Wire and Loop Antennas

Introduction

Wire antennas are among the oldest and most useful radiating structures in electrical engineering. Their importance comes from a favorable combination of simplicity, low cost, mechanical flexibility, and analytically tractable behavior. Even highly sophisticated wireless systems frequently use wire-derived geometries, including dipoles, monopoles, folded dipoles, helices, loops, and printed equivalents.

A wire antenna is formed from a conducting path whose transverse dimensions are small compared with the wavelength. A loop antenna is a special wire antenna in which the conductor forms a closed contour. The electromagnetic behavior of these antennas depends strongly on electrical length, current distribution, conductor geometry, excitation method, ground environment, and proximity to other objects.

At postgraduate level, it is important not merely to memorize standard lengths such as λ/2 or λ/4, but to understand why these dimensions are useful, when the corresponding approximations fail, and how impedance, radiation pattern, bandwidth, efficiency, polarization, and matching interact in practical designs.

Learning Objectives

After completing this chapter, the reader should be able to:

1. Explain the radiation mechanism of a time-varying current on a wire.
2. Distinguish short dipoles, finite-length dipoles, monopoles, folded dipoles, and loop antennas.
3. Derive and interpret the principal far-field expressions for elementary wire and loop antennas.
4. Calculate radiation resistance, directivity, gain, efficiency, and approximate bandwidth under stated assumptions.
5. Select a suitable wire or loop geometry for a communication or sensing application.
6. Analyze the effects of ground, conductor loss, loading, imbalance, and nearby structures.
7. Critically evaluate practical designs and contemporary developments involving wire and loop antennas.

1. Electromagnetic Basis of Wire-Antenna Radiation

An antenna radiates because an accelerated charge, or equivalently a time-varying current, produces electromagnetic fields that detach from the source and propagate outward. In a thin wire, the current varies along the conductor and establishes electric and magnetic fields. At large distance from the antenna, the radiated electric and magnetic fields are transverse to the direction of propagation and are related approximately by the intrinsic impedance of the medium.

For a uniform, lossless medium,

where η is intrinsic impedance in ohms, μ is permeability in henries per metre, and ε is permittivity in farads per metre. In free space, η₀ is approximately 120π Ω, or 377 Ω.

The wavelength is

where λ is wavelength in metres, v is phase velocity, f is frequency in hertz, and β is phase constant in radians per metre. In free space, v = c ≈ 3 × 10⁸ m/s. The approximation must be modified in dielectric or near-ground environments because the effective phase velocity differs from c.

A wire is considered electrically thin when its radius a is much smaller than λ, commonly with a/λ ≪ 1. This assumption permits a one-dimensional current model, although it does not mean that the current is necessarily uniform.

Near, Fresnel, and Far Regions

The field around an antenna is conventionally divided into reactive near-field, radiating near-field, and far-field regions. In the far field, the angular field pattern is essentially independent of distance, while field magnitude decreases approximately as 1/r. For an antenna with maximum dimension D, a commonly used far-field criterion is

provided that r is also sufficiently greater than λ. This criterion is approximate and is most reliable for electrically extended antennas. Measurements made inside the far-field boundary may produce misleading estimates of gain or pattern.

2. Fundamental Antenna Quantities

The radiation intensity U(θ, φ) is the power radiated per unit solid angle. If Pᵣ is total radiated power, then

The directivity is

and the maximum directivity is the maximum of this expression over all directions. Gain includes radiation efficiency:

where ηᵣ is radiation efficiency, dimensionless. If conductor and dielectric losses are represented by loss resistance R_loss and radiation resistance Rᵣ, respectively, then for a simple series model

This relation excludes mismatch loss. If the antenna terminal is connected to a source with reflection coefficient Γ, the accepted-power fraction is 1 − |Γ|². Thus realized gain is commonly written as

The formula assumes a single-port antenna and a reference impedance consistent with the definition of Γ.

Radiation resistance is defined by equating radiated power to the power that would be dissipated in a resistor carrying the same reference current:

If peak current I₀ is used instead, the equivalent expression is Pᵣ = ½I₀²Rᵣ. Confusing peak and rms current is a common source of factor-of-two errors.

3. The Short Electric Dipole

A short electric dipole has total length l satisfying l ≪ λ and a current that is approximately uniform along its length. It is sometimes called a Hertzian dipole when represented as an infinitesimal current element. The short-dipole approximation is analytically valuable but physically idealized: a practical center-fed short dipole usually has a triangular rather than uniform current distribution.

