Learn/ Extra course/Module 7 of 10
Extra Course, Module 7: Antennas as Engineering
Covers NCVEC 2024-2028 Extra Pool, Subelement E9 (Antennas and Transmission Lines). Eight questions on your exam come from this material.
Ray rolls a whiteboard out to the antenna field. "Technician gave you antennas as facts, General gave you antennas as math. Extra gives you antennas as engineering: efficiency budgets, patterns you can predict before you build, matching you can design instead of buy, and the one chart that makes transmission lines visible. Eight sections. This is the module your capstone project lives in."
7.1The Antenna's Balance Sheet
Every antenna keeps books, and radiation resistance is the honest column: the equivalent resistance that would dissipate the same power the antenna actually radiates. It is not a real resistor; it is radiation itself, wearing Ohm's Law. The feed point resistance you measure is the sum of radiation resistance plus loss resistance, and the ratio is everything:
Efficiency = radiation resistance / (radiation resistance + loss resistance)
That one fraction explains three courses of advice. Electrically short antennas (the mobile whips of General Module 8) have very low radiation resistance, so even small loss resistances eat a huge share. Ground-mounted verticals lose power in the dirt, so their efficiency is improved by more and better radials, shrinking the loss term.
The reference standards, formalized: an isotropic radiator is the theoretical antenna radiating equally in all directions, the zero point of dBi. The 2.15 dB offset to dBd carries over from General. From gain and losses comes effective radiated power: transmitter power adjusted by every system gain and loss, referenced to a dipole (ERP) or to isotropic (EIRP). The method is pure decibel bookkeeping: sum the dB, convert. A repeater running 150 watts through 2 dB of feed line loss and 2.2 dB of duplexer loss into a 7 dBd antenna nets +2.8 dB, for an ERP of about 286 watts. The FCC bought this arithmetic for the 630- and 2200-meter limits in Module 1; now you can audit it.
Directivity's measure: beamwidth is the angle between the half-power (3 dB) points of the main lobe, and it trades directly against gain: squeeze the pattern narrower and the gain rises, the balloon metaphor from the Technician course now wearing numbers.
Knowledge Check 7.1
Tap an answer. In your own words first, then check yourself.
1. What is radiation resistance?
2. Why are electrically short antennas inefficient?
3. How is antenna beamwidth defined?
E9A the easy way: all 12 questions, with the right answer
Every pool question in this group. Read the answer, let the tip make it stick.
E9A01 What is an isotropic radiator?
Answer A hypothetical, lossless antenna having equal radiation intensity in all directions used as a reference for antenna gain
Tip An isotropic radiator is an imaginary lossless point that beams equally everywhere, so it makes a clean zero reference for gain.
E9A02 What is the effective radiated power (ERP) of a repeater station with 150 watts transmitter power output, 2 dB feed line loss, 2.2 dB duplexer loss, and 7 dBd antenna gain?
Answer 286 watts
Tip Add dB in signal flow, so 7 - 2 - 2.2 = 2.8 dB net. 150 W times 10^(2.8/10) is about 286 W.
E9A03 What term describing total radiated power takes into account all gains and losses?
Answer Effective radiated power
Tip ERP is the honest number because it folds in every gain and every loss between the transmitter and the air.
E9A04 Which of the following factors affect the feed point impedance of an antenna?
Answer Antenna height
Tip Raise or lower an antenna and the ground couples differently, so height shifts the feed point impedance.
E9A05 What does the term “ground gain” mean?
Answer An increase in signal strength from ground reflections in the environment of the antenna
Tip Ground gain is free signal you get when the reflection off the earth adds in phase with the direct wave.
E9A06 What is the effective radiated power (ERP) of a repeater station with 200 watts transmitter power output, 4 dB feed line loss, 3.2 dB duplexer loss, 0.8 dB circulator loss, and 10 dBd antenna gain?
Answer 317 watts
Tip Sum the dB: 10 - 4 - 3.2 - 0.8 = 2.0 dB net. 200 W times 10^(2.0/10) is about 317 W.
E9A07 What is the effective isotropic radiated power (EIRP) of a repeater station with 200 watts transmitter power output, 2 dB feed line loss, 2.8 dB duplexer loss, 1.2 dB circulator loss, and 7 dBi antenna gain?
Answer 252 watts
Tip EIRP uses dBi directly, so 7 - 2 - 2.8 - 1.2 = 1.0 dB. 200 W times 10^(1.0/10) is about 252 W.
E9A08 Which frequency band has the smallest first Fresnel zone?
Answer 5.8 GHz
Tip The Fresnel zone shrinks as frequency rises, so the highest band here, 5.8 GHz, has the smallest first zone.
E9A09 What is antenna efficiency?
Answer Radiation resistance divided by total resistance
Tip Efficiency is the fraction of resistance that actually radiates, so it is radiation resistance over total resistance.
E9A10 Which of the following improves the efficiency of a ground-mounted quarter-wave vertical antenna?
