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E9E

ANTENNAS AND TRANSMISSION LINES

Impedance matching: matching antennas to feed lines; phasing lines; power dividers

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E9E011 of 10

Which matching system for Yagi antennas requires the driven element to be insulated from the boom?

Why The beta or hairpin match works on a split driven element: the element is made slightly short so it looks capacitive, and a shorted transmission line stub (the hairpin) placed across the feedpoint adds the inductive reactance that cancels it and raises the resistive part to 50 ohms. Because the feed point is a gap at the center of the element, that element cannot be bolted to a grounded metal boom, so it must be mounted on an insulator.
Watch out Gamma, T-match and other shunt-fed schemes are the opposite case: they tap onto a continuous, unbroken element that is deliberately bolted right to the boom, which is why they are popular for DC grounding and static bleed.
Hairpin = split element = insulated. Gamma/T = solid element = bolt it to the boom.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
E9E022 of 10

What antenna matching system matches coaxial cable to an antenna by connecting the shield to the center of the antenna and the conductor a fraction of a wavelength to one side?

Why The gamma match is the unbalanced (coax-friendly) feed for a grounded-center driven element: the braid bonds to the element's center, which is a voltage null and can be at boom/ground potential, while the center conductor runs through a series capacitor to a gamma rod that taps the element a short distance out to one side. Moving that tap point out from center finds a spot where the resistive part matches 50 ohms, and the series capacitor cancels the added inductive reactance. It is the standard driven-element match on Yagis fed with coax.
Watch out The T-match is the same idea but symmetric, with rods tapping the element on both sides for a balanced line, and the delta match spreads a balanced line open into a triangle touching two points either side of center; neither uses a single one-sided tap with the shield at the middle.
Gamma = Greek letter with one leg off to the side; T-match has two legs, delta is a triangle.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
E9E033 of 10

What matching system uses a short length of transmission line connected in parallel with the feed line at or near the feed point?

Why A stub match is a short piece of transmission line, usually shorted or open at its far end, connected in shunt (parallel) with the main feed line at or very near the feed point. A shorted or open line shorter than a quarter wave behaves as a pure reactance, so by choosing its length and position you can cancel the reactive part of the load and transform the remaining resistance to the line impedance. This is the classic single-stub tuner seen as a circle-to-circle move on the Smith chart.
Watch out The gamma and T-matches are different animals: they use conductive rods running alongside the driven element and tapping it at points away from center (the gamma is the single-sided version, the T is the symmetric balanced version), and the delta match fans the feed line out to two points on the element. None of those is a piece of transmission line in parallel with the feed line.
Stub = a stubby length of line hung in parallel; gamma/T/delta = rods tapping the driven element.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
E9E044 of 10

What is the purpose of the series capacitor in a gamma match?

Why A gamma match taps the driven element off-center with a gamma rod running parallel to the element. That rod and its connection behave like a shorted transmission line stub plus added conductor length, so the feed point looks resistive plus a substantial inductive reactance. A capacitor placed in series with the rod contributes negative (capacitive) reactance that cancels the inductive part, leaving a nearly pure resistance close to 50 ohms for the coax. Adjusting the capacitor and the rod tap point together tunes both reactance and resistance to a match.
Watch out Transforming the impedance upward is the job of the tap position along the driven element, not the capacitor; and while the capacitor does happen to block DC, that is incidental, since a gamma match is used on grounded-element beams where DC isolation is not the design goal.
Gamma rod adds +jX, so the series cap supplies -jX. Capacitor cancels coil.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
E9E055 of 10

What Yagi driven element feed point impedance is required to use a beta or hairpin matching system?

Why A beta or hairpin match is simply a shorted transmission line stub or wire loop placed in shunt across the feed point, and it acts as an inductor. For that shunt inductance to form a working L-network, the driven element itself must supply the opposite (capacitive) reactance, which means it is tuned slightly short of resonance, electrically shorter than 1/2 wavelength. The shunt inductor cancels that capacitive reactance and at the same time transforms the element's low radiation resistance (often 20 to 25 ohms on a close-spaced Yagi) up to the 50 ohms the feed line wants.
Watch out An inductive (electrically long) element is what a gamma or omega match wants to work against, since those add series capacitance; adding a shunt hairpin inductor to an already inductive element only makes the mismatch worse. A purely resistive element needs no matching network at all.
Hairpin = inductor, so the element must be capacitive: short element, shunt coil, reactances cancel.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
E9E066 of 10

Which of these transmission line impedances would be suitable for constructing a quarter-wave Q-section for matching a 100-ohm feed point impedance to a 50-ohm transmission line?

