E9 Antennas and Transmission Lines

C. A hypothetical, lossless antenna having equal radiation intensity in all directions used as a reference for antenna gain

An isotropic radiator is an imaginary, lossless point antenna that radiates equally in every direction. No real antenna can do this, but it is the standard reference for antenna gain: gain stated in dBi is relative to an isotropic radiator.

• A. An isotropic radiator radiates equally in all directions, so it is not unidirectional, and it is a theoretical reference rather than a calibrated instrument.
• B. A real horizontally polarized omnidirectional antenna is omnidirectional only in the horizontal plane; an isotropic radiator is hypothetical and radiates equally in all directions.
• D. A spacecraft antenna aimed at Earth is directional, the opposite of an isotropic radiator.

D. 286 watts

Add the gains and losses in dB, then apply the result to the transmitter power: 7 dBd - 2 dB - 2.2 dB = +2.8 dB. ERP = 150 W x 10^(2.8 / 10) = 150 W x 1.905 = 286 W. Because the antenna gain is in dBd, the result is ERP (relative to a dipole).

• A. 469 W is the EIRP: 286 W ERP multiplied by 1.64 (adding 2.15 dB to convert from a dipole to an isotropic reference).
• B. 78.7 W results from treating the net +2.8 dB as a loss (150 W x 10^(-2.8 / 10)).
• C. 420 W results from multiplying 150 W by 2.8, treating the dB figure as a plain power ratio.

C. Effective radiated power

Effective radiated power (ERP) is the transmitter output power adjusted by every gain and loss between the transmitter and the antenna's radiation: feed line, duplexer and other losses, and the antenna's gain over a dipole. It gives the power a reference dipole would need to radiate to produce the same signal in the direction of maximum gain.

• A. Power factor is the ratio of real power to apparent power in an AC circuit, not a measure of radiated power.
• B. Half-power bandwidth is the frequency range between the -3 dB points of a response, not a measure of radiated power.
• D. Apparent power is volts times amperes (in VA) in a circuit with reactance, not radiated power including antenna gain.

B. Antenna height

An antenna's feed point impedance depends partly on its surroundings, especially the ground beneath it. As height changes, the ground reflection couples back to the antenna differently, so the feed point impedance varies with height above ground.

• A. Feed line length changes the impedance seen at the transmitter end of the line, not the impedance at the antenna's feed point.
• C. An antenna tuner changes the impedance the transmitter sees; it does not change the antenna's own feed point impedance.
• D. An antenna is a linear device, so its feed point impedance does not change with power level.

D. An increase in signal strength from ground reflections in the environment of the antenna

Ground gain is the increase in signal strength, in some directions, that comes from radio energy reflected by the ground near the antenna adding in phase with the direct wave. For a horizontal antenna over good ground it can approach 6 dB compared with the same antenna in free space.

• A. Ground gain comes from reflections off the ground, not from electrically grounding the antenna.
• B. Ground gain is not a comparison with a dipole at ground level; it is the extra signal produced by ground reflections.
• C. Ground gain is not a way of forcing net gain to 0 dB; grounding part of an antenna does not do that.

A. 317 watts

Net gain = 10 dBd - 4 dB - 3.2 dB - 0.8 dB = +2 dB. ERP = 200 W x 10^(2 / 10) = 200 W x 1.585 = 317 W. Because the antenna gain is in dBd, the result is ERP.

• B. 2,000 W applies only the 10 dB antenna gain and ignores the 8 dB of losses.
• C. 126 W results from treating the net +2 dB as a 2 dB loss (200 W x 10^(-2 / 10)).
• D. 300 W is 1.5 times 200 W, about 1.76 dB; a 2 dB gain is a factor of 1.585, giving 317 W.

B. 252 watts

Net gain = 7 dBi - 2 dB - 2.8 dB - 1.2 dB = +1 dB. EIRP = 200 W x 10^(1 / 10) = 200 W x 1.259 = 252 W. The antenna gain is already in dBi (relative to isotropic), so this result is the EIRP directly, with no 2.15 dB conversion.

• A. 159 W results from treating the net +1 dB as a 1 dB loss (200 W x 10^(-1 / 10)).
• C. 632 W counts only the 2 dB feed line loss (7 - 2 = 5 dB) and leaves out the duplexer and circulator losses.
• D. 63.2 W treats 5 dB as a loss instead of a gain and also leaves out the duplexer and circulator losses.

A. 5.8 GHz

The radius of the first Fresnel zone is r = √(λ x d1 x d2 / D), so it shrinks as wavelength shortens. The highest frequency listed, 5.8 GHz, has the shortest wavelength and the smallest zone: at the middle of a 1 km path, about 3.6 m, compared with about 9.1 m at 900 MHz.

• B. 3.4 GHz has a longer wavelength than 5.8 GHz, so its first Fresnel zone is larger.
• C. 2.4 GHz has a longer wavelength than 5.8 GHz, so its first Fresnel zone is larger.
• D. 900 MHz has the longest wavelength listed, so it has the largest first Fresnel zone of the four.

B. Radiation resistance divided by total resistance

An antenna's input resistance is its radiation resistance (power that is radiated) plus loss resistance (power turned into heat in conductors, ground and nearby objects). Efficiency is the fraction radiated: radiation resistance divided by total resistance. For example, 36 ohms of radiation resistance with 14 ohms of ground loss gives 36 / 50 = 72 percent.

• A. "Transmission resistance" is not a part of an antenna's resistance; efficiency uses radiation resistance over total resistance.
• C. Total resistance divided by radiation resistance is the efficiency ratio inverted and would always be 1 or greater.
• D. ERP divided by transmitter output includes antenna gain and feed line loss, so it is not antenna efficiency.

A. Installing a ground radial system

A ground-mounted quarter-wave vertical uses the ground as the other half of the antenna, and return currents flowing through lossy soil waste power. A system of ground radials gives those currents a low-resistance path, reducing ground loss and raising efficiency.

• B. Isolating the coax shield from ground does not reduce the ground losses of a vertical.
• C. Shortening the radiator lowers its radiation resistance, so losses become a larger share and efficiency drops.
• D. Only installing radials improves efficiency, so not all the choices are correct.

