REFLECTION AND REFRACTION (TRANSMISSION) OF WAVES
If a travelling wave arrives at a point where the impedance suddenly changes the wave is partly transmitted and partly reflected. Loading points, line-cable junctions and even faults constitute such discontinuities. Independent waves meeting along a line will combine in accordance with their polarity to provide different voltage and current levels at the meeting point. It is convenient to adopt a standard sign convention, and in what follows, forward waves of current and voltage are given the same polarity. If the wave is being reflected the corresponding current and voltage waves are given opposite polarity. This may be illustrated by considering waves of current and voltage being transmitted along a line of characteristic impedance Zc terminated by an impedance Z (fig 2).
Let E and I represent the incident waves, ETand IT represent the transmitted (or refracted) waves and ER and IR the reflected waves. The state of affairs is illustrated in fig 3. The following relations hold good for incident, transmitted and reflected voltage and current waves
The negative sign in equation (3) is because of the fact that ER and IRare travelling in the negative direction of x or backwards on the same line. The transmitted voltage and current will be respectively the algebraic sum of incident and reflected voltage and current waves.
Substituting the values of I, IR and IT from equations (1,2,3) in equation (5), we have
From equations (4) and (6), we have
The coefficients 2Z/ (Z+Zc) and (Z – Zc) / (Z+Zc) are called coefficients of refraction and reflection respectively.
It will be observed that the transmitted or refracted current and voltage always have positive polarity. The polarity of the reflected waves depends on the magnitude relationship between Zc and Z. If Zc> Z, the voltage wave is negative and the current wave is positive, but vice-versa if Z > Zc.
Written by John on March 21st, 2009 with
2 comments.
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