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Amateur Radio Info & Exams - Antennas 3 - Parameters and Patterns

Transmission Lines

There are several forms of transmission line.

The most popular type in Amateur radio is coaxial cable, consisting of a central conductor of solid or stranded wire, surrounded by an insulator, also called the dielectric. Around this is a metallic shield, consisting of braid, or foil and braid; or of a corrugated or smooth copper or aluminium tube.

The nature of the dielectric has some affect on the characteristic impedance, and significant impact on the velocity factor of the cable.

A fairly popular alternative consists of two parallel conductors, such window line, a large version of TV ribbon, with large windows cut out, which are often 450 ohms. The next step up is ladder-line, with some form of spacer, often with un-insulated wire, and an impedance of 600 ohms. High power HF broadcasting often uses open wire feed-lines strung tightly between posts with a pair of glass or ceramic insulators, similar to power or more accurately, old-style open-wire telephone lines. These are also 600 ohms. 300 ohm TV ribbon has some application as well. Little known, but ordinary figure-8 speaker wire, or mains zip-line can be used, especially at HF, to feed dipoles.

Off the exam, there are also a range of more complex open wire arrangements, use on broadcast site, both things like 4-wire balanced systems; and unbalanced ones with a single centre signal wire, and 4 grounded wires, sort of emulating coax.

Velocity Factor

RF energy travels through different cables at different speeds, termed the velocity factor, a factor which represents the proportion of the speed of light at which the signal travels. The slowest propagation, and the lowest VF is in coax using solid polyethylene, a tough translucent plastic, as the dielectric, at around 0.66. PTFE (Teflon) is similar if solid, at 0.695. If either is in foam form, then signals propagate faster, around 0.78 to 0.88, depending on the nature of the foam. Air-spaced cable is listed on Wikipedia as having a VF of "about" 1. As we know, signals cannot exceed c, the speed of light in a vacuum.

Occasionally the VF is written as a percentage.

This velocity factor might not matter if you are connecting a 2 metre rig to a resonant antenna on a vehicle, or connecting to a simple dipole at home, but comes into play when you do cool stuff using fractional wavelengths of coax.

An example of this is the quarter-wave transformer, made using a length of coax. The most common is using a piece of 75 ohm cable to transform from a 100 ohm antenna, such as a loop, to 50 ohm feedline. For a specific frequency, how long this is depends on the VF of the cable.

Thus, if we have RG-59/U, with solid PE, and a VF of 0.66 we multiply the free-space quarter-wave figure by 0.66. Thus, if we are in the CW sub-band at 50 MHz, 300 / 50 x 0.25, we get 1.5 metres. In this case we cut the cable to 1.5 x 0.66 = 0.99 metres. If we have RG-59A/U with a foam dielectric, and thus a VF of 0.78, we need 1.5 x 0.78 = 1.17 metres of cable.

The parallel line discussed above has a fairly high VF, and reverse engineering the question about it, the examiner is now assuming the figure is so close to 1 as to not be calculated.

VF is also applied in the following cases:

Quarter-wavelength Coax - Shorted or Open

If a quarter-wave can transform, as above, then if the end is shorted, then the opposite, an open will appear at the other end; and if opened it appears as a short. Note that this is termed as a very low, or very high impedance. Note that this only applies at the frequency at which it is a quarter-wave.

Off the exam, these can be used as "stub" filters, meaning a shorted quarter-wave, which appears open provides a band-path filter; while an open stub, which appears as a short can be used as a notch filter. A downside of these filters is that while they can be effective for blocking a harmonic at twice the fundamental, they tend to pass signals at 3 times the fundamental, as the stub appears as a 3/4 wave.

Half-wavelength Coax

A half-wave length of cable passes the impedance it "sees" in the load to the source.

In the past, it was said that a VHF feedline should be a multiple of electrical half-wavelengths long.

Eighth-wavelength Coax - Shorted or Open

Two further cases are the shorted and open lengths of 1/8 wavelength. A shorted piece appears inductive reactance, while an open section appears as a capacitive reactance.

Wilkinson divider

In various situations we need to divide power from a single feedline into two loads, typically two antennas. An example is feeding two folded dipoles in a repeater system. Originally designed by Ernest J. Wilkinson for microwave work, and published in 1960, they can be constructed using quarter-wave lines in PCBs, or using coaxial cable. These lines or cables act as transformers, as previously discussed, and as such, you do need to take VF into account.

Optionally, a resistor of twice the system impedance is placed between the two output ports, and this helps cancel noise, and provide isolation between the outputs. This is probably more important if the splitter is feeding amplifiers.

