| "The magnitude and phase angle of the input impedance depends on
the SWR, the (feed) line length, and the (impedance) Zo of the
(feed) line. If the SWR is small, the input impedance is principally resistive
at all line lengths; if the SWR is high, the reactive component may be
relatively large. The input impedance of the line can be represented by a
series circuit of resistance and reactance, where Rs is the
resistive component and Xs is the reactive component. Frequently the
"s" subscripts are omitted, and the series-equivalent impedance
denoted as R + jX. The j is an operator function, used to
indicate that the values for R and X cannot be added directly, but that vector
addition must be used if the overall impedance is to be determined. (This is
analogous to solving a right triangle for the length of its hypotenuse, where R
and X represent the length of its two sides. The length of the hypotenuse
represents Z, the overall impedance.) By convention, a plus sign is assigned to
"j" when the reactance is inductive (R + jX), and a
minus sign is used when the reactance is capacitive (R - jX)." (I
will use this convention throughout this book)(This information is found in theIt is important to note that when you see
the "j" operator with a positive value, the antenna is too
long for the frequency being measured. Just the opposite is true if the
"j" operator is negative. The antenna is too short.
Nonresonant antennas are an exception. ARRL Antenna Handbook,
14th edition, pages 3-6)Since complex impedance (R +/- jX) is now indicated on
readily available antenna test equipment, this simple factor is very valuable
when adjusting antennas for best SWR. |
|
Input impedance
Factors determining the Input
Impedance of a transmission line.
Feed point impedance
The impedance at the feed point of the antenna
may be expressed in terms of R + jX.
|
| It is a
hypothetical antenna radiating or receiving equally in all directions.
Isotropic antennas do not exist physically, but represent a convenient
reference antenna for expressing the directive properties of actual
antennas. |
|
Isotropic
antenna |
"The energy supplied to an antenna is principally dissipated in
two ways: radiation of radio waves and heat loss in the wire and nearby
dielectrics. The radiated energy is the useful part, but it represents a loss
just as much as the energy used in heating the wire is a loss. In either case,
the dissipated power is equal to I2R. With heat losses, R is a real
resistance. For radiation, however, R is a virtual resistance which, if
replaced with an actual resistor of the same value, would dissipate the power
that is actually radiated from the antenna. This resistance is called the
radiation resistance. The total power loss in the antenna is therefore
equal to I2(R0 + R), where R0 is the radiation
resistance and R the real resistance, or ohmic resistance." (ARRL Handbook, 17th edition,
pages 2-6.)
|
|
Radiation Resistance |
| Symbolized by X. Reactance is the opposition to the flow of
alternating current. A capacitive reactance (XC) is the opposition
offered by capacitors, and inductive reactance (XL) is the
opposition offered by a coil or other inductance. Both inductive and capacitive
reactance is measured in ohms. In tuned circuits, resonance occurs when
XC and XL have the same value (and opposite signs). They
cancel themselves. |
|
Reactance |
11
|