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EA3: Systems Dynamics
Electrical Systems
Sridhar Krishnaswamy
28
TRANSMISSION LINES
Consider a length of coaxial cable that connects your Cable TV port to your TV input.
This cable, and other similar things such as your data transmission line, can all be
modeled as a bunch of inductors, resistors and capacitors in an arrangement that we shall
call by the generic term:
transmission line
.
Figure
: A coax cable (courtesy EA3 hyperbook)
The figure above shows a coax cable that has been stripped.
It consists of a conducting
wire surrounded by an insulator ,which is in turn surrounded by a ground sheath.
Every
little segment of this cable has some inductance and some capacitance and some
resistance.
Note the similarity between a coax cable and a slinky.
Every little bit of a
slinky has some mass, some springiness, and some damping.
Earlier we tried to model
this as a set of discrete springs and masses (we neglected dissipative losses). Similarly,
we can model a continuous cable as a system of discrete inductors and capacitors (and
resistors but we will neglect resistive losses here for simplicity. )
You should be able to obtain the first order state equations for this system as follows:
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 Fall '08
 KRISHNASWAMY

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