For a z-directed infinitesimal current element with current amplitude I₀, the far-zone electric field in free space is proportional to

where θ is measured from the dipole axis and r is observation distance. The magnetic field is

The pattern is proportional to sinθ. It is zero along the wire axis and maximum broadside. The three-dimensional pattern is a toroid, often described as a doughnut shape.

For a uniform-current short dipole in free space, the radiation resistance is

The formula assumes l ≪ λ, a thin conductor, uniform current, and free-space operation. For a practical center-fed short dipole with triangular current distribution, the effective radiation resistance is approximately

The difference arises from the current-distribution assumption. The two formulas must not be mixed.

The maximum directivity of the short dipole is 1.5, corresponding to approximately 1.76 dBi. Its gain is lower if conductor, dielectric, or loading losses are present.

Electric-Dipole Field Interpretation

The far field contains no radial electric or magnetic component of comparable magnitude. The electric field is θ-directed, the magnetic field is φ-directed, and both are perpendicular to the outward radial direction. The antenna is linearly polarized in the far field at any fixed azimuthal observation plane.

4. Finite-Length Center-Fed Dipoles

When the dipole length is no longer electrically short, the current distribution must be considered. For a thin, center-fed, straight dipole of total length L, a useful sinusoidal approximation is

for −L/2 ≤ z ≤ L/2, with open-circuit current approaching zero at the ends. This expression assumes a perfectly conducting thin wire, a center feed, sinusoidal standing-wave behavior, and negligible end effects. Actual current distributions deviate near the feed and tips.

For a half-wave dipole, L is close to λ/2, but the exact resonant length is usually somewhat shorter because of end effects and conductor diameter. A practical value may be approximately 0.47λ to 0.49λ, depending on wire radius, surrounding dielectric, height above ground, and required reactance. At resonance, the input resistance of a thin, isolated half-wave dipole is often near 73 Ω, although practical values vary.

The half-wave dipole has a broadside pattern proportional approximately to

where F is normalized field magnitude and θ is measured from the dipole axis. The expression applies to an ideal thin half-wave dipole in free space. The apparent singularity at θ = 0 is removable because the limiting value is zero.

Its maximum directivity is approximately 1.64, or about 2.15 dBi. Compared with the short dipole, it has higher radiation resistance, greater directivity, and generally more manageable feed impedance.

For dipoles longer than λ/2, additional lobes appear. At lengths near λ, the pattern changes substantially and the feed impedance may become reactive or exhibit multiple resonances. Consequently, physical length alone does not determine performance; current distribution and environment must be included.

5. Monopole Antennas and Image Theory

A monopole is a wire antenna mounted over a conducting ground plane. An ideal quarter-wave monopole is approximately λ/4 long and is analyzed using image theory: the ground plane is replaced by an image antenna below the plane. The monopole and its image form a half-wave dipole, but radiation exists only in the upper hemisphere.

For an ideal infinite perfect electric conductor ground plane, the quarter-wave monopole has approximately:

• radiation resistance: 36.5 Ω;
• maximum directivity: approximately 3.28, or 5.15 dBi;
• a null toward the ground plane;
• vertical polarization in the direction of maximum radiation.

The directivity is approximately twice that of the corresponding half-wave dipole because the same power is concentrated into one hemisphere. This statement assumes an ideal ground plane and comparable radiated power; a real ground system introduces loss and pattern distortion.

Finite ground planes require radial wires, a counterpoise, a vehicle body, or another conductive structure to support the return current. Poor ground systems increase loss, alter resonance, and may cause common-mode current on the feed cable. A choke balun or common-mode suppression network is often required when the feedline unintentionally becomes part of the radiator.

6. Folded Dipoles and Balanced Feeding

A folded dipole consists of two parallel conductors joined at their ends, with the feed usually applied at the center of one conductor. For equal-diameter conductors and close spacing, the input resistance near resonance is approximately four times that of a simple half-wave dipole:

Thus, a 73 Ω half-wave dipole may be transformed to approximately 292 Ω. The relation assumes equal conductor currents and negligible spacing effects. Different conductor diameters produce a more general impedance transformation determined by the current ratio and characteristic impedance of the two-wire structure.