Why A quarter-wave transformer (Q-section) transforms impedances according to Z0 = sqrt(Z_load x Z_source). Here sqrt(100 x 50) = sqrt(5000) = 70.7 ohms, so the nearest readily available coax, 75-ohm line, is the practical choice. The section must be a quarter wavelength long at the operating frequency, accounting for the line's velocity factor.
Watch out The 50-ohm and 90-ohm values are too far from the 70.7-ohm geometric mean, and 62 ohms is below it; the answer must land just under the midpoint between 50 and 100, which 75-ohm cable does while also being a standard cable type.
Q-section = geometric mean: sqrt(50 x 100) = 70.7, and the coax you can actually buy at that value is 75 ohms.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
E9E077 of 10

What parameter describes the interaction of a load and transmission line?

Why The reflection coefficient, usually written as the Greek letter gamma, is defined by the mismatch between the load and the line: gamma = (ZL - Z0)/(ZL + Z0). It tells you what fraction of the incident voltage wave bounces back from the load, so it is the one parameter that depends on both the load and the feed line. When ZL equals Z0 the numerator is zero, there is no reflection, and SWR is 1:1; SWR and reflection coefficient are directly related by SWR = (1 + |gamma|)/(1 - |gamma|).
Watch out Characteristic impedance is tempting, but it is a property of the transmission line alone, set by its conductor geometry and dielectric, and says nothing about what load is attached. Velocity factor and dielectric constant are also line-only properties describing propagation speed and insulation.
Reflection = interaction. Only the reflection coefficient uses BOTH ZL and Z0: (ZL - Z0)/(ZL + Z0).
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
E9E088 of 10

What is a use for a Wilkinson divider?

Why A Wilkinson divider is an RF power splitter built from two quarter-wavelength transmission line sections of about 70.7 ohms (the geometric mean of 50 and 100 ohms), with a 100-ohm isolation resistor bridging the two output ports. It takes one 50-ohm input and delivers half the power to each of two 50-ohm loads, while the input still looks like 50 ohms. It is commonly used to feed stacked or phased antenna arrays from a single feed line, and the bridging resistor keeps the two outputs isolated from each other.
Watch out The choices about dividing frequency confuse the word "divider" with a digital frequency divider or prescaler; a Wilkinson divides power, not frequency. Matching a low-impedance source to a high-impedance antenna is the job of a transformer or matching network, not a splitter.
Wilkinson = power splitter, not frequency divider. One 50-ohm in, two 50-ohm outs, quarter-wave 70.7-ohm arms.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
E9E099 of 10

Which of the following is used to shunt feed a grounded tower at its base?

Why A gamma match taps the driven element (or tower) at a point some distance up from ground, running a parallel conductor from the feed point back down to the coax center conductor while the shield bonds to the grounded base. The tap height sets the resistive part of the impedance and a series capacitor in the gamma rod cancels the leftover inductive reactance, so a grounded tower used as a vertical radiator can be matched to 50 ohm coax without breaking the DC ground.
Watch out The beta or hairpin match is a shunt inductor used across a balanced driven element whose feedpoint is capacitive, typically on a Yagi, and it requires a split (not grounded) element. The double-bazooka is a broadbanding coaxial sleeve dipole design, not a tower feed method.
Grounded tower, shunt fed = Gamma. Gamma has one arm, like the Greek letter, tapping the tower above the base.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
E9E1110 of 10

What is the purpose of using multiple driven elements connected through phasing lines?

Why Phasing lines set the relative amplitude and, more importantly, the relative phase of the current fed to each driven element. Because the radiated fields from the elements add in some directions and cancel in others, changing the phase relationship steers and shapes the pattern, giving broadside, end-fire, cardioid or steerable lobes. A classic example is the AM broadcast or 80/40 meter phased vertical array, where changing line lengths or switching phases rotates the null and main lobe.
Watch out Producing a low-angle pattern is only one possible result of one particular phasing arrangement, not the general purpose; phasing lines can also produce high-angle, broadside or bidirectional patterns. Phasing lines do nothing about transmitter harmonics and do not add band coverage.
Phasing lines = pattern control. Phase relationship decides where signals add and where they cancel.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
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