C. Soil conductivity

Return currents from a ground-mounted vertical flow through the soil near the antenna, and the soil's conductivity determines how much power is lost there. Poor (low-conductivity) soil causes more loss, which is why radial systems are used.

• A. SWR describes the match between feed line and antenna, not the loss in the ground under the antenna.
• B. Distance from the transmitter does not determine the ground loss at the antenna.
• D. Take-off angle is a result of the antenna's pattern and surroundings, not what determines ground loss.

A. 3.85 dB

A half-wave dipole has 2.15 dB of gain over an isotropic radiator, so dBd = dBi - 2.15. An antenna with 6 dBi of gain has 6 - 2.15 = 3.85 dBd.

• B. 6.0 dB is the gain over isotropic; gain over a dipole is 2.15 dB less.
• C. 8.15 dB adds 2.15 dB instead of subtracting it; a dipole reference is higher than an isotropic one, so dBd numbers are smaller.
• D. 2.79 dB does not follow from the 2.15 dB difference between a dipole and an isotropic reference.

B. 50 degrees

Beamwidth is the angle between the two points on the main lobe where the response is 3 dB below the peak. In Figure E9-1 the main lobe, centered on 0 degrees, crosses the -3 dB circle at about 25 degrees on each side, so the beamwidth is about 50 degrees.

• A. At 37.5 degrees either side of the peak the lobe is well below -3 dB, so 75 degrees is wider than the half-power beamwidth.
• C. 25 degrees is the angle from the center of the lobe to one -3 dB point, only half the beamwidth.
• D. 30 degrees is narrower than the angle between the two -3 dB points, which is about 50 degrees.

D. 18 dB

Front-to-back ratio compares the response in the main direction (0 degrees) with the response in the opposite direction (180 degrees). In Figure E9-1 the rear lobe at 180 degrees reaches about -18 dB, so the front-to-back ratio is 18 dB.

• A. 36 dB is twice the actual value; the rear lobe reaches about -18 dB, not -36 dB.
• B. 14 dB is the front-to-side ratio, read at 90 degrees, not toward the rear.
• C. 24 dB is the value of one of the labeled circles; the rear lobe extends beyond it to about -18 dB.

D. 14 dB

Front-to-side ratio compares the response in the main direction with the response at right angles to it (90 and 270 degrees). In Figure E9-1 the pattern at 90 degrees is about 14 dB below the main lobe, so the front-to-side ratio is 14 dB.

• A. 12 dB is the value of a labeled circle; the side response is about 14 dB down.
• B. 24 dB is the value of a labeled circle; the side lobes extend well beyond it, to about -14 dB.
• C. 18 dB is the front-to-back ratio, read at 180 degrees, not at the side.

B. 28 dB

In the elevation pattern of Figure E9-2, the forward direction is toward 0 degrees and the rear is toward 180 degrees. The main lobe reaches 0 dB, while the small lobes toward the rear peak about 28 dB lower, so the front-to-back ratio is 28 dB.

• A. 15 dB is far less than the difference between the main lobe and the small rear lobes in the figure.
• C. 3 dB is the half-power point used for beamwidth, not the front-to-back ratio.
• D. 38 dB is more than the difference between the main lobe and the strongest rear lobe, which is about 28 dB.

A. Elevation

Figure E9-2 is a half circle with 0 degrees and 180 degrees at the horizon and 90 degrees straight up, plotted over real ground. That is an elevation pattern, showing how radiation varies with vertical angle above the horizon.

• B. An azimuth pattern is a full 360-degree circle viewed from above, like Figure E9-1, not a half circle from horizon to horizon.
• C. The near field is the region close to the antenna; radiation patterns such as this one describe the far field.
• D. Polarization describes the orientation of the electric field, not a pattern plotted against elevation angle.

C. 7.5 degrees

The elevation angle of peak response is the angle at which the strongest lobe reaches its maximum. In Figure E9-2 the strongest lobe sits close to the horizon, peaking at about 7.5 degrees.

• A. Near 45 degrees there is a higher-angle lobe, but it is weaker than the main lobe.
• B. Near 75 degrees the response is well below the main lobe.
• D. Near 25 degrees there is a second lobe, but it is slightly weaker than the lowest lobe at about 7.5 degrees.

C. They are the same

Antenna gain does not create power; it redistributes it, concentrating radiation in some directions at the expense of others. A lossless directional antenna and an isotropic radiator fed with the same power radiate the same total power.

• A. Gain increases the signal in the favored direction, not the total radiated power.
• B. Front-to-back ratio describes the shape of the pattern, not the total power radiated.
• D. 2.15 dB is the gain of a half-wave dipole over isotropic in its favored direction, not a difference in total radiated power.

D. The region where the shape of the radiation pattern no longer varies with distance

Close to an antenna (the near field), the fields are complex and the pattern changes with distance. Farther out, in the far field, the shape of the radiation pattern stays the same at any distance, and field strength falls in inverse proportion to distance.

• A. The far field is a region around the antenna, not a region of the ionosphere.
• B. The far field is not defined by power dissipating over a period of time.
• C. Field strength in the far field keeps decreasing with distance; it is the pattern shape that stays constant.

B. Method of Moments

Most antenna modeling programs, such as those based on NEC (Numerical Electromagnetics Code), use the Method of Moments. It calculates the current on each part of the antenna and from those currents computes the pattern, gain and feed point impedance.

• A. Graphical analysis is not the method antenna modeling programs use.
• C. Mutual impedance calculations can describe interactions between elements, but the common modeling method is the Method of Moments.
• D. Calculus differentiation with respect to physical properties is not a recognized antenna modeling method.

A. A wire is modeled as a series of segments, each having a uniform value of current

Method of Moments analysis divides each wire into short segments and treats the current along each segment as uniform. Solving for those currents, including how every segment affects every other, gives the antenna's impedance and radiation pattern.

• B. The wire is not modeled as one sine-wave current generator; it is divided into many segments.
• C. The wire is not modeled as one voltage source; a source is placed at the feed point and the segment currents are calculated.
• D. The method assigns each segment a uniform current, not a distinct voltage across it.