Folded dipoles are useful for impedance transformation, broadband arrays, and connection to balanced transmission lines. Since the antenna is balanced, a balanced-to-unbalanced transformer, or balun, is required when it is fed by coaxial cable. Without appropriate balance, feedline radiation can corrupt the intended pattern and electromagnetic compatibility performance.

7. Loop Antennas

A loop antenna is a closed conducting path. Its behavior depends strongly on circumference C relative to wavelength and on whether the loop is electrically small or resonant.

Electrically Small Loop

For a loop with circumference C ≪ λ, the current is approximately uniform. The loop behaves as a magnetic dipole. If A is loop area and I₀ is peak current, the magnetic dipole moment magnitude is

For a single-turn circular loop of radius a,

The radiation resistance of a small loop with N turns is

where A is the area of one turn in square metres. The expression assumes a small loop, uniform current, free space, and negligible mutual coupling between turns. An equivalent form for circumference C is

for a circular loop, because C = 2πa. The strong fourth-power dependence shows why a very small loop has extremely low radiation resistance.

The far-field pattern of a small loop is complementary to that of a short electric dipole. Its field is maximum in the plane of the loop and zero along the loop axis. The loop is often described as a magnetic dipole, whereas the short straight wire is an electric dipole.

The directivity of an ideal small loop is 1.5, the same as that of a short electric dipole. The polarization is linear in a fixed observation direction, but the field orientation differs spatially from that of a straight dipole.

Resonant and Large Loops

When the circumference approaches one wavelength, the uniform-current approximation fails. The loop becomes a distributed resonant structure with standing-wave current. A full-wave loop can have useful radiation resistance and a directional pattern, but the pattern and impedance depend on circumference, conductor diameter, feed position, and loop shape.

A loop may be circular, square, triangular, or electrically equivalent to another closed contour. Shape changes the inductance, capacitance, current distribution, and polarization characteristics. A perimeter near λ is not by itself sufficient to predict resonance because conductor diameter and end geometry also influence the effective electrical length.

Tuning and High-Q Small Loops

A small loop usually has inductive reactance. A tuning capacitor can resonate the loop at the operating frequency. If the total series resistance is R_total = Rᵣ + R_loss, an approximate quality factor is

where X is the reactance magnitude at the tuning point. High Q implies narrow bandwidth. The fractional bandwidth is approximately inversely proportional to Q for a specified small-signal matching criterion, but exact bandwidth depends on the definition of bandwidth, matching network, and acceptable efficiency.

Because Rᵣ is often only a fraction of an ohm, even modest conductor loss can severely reduce efficiency:

For example, if Rᵣ = 0.20 Ω and R_loss = 0.05 Ω, then ηᵣ = 0.20/0.25 = 0.80, or 80%. If R_loss rises to 0.80 Ω, efficiency falls to 20%. This illustrates why high-conductivity conductors, low-loss capacitors, carefully designed joints, and adequate spacing from lossy materials are essential.

Figure: Idealized angular-field comparison. The dipole has nulls on its axis; the small loop has nulls along the loop axis and maximum radiation in the loop plane.

8. Receiving Properties and Polarization

By reciprocity, a passive linear antenna has the same transmitting and receiving pattern at a given frequency. Therefore, the directional and polarization properties determined during transmission also apply during reception.

For a receiving antenna, available received power depends on incident power density, effective aperture, polarization match, impedance match, and propagation conditions. The maximum effective aperture is related to gain by

where A_e,max is in square metres and G is dimensionless gain. This relation assumes a reciprocal antenna in a homogeneous medium and uses gain rather than directivity when losses are present.

Polarization mismatch reduces received power. For unit polarization vectors p_t and p_r, the polarization coupling factor is

where the asterisk denotes complex conjugation. The factor ranges from zero to one. A linearly polarized receiving dipole aligned with the incident electric field has ρ_p = 1; an orthogonal dipole has ρ_p = 0 in the ideal case.

9. Worked Example: Selecting a Half-Wave Dipole

A center-fed dipole is required for 150 MHz operation in free space. Estimate its wavelength and initial physical length, then estimate its ideal radiation resistance.

The wavelength is

An initial half-wave length is L ≈ λ/2 = 1.0 m. A practical resonant dipole may be shortened to approximately 0.47λ–0.49λ, giving an initial range of 0.94–0.98 m. Final length must be established by measurement or full-wave simulation because wire diameter, height, nearby supports, and feed arrangement shift resonance.

