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E9F

ANTENNAS AND TRANSMISSION LINES

Transmission lines: characteristics of open and shorted feed lines; coax versus open wire; velocity factor; electrical length; coaxial cable dielectrics; microstrip

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E9F011 of 12

What is the velocity factor of a transmission line?

Why Velocity factor (VF) is simply the speed of the wave travelling in the line expressed as a fraction of c, the speed of light in free space: VF = v/c. Because the dielectric surrounding the conductors slows propagation, VF is always less than 1, roughly 0.66 for solid polyethylene coax, about 0.8 for foam coax, and 0.95 or more for open wire line. VF also equals 1/sqrt(dielectric constant), and you use it to find physical length: physical length = VF times the free space length.
Watch out The multiplication version would give a meaningless number far larger than c; velocity factor must be a ratio less than one, so the wave speed has to be on top of the fraction. The impedance ratio choices describe standing wave ratio, not velocity factor.
VF = line speed divided by c, always under 1. Coax 0.66, foam 0.8, open wire 0.95.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
E9F022 of 12

Which of the following has the biggest effect on the velocity factor of a transmission line?

Why Velocity factor is the ratio of the speed of a signal in the line to the speed of light in free space, and it is set almost entirely by the dielectric surrounding the conductors: VF = 1/sqrt(er), where er is the relative permittivity of that insulation. Solid polyethylene coax (er about 2.3) gives roughly 0.66, foamed polyethylene about 0.8, and air-spaced open wire line approaches 0.95 or better because there is very little solid material between the conductors. Change the insulating material and the wave speed, and therefore the electrical length of a given physical length, changes with it.
Watch out Characteristic impedance is tempting because it also depends on the dielectric, but it is set by the conductor geometry (the ratio of shield to center conductor diameters) as much as by the insulation, and two lines of the same impedance can have very different velocity factors. Physical length and conductor resistivity affect loss and electrical length in wavelengths, not the propagation speed itself.
Velocity factor lives in the insulation: VF = 1/sqrt(dielectric constant). More air, faster line.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
E9F033 of 12

Why is the electrical length of a coaxial cable longer than its physical length?

Why Inside a coax the dielectric between center conductor and shield slows the wave to a fraction of its free-space speed, described by the velocity factor (about 0.66 for solid polyethylene, 0.78-0.85 for foam, 1.0 for air). Because the wave travels slower, the wavelength inside the cable is shorter, so a given physical piece of cable contains more wavelengths than the same distance in air. That is why, in electrical degrees or wavelengths, the cable measures longer than a tape measure says. To cut a quarter-wave stub you multiply the free-space quarter wavelength by the velocity factor.
Watch out Nothing propagates faster than light in free space, so the choice saying waves move faster in coax is impossible; skin effect relates to conductor loss and current distribution, not to propagation speed.
Slower wave, shorter wavelength, more wavelengths per foot: physical length times VF gives the free-space equivalent.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
E9F044 of 12

What impedance does a 1/2-wavelength transmission line present to an RF generator when the line is shorted at the far end?

Why A transmission line repeats its terminating impedance every half wavelength, so a 1/2-wavelength line is essentially a 1:1 transformer regardless of its characteristic impedance. With a short circuit at the far end, the generator sees that same short, so the input impedance is very low (limited only by line loss). The general relation Zin = Z0(ZL + jZ0 tan(beta*L))/(Z0 + jZL tan(beta*L)) reduces to Zin = ZL when the electrical length is a half wavelength, because tan(180 degrees) = 0.
Watch out Very high impedance is what a quarter-wavelength shorted stub presents, since a quarter wave acts as an impedance inverter; a half wave does not invert, it repeats.
Half wave repeats, quarter wave inverts. Shorted half wave = still a short.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
E9F055 of 12

What is microstrip?

Why Microstrip is a planar transmission line formed right on a printed circuit board: a narrow trace of controlled width running above a continuous ground plane on the other side of the dielectric substrate. The trace width, board thickness and dielectric constant set the characteristic impedance, so designers can print 50 ohm (or other) lines directly into the layout. At microwave frequencies, where connectors and coax jumpers add loss and reflections, these printed constant-impedance interconnects are the practical way to move signals between circuit blocks.
Watch out The idea of tiny coax soldered to the board is tempting because microstrip does the same job, but microstrip has no outer shield at all, just a trace and the ground plane beneath it.
Micro-STRIP = a strip of copper over a ground plane; width plus board thickness set the impedance.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
E9F066 of 12

What is the approximate physical length of an air-insulated, parallel conductor transmission line that is electrically 1/2 wavelength long at 14.10 MHz?

Why A half wavelength in free space is 150/f(MHz) meters, so at 14.10 MHz that is 150/14.10 = 10.64 meters. An air-insulated open-wire line has almost no dielectric loading, so its velocity factor is essentially 1.0 and the physical length matches the free-space electrical length. In feet the same calculation is 492/f(MHz) = about 34.9 feet.
Watch out The choice near 7.0 meters is what you get if you apply a velocity factor of about 0.66, which belongs to solid-polyethylene coax, not open-wire line in air.
Half wave in meters = 150 / f(MHz); air line VF = 1, so no shrink factor.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
E9F077 of 12

How does parallel conductor transmission line compare to coaxial cable with a plastic dielectric?

