Receiving Antennas and System-Level Analysis

Introduction and Context

An antenna is commonly introduced as a transmitting device that converts guided electromagnetic energy into a radiated wave. In a communication, radar, or sensing receiver, however, the antenna performs the reverse operation: it extracts electromagnetic energy from an incident field and delivers a corresponding voltage or power to a receiver. This receiving function cannot be analyzed adequately by considering only physical aperture or gain. It must also account for effective height, polarization, impedance mismatch, noise temperature, receiver sensitivity, and the complete link budget.

Receiving-antenna theory provides the bridge between field quantities and system quantities. It enables an engineer to answer questions such as: What voltage is induced at the terminals by a specified incident electric field? How much received power is available from a distant transmitter? How do polarization and impedance mismatch reduce that power? What is the minimum detectable signal when antenna and receiver noise are included? How should two candidate antennas be compared when their noise temperatures differ?

The central system-level principle is that antenna performance is inseparable from the propagation channel and the receiver. A high-gain antenna may improve received signal power but reduce coverage angle. A physically large antenna may have excellent directivity but poor matching. A low-noise receiver may offer little benefit if antenna loss dominates the system noise temperature. These trade-offs motivate the use of reciprocity, the Friis transmission equation, link budgets, and the figure of merit G/T.

Learning Objectives

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

1. Explain the receiving mechanism using effective height and effective aperture.

2. Relate transmitting and receiving properties through reciprocity.

3. Derive and apply the Friis transmission equation under appropriate assumptions.

4. Construct link budgets in linear and decibel form.

5. Analyze impedance mismatch, polarization mismatch, and pointing losses.

6. Calculate antenna noise temperature, system noise temperature, noise power, and carrier-to-noise ratio.

7. Interpret G/T as a receiving-system figure of merit.

8. Evaluate antenna choices for communication, radar, and sensing systems.

9. Recognize the limitations of ideal formulas in practical environments.

1. Receiving Antennas and Effective Height

Consider a plane wave incident on a receiving antenna. The incident electric field has phasor amplitude E, measured in volts per metre. The antenna develops an open-circuit terminal voltage V_oc. For a linear antenna, the relation may be written as

V_oc = h_e · E,

where h_e is the vector effective height, measured in metres. The dot product shows that only the component of the electric field aligned with the antenna's receiving polarization contributes to the terminal voltage.

For a linearly polarized antenna and a field having the same polarization, the magnitude becomes

|V_oc| = |h_e| |E|.

The effective height is not necessarily the physical length of the antenna. It incorporates current distribution, geometry, frequency, direction of arrival, and polarization. It is therefore a receiving property rather than a simple mechanical dimension.

If the incident wave is not aligned with the receiving polarization, a polarization factor must be included. For unit polarization vectors p_t and p_r,

L_pol = |p_r · p_t|^2,

where 0 ≤ L_pol ≤ 1. For two linear polarizations separated by angle ψ,

L_pol = cos²ψ.

Thus, orthogonal linear polarizations ideally produce zero received power, while a 45-degree orientation produces a power factor of 0.5, or −3.01 dB.

Effective Aperture

The effective aperture A_e is defined as the ratio of available received power to incident power density for a matched, polarization-compatible receiving antenna:

A_e = P_av / S,

where P_av is the maximum available power at the antenna terminals in watts and S is incident power density in watts per square metre.

For an antenna with gain G in the direction of arrival,

A_e = λ²G / (4π),

where λ is wavelength in metres. This relation assumes the gain is defined for the receiving direction and that the antenna is properly matched for maximum power transfer. It is valid for reciprocal antennas in the usual far-field framework.

The effective aperture is not the same as the physical aperture. A reflector may have a physical aperture A_phys but an effective aperture

A_e = η_ap A_phys,

where η_ap is an aperture efficiency satisfying 0 < η_ap ≤ 1. The efficiency includes illumination, phase, spillover, blockage, conductor, dielectric, and polarization effects.