For an ideal thin half-wave dipole, Rᵣ ≈ 73 Ω. If conductor and dielectric losses total 2 Ω, the radiation efficiency is

This estimate excludes mismatch loss. If the antenna is connected to a 50 Ω system without a matching network, the realized gain may be lower even though the radiation efficiency remains high.

10. Practical Design Workflow

A reliable wire-antenna design begins with system requirements rather than a preferred geometry.

1. Define frequency and bandwidth. Determine whether the application is narrowband, multiband, frequency-agile, or ultra-wideband.
2. Specify polarization and coverage. Decide whether broadside, end-fire, omnidirectional azimuth coverage, or null steering is required.
3. Select a topology. Consider dipole, monopole, folded dipole, loop, loaded whip, or a multi-element array.
4. Estimate electrical dimensions. Use λ/2, λ/4, or small-loop relations only as initial approximations.
5. Model the environment. Include ground, enclosure, radome, vehicle body, human proximity, feedline, and nearby conductors.
6. Evaluate impedance and efficiency. Do not judge a design only by return loss; low reflected power can coexist with low radiation efficiency.
7. Provide current-path control. Use baluns, chokes, counterpoises, and adequate grounding where required.
8. Prototype and measure. Use a calibrated vector network analyzer for impedance and an appropriate test range or validated near-field method for pattern and gain.
9. Assess compliance. Verify exposure limits, spurious emissions, electromagnetic compatibility, and applicable spectrum regulations.

Measurement Considerations

A vector network analyzer measures terminal S-parameters, not radiated efficiency directly. A good S₁₁ result indicates impedance matching at the reference plane, but it does not prove that accepted power is radiated. Total efficiency requires techniques such as gain comparison, Wheeler-cap measurements, reverberation-chamber measurements, or calibrated three-dimensional pattern integration.

Cable movement can change common-mode current and create unstable measurements. The feed cable should be routed consistently, and ferrite chokes or baluns should be used when appropriate. Calibration planes, connector repeatability, fixture effects, and chamber reflections must be documented.

11. Applied Case: Compact HF Loop for an Electrically Constrained Site

Background. An illustrative amateur-radio and emergency-communications installation must operate near 14 MHz where a full half-wave dipole would be approximately 10.7 m long. The available balcony space is only 2.5 m by 2.5 m, and the antenna must be removable.

Problem. A compact loop is attractive because its perimeter can fit the available space, but its small radiation resistance and narrow bandwidth create efficiency and tuning challenges.

Analysis. At 14 MHz, λ ≈ 21.4 m. A square loop with perimeter about 8 m is not electrically tiny, but it is still substantially smaller than a full-wave loop. A tuning capacitor can resonate the loop, yet the conductor loss, capacitor loss, balcony railing, and nearby building materials will affect performance. The design must therefore be treated as a coupled electromagnetic structure rather than an isolated theoretical loop.

Approach. The engineering team first models the loop with the balcony railing and support structure included. A high-conductivity tubular conductor is selected, with mechanically robust low-loss joints. A vacuum variable capacitor is used where voltage and current ratings permit. The feed is inductively coupled through a smaller auxiliary loop, which reduces the need for a high-voltage direct feed connection and provides a convenient impedance transformation. A common-mode choke is installed on the coaxial cable.

The team measures resonant frequency, bandwidth, and input match at several physical orientations. Efficiency is estimated by comparing calibrated radiated power with accepted input power rather than relying only on S₁₁. The loop is retuned after installation because the building changes its capacitance and loss.

Outcome. The compact loop provides usable narrowband communication, but its operating bandwidth is much smaller than that of a full-size dipole. Automatic or manual retuning is required when the frequency changes significantly. Raising the loop away from the railing improves efficiency and pattern stability, while careless placement near metal produces detuning and increased loss.

Learning points. Compactness is obtained by accepting trade-offs in bandwidth, efficiency, tuning sensitivity, and power handling. A low return loss alone cannot establish good antenna performance. In constrained installations, environmental modelling, mechanical design, thermal rating, and measurement are as important as the ideal loop equations.

