Determining the Sign of X
When we use the term X or jX, we are referring to the reactive part of the complex
impedance. This reactive part can be either a negative value ( -jX ) which indicates
capacitive reactance or a positive value ( jX or +jX ) which indicates an inductive
reactance. If you do not know the sign of jX or can not read it from the test
instrument you are using, getting accurate results will require a little extra work.
Lets look at some examples.
1. We may not care about the sign of jX if the value of jX is small compared to the
resistance desired. For example lets assume the calculated antenna impedance is
46 + j3 ohms and the SWR is 1.12:1. In this case we may be quite satisfied with the
1.12:1 SWR and no further analysis is required. Does it matter whether it was a
+ j3 ohms or a - j3 ohms if we are not going to do anything about it?
2. We can solve for two results at the antenna end of the transmission line by using
a positive value entry for Series Reactance in the Data Entry field and then calculate
again using a negative value for the entry. This gives two solutions and the ambiguity
must be resolved by some other method such as trial and error in making an antenna
adjustment.
3. In some antenna systems such as simple dipoles and verticals that are intended to
be resonant at the operating frequency, the sign of jX can be determined by changing
the test frequency. Find the resonant frequency where the reactance (jX) is smallest.
As you move slightly below the resonant frequency of the antenna, it becomes
capacitive and the X term is - j ohms. As you move slightly above the resonant
frequency of the antenna, it becomes inductive and the X term is + j ohms. Remember
that we are talking about the calculated antenna resistance and reactance not the
values measured on the test instrument.
4. Another method involves adding a small length of transmission line to the antenna
feed line and observing the change in the measured resistance reading on the test
instrument. Adding transmission line will rotate the impedance point plotted on a
Smith Chart clockwise, in the direction of the Generator. By adding a small length
such as 0.01 wavelength, the resistance will change and the direction of change will
tell you if the reactance is inductive or capacitive i.e. in which half of the Smith
Chart the impedance is located.
If the resistance goes down, the impedance is in the lower half of the Smith Chart
and therefore the reactance is capacitive and the X term is - j ohms.
If the resistance goes up, the impedance is in the upper half of the Smith Chart
and therefore the reactance is inductive and the X term is + j ohms.
This method does have an ambiguity when the X term is very low compared to the
characteristic impedance of the transmission line. In this case it is possible to
add a small length of transmission line and have the resistance value as read from
the test instrument read the same value. This can occur when the impedance is nearly
purely resistive and the added transmission line moves the impedance point on the
Smith Chart from the lower half to the upper half, or vice versa, an equal distance
relative to the horizontal axis of the chart. In this case the addition of a second
short length of transmission line will provide the desired results and the resistance
reading will change as discussed above.
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