For an incident power density S, the maximum available received power is

P_av = S A_e.

For a uniform plane wave in free space with electric-field magnitude E, the average power density is

S = |E|²/(2η_0),

where η_0 ≈ 377 Ω is the intrinsic impedance of free space. This expression uses peak sinusoidal electric-field amplitude. If E is specified as an rms value, the corresponding expression is S = E_rms²/η_0. Mixing peak and rms conventions is a frequent source of a factor-of-two error.

Relationship Between Effective Height and Effective Aperture

For a receiving antenna connected to a load Z_L, the open-circuit voltage is not the voltage delivered to the load. A Thevenin equivalent is useful: the antenna is represented by V_oc in series with impedance Z_A = R_A + jX_A. The load voltage is

V_L = V_oc Z_L/(Z_A + Z_L).

Maximum average power transfer occurs when Z_L = Z_A*; that is, the load impedance is the complex conjugate of the antenna impedance. Under this condition, the available power is

P_av = |V_oc|²/(8R_A),

when V_oc is a peak phasor and R_A is the real part of the antenna impedance. Equivalent formulas may appear with different numerical factors when rms phasors are used. The convention must always be stated.

Combining V_oc = h_e E with the available-power relation and the plane-wave power density leads to the effective-height/effective-aperture relationship. In scalar form for a polarization-matched antenna,

A_e = η_0 |h_e|²/(4R_A).

This form is particularly useful when antenna terminal voltage and impedance are known. It also illustrates that effective height alone does not determine received power; antenna impedance is required as well.

2. Reciprocity and Receiving Properties

The reciprocity theorem states, under linear, passive, and reciprocal material conditions, that the transmission behavior between two antenna ports is unchanged when the source and observation points are interchanged. In antenna engineering, this means that an antenna has the same radiation pattern when transmitting as its receiving pattern when receiving, provided the polarization and direction conventions are handled consistently.

For a reciprocal antenna:

• transmitting gain in a direction equals receiving gain from that direction;
• transmitting and receiving radiation patterns are the same;
• transmitting polarization and receiving polarization are the same;
• effective height is related to the same current distribution that determines radiation.

Reciprocity does not mean that every antenna has identical performance in every direction. It means that the directional behavior is the same in transmit and receive. A directional antenna can therefore provide high gain in one direction and poor response elsewhere in both modes.

Reciprocity may not hold in the ordinary form for nonreciprocal materials or active devices, such as ferrite circulators under bias, magnetized plasma devices, and certain active metamaterial structures. Even in such systems, generalized reciprocity or scattering-matrix methods may be used, but the simple transmit-receive equivalence must not be assumed.

3. The Friis Transmission Equation

For two antennas in free space, separated by distance R, the received power under ideal conditions is given by the Friis transmission equation:

P_r = P_t G_t G_r [λ/(4πR)]².

Here P_t is the power accepted by the transmitting antenna, G_t is transmitter gain toward the receiving antenna, G_r is receiver gain toward the transmitter, λ is wavelength, and R is the separation distance. The equation assumes:

1. Both antennas operate in the far field of one another.

2. The propagation medium is homogeneous and lossless, normally free space.

3. The antennas are polarization matched.

4. The impedance interfaces are matched, so stated powers are accepted or available powers as appropriate.

5. Multipath, atmospheric absorption, scattering, and obstruction are negligible.

6. The antennas are aligned with their intended boresight directions.

The free-space factor

L_fs = [4πR/λ]²

is the inverse of the power-transfer factor and is called free-space path loss in linear form. In decibels,

L_fs(dB) = 20 log10(4πR/λ).

The link equation in decibel form is

P_r(dBm) = P_t(dBm) + G_t(dBi) + G_r(dBi) − L_fs(dB) − L_other(dB),

where L_other represents polarization, mismatch, feeder, pointing, atmospheric, and other losses. Gains in dBi are referenced to an isotropic radiator. If antenna gain is replaced by directivity, radiation efficiency must be included because G = η_rad D.