Why Open-wire or ladder line uses mostly air as its dielectric, with only small spacers touching the conductors, so dielectric heating losses are minimal. The conductors are also spaced widely, which raises the characteristic impedance and lowers the current for a given power, reducing I-squared-R loss. Solid plastic dielectric coax, by contrast, dissipates energy in the polyethylene, especially at VHF and above. That is why open wire is preferred for long runs and for feeding antennas at high SWR.
Watch out The velocity factor choice has it backwards: air-spaced line runs about 0.9 to 0.95, while solid polyethylene coax is near 0.66. SWR and reflection coefficient are set by the load and the line impedance, not by the type of line construction.
Air beats plastic: open wire has less dielectric, so less loss and a higher velocity factor.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
E9F088 of 12

Which of the following is a significant difference between foam dielectric coaxial cable and solid dielectric coaxial cable, assuming all other parameters are the same?

Why Foam dielectric is mostly air with a plastic matrix, so its dielectric constant is lower than solid polyethylene. That raises the velocity factor (roughly 0.78 to 0.85 versus about 0.66 for solid PE) and cuts dielectric losses, so foam cable has lower attenuation per hundred feet. The tradeoff is that the softer, less dense material breaks down at a lower voltage and the center conductor can migrate under compression, so the safe maximum operating voltage is lower.
Watch out Each single-item choice is true on its own, which is the trap: picking just the velocity factor or just the loss statement misses that all three describe foam cable.
Foam = more air: faster (higher VF), lower loss, but weaker insulation. Three true statements means pick them all.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
E9F099 of 12

What impedance does a 1/4-wavelength transmission line present to an RF generator when the line is shorted at the far end?

Why A transmission line an odd multiple of 1/4 wavelength long acts as an impedance inverter: Zin = Z0^2 / ZL. With the far end shorted, ZL is essentially zero, so Zin goes toward infinity and the generator sees a very high impedance. This is why shorted quarter-wave stubs behave like parallel resonant circuits at their design frequency and are used as notch filters and metal insulators.
Watch out Very low impedance is what a shorted line presents when it is a half wavelength (or any multiple of a half wavelength) long, since a half-wave line repeats the load impedance rather than inverting it.
Quarter wave flips it: short in, open out; open in, short out. Half wave repeats what it sees.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
E9F1010 of 12

What impedance does a 1/8-wavelength transmission line present to an RF generator when the line is shorted at the far end?

Why For a shorted line the input impedance is jZ0 tan(theta), where theta is the electrical length. At 1/8 wavelength theta is 45 degrees, so the input impedance is +jZ0, a purely inductive reactance whose magnitude equals the characteristic impedance. Any shorted line shorter than 1/4 wavelength looks inductive; it only becomes a parallel-resonant open circuit at exactly 1/4 wavelength.
Watch out Capacitive reactance is what a 1/8-wavelength line with an open far end presents, since an open line behaves the opposite way from a shorted one. The choice saying zero would only apply to a short line very much shorter than 1/8 wavelength, or a half-wavelength line, which repeats the short.
Short stays short: shorted stub under 1/4 wave acts inductive; open stub under 1/4 wave acts capacitive.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
E9F1111 of 12

What impedance does a 1/8-wavelength transmission line present to an RF generator when the line is open at the far end?

Why An open-ended line shorter than a quarter wavelength behaves like a capacitor. The input impedance of a lossless open line is Zin = -jZ0 cot(βl); at 1/8 wavelength βl = 45 degrees and cot(45°) = 1, so Zin = -jZ0, a pure capacitive reactance equal in magnitude to the characteristic impedance. Only at 1/4 wavelength does the open line transform into a short, and beyond that it turns inductive.
Watch out An inductive reactance is what a 1/8-wavelength line with a shorted far end presents; infinite impedance applies only to a very short open stub or a half-wavelength open line.
Open stub starts as a capacitor, shorted stub starts as an inductor. At 1/8 wave the magnitude is exactly Z0.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
E9F1212 of 12

What impedance does a 1/4-wavelength transmission line present to an RF generator when the line is open at the far end?

Why A quarter-wavelength line acts as an impedance inverter: Zin = Z0 squared divided by ZL. With the far end open, ZL is essentially infinite, so Zin goes to nearly zero and the generator sees a very low impedance, like a short. In physical terms the open end forces a voltage maximum and current zero, and a quarter wave back along the line those conditions reverse to a current maximum and voltage minimum.
Watch out Very high impedance is what a quarter-wave line shows when the far end is shorted, and it is also what an open half-wave line (or any multiple of a half wave) repeats back to the input.
Quarter wave flips it: open far end looks shorted, shorted far end looks open. Half wave repeats what it sees.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
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