C. The computed feed point impedance may be incorrect

Method of Moments accuracy depends on having enough segments to represent how current varies along the wire. A common guideline is at least 10 segments per half-wavelength; with fewer, the computed currents, and so the feed point impedance, may be wrong.

• A. Ground conductivity is a separate model setting, not something the number of wire segments controls.
• B. The segment count affects calculation accuracy; it does not make the design favor harmonic radiation.
• D. Segments exist only in the computer model, so their number has nothing to do with mechanical stability.

D. A figure-eight oriented along the axis of the array

Two verticals a half wavelength apart and fed 180 degrees out of phase cancel broadside to the array but add along its axis: a wave traveling from one to the other is delayed 180 degrees, which offsets the 180-degree feed difference. The result is a figure-eight pattern pointing along the line through the two antennas (end-fire).

• A. A cardioid comes from quarter-wavelength spacing with a 90-degree phase difference.
• B. Two elements with a 180-degree phase difference produce nulls broadside, so the pattern is not omnidirectional.
• C. A broadside figure-eight comes from feeding the half-wave-spaced pair in phase.

A. Cardioid

With quarter-wavelength spacing and a 90-degree phase difference, the signals add in the direction of the element whose current lags and cancel in the opposite direction, where the 90-degree spacing delay and 90-degree feed difference combine to 180 degrees. The result is a heart-shaped (cardioid) pattern with one null.

• B. An end-fire figure-eight comes from half-wavelength spacing fed 180 degrees out of phase.
• C. A broadside figure-eight comes from half-wavelength spacing fed in phase.
• D. The 90-degree phasing makes the pattern strongly directional, not omnidirectional.

C. A figure-eight broadside to the axis of the array

Two verticals fed in phase add perpendicular to the line joining them, where their signals arrive together. Along the line, the half-wavelength spacing adds 180 degrees of delay and the signals cancel. The result is a figure-eight broadside to the array.

• A. The cancellation along the array's axis makes the pattern a figure-eight, not omnidirectional.
• B. A cardioid comes from quarter-wavelength spacing with a 90-degree phase difference.
• D. An end-fire figure-eight comes from feeding the pair 180 degrees out of phase.

B. Additional lobes form with major lobes increasingly aligned with the axis of the antenna

As an unterminated long wire is made longer (in wavelengths), its pattern breaks up into more lobes, and the main lobes move closer to the direction of the wire itself. A wire several wavelengths long has its strongest lobes at fairly small angles to the wire.

• A. Making the wire longer adds lobes rather than reducing them, and the main lobes move toward the wire's axis, not broadside.
• C. Lengthening the wire mainly adds lobes and swings them toward the wire's axis; it does not raise the elevation angle.
• D. The main effect of added length is more lobes aligned closer to the wire, not a higher elevation angle.

A. To create a similar feed point impedance on multiple bands

Feeding a dipole about one third of the way from one end, rather than at the center, places the feed point where the impedance is roughly similar (a few hundred ohms) on several harmonically related bands. A single balun, often 4:1, can then match it to coax on all those bands.

• B. Off-center feeding is chosen for a similar feed point impedance across bands, not to suppress lobes at higher frequencies.
• C. The wire's length still sets its resonant frequencies; moving the feed point does not make it resonant over a wider range.
• D. Off-center feeding is unbalanced and tends to increase common-mode current on the feed line, so chokes are often added.

B. It changes the radiation pattern from bidirectional to unidirectional

On an unterminated rhombic or long wire, current reflects from the far end and radiates in both directions. A terminating resistor of about the right value at the far end absorbs the wave instead of reflecting it, so the antenna radiates and receives mainly toward the terminated end: the pattern becomes unidirectional.

• A. The resistor absorbs the wave that reaches the far end; it prevents reflection rather than sending power back toward the transmitter.
• C. Termination changes the pattern's direction, not the antenna's polarization.
• D. The terminating resistor is not used to reduce ground loss; it dissipates power that would otherwise reflect.

A. 300 ohms

A two-wire folded dipole made from equal-diameter conductors steps up the feed impedance by a factor of 4. With an ordinary half-wave dipole at about 73 ohms, the folded dipole's feed point is about 4 x 73 = 292, or roughly 300 ohms, a good match for 300-ohm twin-lead.

• B. About 72 ohms is the feed point impedance of an ordinary half-wave dipole in free space, not a folded one.
• C. 50 ohms is a common coax impedance, not the feed point impedance of a folded dipole.
• D. 450 ohms is a common impedance of window (ladder) line, not the typical feed impedance of a two-wire folded dipole.

C. A half-wave dipole with an additional parallel wire connecting its two ends

A folded dipole is a half-wave dipole with a second conductor running parallel to it and joined to it at both ends, forming a long, narrow loop. The feed point is at the center of one conductor, which raises the feed impedance to about 300 ohms and widens the bandwidth.

• A. A folded dipole is a half wavelength long, not a quarter wavelength.
• B. Bending the ends of a dipole downward produces a drooping or bent dipole, not a folded dipole.
• D. A folded dipole has essentially the same pattern and gain as an ordinary dipole; it is not designed for forward gain.

A. A wire antenna center-fed through a specific length of open-wire line connected to a balun and coaxial feed line

A G5RV is a center-fed wire antenna (about 102 feet in its full-size version) fed through a specific length of open-wire or ladder line, which acts as a matching section. That line connects to a balun or directly to coax that runs to the station.

• B. A G5RV uses no traps; multiband operation comes from the antenna and matching-section lengths, usually with a tuner.
• C. A G5RV is a single wire dipole, not a phased array of loops.
• D. Using shorted coax as the radiating elements describes a coaxial dipole design such as a double bazooka, not a G5RV.

B. An end-fed half-wavelength dipole

A Zepp antenna is a half-wavelength dipole fed at one end, originally with open-wire line. The name comes from its early use trailing from Zeppelin airships.

