A Short Tutorial on Transmission Lines in Pulse Generator Systems |
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Transmission lines are routinely used for high bandwidth communication and power transfer. They come in a wide variety of geometries and sizes and operate over enourmous frequency ranges. The transmission lines discussed here are typically simple coaxial cables, strip or microstrip geometries. The bandwidths of interest will be from DC to a few GHz.
Pulse generators use transmission lines not only for pulse transmission but also for pulse forming. In addition they are used for impedance matching and pulse inversion. There are a few relationships that are required to be known in order to understand the operation of trasnmission lines within pulser systems.
Loss free transmission lines exhibit a characteristic impedance such that the voltage and current are in a ratio that depends on the following factors:-
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The majority of lines have a relative permiability of 1, i.e. they have no magnetic materials in them where the magnetic field exists. In this case the geometry and the dielectric constant of the insulator fix the characteristic impedance.
The characteristic impedance Z0 =
where and
are the inductance and capacitance per unit length
Generally the group velocity of a wave (i.e. the velocity of a pulse) in such a line is given by:-
where c is the velocity of light in vacuo.
Coaxial cables
Coaxial cables with simple inner conductors have impedances typically in the range 10 Ω to 100Ω
the impedance is given by where b and a are the outer and internal diameters of the dielectric. Empirical formulae are available for a wide range of geometries, see for example, Microwave Engineers' Handbook, Volume 1, published by Artech House, Inc.
Stripline and Microstrip
In planar geometry there are two main configurations, the stripline and the microstrip. Stripline systems have a live electrode between two ground planes and microstrip has a single ground plane.
Empirical equations have been developed for the impedance of such lines. For the simple case of a microstrip with a much wider ground plane and no magnetic materials we offer the following small application for calculation (Macintosh compatible only).
Download Microstrip for Classic Macintosh (18kbytes). To run ClassicOS 9.0.4 under Mohave click here.