An important interpretation follows from the Friis equation. At fixed physical aperture, increasing frequency can increase gain approximately in proportion to 1/λ², while the explicit λ² factor in the transmission term decreases. In a physically fixed-aperture system, these effects may approximately balance. At fixed antenna gain, however, received power decreases as λ² when frequency increases. Statements about frequency dependence must therefore specify what is held constant.

Near-Field and Far-Field Conditions

The Friis equation is a far-field result. For an antenna with maximum dimension D, a commonly used Fraunhofer distance is

R_ff ≥ 2D²/λ,

with the additional practical requirement that R be several wavelengths. In the reactive near field and radiating near field, the field is not adequately represented as a uniform plane wave, and mutual coupling or spatial field variation can invalidate the simple formula.

4. Generalized Link Budgets

A link budget is an accounting framework for signal power. A useful general form is

P_r = P_t + G_t + G_r − L_fs − L_pol − L_mis − L_feed − L_point − L_atm − L_other,

when all quantities are expressed in decibels and powers in dB or dBm. Gains and losses must be defined consistently: a loss is a positive number subtracted from the budget.

Impedance-Mismatch Loss

If the antenna and receiver are not conjugately matched, the fraction of available antenna power delivered to the receiver is

τ = 1 − |Γ|²,

where Γ is the voltage reflection coefficient at the interface. The mismatch loss is

L_mis(dB) = −10 log10(τ) = −10 log10(1 − |Γ|²).

For |Γ| = 0.3, τ = 0.91 and the loss is approximately 0.41 dB. For |Γ| = 1, no power is delivered in the idealized model and the loss tends to infinity.

The reflection coefficient may be calculated from antenna and load impedances as

Γ = (Z_L − Z_A*)/(Z_L + Z_A),

when the reference is the antenna port and conjugate matching is the condition for maximum power transfer. In practical microwave measurement, Γ is usually defined relative to a real reference impedance, commonly 50 Ω; the system definition must then be used consistently.

Polarization Loss

Polarization mismatch is represented by

L_pol(dB) = −10 log10(|p_r · p_t|²).

For linear polarization angle ψ, this becomes −10 log10(cos²ψ). Circular polarization introduces handedness effects. A right-hand circularly polarized wave received by an ideal left-hand circularly polarized antenna is rejected, whereas an antenna with the same handedness can receive it. Elliptical polarization requires the full complex polarization vectors or polarization-loss factor.

Other Practical Losses

Feeder loss occurs before the low-noise amplifier and reduces received signal power. It also contributes noise, so it is more harmful than an equivalent loss after amplification. Pointing loss results from angular displacement from the antenna boresight and should be derived from the measured or modeled radiation pattern. Atmospheric and rain attenuation become important at microwave and millimetre-wave frequencies. Shadowing, multipath fading, terrain blockage, and foliage loss may dominate the deterministic free-space term in terrestrial systems.

5. Noise in Receiving Systems

Thermal noise is generated by resistive and lossy components. The available noise power from a matched resistor at physical temperature T is

N = kTB,

where k = 1.380649 × 10^−23 J/K is Boltzmann's constant, T is absolute temperature in kelvin, and B is noise bandwidth in hertz. The corresponding noise power spectral density is kT W/Hz.

The noise figure of a receiver is commonly defined at a reference temperature T_0 = 290 K:

F = (S/N)_in/(S/N)_out,

and noise temperature is

T_e = (F − 1)T_0.

Noise figure is dimensionless; its decibel form is NF = 10 log10 F.

Antenna and System Noise Temperature

An antenna receives not only the desired signal but also noise from the sky, ground, atmosphere, cosmic background, man-made sources, and losses in the antenna structure. Its noise temperature T_A is defined through the equivalent available noise power kT_A B.