Answer Installing a ground radial system
Tip A ground-mounted vertical uses the earth as its return, so burying radials cuts ground loss and lifts efficiency.
E9A11 Which of the following determines ground losses for a ground-mounted vertical antenna operating on HF?
Answer Soil conductivity
Tip The vertical leans on the soil for its return path, so how well that dirt conducts sets the ground loss.
E9A12 How much gain does an antenna have compared to a half-wavelength dipole if it has 6 dB gain over an isotropic radiator?
Answer 3.85 dB
Tip dBd is dBi minus 2.15, the dipole's own edge over isotropic, so 6 dBi becomes about 3.85 dBd.
7.2Patterns You Can Predict
Antenna software turned pattern prediction from art to engineering, and the pool wants the method: antenna modeling by the method of moments, in which the wire is divided into segments and the current in each segment is computed. More segments, more accuracy, longer computation: the modeler's eternal dial. What the model produces is the far field pattern, the region where the pattern's shape no longer depends on distance from the antenna, which is the pattern that matters to anyone you contact.
Reading the plots is its own literacy. An azimuth or elevation pattern (like the pool's Figure E9-1) yields the numbers by inspection: gain from the main lobe's reach, front-to-back ratio by comparing the main lobe to the 180-degree point, beamwidth between the 3 dB points. The pool's figure questions are pure plot-reading, and practicing on your own model's output makes them free points.
Website note: this page will include a sample azimuth plot with the gain, beamwidth, and front-to-back readings traced, standing in for pool Figure E9-1, plus your modeling capstone's own plots as worked examples.
The modeling habit pays off immediately in your capstone (E-S2 requires modeling, building, and comparing), and the comparison step is where the education lives: the model assumed perfect ground and exact dimensions; the antenna hangs in a real yard. The gap between them is a list of everything this module teaches.
Quiz yourself: read the pattern yourself
Knowledge Check 7.2
Tap an answer. In your own words first, then check yourself.
1. How does method-of-moments modeling represent an antenna?
2. What is the far field?
3. What is the tradeoff of using more segments in a model?
E9B the easy way: all 11 questions, with the right answer
Every pool question in this group. Read the answer, let the tip make it stick.
E9B01 What is the 3 dB beamwidth of the antenna radiation pattern shown in Figure E9-1?
Answer 50 degrees
Tip The 3 dB beamwidth is the angle between the half-power points on either side of the main lobe, read here as 50 degrees.
E9B02 What is the front-to-back ratio of the antenna radiation pattern shown in Figure E9-1?
Answer 18 dB
Tip Front-to-back compares the main lobe to the lobe pointing straight behind it, measured at 18 dB on this pattern.
E9B03 What is the front-to-side ratio of the antenna radiation pattern shown in Figure E9-1?
Answer 14 dB
Tip Front-to-side compares the main lobe to the lobe off the side, which reads 14 dB on this pattern.
E9B04 What is the front-to-back ratio of the radiation pattern shown in Figure E9-2?
Answer 28 dB
Tip Again compare the forward peak to the lobe 180 degrees behind, which measures 28 dB on this pattern.
E9B05 What type of antenna pattern is shown in Figure E9-2?
Answer Elevation
Tip An elevation pattern slices the beam vertically to show takeoff angle, which is what Figure E9-2 displays.
E9B06 What is the elevation angle of peak response in the antenna radiation pattern shown in Figure E9-2?
Answer 7.5 degrees
Tip The peak of the lowest lobe in the elevation plot sits at the takeoff angle, here about 7.5 degrees.
E9B07 What is the difference in radiated power between a lossless antenna with gain and an isotropic radiator driven by the same power?
Answer They are the same
Tip Gain only reshapes where the energy goes, so a lossless gain antenna radiates the same total power as isotropic.
E9B08 What is the far field of an antenna?
Answer The region where the shape of the radiation pattern no longer varies with distance
Tip In the far field the pattern has settled, so its shape stays fixed and only the level drops with distance.
E9B09 What type of analysis is commonly used for modeling antennas?
Answer Method of Moments
Tip Method of Moments is the workhorse modeler, slicing wires into segments and solving the currents on each.
E9B10 What is the principle of a Method of Moments analysis?
Answer A wire is modeled as a series of segments, each having a uniform value of current
Tip Method of Moments chops each wire into short segments and treats the current as uniform across each one.
E9B11 What is a disadvantage of decreasing the number of wire segments in an antenna model below 10 segments per half-wavelength?
Answer The computed feed point impedance may be incorrect
Tip Too few segments, below about 10 per half wave, and the math gets coarse, so the computed feed impedance can be off.
7.3Wires, Phasing, and the Ground Beneath
The wire-antenna drawer, Extra depth:
- The folded dipole wraps the dipole back on itself, multiplying feed impedance by four: about 300 ohms, which is why 300-ohm twin-lead and folded dipoles grew up together.
- The terminated rhombic is the wire antenna scaled to ambition: unidirectional, extremely wideband, requiring acres and a terminating resistor that burns half the power to buy its clean unidirectional pattern.