• A. Switching phasing lines to steer a horizontal array describes a switchable phased array, not a Zepp.
• C. Omnidirectional satellite antennas include the turnstile and eggbeater, not the Zepp.
• D. Switching phasing lines to steer a vertical array describes a phased vertical array, not a Zepp.

D. Radiation at low angles increases

Seawater is a much better conductor than soil, so the ground reflection near a vertical antenna loses far less energy and stays in phase to lower angles. The result is stronger radiation at low elevation angles, which favors long-distance contacts.

• A. Seawater increases low-angle radiation from a vertical; it does not decrease it.
• B. Seawater mainly strengthens low-angle radiation from a vertical; it does not add high-angle lobes.
• C. Seawater does not merge separate lobes into one; its effect is to strengthen the low-angle response.

C. A center-fed 1.25-wavelength dipole antenna

An extended double Zepp is a center-fed dipole with each half 5/8 wavelength long, for a total of 1.25 wavelengths. That length gives more broadside gain than a half-wave dipole, about 3 dB, before the pattern breaks into more lobes.

• A. An extended double Zepp is center-fed, not end-fed, and it is 1.25 wavelengths long, not 1 wavelength.
• B. An extended double Zepp is 1.25 wavelengths long (two 5/8-wavelength halves), not 1.5 wavelengths.
• D. An extended double Zepp is center-fed and 1.25 wavelengths long, not end-fed and 2 wavelengths long.

B. The takeoff angle of the lowest elevation lobe decreases

The pattern of a horizontal antenna over ground is shaped by its reflection from the ground. Raising the antenna (in wavelengths) moves the lowest lobe closer to the horizon, so its takeoff angle decreases; for example, a half-wave-high dipole's lowest lobe peaks at about 30 degrees, and a one-wavelength-high dipole's at about 15 degrees.

• A. Raising the antenna lowers the takeoff angle of the lowest lobe; it does not raise it.
• C. Height above ground mainly changes the elevation pattern, not the horizontal beamwidth.
• D. Height above ground mainly changes the elevation pattern, not the horizontal beamwidth.

B. The main lobe takeoff angle decreases in the downhill direction

On a slope, the ground falls away in the downhill direction, so the antenna is effectively higher above the reflecting ground that way and the reflection tilts the main lobe downward. The main lobe takeoff angle decreases in the downhill direction (and increases toward the uphill side).

• A. The takeoff angle decreases, not increases, in the downhill direction; it increases toward the uphill side.
• C. Sloping ground mainly changes the elevation angle of the main lobe, not the horizontal beamwidth.
• D. Sloping ground mainly changes the elevation angle of the main lobe, not the horizontal beamwidth.

D. 6 dB

The gain of an ideal parabolic dish is proportional to its area measured in wavelengths, so it rises with the square of frequency. Doubling the frequency increases gain by 2² = 4 times, and 10 x log(4) = 6 dB.

• A. 2 dB is too small; doubling frequency quadruples the gain of an ideal dish, a 6 dB increase.
• B. 3 dB is a doubling of gain, but doubling frequency quadruples the gain of an ideal dish (6 dB).
• C. 4 dB does not follow from the square-law relationship; a factor of 4 is 6 dB.

C. 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

Circular polarization needs two linear fields at right angles to each other and 90 degrees apart in phase. Mounting two Yagis on the same boom axis with their elements perpendicular (a crossed Yagi), with driven elements at the same point on the boom and fed 90 degrees out of phase, produces it.

• A. Elements in parallel planes have the same polarization, so phasing them 90 degrees does not create the right-angle fields needed for circular polarization.
• B. Stacking two Yagis with parallel elements fed in phase increases gain but keeps the same linear polarization.
• D. Collinear Yagis fed 180 degrees apart have the same linear polarization; that does not create circular polarization.

A. Near the center of the vertical radiator

On a short whip, current is nearly constant below a loading coil and tapers toward zero above it. Placing the coil near the center keeps high current along the lower half (raising radiation resistance) without needing the very large, lossy coil that a position near the top would require, so center loading is the efficient compromise.

• B. With the coil at the base, current tapers along the whole whip from base to tip, giving lower radiation resistance and lower efficiency than center loading.
• C. The voltage maximum is at the top of the whip, where a coil would need a very large inductance and would be lossy.
• D. A voltage minimum is not the criterion for coil placement; near the center is the efficient compromise.

C. To maximize efficiency

A loading coil's resistance wastes power as heat. A coil with a high ratio of reactance to resistance (high Q) provides the needed inductance with little loss, which maximizes the antenna's efficiency.

• A. Coil Q is chosen to reduce loss, not to suppress harmonics.
• B. The coil's reactance-to-resistance ratio does not set the radiation angle.
• D. A high reactance-to-resistance ratio is a high coil Q; the goal is low loss, not low Q.

D. 1/2 wavelength

A Yagi's driven element is a dipole, about one-half wavelength long, fed at its center. The parasitic elements around it are slightly longer (reflector) or shorter (directors).

• A. 234 divided by frequency in MHz gives a quarter wavelength in feet, the length of a vertical or one half of a dipole.
• B. 1005 divided by frequency in MHz gives about a full wavelength in feet, the length of a quad loop, not a Yagi driven element.
• C. A quarter wavelength is the length of a vertical monopole, not a Yagi's dipole driven element.

B. It is decreased

An electrically short antenna has low radiation resistance and a large reactance that a loading coil must cancel. The result is a high-Q system whose reactance changes quickly with frequency, so the SWR bandwidth is narrower than that of a full-size antenna.

• A. Loading coils raise the system Q, which narrows rather than increases the SWR bandwidth.
• C. A coil at the feed point still makes a high-Q system, so the bandwidth is narrowed, not unchanged.
• D. Coil location affects efficiency, but loading still narrows the SWR bandwidth.

D. Improved radiation efficiency

A top hat or other capacitive loading at the top of a short vertical keeps the current high farther up the radiator. The more uniform current raises the radiation resistance and reduces the loading inductance needed, so a larger share of the power is radiated rather than lost: radiation efficiency improves.