If an antenna is followed by a receiver with equivalent input noise temperature T_e, then, for a matched connection, the system noise temperature referred to the antenna terminals is approximately

T_sys = T_A + T_e.

If a passive feeder with linear loss L at physical temperature T_p lies between the antenna and receiver, its output-referred contribution must be included carefully. Referred to the receiver input, a passive attenuator at T_p has effective noise temperature (L − 1)T_p. Referred to the antenna terminals, the system expression is commonly written

T_sys = T_A + (L − 1)T_p + L T_e,

where L is the feeder power-loss ratio, L ≥ 1, and T_e is receiver equivalent input noise temperature. This assumes a matched passive network and consistent reference planes.

The noise power at the receiver input is

N = k T_sys B.

For a desired received signal power C, the carrier-to-noise ratio is

C/N = P_r/(kT_sys B).

In decibels, using P_r in watts,

C/N(dB) = 10 log10(P_r) − 10 log10(kT_sys B).

If P_r is in dBm, the thermal noise power at 290 K is approximately −174 dBm/Hz plus 10 log10(B) plus the noise figure in dB, subject to the chosen reference and receiver model.

6. G/T and Receiving-System Merit

For satellite communication, radio astronomy, radar, and deep-space links, the receiving figure of merit is often

G/T = G_r/T_sys,

where G_r is receive antenna gain in the signal direction and T_sys is system noise temperature in kelvin. In decibels,

G/T(dB/K) = G_r(dBi) − 10 log10[T_sys(K)].

A larger G/T indicates better ability to produce carrier-to-noise ratio for a given incident flux density. It is a system metric, not merely an antenna metric. Increasing gain improves G/T, but increasing gain may also increase physical loss, pointing sensitivity, or antenna noise temperature. Consequently, the best design is not necessarily the antenna with maximum gain.

For a received plane-wave flux density S, the available signal power is S A_e. Since A_e = λ²G/(4π),

C/N = [S λ² G/(4π)]/[kT_sys B].

This expression shows directly why G/T is useful: for fixed wavelength, bandwidth, and incident flux density, performance is proportional to G/T.

7. Worked Example: A Microwave Receiving Link

Consider a 12 GHz line-of-sight link with R = 20 km. The transmitter delivers 2 W to an antenna with gain 24 dBi. The receiving antenna gain is 30 dBi. Assume matched interfaces, aligned antennas, and no additional losses initially. Determine the free-space path loss and received power.

The wavelength is

λ = c/f = (3 × 10^8)/(12 × 10^9) = 0.025 m.

The free-space loss is

L_fs = 20 log10(4πR/λ)

= 20 log10[(4π × 20,000)/0.025]

≈ 140.46 dB.

The transmitter power in dBm is

P_t = 10 log10(2 W/1 mW) ≈ 33.01 dBm.

Therefore,

P_r = 33.01 + 24 + 30 − 140.46

≈ −53.45 dBm.

Now suppose the polarization factor is 0.5, the receive-interface reflection coefficient magnitude is 0.3, and feeder loss before the receiver is 1.5 dB. Polarization loss is 3.01 dB, mismatch loss is

−10 log10(1 − 0.3²) = 0.41 dB.

The revised received power is

P_r ≈ −53.45 − 3.01 − 0.41 − 1.5 = −58.37 dBm.

If the system noise temperature is 600 K and noise bandwidth is 1 MHz, then

N = kT_sysB

= (1.380649 × 10^−23)(600)(10^6)

= 8.284 × 10^−15 W.

In dBm, this is approximately −110.82 dBm. Hence

C/N ≈ −58.37 − (−110.82) = 52.45 dB.

This large value is an idealized result because fading, interference, implementation losses, and the distinction between occupied bandwidth and noise bandwidth may substantially reduce practical margin.