- Plain long wires develop gain as they grow, and their lobes align closer to the wire's axis as length increases, the pattern folding forward along the wire.
Phased arrays are Module 3's phase mathematics radiating: two elements, one geometry lever (spacing) and one electrical lever (feed phase):
- Quarter-wave spacing, fed 90 degrees apart: a cardioid, the heart-shaped pattern with one deep null, beloved of direction finders and low-band receivers.
- Half-wave spacing, fed in phase: broadside figure-eight, gain perpendicular to the pair.
- Half-wave spacing, fed 180 degrees apart: end-fire figure-eight, gain along the line of the pair.
Same two verticals, three different antennas, chosen with a feed line.
Ground finishes the section as an active element: the elevation lobes of every horizontal antenna are interference patterns between direct and ground-reflected waves, which is how height sets takeoff angle. Ground quality scales the effect: over saltwater, with its high conductivity, a vertical's low-angle radiation is dramatically enhanced, the reason DXpeditions camp on beaches, and sloping terrain tilts the whole pattern with it.
Knowledge Check 7.3
Tap an answer. In your own words first, then check yourself.
1. What is the approximate feed point impedance of a folded dipole?
2. Two vertical elements a quarter wavelength apart, fed 90 degrees out of phase, produce what pattern?
3. Why do verticals near saltwater work DX so well?
E9C the easy way: all 14 questions, with the right answer
Every pool question in this group. Read the answer, let the tip make it stick.
E9C01 What type of radiation pattern is created by two 1/4-wavelength vertical antennas spaced 1/2-wavelength apart and fed 180 degrees out of phase?
Answer A figure-eight oriented along the axis of the array
Tip Half-wave spacing fed 180 out cancels broadside and reinforces end on, giving a figure eight along the array axis.
E9C02 What type of radiation pattern is created by two 1/4-wavelength vertical antennas spaced 1/4-wavelength apart and fed 90 degrees out of phase?
Answer Cardioid
Tip Quarter-wave spacing fed 90 degrees apart steers all the energy one way, forming a one-direction cardioid.
E9C03 What type of radiation pattern is created by two 1/4-wavelength vertical antennas spaced 1/2-wavelength apart and fed in phase?
Answer A figure-eight broadside to the axis of the array
Tip Half-wave spacing fed in phase adds broadside and cancels end on, so the figure eight points across the array.
E9C04 What happens to the radiation pattern of an unterminated long wire antenna as the wire length is increased?
Answer Additional lobes form with major lobes increasingly aligned with the axis of the antenna
Tip Make a long wire longer and it grows more lobes that swing in toward the wire's own axis.
E9C05 What is the purpose of feeding an off-center-fed dipole (OCFD) between the center and one end instead of at the midpoint?
Answer To create a similar feed point impedance on multiple bands
Tip Feeding off center lands on a feed impedance that repeats across several harmonic bands, so one balun serves many.
E9C06 What is the effect of adding a terminating resistor to a rhombic or long-wire antenna?
Answer It changes the radiation pattern from bidirectional to unidirectional
Tip A terminating resistor soaks up the reverse wave, turning a bidirectional long wire into a one-way pattern.
E9C07 What is the approximate feed point impedance at the center of a two-wire half-wave folded dipole antenna?
Answer 300 ohms
Tip The folded dipole's two parallel wires split the current and raise the center feed impedance to about 300 ohms.
E9C08 What is a folded dipole antenna?
Answer A half-wave dipole with an additional parallel wire connecting its two ends
Tip A folded dipole is just a half-wave dipole with a second wire bridging its two ends into a thin loop.
E9C09 Which of the following describes a G5RV antenna?
Answer A wire antenna center-fed through a specific length of open-wire line connected to a balun and coaxial feed line
Tip The G5RV is center fed by a set length of open-wire line feeding a balun and coax, letting one wire work many bands.
E9C10 Which of the following describes a Zepp antenna?
Answer An end-fed half-wavelength dipole
Tip A Zepp is an end-fed half wave, named for the airships that trailed one as a wire antenna.
E9C11 How is the far-field elevation pattern of a vertically polarized antenna affected by being mounted over seawater versus soil?
Answer Radiation at low angles increases
Tip Seawater is a near-perfect mirror for RF, so a vertical over it throws more signal at the low angles DX needs.
E9C12 Which of the following describes an extended double Zepp antenna?
Answer A center-fed 1.25-wavelength dipole antenna
Tip An extended double Zepp stretches each side past a half wave to a 1.25-wavelength center-fed dipole for extra broadside gain.
E9C13 How does the radiation pattern of a horizontally polarized antenna vary with increasing height above ground?
Answer The takeoff angle of the lowest elevation lobe decreases
Tip Raise a horizontal antenna higher and the lowest lobe flattens, so its takeoff angle drops for better DX.
E9C14 How does the radiation pattern of a horizontally-polarized antenna mounted above a long slope compare with the same antenna mounted above flat ground?