12. Limitations, Safety, and Regulation

Wire and loop formulas are approximations. They become unreliable when the conductor is not thin, when the antenna is close to a lossy or conductive object, when the ground is finite, when multiple conductors are strongly coupled, or when the structure is electrically large. Full-wave numerical methods such as the method of moments, finite-element methods, and finite-difference time-domain analysis are useful, but their results remain dependent on accurate geometry, material data, meshing, excitation, and boundary conditions.

High-Q loop capacitors can develop dangerous radio-frequency voltage even at modest transmitter power. Designers must consider voltage breakdown, current heating, arcing, insulation, and accidental contact. Antennas installed near buildings must satisfy structural, lightning-protection, and occupational radio-frequency exposure requirements.

Regulatory compliance includes permitted frequency bands, spectral masks, maximum effective isotropic radiated power, spurious-emission limits, and site-specific restrictions. A design that performs well electromagnetically may still be unacceptable if it creates interference or exceeds exposure limits.

13. Contemporary Developments

Modern wire antennas increasingly combine classical geometries with digital modelling, reconfigurable components, and additive or printed manufacturing. PIN diodes, varactors, RF microelectromechanical switches, and tunable materials can alter electrical length or matching state. These technologies support frequency-agile and multi-band operation, but they introduce bias networks, nonlinearities, loss, control complexity, and possible intermodulation.

Machine-learning tools can assist surrogate modelling, parameter optimization, and fault diagnosis. They do not replace electromagnetic reasoning: training data must span relevant geometries and environments, and optimized solutions must be verified using physics-based simulation and measurement. Explainability, manufacturing tolerances, and extrapolation risk are especially important in safety-critical or regulated systems.

Research also examines electrically small antennas, metamaterial-inspired loading, conformal wearable antennas, transparent conductors, and electrically coupled multi-antenna systems. Fundamental limitations involving stored energy, quality factor, loss, and bandwidth remain relevant regardless of the optimization method.

Best-Practice Checklist

• State the electrical-size and current-distribution assumptions before using a formula.
• Distinguish radiation resistance from total input resistance.
• Report gain, directivity, radiation efficiency, and realized gain separately.
• Treat feedline currents and the ground system as part of the antenna when appropriate.
• Include the installation environment in simulation and measurement.
• Use peak or rms current consistently in power calculations.
• Evaluate bandwidth using a specified criterion, not only a visual impedance plot.
• Check voltage, current, thermal, structural, exposure, and regulatory limits.
• Validate numerical predictions with calibrated measurements.

Chapter Summary

Wire antennas radiate through time-varying current and are governed by electrical size, current distribution, geometry, and environment. The short electric dipole has a sinθ pattern, low radiation resistance proportional to (l/λ)², and maximum radiation broadside to the wire. The finite half-wave dipole has a sinusoidal current distribution, approximately 73 Ω radiation resistance in free space, and about 2.15 dBi directivity. A quarter-wave monopole over an ideal ground plane uses image theory and concentrates radiation into the upper hemisphere. Folded dipoles provide impedance transformation but require balanced feeding.

Small loops act as magnetic dipoles. Their radiation resistance varies with the square of N A/λ², or with the fourth power of electrical circumference, making efficiency a central design challenge. Resonant loops can be compact but are generally narrowband and sensitive to conductor and capacitor loss. Reciprocity connects transmitting and receiving behavior, while effective aperture and polarization mismatch determine received power.

Practical design requires more than selecting a standard length. The engineer must account for matching, feedline currents, ground, nearby objects, measurement uncertainty, safety, and regulation. Contemporary tuning and optimization technologies extend the usefulness of classical wire and loop forms, but they do not eliminate the underlying electromagnetic trade-offs.

Key Terms

Radiation resistance: Equivalent resistance that represents power radiated by an antenna.

Radiation efficiency: Ratio of radiated power to accepted antenna input power.

Directivity: Ratio of radiation intensity in a direction to the average radiation intensity.

Gain: Directivity multiplied by radiation efficiency.

Realized gain: Gain including impedance mismatch loss.

Short dipole: Electrically short straight antenna with approximately uniform or triangular current.

Hertzian dipole: Ideal infinitesimal current element used in electromagnetic analysis.

Half-wave dipole: Center-fed dipole whose total length is approximately half a wavelength.

Monopole: Antenna operated over a conducting ground plane or counterpoise.

Image theory: Method replacing a conductor boundary with an equivalent image source.

Folded dipole: Two-conductor folded antenna commonly used for impedance transformation.