A common configuration takes a 50 ohm input, and uses two λ/4 lengths of 70 to 75 Ω and outputs at 50 ohms. Given a 50 ohms load, coax of around 70 ohms, the driven end of EACH coax will present a 100 ohm impedance. Place two in parallel, and we see 50 ohms. Nice!

Thus the resistor between the outputs, if used, would be 100 ohms.

Another use is to feed the two feedpoints spaced 90 degrees along the boom on a × or + format circularly polarised Yagi, used for VHF or UHF satellite work.

Two additional features of the Wilkinson is that the levels on both outputs are at the same level (that is, the division is equal), and the same phase.

Yagi feedpoint methods

Yagi and similar antennas often have the driven element split into two sections at the point it crosses the boom, and plastic used to mount the elements, with the disadvantages that it is weaker, and the plastic eventually degrades. Several other arrangements, which use a continuous driven element, and also allow them to be grounded (that, is, directly connected to the boom. Some are named for the Greek character which they look most like.

The Delta match looks like the upper-case delta Δ. The feedline is spread to connect some distance either side of the centre-point of the driven element.

The Gamma match looks like an upper-case Γ. Most often this consists of a coaxial connection, with the shield connected to the centre point. The inner is connected via a capacitor to a tube running parallel to the element, and connected some distance from the centre point. While a discreet capacitor may be included, often the connection from the coax is to a thick wire running within, and insulated from, the tube, forming a capacitor.

The Stub match typically consists of a hairpin shaped loop or stub of aluminium wire.

Relevant Questions

These are actual questions from the NCVEC Extra exam pool.

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?
A. The gamma matching system
B. The delta matching system
C. The omega matching system
D. The stub matching system

This is the delta match, so named because the feedline splays into a triangle, or delta shape, Δ, answer B.

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?
A. The gamma match
B. The delta match
C. The epsilon match
D. The stub match

The is the Gamma match, Γ, answer A.

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?
A. The gamma match
B. The delta match
C. The omega match
D. The stub match

The match which uses a section or stub of transmission line is the stub match, answer D.

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

The capacitor cancels the inductance of the matching network, answer B.

How must an antenna's driven element be tuned to use a hairpin matching system?
A. The driven element reactance must be capacitive
B. The driven element reactance must be inductive
C. The driven element resonance must be lower than the operating frequency
D. The driven element radiation resistance must be higher than the characteristic impedance of the transmission line

The element mast be made capacitive to counter the inductive nature of the hairpin match, answer A.

Which of these feed line impedances would be suitable for constructing a quarter-wave Q-section for matching a 100-ohm loop to 50-ohm feed line?
A. 50 ohms
B. 62 ohms
C. 75 ohms
D. 450 ohms

Half-way between 100 and 50 is 75 ohms, answer C.

What parameter describes the interactions at the load end of a mismatched transmission line?
A. Characteristic impedance
B. Reflection coefficient
C. Velocity factor
D. Dielectric constant

Mismatch generates reflections, so it is reflection coefficient, answer B.

What is a use for a Wilkinson divider?
A. It divides the operating frequency of a transmitter signal so it can be used on a lower frequency band
B. It is used to feed high-impedance antennas from a low-impedance source
C. It is used to divide power equally between two 50 ohm loads while maintaining 50 ohm input impedance
D. It is used to feed low-impedance loads from a high-impedance source

The Wilkinson divides power equally between two outputs, while preserving impedance. Answer C.

Which of the following is used to shunt-feed a grounded tower at its base?
A. Double-bazooka match
B. Hairpin match
C. Gamma match
D. All of these choices are correct

A Gamma match can also be used to feed a grounded tower, answer C.

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?
A. 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
B. Insert a 1/2 wavelength piece of 300 ohm twin-lead in series between the antenna terminals and the 50 ohm feed cable
C. 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
D. Connect 1/2 wavelength shorted stub of 75 ohm cable in parallel with the 50 ohm cable where it attaches to the antenna

Once again, it is the 1/4 length of 75 ohm coax, answer C.

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

Phasing lines ensure that each of the driven elements is driven with the correct phase, so they work in concert, answer A.

If you see a phased array VHF TV antenna, popular in rural Australia, or a bow-tie UHF one, you will see the central feedpoint, with parallel tubes of wires running to the two centre-most driven elements, then these lines crossing over to feed the two outer-most.

What is the velocity factor of a transmission line?
A. The ratio of the characteristic impedance of the line to the terminating impedance
B. The index of shielding for coaxial cable
C. The velocity of the wave in the transmission line multiplied by the velocity of light in a vacuum
D. The velocity of the wave in the transmission line divided by the velocity of light in a vacuum

This is the velocity at which a radio wave travels in the cable divided by the speed of light, answer D.

