biljic, V. D. Likar-Smiljanic, and T. K. Sarkar, 2001, Wide-
band frequency domain characterization of FR-4 and time domain causality, IEEE
Transactions on Electromagnetic Compatability , vol. 43, no. 4, Nov., pp. 662-667.
Elliot, R., 1993. Electromagnetics , IEEE Press, Piscataway, NJ.
Hall, Stephen, Steven G. Pytel, Paul G. Huray, Daniel Hua, Anusha Moonshiram, Gary
A. Brist, and Edin Sijercic, 2007, Multi-GHz causal transmission line modeling using
a 3-D hemispherical surface roughness approach, IEEE Transactions on Microwave
Theory and Techniques , vol. 55, no. 12, Dec.
Hamilton, Paul, Gary Brist, Guy Barnes, Jr., and Jason Schrader, 2007, Humidity depen-
dent losses in FR4 dielectric, presented at the IPC Apex Conference.
Huray, Paul, 2009, Foundations of Signal Integrity , Wiley, Hoboken, NJ.
Jackson, J. D., 1998, Classical Electrodynamics , 3rd ed., Wiley, New York.
Johnk, Carl T. A., 1988, Engineering Electromagnetic Fields and Waves , Wiley, New
York.
LePage, Wilbur P., 1980, Complex Variables and the Laplace Transform , Dover Publica-
tions, New York.
Pauling, Linus, 1948, The Nature of the Chemical Bond , Cornell University Press, Ithaca,
NY.
Pytel, Steven G., 2007, Multi-gigabit data signaling rates for PWBs including dielectric
losses and effects of surface roughness, Ph.D. dissertation, Department of Electrical
Engineering, University of South Carolina.

PROBLEMS

6-1 If the dielectric permittivity of a dielectric is known to be ε r = 4 . 2 and

0 . 021 at 1 GHz, plot the frequency dependent values ε r (f ) and
tan δ(f ) from 1 MHz to 20 GHz.
6-2 Given the plot of the dielectric permittivity in Figure 6-27a and the loss
tangent plot in Figure 6-27b, derive an equation for a frequency-dependent
dielectric model.
6-3 Given the real part of the dielectric permittivity in Figure 6-28, calculate
the loss tangent.

tan δ =