• A. Lower Q, and so somewhat wider bandwidth, can accompany top loading, but the main advantage is improved radiation efficiency; Q by itself does not measure how much power is radiated.
• B. A top hat adds weight and wind load, so greater structural strength is not an advantage.
• C. Higher losses would be a disadvantage; top loading improves efficiency, so losses take a smaller share of the power.

B. SWR bandwidth decreases

An antenna's Q describes how sharply its reactance changes around resonance. A higher-Q antenna's impedance changes faster with frequency, so the range over which SWR stays low (the SWR bandwidth) gets narrower.

• A. Higher Q narrows the SWR bandwidth; it does not widen it.
• C. Q is related to bandwidth, not directly to gain.
• D. Common-mode current on the feed line depends on balance and feed arrangement, not on the antenna's Q.

D. To resonate the antenna by cancelling the capacitive reactance

An antenna shorter than resonant length has capacitive reactance at its feed point. A loading coil adds inductive reactance that cancels it, bringing the antenna to resonance so it presents a mostly resistive load.

• A. A loading coil cancels reactance (reducing net reactance), and it narrows the SWR bandwidth rather than increasing it.
• B. A loading coil adds its own resistance loss; it does not lower losses.
• C. A loading coil raises the antenna system's Q; it does not lower it.

B. Radiation resistance decreases

Below its resonant frequency, a whip is electrically shorter, and radiation resistance falls rapidly as an antenna becomes shorter in wavelengths (roughly with the square of its electrical length). So the radiation resistance decreases, which makes losses a bigger share of the total.

• A. A whip is electrically shorter below resonance, and that lowers its radiation resistance rather than raising it.
• C. Resistance is the real part of impedance; the imaginary part is reactance, so radiation resistance cannot become imaginary.
• D. Radiation resistance depends on electrical length, which changes with frequency.

D. Higher gain

With typical element spacing, a two-element Yagi using a driven element and reflector gives somewhat more forward gain than one using a driven element and director. That gain advantage is why most two-element Yagis use a reflector.

• A. The choice of reflector over director is made for gain, not to lower SWR, which a matching network handles.
• B. Receiving directivity factor is a receiving-antenna measure, not the reason two-element Yagis use reflectors.
• C. Front-to-side ratio is not the reason; the reflector version is chosen for its higher gain.

C. Control of phase shift

A parasitic element is not fed directly; it is excited by the driven element's field. Making it longer than resonance (inductive, a reflector) or shorter (capacitive, a director) controls the phase of its induced current, which sets whether its radiation adds forward or backward.

• A. Element lengths are set for electrical phase, not for wind torque.
• B. Element lengths are set for electrical phase, not for mechanical balance.
• D. Detuning the elements controls the phase of their currents; it is not done to minimize losses.

B. Beta or hairpin

A beta or hairpin match connects to both halves of a split driven element at its center, as a balanced feed, so the element must be insulated from the boom. Gamma and T matches connect to points out along a continuous element, whose center can be attached directly to the boom.

• A. A gamma match feeds a continuous element whose center can be attached to the boom.
• C. Shunt feeding taps onto a continuous, grounded element, so it does not require insulating it from the boom.
• D. A T-match is a balanced version of the gamma match and also works with a continuous element attached to the boom at its center.

A. Gamma match

In a gamma match, the coax shield connects to the electrical center of the driven element, and the center conductor connects through a series capacitor to a rod that taps the element a short distance to one side. Moving the tap point adjusts the impedance transformation.

• B. A delta match fans out from a balanced feed line to two points equally spaced on either side of the center.
• C. A T-match taps both sides of the center symmetrically; it is a balanced version of the gamma.
• D. A stub match uses a short section of transmission line in parallel with the feed line, not a tap on one side of the element.

D. Stub match

A stub match connects a short section of transmission line, open or shorted at its far end, in parallel with the feed line at or near the feed point. The stub's reactance, set by its length and position, cancels the load's reactance so the line sees a match.

• A. A gamma match taps the driven element with a rod and series capacitor; it is not a stub in parallel with the feed line.
• B. A delta match fans the feed line out to two points on the element; it is not a stub in parallel with the feed line.
• C. A T-match taps both sides of the element with rods; it is not a stub in parallel with the feed line.

B. To cancel unwanted inductive reactance

The gamma rod and the element section it parallels form an inductive loop, adding inductive reactance at the feed. The series capacitor cancels that reactance, leaving a resistive match to the coax.

• A. DC isolation is not the purpose; the capacitor is there to cancel the gamma rod's inductive reactance.
• C. The capacitor is in series to cancel reactance at the operating frequency, not to form a harmonic rejection notch.
• D. The impedance transformation comes from the tap point along the element; the capacitor cancels reactance.

A. Capacitive (driven element electrically shorter than 1/2 wavelength)

A hairpin is a shunt inductor across the feed point. It works with a driven element that is slightly shorter than a half wavelength, so its feed point is capacitive: the capacitive reactance and the hairpin's inductance form an L network that transforms the element's low resistance up to the feed line's impedance.

• B. An inductive driven element would need a capacitive shunt; the hairpin adds inductance and requires a capacitive element.
• C. A purely resistive element has no capacitive reactance for the hairpin's inductance to work against.
• D. A purely reactive load would accept no power; the hairpin needs a feed point with resistance plus capacitive reactance (an element shorter than resonant).

C. 75 ohms

A quarter-wave matching section needs a characteristic impedance equal to the geometric mean of the two impedances: Z0 = √(50 x 100) = 70.7 ohms. 75-ohm line is closest; it transforms the 100-ohm load to 75² / 100 = 56.25 ohms, an SWR of about 1.13 on the 50-ohm line.

• A. A 50-ohm quarter-wave section transforms 100 ohms to 50² / 100 = 25 ohms, an SWR of 2 on the 50-ohm line.
• B. A 62-ohm section transforms 100 ohms to about 38 ohms, a worse match than 75 ohms gives.
• D. A 90-ohm section transforms 100 ohms to 81 ohms, a worse match than 75 ohms gives.

B. Reflection coefficient

The reflection coefficient describes how a load and a transmission line interact: Γ = (ZL - Z0) / (ZL + Z0), the ratio of reflected to forward voltage at the load. It is 0 for a matched load and has a magnitude of 1 for an open or short.

