In the section preceding this section, we discovered that the velocity of the wave (orsignal) in the transmission line is less than the free-space velocity (i.e., less than thespeed of light). Further, we discovered in Eq. 3.3 that velocity is related to the di-electric constant of the insulating material that separates the conductors in thetransmission line. Velocity factor vis usually specified as a decimal fraction of c,the speed of light (3 ×108m/s). For example, if the velocity factor of a transmissionline is rated at “0.66,” then the velocity of the wave is 0.66c, or (0.66) (3 ×108m/s)= 1.98 ×108m/s.Velocity factor becomes important when designing things like transmission linetransformers, or any other device in which the length of the line is important. In mostcases, the transmission line length is specified in terms of electrical length, whichcan be either an angular measurement (e.g., 180° orπradians), or a relative measurekeyed to wavelength (e.g., one-half wavelength, which is the same as 180°). Thephysical lengthof the line is longer than the equivalent electrical length. For exam-ple, let’s consider a 1-GHz half-wavelength transmission line.A rule of thumb tells us that the length of a wave (in meters) in free space is 0.30/F,where frequencyFis expressed in gigahertz; therefore, a half-wavelength line is 0.15/F
At 1 GHz, the line must be 0.15 m/1 GHz = 0.15 m. If the velocity factor is 0.80, then thephysical lengthof the transmission line that will achieve the desired electrical lengthis [(0.15 m) (v)]/F= [(0.15 m) (0.80)]/1 GHz = 0.12 m. The derivation of the rule ofthumb is “left as an exercise for the student.” (Hint: It comes from the relationship be-tween wavelength, frequency, and velocity of propagation for any form of wave.)There are certain practical considerations regarding velocity factor that resultfrom the fact that the physical and electrical lengths are not equal. For example, ina certain type of phased-array antenna design, radiating elements are spaced a half-wavelength apart, and must be fed 180° (half-wave) out of phase with each other.The simplest interconnect is to use a half-wave transmission line between the 0°element and the 180° element. According to the standard wisdom, the transmissionline will create the 180° phase delay required for the correct operation of the an-tenna. Unfortunately, because of the velocity factor, the physical length for a one-half electrical wavelength cable is shorter than the free-space half-wave distancebetween elements. In other words, the cable will be too short to reach between theradiating elements by the amount of the velocity factor!Clearly, velocity factor is a topic that must be understood before transmissionlines can be used in practical situations. Table 3-1 shows the velocity factors for sev-eral types of popular transmission line. Because these are nominal values, the actualvelocity factor for any given line should be measured.
Transmission lines are capable of generating noise and spurious voltages that areseen by the system as valid signals. Several such sources exist. One source is thecoupling between noise currents flowing in the outer conductor and the inner con-ductor. Such currents are induced by nearby electromagnetic interference and othersources (e.g., connection to a noisy groundplane). Although coaxial design reducesnoise pickup, compared with parallel line, the potential for EMI exists. Selection ofhigh-grade line, with a high degree of shielding, reduces the problem.Another source of noise is thermal noises in the resistances and conductances.This type of noise is proportional to resistance and temperature.
There is also noise created by mechanical movement of the cable. One speciesresults from the movement of the dielectric against the two conductors. This form ofnoise is caused by electrostatic discharges in much the same manner as the sparkcreated by rubbing a piece of plastic against woolen cloth.A second species of mechanically generated noise is piezoelectricityin the di-electric. Although more common in cheap cables, one should be aware of it. Me-chanical deformation of the dielectric causes electrical potentials to be generated.Both species of mechanically generated noise can be reduced or eliminated byproper mounting of the cable. Although rarely a problem at lower frequencies, suchnoise can be significant at microwave frequencies when signals are low.
Coaxial cable capacitance
A coaxial transmission line possesses a certain capacitance per unit of length. This capacitance is defined by :
A long run of coaxial cable can build up a large capacitance. For example, acommon type of coax is rated at 65 pF/m. A 150-m roll thus has a capacitance of 65 pF/m ×(150 m), or 9750 pF. When charged with a high voltage, as is done inbreakdown voltage tests at the factory, the cable acts like a charged high-voltagecapacitor. Although rarely (if ever) lethal to humans, the stored voltage in newcable can deliver a nasty electrical shock and can irreparably damage electronic components.
Coaxial cable cutoff frequency Fo
The normal mode in which a coaxial cable propagates a signal is as a transverseelectromagnetic (TEM) wave, but others are possible—and usually undesirable.There is a maximum frequency above which TEM propagation becomes a prob-lem, and higher modes dominate. Coaxial cable should notbe used above a fre-quency of
where
F is the TEM-mode cutoff frequency
D is the diameter of the outer conductor, in inchesdis the diameter of the inner conductor, in inches
e is the dielectric constant
When maximum operating frequencies for cable are listed, it is the TEM modethat is cited. Beware of attenuation, however, when making selections for microwavefrequencies. A particular cable may have a sufficiently high TEM-mode frequency,but still exhibit a high attenuation per unit length at X or Ku bands.
(from Practical Antenna :by Joseph Carr) If you wantget hardcopy of this Practical Antenna Theory ,You canbuy this book :Practical Antenna Handbook by Joseph Carr:
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