A hairpin match, also known as a Beta match, is a technique used in antenna design to match the impedance of the feedline to the antenna's driven element. It typically involves placing a small coil or loop of wire (often resembling a hairpin shape) across the terminals of the antenna. This coil acts as an inductor, which is used to adjust the impedance and improve the antenna's performance by minimizing reflection of radio frequency energy back down the transmission line

Silly hint: 5th Element "Bada Boom" helps to remember Beta from answer and boom from question

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A Gamma-match can match impedance below 50 ohms right up to that 50 ohms which your transceiver wants to see. A Yagi antenna almost never has an impedance of 50 ohms.

REF: http://www.dx-antennas.com/Gamma_match.htm

Silly Hint: Fraction starts with an F, which is one letter in the alphabet before G, which is the first letter in Gamma

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Hint: A “SHORT length” = A “STUB.”

In microwave and radio-frequency engineering, a stub is a length of transmission line or waveguide that is connected at one end only. The free end of the stub is either left open-circuit or (especially in the case of waveguides) short-circuited. Neglecting transmission line losses, the input impedance of the stub is purely reactive; either capacitive or inductive, depending on the electrical length of the stub, and on whether it is open or short circuit. Stubs may thus be considered to be frequency-dependent capacitors and frequency-dependent inductors. Because stubs take on reactive properties as a function of their electrical length, stubs are most common in UHF or microwave circuits where the line lengths are more manageable. Stubs are commonly used in antenna impedance matching circuits and frequency selective filters.

http://en.wikipedia.org/wiki/Stub_(electronics)

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The PVC insulation that encases the center conductor of a coaxial cable is within the outer tube that provides a series capacitance of some gamma-type matching networks.
The inductive reactance is cancelled by the series capacitance within the matching network. This will lead to a defined resonance.

Hint: "Matching Network" is in the answer.

Memory tip: The TV series was cancelled by the network

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Hint: Hairpins are shorter with a small gap in them much like the gap in a Capacitor

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When implementing a quarter-wave Q-section (also called a quarter wave impedance transformer), the impedance \(Z_o\) of the quarter wave section should be equal to \(\sqrt{Z_{in} Z_L}\). In this case: \(Z_o = \sqrt{50 * 100} = 70.71 \Omega\), which is closest to 75 ohms.

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The reflection coefficient is defined as

\[\Gamma = {(Z_L - Z_0) \over (Z_L + Z_0)}\]

where \(Z_L\) is the impedance of the load and \(Z_0\) is the characteristic impedance of the transmission line. If \(Z_0\) and \(Z_L\) are the same, the reflection coefficient (\(\Gamma\)) is zero. And the reflection coefficient increases the more \(Z_L\) and \(Z_0\) differ, indicating stronger mismatch between the load and transmission line.

Silly hint:the transmission line "reflected" on his behavior the day he lost Mrs Load

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A WIlkinson Power Divider is used in microwave circuitry to split the power coming into the divider's input port into two output ports. Each port has the same impedance and the two output ports are of equal power and are isolated from each other, which minimizes crosstalk between ports. The Wilkinson Divider is passive, so it works equally well as a power combiner due to reciprocity.

Hint: it divides the power "50/50" between two 50 ohm loads.

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The gamma match is an effective method of connecting a 50-ohm coaxial cable feed line to a grounded tower so it can be used as a vertical antenna.

The gamma match is the name of an antenna matching system that matches an unbalanced feed line to an antenna by feeding the driven element both at the center of the element and at a fraction of a wavelength to one side of center.

Mnemonic: A Grounded tower needs a Gamma match.

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These arrays are constructed by using physically identical antennas that are fed with phasing lines that create the necessary phase differences between them. This ensures that each element radiates a signal with the necessary phase to create the desired antenna pattern.

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