Answer: The delta matching system

An easy way to remember this is the two lines help form a triangle, or the Greek letter used as the fourth letter in the phonetic alphabet - \(\Delta\).

For a visual representation between a delta and a gamma match, see: here

Hint: The question says 'higher' impedance. Think Delta planes fly 'higher'.

Hint: The Greek letter Delta is used to indicate "change" in math and science, and we're changing impedance in the system.

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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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Memorization trick: a SECTION of transmission line = a STUB (like a movie ticket stub is a section of the ticket)

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.

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Think of the hairpin as a coil. It is a conductor with an inductive reactance. A tuned antenna is resonant which means inductive and capacitive reactances cancel each other out. For an inductor to tune an antenna the antenna must be capacitive.

Hint: Hairpin = Inductor, Inductors cancel Capacitors, to tune, we must have cancelled reactance. Thus The driven element reactance must be capacitive

Hint #2: Hairpin goes on your head. So does a baseball cap (Capacitive).

Silly hint: Reactance must be Capacitive so put a "Hairpin" in your "Cap"

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The equivalent lumped-constant network for a hairpin matching system of a 3-element Yagi is a shunt inductor.

Remember that the driven element must be capacitive. The hairpin matching system must be inductive. Hence, a shunt inductor is its equivalent.

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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.

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Think of logic behind this problem. One ratio number must be higher than the other (it is the whole point of ratios). This is where SWR comes into play. SWR compares the impedance together.

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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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The impedance of a quarter wavelength matching transformer can be found by taking the square root of the product of the two impedances to be matched.

For this problem a 100 ohm impedance must be matched to a 50 ohm impedance.

\[\sqrt{50 \times 100}=\sqrt{5000} \approx 70.71\approx75\]

Therefore, a quarter (1/4) wavelength piece of 75-ohm coax should match the two impedances relatively well.

The formula for the impedance of a quarter wavelength matching transformer is: \[Z_{\text{in}}=\frac{Z_0^2}{Z_L}\Rightarrow Z_0=\sqrt{Z_{\text{in}}Z_L}\] where:

• \(Z_{\text{in}}\) is the input impedance

• \(Z_0\) is the characteristic impedance

• \(Z_L\) is the load impedance

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Universal stubs are most used in VHF and higher applications to keep the feed line manageable. They are called universal because it can match unknown feed line and antenna impedances.

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Memorization trick:

Each band goes on stage in phases at a concert

Also, driven element is mentioned in question and answer

Some beam antennas use multiple driven elements in order to make them multi-band antennas. The primary purpose of a phasing line when used with an antenna having multiple driven elements is that it ensures that each driven element operates in concert with the others to create the desired antenna pattern.

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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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