Loop antenna: Closed conducting antenna structure.

Small loop: Loop with circumference much less than one wavelength.

Magnetic dipole: Equivalent magnetic-current source used to describe a small loop.

Radiation pattern: Angular distribution of radiated field or power.

Polarization: Orientation and time behavior of the electric-field vector.

Balun: Device that connects balanced and unbalanced circuits while controlling common-mode current.

Counterpoise: Conductive return structure used with a monopole or compact antenna.

Quality factor Q: Measure of stored energy relative to energy dissipated per cycle.

Effective aperture: Receiving area associated with antenna gain and wavelength.

Review Questions

Short Answer Questions

1. Why is the radiation pattern of a short dipole zero along its axis?
2. State the assumptions behind the short-dipole radiation-resistance formula.
3. What is the purpose of a ground plane beneath a monopole?
4. Why are small loop antennas often narrowband?
5. Distinguish directivity, gain, and realized gain.

Long Answer Questions

1. Explain the current distribution and radiation pattern of a center-fed half-wave dipole.
2. Derive the relationship between the radiation resistance of a small circular loop and its area.
3. Discuss image theory for a quarter-wave monopole and identify the limitations of the ideal ground-plane model.
4. Compare folded dipoles and simple dipoles in terms of impedance, balance, and applications.
5. Explain a complete measurement procedure for determining the practical performance of a wire antenna.

Analytical / Application Questions

1. A 100 MHz center-fed dipole is constructed from thin wire. Estimate its free-space half-wave length and explain why the final resonant length may differ from that estimate.
2. A small loop has radiation resistance 0.12 Ω and loss resistance 0.18 Ω. Calculate its radiation efficiency and explain two engineering methods for improving it.
3. An antenna has directivity 4.0, radiation efficiency 0.75, and mismatch reflection coefficient magnitude 0.30. Calculate its realized gain and interpret the result.

Multiple Choice Questions with Answers

Question 1

For an ideal short electric dipole, the far-field pattern is maximum in which direction?

A. Along the dipole axis

B. Broadside to the dipole

C. Only toward the feed point

D. Uniformly in all directions

Correct Answer: B. Broadside to the dipole

Question 2

Under the stated thin-wire approximation, the radiation resistance of a uniform-current short dipole is proportional to:

A. l/λ

B. (l/λ)²

C. (λ/l)²

D. (l/λ)⁴

Correct Answer: B. (l/λ)²

Question 3

The approximate input resistance of an equal-conductor folded dipole is how many times that of a comparable simple half-wave dipole?

A. One-half

B. One

C. Two

D. Four

Correct Answer: D. Four

Question 4

An ideal quarter-wave monopole over an infinite perfect ground plane has approximately what radiation resistance?

A. 18.25 Ω

B. 36.5 Ω

C. 73 Ω

D. 300 Ω

Correct Answer: B. 36.5 Ω

Question 5

A small loop antenna is most accurately modeled in the electrically small limit as a:

A. Magnetic dipole

B. Uniform plane wave

C. Transmission-line termination

D. Half-wave electric dipole

Correct Answer: A. Magnetic dipole

Question 6

If a small loop has radiation resistance 0.20 Ω and loss resistance 0.05 Ω, its radiation efficiency is:

A. 20%

B. 25%

C. 80%

D. 95%

Correct Answer: C. 80%

Question 7

At 150 MHz in free space, the wavelength is approximately:

A. 0.5 m

B. 1.0 m

C. 2.0 m

D. 4.0 m

Correct Answer: C. 2.0 m

Question 8

Which quantity includes impedance mismatch loss in addition to antenna radiation efficiency and directivity?

A. Radiation resistance

B. Realized gain

C. Radiation intensity

D. Intrinsic impedance

Correct Answer: B. Realized gain

Question 9

For a reciprocal antenna, reciprocity implies that the transmitting and receiving:

A. Patterns are the same at the same frequency

B. Terminal resistances are always zero

C. Polarizations must always be circular

D. Ground systems have no effect

Correct Answer: A. Patterns are the same at the same frequency

Question 10

The radiation resistance of a small loop is strongly affected by which dependence?

A. It is proportional to the square of electrical area factor N A/λ²

B. It is independent of wavelength

C. It is proportional only to conductor length

D. It is always approximately 73 Ω

Correct Answer: A. It is proportional to the square of electrical area factor N A/λ²