Answer The main lobe takeoff angle decreases in the downhill direction
Tip Over a downhill slope the ground reflection tilts the beam lower, so the takeoff angle drops in the downhill direction.
7.4Dishes and the Physics of Short
Two extremes of the antenna world share this section.
The parabolic dish is gain by geometry: its aperture captures energy proportional to area measured in wavelengths, so doubling the frequency adds 6 dB of gain from the same dish. The same three-foot dish that is modest at 2.4 GHz is formidable at 10 GHz, which is the economic engine of amateur microwave work.
The electrically short antenna is the opposite problem, and Extra finally supplies the full physics behind the General course's mobile whip:
- A short antenna's feed point shows capacitive reactance (it is an unfinished antenna, and unfinished antennas look like capacitors), so loading inductance exists to cancel that capacitive reactance and bring the feed point to resonance. The loading coil is a conjugate match, not a lengthener in any physical sense.
- Coil placement is an efficiency decision: moving the coil from the base toward the center of the whip improves the current distribution along the radiator and with it the radiation efficiency. Better still is top loading (the capacitance hat from General Module 8): finishing the antenna capacitively at the tip keeps current high along the whole radiator, the most efficient fix of all.
- The coil itself must be high Q to keep its loss resistance small, because Section 7.1's balance sheet is brutal here: with radiation resistance of a few ohms, every ohm of coil loss is a large slice of your power. And Q keeps its Module 3 bill: the higher the Q, the narrower the bandwidth, the retune-across-the-band behavior your mobile antenna has always had, now fully accounted for.
Knowledge Check 7.4
Tap an answer. In your own words first, then check yourself.
1. What happens to a parabolic dish's gain when the operating frequency doubles?
2. What does a loading coil actually do for a short whip?
3. Why must mobile loading coils be high Q?
E9D the easy way: all 12 questions, with the right answer
Every pool question in this group. Read the answer, let the tip make it stick.
E9D01 How much does the gain of an ideal parabolic reflector antenna increase when the operating frequency is doubled?
Answer 6 dB
Tip A dish gain rises with frequency squared, so doubling the frequency gains a factor of four, which is 6 dB.
E9D02 How can two linearly polarized Yagi antennas be used to produce circular polarization?
Answer Arrange two Yagis on the same axis and perpendicular to each other with the driven elements at the same point on the boom and fed 90 degrees out of phase
Tip Cross two Yagis on one boom at right angles and feed them 90 degrees apart to spin the field into circular polarization.
E9D03 What is the most efficient location for a loading coil on an electrically short whip?
Answer Near the center of the vertical radiator
Tip Current is highest near the base and loading works best where current flows, so center loading beats a base coil.
E9D04 Why should antenna loading coils have a high ratio of reactance to resistance?
Answer To maximize efficiency
Tip A loading coil's resistance just burns power, so a high reactance-to-resistance ratio keeps it efficient.
E9D05 Approximately how long is a Yagi’s driven element?
Answer 1/2 wavelength
Tip A Yagi's driven element is the real radiator, cut to the usual resonant half wavelength.
E9D06 What happens to SWR bandwidth when one or more loading coils are used to resonate an electrically short antenna?
Answer It is decreased
Tip Loading coils raise the antenna's Q, and higher Q is narrower, so the SWR bandwidth shrinks.
E9D07 What is an advantage of top loading an electrically short HF vertical antenna?
Answer Improved radiation efficiency
Tip Top loading, like a capacity hat, keeps current high up the whip, so more of it radiates and efficiency improves.
E9D08 What happens as the Q of an antenna increases?
Answer SWR bandwidth decreases
Tip Higher Q means a sharper resonance, so as Q climbs the SWR bandwidth narrows.
E9D09 What is the function of a loading coil in an electrically short antenna?
Answer To resonate the antenna by cancelling the capacitive reactance
Tip A short antenna looks capacitive, so the loading coil adds inductance to cancel that reactance and hit resonance.
E9D10 How does radiation resistance of a base-fed whip antenna change below its resonant frequency?
Answer Radiation resistance decreases
Tip Drop below resonance and a base-fed whip looks shorter electrically, so its radiation resistance falls.
E9D11 Why do most two-element Yagis with normal spacing have a reflector instead of a director?
Answer Higher gain
Tip A reflector set behind the driven element yields a bit more gain than a director in a normal two-element Yagi.
E9D12 What is the purpose of making a Yagi’s parasitic elements either longer or shorter than resonance?
Answer Control of phase shift
Tip Tuning parasitic elements off resonance sets how much their reradiated current leads or lags, which controls phase.
7.5Matching, Designed
The General course bought matching devices; this section designs them.
- The gamma match (from General, now with its missing part explained): the matching rod paralleling the driven element is inductive, and the series capacitor exists to cancel that inductive reactance. The whole assembly taps the element at the 50-ohm point without breaking it, hence no insulation from the boom. Its wire-antenna cousin, the delta match, fans the feed line out to attach at two points spread along an unbroken element, the spread choosing the impedance the same way the gamma's tap point does. And the hairpin (beta) match from your General course keeps its place here: a shorted stub across the feed point supplying the inductance that a slightly shortened driven element needs.