• A. Characteristic impedance is a property of the line alone, set by its construction, not of the line and load together.
• C. Velocity factor is a property of the line's construction, not of its interaction with the load.
• D. Dielectric constant is a property of the insulating material, not of how a load interacts with the line.

C. To divide power equally between two 50-ohm loads while maintaining 50-ohm input impedance

A Wilkinson divider splits power equally between two outputs, each terminated in 50 ohms, while presenting a 50-ohm input impedance. Its quarter-wave sections and a resistor between the outputs also isolate the outputs from each other; it is commonly used to feed two antennas in a phased or stacked array.

• A. A Wilkinson divider divides power, not frequency; it does not move a signal to a lower band.
• B. Feeding a high-impedance antenna from a low-impedance source is a job for a matching network or transformer.
• D. Dividing an input frequency for a counter is the job of a prescaler, not a power divider.

C. Gamma match

A grounded tower can be used as a vertical antenna by shunt feeding it: a gamma match connects the coax shield to the grounded base and the center conductor, through a series capacitor, to a wire tapping the tower partway up. Adjusting the tap height and capacitor gives a match without insulating the tower from ground.

• A. A double bazooka is a type of coaxial dipole antenna, not a way to shunt feed a tower.
• B. A beta or hairpin match feeds a split, insulated element, so it does not suit a grounded tower.
• D. Only the gamma match is used this way, so not all the choices are correct.

A. To control the antenna’s radiation pattern

Feeding several driven elements through phasing lines sets the relative phase (and amplitude) of the current in each element. The way their fields add and cancel then controls the radiation pattern, for example making a broadside, end-fire or cardioid pattern.

• B. Harmonic radiation is reduced with filters, not with phasing lines between driven elements.
• C. Phasing lines are cut for a particular band; they do not make single-band antennas work on other bands.
• D. Phasing mainly shapes and steers the pattern; a low radiation angle depends mostly on antenna type, height and ground.

D. The velocity of a wave in the transmission line divided by the velocity of light in a vacuum

Velocity factor is the speed of a wave in the transmission line divided by the speed of light in a vacuum. For example, a solid-polyethylene coax with a velocity factor of 0.66 carries signals at 66 percent of the speed of light.

• A. The ratio of characteristic impedance to termination impedance relates to mismatch and SWR, not velocity factor.
• B. The ratio of termination impedance to characteristic impedance relates to mismatch and SWR, not velocity factor.
• C. Velocity factor is a ratio of speeds, so it divides by the speed of light; multiplying gives a meaningless quantity.

C. The insulating dielectric material

Velocity factor depends mainly on the insulating material (dielectric) between the conductors: it is about 1 / √(dielectric constant). Solid polyethylene gives about 0.66, foam about 0.8 or higher, and air close to 1.

• A. Characteristic impedance and velocity factor are separate; two lines with the same impedance can have different velocity factors if their dielectrics differ.
• B. Velocity factor does not depend on how long the line is.
• D. The center conductor's resistivity affects loss, not the speed of the wave.

D. Electromagnetic waves move more slowly in a coaxial cable than in air

Waves travel more slowly in coax than in air because of the dielectric, so a wavelength in the cable is physically shorter. A given physical length of cable therefore contains more wavelengths, making its electrical length longer than its physical length.

• A. Skin effect affects loss in the conductors, not how fast the wave travels or the electrical length.
• B. Skin effect affects loss in the conductors, not how fast the wave travels or the electrical length.
• C. Waves travel more slowly in coax than in air, not faster.

B. Very low impedance

A half-wavelength line repeats its load impedance at its input. With a short at the far end, the generator sees a short again: a very low impedance.

• A. A very high impedance appears at the input of a shorted quarter-wavelength line, not a half-wavelength one.
• C. A line presents its characteristic impedance at its input, whatever its length, when it is terminated in that impedance; a shorted or open line does not.
• D. The input impedance depends on the line and its termination, not on the generator's output impedance.

D. Precision printed circuit conductors above a ground plane that provide constant impedance interconnects at microwave frequencies

Microstrip is a precisely sized printed circuit conductor running over a ground plane on the other side of the board. Its width and the board's thickness and dielectric set a constant characteristic impedance, making it a transmission line for connecting microwave circuits.

• A. Microstrip is a printed transmission line, not a shielding material.
• B. Microstrip is a printed conductor over a ground plane, not miniature coax.
• C. Microstrip is printed on the board, not made from short lengths of coax.

C. 10.6 meters

Wavelength in meters is 300 / f in MHz: 300 / 14.10 = 21.3 m, and half of that is 10.6 m. Air-insulated parallel line has a velocity factor close to 1, so its physical length is about equal to its electrical length: about 10.6 m.

• A. 7.0 m applies a velocity factor of 0.66, typical of solid-polyethylene coax, not air-insulated line.
• B. 8.5 m applies a velocity factor of 0.8, which is too low for air-insulated line.
• D. 13.3 m divides by 0.8 instead of multiplying; a velocity factor below 1 makes the physical length shorter, not longer.

A. Lower loss

Parallel-conductor (open-wire or ladder) line is mostly air between the conductors, so it has much less dielectric loss than coax with a plastic dielectric. It typically has lower loss per unit length, especially when SWR on the line is high.

• B. SWR depends on the mismatch between the load and the line's characteristic impedance, not on the type of line.
• C. Reflection coefficient depends on the load and the line's characteristic impedance, not on whether the line is coax or parallel conductor.
• D. Parallel-conductor line has a higher velocity factor than plastic-dielectric coax, not a lower one.

D. All these choices are correct

Foam dielectric is partly gas, so compared with solid dielectric of the same type it has a lower dielectric constant and lower loss. That gives it a higher velocity factor and lower loss per unit length, but the foam withstands less voltage before breaking down, lowering the safe maximum voltage.

• A. True: foam has lower dielectric strength than solid dielectric, so it breaks down at a lower voltage, but this is only one of the differences.
• B. True: foam dielectric has lower dielectric loss, but this is only one of the differences.
• C. True: foam's lower dielectric constant gives it a higher velocity factor, but this is only one of the differences.

