Finite-length transmission lines

Chapter 14.4 Finite-length transmission lines

Lessons In Electric Circuits Volume II – AC Book
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Lessons In Electric Circuits Volume II – AC Book

  • 482CHAPTER 14. TRANSMISSION LINESimpedance (Z0) increases as the conductor spacing increases. If the conductors are moved away fromeach other, the distributed capacitance will decrease (greater spacing between capacitor “plates”),and the distributed inductance will increase (less cancellation of the two opposing magnetic fields).Less parallel capacitance and more series inductance results in a smaller current drawn by the linefor any given amount of applied voltage, which by definition is a greater impedance. Conversely,bringing the two conductors closer together increases the parallel capacitance and decreases the se-ries inductance. Both changes result in a larger current drawn for a given applied voltage, equatingto a lesser impedance.Barring any dissipative effects such as dielectric “leakage” and conductor resistance, the char-acteristic impedance of a transmission line is equal to the square root of the ratio of the line’sinductance per unit length divided by the line’s capacitance per unit length:Where,Z0 = Characteristic impedance of lineZ0 = LCL = Inductance per unit length of lineC = Capacitance per unit length of line• REVIEW:• A transmission line is a pair of parallel conductors exhibiting certain characteristics due todistributed capacitance and inductance along its length.• When a voltage is suddenly applied to one end of a transmission line, both a voltage “wave”and a current “wave” propagate along the line at nearly light speed.• If a DC voltage is applied to one end of an infinitely long transmission line, the line will drawcurrent from the DC source as though it were a constant resistance.• The characteristic impedance (Z0) of a transmission line is the resistance it would exhibit if itwere infinite in length. This is entirely different from leakage resistance of the dielectric sepa-rating the two conductors, and the metallic resistance of the wires themselves. Characteristicimpedance is purely a function of the capacitance and inductance distributed along the line’slength, and would exist even if the dielectric were perfect (infinite parallel resistance) and thewires superconducting (zero series resistance).• Velocity factor is a fractional value relating a transmission line’s propagation speed to thespeed of light in a vacuum. Values range between 0.66 and 0.80 for typical two-wire lines andcoaxial cables. For any cable type, it is equal to the reciprocal (1/x) of the square root of therelative permittivity of the cable’s insulation.14.4Finite-length transmission linesA transmission line of infinite length is an interesting abstraction, but physically impossible. Alltransmission lines have some finite length, and as such do not behave precisely the same as an