I have been struggling with the following problem,
which is intended to have some of the
characteristics of a printed circuit board
signalling environment. I hope that someone
here can help answer my questions, and/or
point me to appropriate analysis techniques.
Say we have one perfectly conducting plane, A. Parallel
to A and at a distance t is a second perfectly
conducting plane, B. Plane B is perforated by two
small holes separated by a distance L. A thin wire
(via) of length Lv passes through each hole.
At the connection point between one via and plane A
is an ideal voltage source with 50 ohm source impedance.
At the connection point between the other via and
plane A is a 50 ohm resistance. The two vias are joined
by a thin strip (trace) of perfect conductor at
height (Lv-t) above plane B. Both planes are infinite
in extent; dielectric has relative permittivity of 1.
_____ | _____________________________ | _____ plane B
______V_______________________________R______ plane A
I'd like to understand how this structure functions.
1) What is the voltage across the load resistor as
a function of frequency if the source voltage
is a 1 V sinusoid?
2) How does this change if I connect a wire between
planes A and B at some remote location? ... if I
add a DC voltage source in series with this wire?
3) What is the voltage across the load resistor if
the source voltage is a square wave with a
given rise/fall time?
4) For each of the above excitations, what is the
current density on each conductor?
5) Can one say that above a certain frequency almost
no current flows on plane A, and below another
frequency almost no current flows on plane B?
Is there a quick way to find these frequencies?
6) How sensitive are the answers to the above questions
to via dimensions (wire and perforation diameters,
Should I use a full-wave field solver on the entire
structure? Can I partition the problem into two vias
and a transmission line, solve statically, then use
spice? Or can I use some closed-form approximations?
All suggestions are most welcome. Thanks!
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