A. Very high impedance

A quarter-wavelength line inverts its load impedance: a low impedance at one end appears as a high impedance at the other. A short at the far end therefore looks like a very high impedance (ideally an open circuit) to the generator.

• B. A very low impedance appears at the input of a shorted half-wavelength line, not a quarter-wavelength one.
• C. A line presents its characteristic impedance at its input, whatever its length, when it is terminated in that impedance; a shorted or open line does not.
• D. The input impedance depends on the line and its termination, not on the generator's output impedance.

C. An inductive reactance

A shorted line less than a quarter wavelength long acts as an inductor. At 1/8 wavelength (45 degrees) the input reactance is X = Z0 x tan(45°) = Z0, an inductive reactance with the same number of ohms as the line's characteristic impedance.

• A. A capacitive reactance appears at the input of an open 1/8-wavelength line, not a shorted one.
• B. The reactance has the same number of ohms as Z0, but it is a pure inductive reactance, not the resistive Z0 a matched line presents.
• D. A shorted line shows zero impedance at its input when it is a half wavelength long (or a multiple of that), not at 1/8 wavelength.

C. A capacitive reactance

An open line less than a quarter wavelength long acts as a capacitor. At 1/8 wavelength (45 degrees) the input reactance is X = Z0 / tan(45°) = Z0, a capacitive reactance with the same number of ohms as the line's characteristic impedance.

• A. The reactance has the same number of ohms as Z0, but it is a pure capacitive reactance, not the resistive Z0 a matched line presents.
• B. An inductive reactance appears at the input of a shorted 1/8-wavelength line, not an open one.
• D. An ideally infinite impedance appears at the input of an open line a half wavelength long, not 1/8 wavelength.

D. Very low impedance

A quarter-wavelength line inverts its load impedance. An open at the far end therefore appears as a very low impedance (ideally a short) at the generator.

• A. A line presents its characteristic impedance at its input, whatever its length, when it is terminated in that impedance; a shorted or open line does not.
• B. The line's input impedance is set by the line and its termination, not by the generator.
• C. A very high impedance appears at the input of an open half-wavelength line or a shorted quarter-wavelength line.

A. Impedance along transmission lines

A Smith chart is a graphical calculator for impedances on transmission lines. Plotting a load impedance and moving around the chart by a line's electrical length shows the impedance at any point along the line.

• B. Radiation resistance depends on the antenna's size and shape; it is calculated or modeled, not found with a Smith chart.
• C. Antenna radiation patterns come from modeling or measurement, not from a Smith chart.
• D. Radio propagation is predicted with propagation tools, not with a Smith chart.

B. Resistance circles and reactance arcs

A Smith chart's coordinates are circles of constant resistance and arcs of constant reactance. Any impedance plots at the point where its resistance circle and reactance arc cross.

• A. A Smith chart plots resistance and reactance, not voltage and current.
• C. A Smith chart has no voltage or current chords; it uses resistance circles and reactance arcs.
• D. Constant-resistance values on a Smith chart are circles, not lines, and reactance values are arcs.

C. Impedance and SWR values in transmission lines

Smith charts are used to find impedance and SWR along transmission lines, for example the impedance at the transmitter end of a line feeding a mismatched antenna, and to design matching networks.

• A. Beam headings come from great-circle maps and radiation patterns from modeling, not from a Smith chart.
• B. Satellite azimuth and elevation come from tracking software or calculations, not from a Smith chart.
• D. Propagation reliability is estimated with propagation prediction programs, not with a Smith chart.

C. Resistance and reactance

A Smith chart is made of two families: circles of constant resistance and arcs of constant reactance. Inductive reactance is plotted in the upper half and capacitive reactance in the lower half.

• A. Inductance and capacitance appear on the chart as reactance values; the families are resistance and reactance.
• B. Voltage is not one of the families of curves on a Smith chart.
• D. Voltage is not plotted on a Smith chart; impedance is located by its resistance and reactance.

A. Determine the length and position of an impedance matching stub

A common Smith chart task is designing a stub match: the chart shows how far from the load to place a stub and how long the stub must be to cancel the reactance there.

• B. Characteristic impedance from physical dimensions is calculated with a formula, not a Smith chart.
• C. Antenna gain comes from modeling or measurement, not a Smith chart.
• D. Line loss per 100 feet comes from manufacturer data or calculation, not a Smith chart.

B. Reactance axis

The large outer circle of a Smith chart is where resistance is zero, so every point on it is a pure reactance. It is called the reactance axis, and the reactance arcs end on it.

• A. "Prime axis" is not a Smith chart term; the center point is called the prime center.
• C. The outer circle is not called the impedance axis; it represents pure reactance.
• D. "Polar axis" is not the name of the Smith chart's outer circle.

D. The resistance axis

The horizontal line through the center of a Smith chart is where reactance is zero, so it holds the pure resistances, from zero on the left to infinity on the right. It is the resistance axis and is the only straight line on the chart.

• A. The reactance axis is the large outer circle, not a straight line.
• B. A Smith chart has no current axis.
• C. A Smith chart has no voltage axis.

C. Reassign the prime center’s impedance value

Normalizing assigns the chart's prime center a reference impedance, usually the line's characteristic impedance, and divides every impedance by it. On a 50-ohm system, 50 ohms plots at the center as 1.0 and 100 + j50 ohms plots as 2 + j1.

• A. Normalizing does not swap axes; it scales impedances by the value assigned to the prime center.
• B. Normalizing does not relabel the resistance axis with reactance values.
• D. Normalizing does not move the prime center; it assigns the center an impedance value.

A. Constant-SWR circles

Constant-SWR circles, centered on the prime center, are often added to a Smith chart. Moving along a lossless line keeps SWR constant, so the impedance travels around such a circle; this makes the circles useful when designing matching networks.

• B. Line length is read from the wavelength scales around the outside of the chart, not from added circles.
• C. There are no coaxial-length circles on a Smith chart.
• D. Radiation patterns are not shown on a Smith chart.