8. Application Case: Earth-Station Receiver Selection

Background

This illustrative case concerns a satellite ground station receiving a weak downlink at Ku-band. Two candidate reflector antennas are available. Antenna A has receive gain 42 dBi and contributes an antenna-plus-feed noise temperature of 95 K. Antenna B has gain 44 dBi but, because of a lossy feed and increased spillover toward warm ground, its antenna-plus-feed noise temperature is 145 K. The receiver equivalent input noise temperature is 55 K for both options.

Problem

Which antenna provides the superior receiving-system figure of merit, assuming both are correctly pointed and have the same bandwidth and polarization performance?

Analysis

For Antenna A,

T_sys,A = 95 + 55 = 150 K.

Thus,

G/T_A = 42 − 10 log10(150) ≈ 42 − 21.76 = 20.24 dB/K.

For Antenna B,

T_sys,B = 145 + 55 = 200 K,

and

G/T_B = 44 − 10 log10(200) ≈ 44 − 23.01 = 20.99 dB/K.

Outcome

Antenna B is better by approximately 0.75 dB in G/T despite its substantially higher noise temperature. The 2 dB gain increase more than compensates for the noise-temperature penalty. However, if Antenna B also had 1 dB greater pointing loss or significant rain attenuation due to a lower elevation angle, the system-level choice could change.

Learning Points

The case demonstrates why gain alone is insufficient. G/T combines useful signal collection with noise generation. It also shows that the final selection must include operational losses, pointing stability, environmental exposure, maintenance, and regulatory constraints.

9. Receiving Antennas in Radar and Sensing

In monostatic radar, the same antenna often transmits and receives. Reciprocity permits use of the same gain pattern in the radar range equation, while the receive chain determines noise performance and detection probability. A narrow beam improves angular discrimination and gain but increases pointing requirements. A low sidelobe level reduces interference and clutter pickup but may require a more complex aperture or feed.

In passive sensing and radio astronomy, the antenna receives naturally occurring radiation rather than a cooperative transmitter. System temperature, calibration stability, beam efficiency, and sidelobe response become critical. A sidelobe directed toward a hot ground region can increase antenna noise temperature even when boresight performance appears excellent.

In distributed sensor networks, small antennas may be selected for coverage rather than maximum gain. Diversity antennas exploit spatial, polarization, or pattern differences to reduce fading. The receiver may combine branches using selection combining, equal-gain combining, or maximal-ratio combining. These methods do not eliminate the need for accurate antenna correlation and noise characterization.

10. Limitations and Advanced Design Considerations

The Friis equation is deterministic and single-path. In real channels, the received signal may be the vector sum of multiple paths, producing constructive or destructive interference. Statistical fading margins are therefore added to the link budget. A link budget that omits fading margin may be adequate for a laboratory line-of-sight test but unreliable for a mobile or terrestrial deployment.

Antenna gain is frequency-dependent. Wideband systems cannot always use a single gain value or a single center frequency. Group delay, impedance variation, polarization variation, and beam squint may affect waveform fidelity and link quality.

Noise temperature is also frequency- and direction-dependent. The approximation T_sys = T_A + T_e assumes a clear reference plane and matched interfaces. Active antennas, lossy matching networks, frequency converters, and digital beamformers require more detailed noise-wave or multiport analysis.

The effective aperture relation assumes reception from the far field. For near-field wireless power transfer, RFID coupling, implant communications, or compact antenna test ranges, mutual impedance and mode coupling may be more appropriate than plane-wave aperture theory.

Environmental and regulatory considerations are part of professional antenna analysis. Transmit power, equivalent isotropically radiated power, spectral masks, exposure limits, interference coordination, and frequency licensing constrain feasible designs. Receive systems must also address cybersecurity and privacy when sensing human activity or geolocation. Data collected by radar and passive sensors may require access control, retention policies, and lawful-use governance.