If a signal travels at 200,000,000 metres per second, this over 300,000,000 is 0.667, the VF of typical coax with a solid PE (polyethylene) dielectric.

Which of the following has the biggest effect on the velocity factor of a transmission line?
A. The termination impedance
B. The line length
C. Dielectric materials used in the line
D. The center conductor resistivity

This is the nature of the dielectric material, including whether is is solid or foamed, answer C.

Why is the physical length of a coaxial cable transmission line shorter than its electrical length?
A. Skin effect is less pronounced in the coaxial cable
B. The characteristic impedance is higher in a parallel feed line
C. The surge impedance is higher in a parallel feed line
D. Electrical signals move more slowly in a coaxial cable than in air

Signals travel more slowly in coax than in air, answer D.

What impedance does a 1/2 wavelength transmission line present to a generator when the line is shorted at the far end?
A. Very high impedance
B. Very low impedance
C. The same as the characteristic impedance of the line
D. The same as the output impedance of the generator

A half-wave of coax transfers the impedance, so it looks like a short (very low impedance) in this case, answer B.

What is the approximate physical length of a solid polyethylene dielectric coaxial transmission line that is electrically 1/4 wavelength long at 14.1 MHz?
A. 10.6 meters
B. 5.3 meters
C. 4.3 meters
D. 3.5 meters

This is in the 20 metre band, so the a quarter-wave is space is about 5 metres. Solid polyethylene has a VF of 0.66, so this is about 3.3 metres, nearest to answer D.

Calculating it properly is 299.7 / 14.1 = 21.255 metre. Thus it is 21.255 / 4 x 0.66 = 3.507 metres.

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?
A. 7.0 meters
B. 8.5 meters
C. 10.6 meters
D. 13.3 meters

This is the 20 metre band, so half-wave is around 10 metres. Calculating it, 299.7 / 14.1 = 21.255 m. 21.255 / 2 x 0.94 = 10.627 metres, answer C.

You will note they have not factored in a VF, as this is fairly high (close to 1) with this cable type.

How does ladder line compare to small-diameter coaxial cable such as RG-58 at 50 MHz?
A. Lower loss
B. Higher SWR
C. Smaller reflection coefficient
D. Lower velocity factor

The only valid answer is that is has lower loss, answer A.

Which of the following is a significant difference between foam dielectric coaxial cable and solid dielectric cable, assuming all other parameters are the same?
A. Foam dielectric has lower safe operating voltage limits
B. Foam dielectric has lower loss per unit of length
C. Foam dielectric has higher velocity factor
D. All of these choices are correct

All factors are fairly logical, and are correct, answer D.

What is the approximate physical length of a foam polyethylene dielectric coaxial transmission line that is electrically 1/4 wavelength long at 7.2 MHz?
A. 10.4 meters
B. 8.3 meters
C. 6.9 meters
D. 5.2 meters

40 metre band, so a quarterwave is 10 metres in free space, multiply by the VF of 0.8, and we get about 8 metres, answer B.

Doing it properly, 299.7 / 7.2 x 0.25 x 0.80 = 10.40625 x 0.80 = 8.325 metres.

What impedance does a 1/8 wavelength transmission line present to a generator when the line is shorted at the far end?
A. A capacitive reactance
B. The same as the characteristic impedance of the line
C. An inductive reactance
D. Zero

Like most closed loops, this is an inductive reactance, answer C.

What impedance does a 1/8 wavelength transmission line present to a generator when the line is open at the far end?
A. The same as the characteristic impedance of the line
B. An inductive reactance
C. A capacitive reactance
D. Infinite

This presents a capacitive reactance, answer C.

Like two insulated conductors in parallel, this behaves like a regular capacitor.

What impedance does a 1/4 wavelength transmission line present to a generator when the line is open at the far end?
A. The same as the characteristic impedance of the line
B. The same as the input impedance to the generator
C. Very high impedance
D. Very low impedance

A quarter-wave section reverses the impedance, so it appears like a near short (low impedance), answer D.

What impedance does a 1/4 wavelength transmission line present to a generator when the line is shorted at the far end?
A. Very high impedance
B. Very low impedance
C. The same as the characteristic impedance of the transmission line
D. The same as the generator output impedance

This will appear as an open, or near open circuit (high impedance), answer A.

On to: Antennas 4 - Smith Charts; Loops and Beverage Antennas

You can find links to lots more on the Learning Material page.

Written by Julian Sortland, VK2YJS & AG6LE, July 2022.

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