D. Points with constant reactance

The arcs on a Smith chart each connect points of equal reactance, inductive above the resistance axis and capacitive below it. The full circles connect points of equal resistance.

• A. Frequency is not plotted directly on a Smith chart.
• B. SWR is shown by constant-SWR circles centered on the prime center, not by the reactance arcs.
• C. Points of constant resistance lie on the full circles, not the arcs.

B. In fractions of transmission line electrical wavelength

The scales around the edge of a Smith chart are marked in fractions of a wavelength along the transmission line, measured as electrical length. One full trip around the chart equals a half wavelength of line.

• A. The scales are in fractions of wavelength, not frequency.
• C. The wavelength scales refer to the transmission line, not the antenna.
• D. The scales are in fractions of transmission line wavelength, not antenna frequency.

D. It should be at least one wavelength long

A Beverage is a long, low wire receiving antenna, usually terminated at the far end. It needs to be at least one wavelength long at the operating frequency to develop useful directivity; longer generally gives more directivity.

• A. A Beverage needs to be at least a wavelength long; a quarter wavelength is far too short.
• B. Beverages are mounted low, typically a few feet to about 10 feet above ground, not over a wavelength high.
• C. A Beverage is a long single wire, not a four-sided loop.

A. Atmospheric noise is so high that directivity is much more important than losses

On 160 and 80 meters, atmospheric noise is strong enough to set the reception limit. An inefficient receiving antenna lowers signal and noise together, so what improves reception is directivity that rejects noise and interference from other directions.

• B. Good low-band receiving antennas such as Beverages work close to the ground; half-wavelength height is not required.
• C. Because atmospheric noise is high, some feed line loss reduces signal and noise together and is not critical.
• D. Only the statement about directivity is generally true, so not all the choices are correct.

D. Peak antenna gain compared to average gain over the hemisphere around and above the antenna

Receiving directivity factor (RDF) compares an antenna's gain in its peak direction with its average gain over the whole hemisphere around and above it. A high RDF means the antenna favors the wanted direction over noise arriving from all others.

• A. Forward gain compared with reverse gain is the front-to-back ratio.
• B. Directivity compared with isotropic describes gain in dBi, not RDF.
• C. Directivity compared with a dipole describes gain in dBd, not RDF.

B. It eliminates unbalanced capacitive coupling to the antenna’s surroundings, improving the depth of its nulls

A small loop can pick up signals through stray capacitive coupling to nearby objects and to the feed line, acting like a small unbalanced vertical. An electrostatic shield removes this unwanted coupling so the loop responds only as a balanced loop, which makes its nulls deeper and its bearings sharper.

• A. The shield is used to remove unbalanced coupling, not to add loading or increase bandwidth.
• C. The shield does not address strong out-of-band signals; that is a receiver selectivity problem.
• D. The shield does not improve the match to the feed line; its purpose is to deepen the nulls.

A. It has a bidirectional null pattern

A small loop has two equally deep nulls, 180 degrees apart, along the loop's axis. A null tells you the line the signal comes from but not which of the two opposite directions, so a second bearing or a sense antenna is needed to resolve the ambiguity.

• B. A small loop's nulls are sharp and well defined; that is what makes it useful for direction finding.
• C. Small loops are widely used for direction finding on MF and HF, not only on VHF and higher.
• D. Only the bidirectional null is a challenge, so not all the choices are correct.

D. Minimum variation in SWR over the desired frequency range

When a Beverage is terminated in a resistance close to its characteristic impedance, little energy reflects from the far end, and the feed point impedance stays nearly constant with frequency. So the correct termination shows as the least variation in SWR across the frequency range.

• A. Feed point DC resistance does not indicate the correct RF termination.
• B. The goal of termination is maximum front-to-back ratio, not minimum.
• C. Correct termination is judged by a steady SWR across the band, not by the current in the terminating resistor.

B. Absorb signals from the reverse direction

Signals arriving from the terminated end travel toward that end of the wire and are absorbed in the termination resistor instead of reflecting back to the receiver. Signals from the other direction travel toward the receiver end, so the antenna becomes unidirectional.

• A. The resistor's purpose is to reject signals from the rear, not to increase front-to-side ratio.
• C. Termination makes the SWR steady across frequency, broadening rather than decreasing the SWR bandwidth.
• D. The termination resistor does not affect harmonic reception.

A. It modifies the pattern of a DF antenna to provide a null in only one direction

A loop's figure-eight pattern has two nulls, which leaves a 180-degree ambiguity. A sense antenna, usually a small vertical, is combined with the loop in the right phase and amplitude to turn the pattern into a cardioid with a single null, showing which direction the signal comes from.

• B. The sense antenna's job is to resolve direction ambiguity, not to increase sensitivity.
• C. A sense antenna does not let the array receive at different vertical angles.
• D. A sense antenna is not a diversity antenna for canceling multipath.

A. Cardioid

A pennant (or flag) is a single-turn loop with a resistor in one side. The terminating resistor makes the loop respond like a combination of a small loop and a short vertical, giving a cardioid pattern with a single null, useful for low-band receiving.

• B. A bidirectional, figure-eight pattern comes from a small loop without a termination.
• C. The terminated loop is directional, not omnidirectional.
• D. "Hyperbolic" is not a type of antenna radiation pattern.

C. By increasing the number of turns and/or the area enclosed by the loop

A receiving loop's output voltage is proportional to the number of turns and the area each turn encloses. Adding turns, enlarging the loop, or both increases the voltage it delivers.

• A. Reducing a shield's permeability does not increase the loop's output.
• B. Using high-impedance wire for a coupling loop does not raise the loop's output voltage.
• D. Only more turns and larger area increase the output, so not all the choices are correct.

B. A single null

A cardioid pattern has one deep null opposite its broad maximum. Rotating the antenna until the signal fades into that single null gives a bearing without the 180-degree ambiguity of a loop's two nulls.

• A. A cardioid's peak is broad, not sharp; the useful feature is its single null.
• C. Broadband response is not what makes a cardioid useful for direction finding.
• D. A high radiation angle is not a direction-finding advantage of a cardioid.