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Subelement E9
ANTENNAS AND TRANSMISSION LINES
Section E9E
Matching: matching antennas to feed lines; phasing lines; power dividers
What system matches a higher impedance transmission line to a lower impedance antenna by connecting the line to the driven element in two places spaced a fraction of a wavelength each side of element center?
• The gamma matching system
The delta matching system
• The omega matching system
• The stub 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 - $\Delta$.

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What 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?
The gamma match
• The delta match
• The epsilon match
• The stub match

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.

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What is the name of the matching system that uses a section of transmission line connected in parallel with the feed line at or near the feed point?
• The gamma match
• The delta match
• The omega match
The stub match

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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What is the purpose of the series capacitor in a gamma-type antenna matching network?
• To provide DC isolation between the feed line and the antenna
To cancel the inductive reactance of the matching network
• To provide a rejection notch that prevents the radiation of harmonics
• To transform the antenna impedance to a higher value

Hint: "Matching Network" is in the answer.

kg5kou

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 in-turn lead to a defined resonance.

-KE0IPR

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How must the driven element in a 3-element Yagi be tuned to use a hairpin matching system?
The driven element reactance must be capacitive
• The driven element reactance must be inductive
• The driven element resonance must be lower than the operating frequency
• The driven element radiation resistance must be higher than the characteristic impedance of the transmission line

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.

-w1sop-2

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

-KE0IPR

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What is the equivalent lumped-constant network for a hairpin matching system of a 3-element Yagi?
• Pi-network
• Pi-L-network
A shunt inductor
• A series capacitor

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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What term best describes the interactions at the load end of a mismatched transmission line?
• Characteristic impedance
Reflection coefficient
• Velocity factor
• Dielectric constant

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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Which of the following measurements is characteristic of a mismatched transmission line?
• An SWR less than 1:1
• A reflection coefficient greater than 1
• A dielectric constant greater than 1
An SWR greater than 1:1

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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Which of these matching systems 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?
• Double-bazooka match
• Hairpin match
Gamma match
• All of these choices are correct

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.

-KE0IPR

Mnemonic: A Grounded tower needs a Gamma match.

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Which of these choices is an effective way to match an antenna with a 100 ohm feed point impedance to a 50 ohm coaxial cable feed line?
• Connect a 1/4-wavelength open stub of 300 ohm twin-lead in parallel with the coaxial feed line where it connects to the antenna
• Insert a 1/2 wavelength piece of 300 ohm twin-lead in series between the antenna terminals and the 50 ohm feed cable
Insert a 1/4-wavelength piece of 75 ohm coaxial cable transmission line in series between the antenna terminals and the 50 ohm feed cable
• Connect 1/2 wavelength shorted stub of 75 ohm cable in parallel with the 50 ohm cable where it attaches to the antenna

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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What is an effective way of matching a feed line to a VHF or UHF antenna when the impedances of both the antenna and feed line are unknown?
• Use a 50 ohm 1:1 balun between the antenna and feed line
Use the universal stub matching technique
• Connect a series-resonant LC network across the antenna feed terminals
• Connect a parallel-resonant LC network across the antenna feed terminals

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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What is the primary purpose of a phasing line when used with an antenna having multiple driven elements?
It ensures that each driven element operates in concert with the others to create the desired antenna pattern
• It prevents reflected power from traveling back down the feed line and causing harmonic radiation from the transmitter
• It allows single-band antennas to operate on other bands
• It makes sure the antenna has a low-angle radiation pattern

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.

-KE0IPR

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What is a use for a Wilkinson divider?
• It divides the operating frequency of a transmitter signal so it can be used on a lower frequency band
• It is used to feed high-impedance antennas from a low-impedance source