PORTION AU0KGL1N£

Fig* 3, Voitage distribution on transmission line having measurable standing wave ratio looks like this, if measured at various points along the line. Maximum-voltage points repeat every half-wavelength along line, as do minimum points. Ratio of maximum voltage to minimum voltage is one meaning of SWR; other meanings are equally valid as discussed in text. Note that voltage distribution does not follow a sine-wave pattern, will find the same actual voltage as that which exists across the open'circuit. The current phase shift is 180+180+180 or 540 degrees, which corresponds to a 180 degree change. The incident and reflected currents cancel each other out. Once again we find the same condition that existed at the open circuit.

As we move back on the line, at every l4-wave interval we will find these conditions alternating. Every half-wave the conditions of the open circuit full voltage with zero current- are duplicated, and at the intermediate !4-wave points (usually called "odd quarter-wave" points) the opposite condition—zero voltage with hiaximum current-exists, It s brought about entirely by the phase relationship between incident and reflected waves, which is determined in part by the reflection coefficient at the open circuit and in part by the distance from our measuring point to the open-

Let's try another example. Instead of an open circuit, let's short the line out.

This gives us zero voltage across the short, together with maximum current. Curiously enough, that's the same condition we found at a distance of lA wave in from an open circuit.

To get the zero voltage, we must have again a reflection coefficient of L0 at the short, with 180 degrees phase shift for voltage and 0 degrees phase shift for currenls at the reflecting point. Thafs the only way we can make the incident and reflected waves come out lo match the measurable conditions at the short.

If we now move back a quarter wavelength on the line, we'll find a voltage phase difference between incident and reflected waves of 90+180+40 degrees, which amounts to no shift at all, and a current phase difference of 90+0+90 degrees, or ] 80 degrees, which produces cancellation. Full voltage and no current! The open-circuit condition, no less.

Regardless of our termination, we find that the terminating condition is repeated at half-wave intervals back from the load end of the line, and that its "opposite" occurs at the intervening 14-wave points.

Let's look in a little more detail at that "opposite \ Waen we terminated in an open circuit, which featured high impedance and almost no current flow, at the quarter-wave point we apparently had a short circuit, with low impedance and maximum current flow. When we terminated in a short, or low impedance, we found at the '/¿-wave point an apparent open, or high impedance. We found, in effect, that a *4-wave length of transmission line acts as a transformer to change high impedances to low, and vice versa.

Before we explore this idea any deeper, let's take one more example. What happens if we terminate a transmission line in another, identical, infinitely long transmission line?

Reflection coefficient, you'll remember, we defined as the ratio of incident to reflected voltage and we added that it could be described in terms of the ratio of impedances also. If the two impedances are identical, the reflection coefficient must be zero. And if it is zero, then the reflected wave cannot exist; the actual voltage on the line and the incident wave must be equal to each other. In such a case, the line is said to be "matched," As it happens, we could substitute a resistor in place of any part of the infinitely long line, and if the impedance remained identical, nothing would change. This is the principle behind efforts lo "match1' antennas-and the success of our efforts to match impedances is measured in terms of a standing wave ratio or SWR.

We'll get into SWR in detail just a little later, after cleaning up a few loose ends about the major characteristics of a transmission line, We have determined that a line has capacitance, inductance, resistance, impedance, and attenuation, and that the energy in it at any point can be accounted for by incident and reflected waves travelling in opposite directions along the line. We have also determinded that any change of impedance along the line will cause a reflection, and thai the amount of reflection is indicated by the reflection coefficient,

Was this article helpful?

## Post a comment