11. Best Practices for System-Level Analysis

1. Define all reference planes: transmitter output, antenna port, feeder input, receiver input, and detector output.

2. State whether powers are available, accepted, delivered, peak, rms, dBW, or dBm.

3. Use gain rather than directivity unless radiation efficiency is explicitly included.

4. Check far-field validity before applying Friis.

5. Include polarization and mismatch factors separately rather than hiding them in an unexplained margin.

6. Calculate noise temperature at a clearly defined reference plane.

7. Use measured antenna patterns for pointing and sidelobe analyses whenever possible.

8. Include fading, atmospheric, implementation, and maintenance margins for operational systems.

9. Perform sensitivity analysis: determine which parameter most strongly affects C/N or G/T.

10. Validate analytical results with electromagnetic simulation, calibrated measurements, and, where necessary, field trials.

Contemporary Developments

Modern phased arrays and digital beamforming make receiving performance a multi-element problem. Individual-element mismatch, mutual coupling, scan loss, calibration error, and beamformer quantization can alter both gain and noise figure. In massive MIMO systems, spatial degrees of freedom may be more important than a single antenna's peak gain.

Machine learning is increasingly used for antenna calibration, interference classification, adaptive beam selection, and channel prediction. Such methods should supplement, not replace, physically validated link and noise models. Training-data bias, out-of-distribution behavior, and explainability are important when an adaptive receiver controls safety-critical or spectrum-sharing functions.

Reconfigurable intelligent surfaces and programmable metasurfaces have stimulated new receiving-system models. Their practical value depends on loss, control overhead, phase quantization, channel estimation, and energy consumption. Claims of large link improvement should be tested against a complete power and noise budget rather than idealized aperture assumptions.

Chapter Summary

Receiving antennas convert incident electromagnetic fields into terminal voltage and available power. Effective height describes the voltage response, while effective aperture describes the power-collection capability. For reciprocal antennas, transmitting and receiving patterns, gain, and polarization properties are closely related.

The Friis transmission equation provides the basic far-field free-space link relation. Practical link budgets extend it by including polarization loss, impedance mismatch, feeder loss, pointing loss, atmospheric attenuation, and fading margin. Noise must be analyzed through antenna temperature, receiver equivalent noise temperature, system noise temperature, and the relation N = kT_sysB. The receiving figure of merit G/T combines gain and noise temperature and is especially valuable for satellite, radar, radio astronomy, and weak-signal systems.

Reliable system analysis requires explicit assumptions, consistent reference planes, correct units, and awareness of near-field, multipath, wideband, environmental, and regulatory limitations. The most effective engineering choice is a system-level compromise among gain, noise, bandwidth, coverage, pointing, cost, reliability, and compliance.

Key Terms

Effective height: Vector quantity relating incident electric field to open-circuit receiving voltage.

Effective aperture: Ratio of available received power to incident power density.

Reciprocity: Property whereby transmission behavior is unchanged when source and observation locations are interchanged in a reciprocal system.

Antenna gain: Directivity multiplied by radiation efficiency.

Polarization loss: Reduction in received power caused by mismatch between transmit and receive polarization states.

Mismatch loss: Power loss caused by imperfect impedance matching.

Friis transmission equation: Far-field free-space relation for power received between two antennas.

Free-space path loss: Inverse of the free-space power-transfer factor, expressed commonly in decibels.

Link budget: Accounting of transmitted power, gains, and system losses.

Antenna noise temperature: Equivalent temperature representing noise received or generated by an antenna system.

Receiver noise temperature: Equivalent input temperature representing receiver-added noise.

System noise temperature: Total equivalent noise temperature referred to a specified system reference plane.

Noise figure: Degradation of signal-to-noise ratio caused by a receiver relative to an ideal reference.

G/T: Receive antenna gain divided by system noise temperature.

Far field: Region where the radiated field approximates a locally uniform plane wave with stable angular pattern.

Available power: Maximum power deliverable by a source to a conjugately matched load.

Reflection coefficient: Complex ratio of reflected to incident voltage wave.

Aperture efficiency: Ratio of effective aperture to physical aperture.

Fading margin: Additional link-budget allowance for random signal fluctuations.

