TERMINATION IN A RESISTANCE NOT EQUAL TO THE CHARACTERISTIC IMPEDANCE (Z_{0})

Whenever the termination is not equal to Z_{0}, reflections occur on the line.
For example, if the terminating element contains resistance, it absorbs some energy, but
if the resistive element does not equal the Z_{0} of the line, some of the energy
is reflected. The amount of voltage reflected may be found by using the equation:

Where:

E_{R} = the reflected voltage

E_{i} = the incident voltage

R_{R} = the terminating resistance

Z_{0}= the characteristic impedance of the line

If you try different values of R_{L} in the preceding equation, you will find
that the reflected voltage is equal to the incident voltage only when R_{L} equals
0 or is infinitely large. When R_{L}equals Z_{0}, no reflected voltage
occurs. When R_{L}is greater than Z_{0}, E_{R} is positive, but
less than E_{i}. As R_{L} increases and approaches an infinite value, E_{R}
increases and approaches E_{i} in value. When R_{L} is smaller than Z_{0},
E_{R} has a negative value. This means that the reflected voltage is of opposite
polarity to the incident wave at the termination of the line. As R_{L} approaches
zero, E_{R} approaches E_{i} in value. The smaller the value of E_{R},
the smaller is the peak amplitude of the standing waves and the higher are the minimum
values.

TERMINATION IN A RESISTANCE GREATER THAN Z_{0}

When R_{L} is greater than Z_{0}, the end of the line is somewhat like
an open circuit; that is, standing waves appear on the line. The voltage maximum appears
at the end of the line and also at half-wave intervals back from the end. The current is
minimum (not zero) at the end of the line and maximum at the odd quarter-wave points.
Since part of the power in the incident wave is consumed by the load resistance, the
minimum voltage and current are less than for the standing waves on an open-ended line.
Figure 3-34, view G, illustrates the standing waves for this condition.

TERMINATION IN A RESISTANCE LESS THAN Z_{0}

When R_{L} is less than Z_{0}, the termination appears as a short
circuit. The standing waves are shown in figure 3-34, view H. Notice that the line
terminates in a current LOOP (peak) and a voltage NODE (minimum). The values of the
maximum and minimum voltage and current approach those for a shorted line as the value of
R_{L} approaches zero.

A line does not have to be any particular length to produce standing waves; however, it
cannot be an infinite line. Voltage and current must be reflected to produce standing
waves. For reflection to occur, a line must not be terminated in its characteristic
impedance. Reflection occurs on lines terminated in opens, shorts, capacitances, and
inductances, because no energy is absorbed by the load. If the line is terminated in a
resistance not equal to the characteristic impedance of the line, some energy will be
absorbed and the rest will be reflected.

The voltage and current relationships for open-ended and shorted lines are opposite to
each other, as shown in figure 3-34, views C and D. The points of maximum and minimum
voltage and current are determined from the output end of the line, because reflection
always begins at that end.

Q.26 A nonresonant line is a line that has no standing waves of current and voltage on
it and is considered to be flat. Why is this true?

Q.27 On an open line, the voltage and impedance are maximum at what points on the line?

STANDING-WAVE RATIO

The measurement of standing waves on a transmission line yields information about
equipment operating conditions. Maximum power is absorbed by the load when Z_{L} =
Z_{0}. If a line has no standing waves, the termination for that line is correct
and maximum power transfer takes place.

You have probably noticed that the variation of standing waves shows how near the rf
line is to being terminated in Z_{0}. A wide variation in voltage along the length
means a termination far from Z_{0}. A small variation means termination near Z_{0}.
Therefore, the ratio of the maximum to the minimum is a measure of the perfection of the
termination of a line. This ratio is called the STANDING-WAVE RATIO (swr) and is always
expressed in whole numbers. For example, a ratio of 1:1 describes a line terminated in its
characteristic impedance (Z_{0}).

Voltage Standing-Wave Ratio

The ratio of maximum voltage to minimum voltage on a line is called the VOLTAGE
STANDING-WAVE RATIO (vswr). Therefore:

The vertical lines in the formula indicate that the enclosed quantities are absolute
and that the two values are taken without regard to polarity. Depending on the nature of
the standing waves, the numerical value of vswr ranges from a value of 1 (Z_{L} =
Z_{0}, no standing waves) to an infinite value for theoretically complete
reflection. Since there is always a small loss on a line, the minimum voltage is never
zero and the vswr is always some finite value. However, if the vswr is to be a useful
quantity, the power losses along the line must be small in comparison to the transmitted
power.

Power Standing-Wave Ratio

The square of the voltage standing-wave ratio is called the POWER STANDING-WAVE RATIO
(pswr). Therefore:

This ratio is useful because the instruments used to detect standing waves react to the
square of the voltage. Since power is proportional to the square of the voltage, the ratio
of the square of the maximum and minimum voltages is called the power standing-wave ratio.
In a sense, the name is misleading because the power along a transmission line does not
vary.

Current Standing-Wave Ratio

The ratio of maximum to minimum current along a transmission line is called CURRENT
STANDING-WAVE RATIO (iswr). Therefore:

This ratio is the same as that for voltages. It can be used where measurements are made
with loops that sample the magnetic field along a line. It gives the same results as vswr
measurements.

Q.28 At what point on an open-circuited rf line do voltage peaks occur?

Q.29 What is the square of the voltage standing-wave ratio called?

Q.30 What does vswr measure?