- Stub matching wields Section 7.6's transmission-line reactances deliberately: a shorted or open stub of the right length places a computed reactance in parallel with the feed point, cancelling what the antenna presents. A stub is a capacitor or inductor made of coax, free from a scrap box. The same line-length arithmetic serves Section 7.3's arrays as phasing lines: measured lengths of feed line delivering the 90- or 180-degree feed relationships that steer the pattern.
- The quarter-wave transformer is matching by geometry: a quarter wavelength of line whose impedance is the geometric mean of the two impedances to be matched, Z = the square root of Z1 times Z2. Match a 100-ohm antenna to 50-ohm coax through a quarter wave of 70-ohm line (75-ohm cable, close enough, is the classic trick); match 50 to 200 through 100-ohm line. Module 3's transformer arithmetic, rebuilt from cable.
- The Wilkinson divider solves the phased-array plumbing problem: it divides power equally between two loads while maintaining match and providing isolation between the output ports, so the two antennas of Section 7.3's array each get their share without talking to each other through the splitter.
Knowledge Check 7.5
Tap an answer. In your own words first, then check yourself.
1. Why does a gamma match include a series capacitor?
2. What line impedance quarter-wave-matches a 200-ohm load to 50-ohm coax?
3. What does a Wilkinson divider provide beyond splitting power?
E9E the easy way: all 10 questions, with the right answer
Every pool question in this group. Read the answer, let the tip make it stick.
E9E01 Which matching system for Yagi antennas requires the driven element to be insulated from the boom?
Answer Beta or hairpin
Tip The beta or hairpin shunts the feed point, so the driven element must float, insulated from the boom.
E9E02 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?
Answer Gamma match
Tip A gamma match taps the center for the shield and clamps the center conductor out to one side a short distance.
E9E03 What matching system uses a short length of transmission line connected in parallel with the feed line at or near the feed point?
Answer Stub match
Tip A stub match hangs a short piece of line in parallel near the feed point to tune out the mismatch.
E9E04 What is the purpose of the series capacitor in a gamma match?
Answer To cancel unwanted inductive reactance
Tip A gamma rod adds inductance, so a series capacitor is fitted to cancel that unwanted inductive reactance.
E9E05 What Yagi driven element feed point impedance is required to use a beta or hairpin matching system?
Answer Capacitive (driven element electrically shorter than 1/2 wavelength)
Tip The beta or hairpin only tunes out capacitance, so it needs a driven element made a touch short to look capacitive.
E9E06 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?
Answer 75 ohms
Tip A quarter-wave Q-section uses the geometric mean, root of 100 times 50 is about 71 ohms, so 75-ohm line fits.
E9E07 What parameter describes the interaction of a load and transmission line?
Answer Reflection coefficient
Tip The reflection coefficient is the ratio of reflected to forward wave, describing how load and line interact.
E9E08 What is a use for a Wilkinson divider?
Answer To divide power equally between two 50-ohm loads while maintaining 50-ohm input impedance
Tip A Wilkinson divider splits power evenly to two 50-ohm loads while keeping a matched 50-ohm input.
E9E09 Which of the following is used to shunt feed a grounded tower at its base?
Answer Gamma match
Tip Shunt feeding a grounded tower uses a gamma match, tapping the tower itself as the radiator.
E9E11 What is the purpose of using multiple driven elements connected through phasing lines?
Answer To control the antenna’s radiation pattern
Tip Feeding several driven elements through phasing lines sets their relative timing, which shapes the radiation pattern.
7.6The Transmission Line's Secret Life
A transmission line does more than carry power; cut to the right lengths, it becomes components.
Velocity factor first: the ratio of the wave's velocity in the line to its velocity in free space, set by the dielectric (Module 2's index of refraction, indoors). Solid polyethylene coax runs about 0.66; foam, around 0.8. The consequence: a line's electrical length exceeds its physical length, so a quarter wavelength of solid-dielectric coax at 14.1 MHz is not 17.5 feet of cable but 17.5 x 0.66, about 11.5 feet. Every stub and transformer from Section 7.5 is cut by this arithmetic.
Now the secret life. A line terminated in a short or open reflects everything, and at the input, the reflection reads as pure reactance that depends on length:
- Shorted quarter wave: looks open (very high impedance). Open quarter wave: looks shorted. The quarter wave inverts.
- Shorted eighth wave: inductive reactance. Open eighth wave: capacitive reactance. The stub components of Section 7.5, specified.
- Half wave (shorted or open): repeats its far-end condition exactly. The half wave is a mirror, which is also why a half wave of any line reproduces the antenna's impedance at the shack end, a measurement trick worth remembering.