Reference plane: Defined location to which power, gain, loss, or noise quantities are referred.

Review Questions

Short Answer Questions

1. Define effective height and explain its physical significance.

2. State the assumptions required for applying the Friis transmission equation.

3. What is the difference between antenna gain and directivity?

4. Define system noise temperature and explain why the reference plane matters.

5. Why is G/T a useful receiving-system figure of merit?

Long Answer Questions

1. Derive the relationship between effective aperture, antenna gain, and wavelength, and discuss its assumptions.

2. Explain reciprocity in antenna systems and identify situations in which simple reciprocity may not apply.

3. Develop a complete decibel link budget including free-space loss, polarization loss, mismatch loss, and feeder loss.

4. Explain antenna noise temperature, receiver noise temperature, and the calculation of total system noise temperature.

5. Discuss the limitations of the Friis equation in multipath, near-field, wideband, and millimetre-wave environments.

Analytical / Application Questions

1. A 10 GHz link has 5 W transmitter power, 20 dBi transmit gain, 28 dBi receive gain, and a 15 km separation. Calculate the ideal free-space received power in dBm, then recalculate it with 2 dB feeder loss and 1 dB polarization loss.

2. Two receiving antennas have gains of 38 dBi and 41 dBi, with system noise temperatures of 180 K and 310 K, respectively. Calculate G/T for each and determine which antenna is preferable.

3. A receiver has a 2 MHz noise bandwidth, 800 K system noise temperature, and input signal power of −95 dBm. Calculate the noise power and C/N, and identify two practical effects that could reduce the measured C/N.

Multiple Choice Questions with Answers

Question 1

Which quantity relates incident electric field to open-circuit voltage at a receiving antenna?

A. Effective height

B. Effective aperture

C. Radiation resistance

D. Free-space path loss

Correct Answer: A. Effective height

Question 2

For a reciprocal antenna, which property is shared between transmitting and receiving operation?

A. Physical temperature only

B. Radiation pattern

C. Load impedance only

D. Cable attenuation only

Correct Answer: B. Radiation pattern

Question 3

The effective aperture of an antenna with gain G at wavelength λ is

A. 4πG/λ²

B. λG/(4π)

C. λ²G/(4π)

D. G/(4πλ²)

Correct Answer: C. λ²G/(4π)

Question 4

If two linearly polarized antennas are oriented at 45 degrees, the ideal polarization power factor is

A. 0

B. 0.25

C. 0.5

D. 1

Correct Answer: C. 0.5

Question 5

The Friis transmission equation is primarily valid when the antennas are

A. In the reactive near field

B. In the far field and in free space

C. Electrically connected directly

D. Perfectly electrically small

Correct Answer: B. In the far field and in free space

Question 6

For a reflection-coefficient magnitude of 0.3, the fraction of available power delivered through the interface is

A. 0.09

B. 0.30

C. 0.70

D. 0.91

Correct Answer: D. 0.91

Question 7

Thermal noise power for a matched system is given by

A. kT/B

B. kTB

C. T/(kB)

D. kB/T

Correct Answer: B. kTB

Question 8

The receiving figure of merit G/T increases when

A. Gain decreases and noise temperature increases

B. Gain increases while system noise temperature remains constant

C. Bandwidth increases only

D. Mismatch loss increases

Correct Answer: B. Gain increases while system noise temperature remains constant

Question 9

A system has gain 40 dBi and noise temperature 100 K. Its G/T is approximately

A. 20 dB/K

B. 40 dB/K

C. 60 dB/K

D. −20 dB/K

Correct Answer: A. 20 dB/K

Question 10

A passive feeder with power-loss ratio L before a receiver contributes, when referred to the antenna terminals, a receiver-noise term proportional to

A. T_e/L

B. (L−1)T_p + LT_e in the complete expression

C. T_p/L only

D. L/T_e

Correct Answer: B. (L−1)T_p + LT_e in the complete expression