ELEC 390
Theory and Applications of Electromagnetics
Spring 2012
Representative Topics for Individual Investigation Assignment
For this assignment, you must select a topic or task within the scope of the course but outside
those that will be covered in the lectures. You may choose a topic in a portion of the textbook not
covered by the course or a topic not included in the textbook. With that in mind, I am providing
the following list of representative topics. You may choose a topic from this list, but you do not
have to. You may choose another topic.
Remember that the primary purpose of this exercise is to demonstrate that you have mastered
through your own work a topic relevant to the course beyond the normal coverage of it. You
should acquire enough knowledge about the topic to achieve one of the following:
1. Carry a derivation to a more technically sophisticated level,
2. Apply theory to a challenging real-world problem, or
3. Provide some other evidence of your mastery of the subject.
Note that several topics listed below involve derivations. If you choose one of those topics, the
derivation you present must include details that go well beyond what the textbook provides, and
you must demonstrate a deep understanding of the derivation. Derivations that are well
developed in the textbook should be avoided, unless you plan to provide an insight that the
textbook omits.
Examples of Acceptable Topics (Updated 9:30 pm Monday, Apr. 16)
If a topic is labeled as “TAKEN,” that means someone else has chosen it for their presentation,
and it is no longer available.
1. [TAKEN] Prove that the total reactive power Q absorbed or delivered (during the reference
half-cycle) of a loaded transmission line of length l, characteristic impedance Zo, and a
reflection coefficient at the load of  is given by
Q
2  Vo
Zo
2
sin  r  2 l   sin  r .
2. [TAKEN] Derive the formula for the transmission line parameter L′, the inductance per unit
length, for a coaxial line.
3. Derive the formula for L′ for a two-wire line. (If necessary, you may assume (D/d)2 >> 1.)
4. [TAKEN] Derive the formula for L′ for a parallel-plate line. (If necessary, you may assume w
>> h.)
5. [TAKEN] Derive the formula for the transmission line parameter C′, the capacitance per unit
length, for a coaxial line.
6. [TAKEN] Derive the formula for C′ for a two-wire line. (If necessary, you may assume
(D/d)2 >> 1.)
7. [TAKEN] Derive the formula for C′ for a parallel-plate line. (If necessary, you may assume
w >> h.)
8. Derive the formula for the transmission line parameter R′, the resistance per unit length, for a
coaxial line.
9. [TAKEN] Derive the formula for R′ for a two-wire line. (If necessary, you may assume
(D/d)2 >> 1.)
10. Derive the formula for R′ for a parallel-plate line. (If necessary, you may assume w >> h.)
11. Derive the formula for the transmission line parameter G′, the conductance per unit length,
for a coaxial line.
12. Derive the formula for G′ for a two-wire line. (If necessary, you may assume (D/d)2 >> 1.)
13. Derive the formula for G′ for a parallel-plate line. (If necessary, you may assume w >> h.)
14. [TAKEN] Explain the derivation of the formula for rL-circles on the Smith chart.
15. [TAKEN] Explain the derivation of the formula for xL-circles on the Smith chart.
16. [SHUNT AND SERIES STUBS TAKEN] Explain how to use the Smith chart to design a
single-stub matching system with either a shunt or series stub.
17. [TAKEN] Produce a bounce diagram to describe the transient propagation along a
transmission line with arbitrary source and load impedances (limiting to real impedances is
okay).
18. [TAKEN] Derive the transformation equations to convert unit vectors from one coordinate
system to another. Coordinate systems must be limited to Cartesian, spherical, or cylindrical.
19. [TAKEN] Derive the transformation equations to convert differential vector length (dl),
differential vector surface area (ds), or differential volume (dV) from one coordinate system
to another. Coordinate systems must be limited to Cartesian, spherical, or cylindrical.
20. [TAKEN] Derive the formula for the input impedance of a lossy loaded transmission line:
Z in l   Z o
Z L  Z o tanh  l 
, where
Z o  Z L tanh  l 
    j ,
and discuss one or more important implications of it in general or specific applications.
21. [TAKEN] Derive the Telegrapher’s equations from Maxwell’s equations.