The medium itself completes the ledger from three courses of feed line talk: open-wire line carries the lowest loss of the practical lines, coax buys convenience with loss, and at microwave the transmission line dissolves into the circuit board itself as microstrip: a precisely dimensioned trace over a ground plane, the controlled-impedance line that connects Module 4's MMICs.
Knowledge Check 7.6
Tap an answer. In your own words first, then check yourself.
1. What sets a transmission line's velocity factor?
2. What does a shorted quarter-wave stub look like at its input?
3. What is microstrip?
E9F the easy way: all 12 questions, with the right answer
Every pool question in this group. Read the answer, let the tip make it stick.
E9F01 What is the velocity factor of a transmission line?
Answer The velocity of a wave in the transmission line divided by the velocity of light in a vacuum
Tip Velocity factor is how fast the wave travels in the line compared to light in a vacuum, always a number under one.
E9F02 Which of the following has the biggest effect on the velocity factor of a transmission line?
Answer The insulating dielectric material
Tip The dielectric packed around the conductors slows the wave the most, so it dominates the velocity factor.
E9F03 Why is the electrical length of a coaxial cable longer than its physical length?
Answer Electromagnetic waves move more slowly in a coaxial cable than in air
Tip Waves crawl slower through coax dielectric than through air, so the cable is electrically longer than its physical length.
E9F04 What impedance does a 1/2-wavelength transmission line present to an RF generator when the line is shorted at the far end?
Answer Very low impedance
Tip A half-wave line repeats what it sees, so a short at the far end looks like a near short at the generator.
E9F05 What is microstrip?
Answer Precision printed circuit conductors above a ground plane that provide constant impedance interconnects at microwave frequencies
Tip Microstrip is a printed trace riding above a ground plane that holds steady impedance for microwave interconnects.
E9F06 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?
Answer 10.6 meters
Tip Air line VF is near one, so a full wave at 14.10 MHz is 300/14.1 = 21.3 m and the half wave is about 10.6 m.
E9F07 How does parallel conductor transmission line compare to coaxial cable with a plastic dielectric?
Answer Lower loss
Tip Open-wire line runs mostly through air with little dielectric, so it beats plastic-filled coax on loss.
E9F08 Which of the following is a significant difference between foam dielectric coaxial cable and solid dielectric coaxial cable, assuming all other parameters are the same?
Answer All these choices are correct
Tip Foam dielectric changes several traits at once, velocity factor, loss, and more, so all the listed differences hold.
E9F09 What impedance does a 1/4-wavelength transmission line present to an RF generator when the line is shorted at the far end?
Answer Very high impedance
Tip A quarter-wave line inverts impedance, so a short at the far end becomes a very high impedance at the generator.
E9F10 What impedance does a 1/8-wavelength transmission line present to an RF generator when the line is shorted at the far end?
Answer An inductive reactance
Tip A shorted line under a quarter wave acts like a coil, so an eighth-wave short looks like inductive reactance.
E9F11 What impedance does a 1/8-wavelength transmission line present to an RF generator when the line is open at the far end?
Answer A capacitive reactance
Tip An open line under a quarter wave acts like a capacitor, so an eighth-wave open looks like capacitive reactance.
E9F12 What impedance does a 1/4-wavelength transmission line present to an RF generator when the line is open at the far end?
Answer Very low impedance
Tip A quarter-wave line inverts impedance, so an open at the far end becomes a very low impedance at the generator.
7.7The Smith Chart
One page of curves makes Section 7.6 visible: the Smith chart, whose coordinate system consists of resistance circles and reactance arcs. Every possible impedance is one point; the chart's uses are impedance, SWR, and transmission line calculations performed as geometry.
The working rules:
- The chart is normalized, customarily to 50 ohms, so the center point (1.0) is a perfect 50-ohm match. Divide your impedance by 50, plot, work, multiply back.
- Moving along a transmission line rotates the impedance point around the chart, distance marked on the wavelength scales around the perimeter. A half wavelength is one full lap, which is Section 7.6's half-wave mirror drawn as a circle.
- Points of equal mismatch trace constant-SWR circles centered on the chart's center: the third family of circles, drawn in by the user. A lossless line moves your impedance around its SWR circle; a matching network's job is spiraling that point into the center.
Your NanoVNA has been drawing this chart since Module 3's tie-in; now the display is readable. The gamma capacitor, the stub, the quarter-wave transformer: each Section 7.5 device is one specific move on this chart, and designing a match becomes navigation.
Website note: the pool's Figure E9-3 Smith chart (horizontal orientation, per the January 2024 errata) will be reproduced with a worked match traced onto it.
Quiz yourself: a 100 - j50 ohm match traced to center
Knowledge Check 7.7
Tap an answer. In your own words first, then check yourself.
1. What are the two families of printed curves on a Smith chart?
2. What does moving along a lossless transmission line do to an impedance plotted on the chart?
3. What do the scales around the chart's perimeter measure?
E9G the easy way: all 11 questions, with the right answer
Every pool question in this group. Read the answer, let the tip make it stick.
E9G01 Which of the following can be calculated using a Smith chart?
Answer Impedance along transmission lines
Tip The Smith chart's whole job is transmission lines, so you use it to find impedance at any point along the line.
E9G02 What type of coordinate system is used in a Smith chart?
Answer Resistance circles and reactance arcs
Tip The Smith chart trades x-y axes for resistance circles and reactance arcs riding on the reflection plane.
E9G03 Which of the following is often determined using a Smith chart?
Answer Impedance and SWR values in transmission lines
Tip The Smith chart is built for line problems, so it readily gives both impedance and SWR along a feed line.
E9G04 What are the two families of circles and arcs that make up a Smith chart?
Answer Resistance and reactance
Tip The chart is woven from two families, constant-resistance circles and constant-reactance arcs.
E9G05 Which of the following is a common use for a Smith chart?
Answer Determine the length and position of an impedance matching stub
Tip A classic Smith chart task is sizing a matching stub, finding where to place it and how long to cut it.
E9G06 On the Smith chart shown in Figure E9-3, what is the name for the large outer circle on which the reactance arcs terminate?
Answer Reactance axis
Tip The big outer rim where every reactance arc ends is the reactance axis of the Smith chart.
E9G07 On the Smith chart shown in Figure E9-3, what is the only straight line shown?
Answer The resistance axis
Tip The one perfectly straight line running across the Smith chart is the resistance axis.
E9G08 How is a Smith chart normalized?
Answer Reassign the prime center’s impedance value
Tip You normalize a Smith chart by reassigning the prime center value, usually to the line's characteristic impedance.
E9G09 What third family of circles is often added to a Smith chart during the process of designing impedance matching networks?
Answer Constant-SWR circles
Tip Designers overlay constant-SWR circles as a third family to track mismatch while they work a match.
E9G10 What do the arcs on a Smith chart represent?
Answer Points with constant reactance
Tip Each arc on the Smith chart is a track of points sharing one constant value of reactance.
E9G11 In what units are the wavelength scales on a Smith chart calibrated?
Answer In fractions of transmission line electrical wavelength
Tip The chart's wavelength scales are marked in fractions of a wavelength of the transmission line itself.
7.8Antennas That Only Listen
The receiving-antenna drawer, where efficiency stops mattering and directivity is everything. The license for that trade: on the low bands, atmospheric noise towers over receiver noise, so an inefficient antenna loses signal and noise together, costing nothing in signal-to-noise while its pattern can be optimized purely for rejection.
- The Beverage (introduced at General) gets its design rule: for good directivity it must be one or more wavelengths long, the terminated long wire earning its low-band listening crown by length.
- The shielded loop solves a different problem: its electrostatic shield rejects locally generated electric-field noise, receiving the magnetic component cleanly, which makes it the small-lot and portable listening antenna of choice.
- Radio direction finding assembles three courses of pieces into a discipline. The small loop's sharp nulls broadside (from General) do the pointing, but a loop alone reads two bearings 180 degrees apart; adding a sense antenna resolves the ambiguity to a single direction. Then triangulation: bearings taken from two or more locations, crossed on a map, yield the transmitter. That is the machinery inside the Technician course's foxhunt and the Volunteer Monitors' beam-heading comparisons from General, now specified well enough to build.
Knowledge Check 7.8
Tap an answer. In your own words first, then check yourself.
1. Why is antenna efficiency almost irrelevant for 160-meter receiving?
2. How long should a Beverage be for good directivity?
3. What resolves an RDF loop's 180-degree bearing ambiguity?
E9H the easy way: all 11 questions, with the right answer
Every pool question in this group. Read the answer, let the tip make it stick.
E9H01 When constructing a Beverage antenna, which of the following factors should be included in the design to achieve good performance at the desired frequency?
Answer It should be at least one wavelength long
Tip A Beverage leans on wave tilt along a long wire, so make it at least a full wavelength to work well.
E9H02 Which is generally true for 160- and 80-meter receiving antennas?
Answer Atmospheric noise is so high that directivity is much more important than losses
Tip On 160 and 80 the band roars with atmospheric noise, so a quiet directional pattern beats chasing low loss.
E9H03 What is receiving directivity factor (RDF)?
Answer Peak antenna gain compared to average gain over the hemisphere around and above the antenna
Tip RDF rates a receiving antenna by its peak gain against the average gain over the whole sky around it.
E9H04 What is the purpose of placing an electrostatic shield around a small-loop direction-finding antenna?
Answer It eliminates unbalanced capacitive coupling to the antenna’s surroundings, improving the depth of its nulls
Tip A shield around a DF loop blocks stray capacitive pickup, so the loop stays balanced and its nulls go deep.
E9H05 What challenge is presented by a small wire-loop antenna for direction finding?
Answer It has a bidirectional null pattern
Tip A small loop has two nulls facing opposite ways, so by itself it cannot tell which direction the signal came from.
E9H06 What indicates the correct value of terminating resistance for a Beverage antenna?
Answer Minimum variation in SWR over the desired frequency range
Tip Set a Beverage termination for the flattest SWR across the band, which marks the resistance that matches the line.
E9H07 What is the function of a Beverage antenna’s termination resistor?
Answer Absorb signals from the reverse direction
Tip The Beverage's terminating resistor swallows the backward wave, leaving a clean one-way receive pattern.
E9H08 What is the function of a sense antenna?
Answer It modifies the pattern of a DF antenna to provide a null in only one direction
Tip A sense antenna adds a bit of omnidirectional pickup to a loop, collapsing its two nulls into a single one.
E9H09 What type of radiation pattern is created by a single-turn, terminated loop such as a pennant antenna?
Answer Cardioid
Tip A terminated single-turn loop like a pennant soaks up the back signal, giving a one-way cardioid pattern.
E9H10 How can the output voltage of a multiple-turn receiving loop antenna be increased?
Answer By increasing the number of turns and/or the area enclosed by the loop
Tip A receive loop picks up more voltage when you add turns or enlarge the area it encloses.
E9H11 What feature of a cardioid pattern antenna makes it useful for direction-finding antennas?
Answer A single null
Tip A cardioid has just one null, so you can swing it to a sharp minimum and read a single clear bearing.
Review: every Exam Anchor from this module
E9A Radiation resistance: the resistance equivalent to the radiated power. Feed point resistance = radiation + loss resistance; efficiency is their ratio. Short antennas: very low radiation resistance. Vertical efficiency: improved with a better radial system. Isotropic radiator: equal radiation in all directions, the dBi reference. ERP/EIRP: power adjusted by all gains and losses (150 W, -2, -2.2, +7 dBd = about 286 W ERP). Beamwidth: angle between half-power points; higher gain, narrower beamwidth.
E9B Method of moments: the wire is modeled as segments and the current in each is calculated; more segments give more accuracy. Far field: where the pattern shape is independent of distance. Pattern plots: read gain from the main lobe, front-to-back from the 180-degree comparison, beamwidth between half-power points (Figure E9-1 questions are plot-reading).
E9C Folded dipole: about 300 ohms. Terminated rhombic: unidirectional, wideband, large, and terminated in a resistor. Long wires: lobes align toward the wire as length grows. Two-element phasing: 90 degrees at 1/4-wave spacing = cardioid; in phase at 1/2 wave = broadside figure-eight; 180 degrees at 1/2 wave = end-fire figure-eight. Ground reflections form the elevation lobes; saltwater's conductivity enhances low-angle vertical radiation.
E9D Parabolic dish: +6 dB each time frequency doubles. Short antennas present capacitive reactance; loading inductance cancels it. Center loading beats base loading on radiation efficiency; top loading (capacitance hat) is better still. Loading coils must be high Q to limit loss against the antenna's very low radiation resistance; high Q narrows operating bandwidth.
E9E Gamma match series capacitor: cancels the matching section's inductive reactance. Delta match: feed line fanned to two attachment points on an unbroken element. Hairpin/beta match: shorted stub supplying inductance at the feed point. Phasing lines: measured line lengths setting element feed phase. Stubs: shorted or open line sections supplying cancelling reactance. Quarter-wave transformer: line impedance equals the square root of the product of the two impedances (50 to 100 via about 70-75 ohms; 50 to 200 via 100 ohms). Wilkinson divider: equal power split with isolation between output ports.
E9F Velocity factor: line velocity over free-space velocity, set by the dielectric; solid polyethylene about 0.66. Physical length = electrical length times VF (quarter wave at 14.1 MHz in 0.66 coax: about 11.5 feet). Shorted 1/4 wave: open at input; open 1/4 wave: short. Shorted 1/8 wave: inductive; open 1/8 wave: capacitive. Half wave: repeats the termination. Open-wire line: lowest loss. Microstrip: controlled-impedance PCB transmission line for microwave.
E9G Smith chart coordinates: resistance circles and reactance arcs. Uses: impedance, SWR, and transmission-line calculations. Normalized (prime center = 1.0, customarily 50 ohms). Wavelength scales on the perimeter track movement along a line; constant-SWR circles are centered on the chart center.
E9H Low-band receive: atmospheric noise dominates, so antenna efficiency matters little and directivity matters greatly. Beverage: one or more wavelengths long for directivity. Shielded loop: rejects local electric-field noise. RDF: loop nulls point, a sense antenna resolves the 180-degree ambiguity, and triangulation from multiple bearings locates the source.
Before you move on
The whiteboard in the antenna field is full: efficiency as a balance sheet, patterns as computable predictions, phasing as design, matching as navigation on one elegant chart, and transmission lines living their secret second life as components. This module and your E-S2 capstone are the same material; the exam checks whether you know it, the capstone checks whether you built it.
Module 8 turns the instruments on everything you have made: spectrum analyzers, vector network analysis, and the receiver specifications that separate marketing from engineering.
© 2026 Anthony Pelfanio, K4DIA. All rights reserved.