Broadband, Frequency-Independent and Electrically Small Antennas

Introduction and Context

Conventional resonant antennas, such as half-wave dipoles and microstrip patches, generally provide efficient radiation over a limited fractional bandwidth. Modern wireless, radar, sensing, satellite, and electronic-warfare systems often require operation over several octaves, rapid frequency agility, multiple separated bands, or physical dimensions much smaller than the free-space wavelength. These requirements motivate three related but distinct antenna classes:

1. Broadband antennas, whose impedance and radiation characteristics remain acceptable over a specified continuous frequency range.

2. Frequency-independent antennas, designed so that their electromagnetic behavior is governed primarily by angles or scale ratios rather than by an absolute dimension.

3. Electrically small antennas, whose maximum dimension is much less than a wavelength and which consequently face fundamental bandwidth, efficiency, and matching limitations.

A broadband antenna is not necessarily frequency-independent, and an electrically small antenna is not automatically broadband. The design problem is therefore one of balancing bandwidth, efficiency, size, gain, polarization, manufacturability, and environmental sensitivity.

Learning Objectives

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

• distinguish broadband, frequency-independent, ultrawideband, and electrically small antennas;
• explain the operation and design logic of helices, spirals, log-periodic antennas, and Vivaldi antennas;
• evaluate impedance bandwidth, radiation efficiency, gain, polarization, and group-delay behavior;
• apply Chu–Harrington and Bode–Fano limits to small-antenna design;
• analyze matching networks, quality factor, miniaturization methods, and their efficiency penalties;
• design and assess multiband and broadband antenna systems;
• make defensible engineering trade-offs in practical applications.

1. Bandwidth, Frequency Independence, and Electrical Size

1.1 Bandwidth definitions

The fractional bandwidth is commonly defined as

\[

B_f=\frac{f_H-f_L}{f_C}, \qquad f_C=\frac{f_H+f_L}{2},

\]

where \(f_L\) and \(f_H\) are the lower and upper operating frequencies and \(f_C\) is the arithmetic center frequency. Percentage bandwidth is \(100B_f\) percent. For very wide ranges, the ratio \(f_H/f_L\), or bandwidth in octaves,

\[

N_{oct}=\log_2\left(\frac{f_H}{f_L}\right),

\]

is often more informative. These definitions describe frequency span only; a frequency range is useful only when criteria such as input-voltage-standing-wave ratio (VSWR), realized gain, efficiency, polarization purity, and radiation-pattern stability are also specified.

For a one-port antenna, the reflection coefficient is

\[

\Gamma(f)=\frac{Z_{in}(f)-Z_0}{Z_{in}(f)+Z_0},

\]

where \(Z_{in}\) is the antenna input impedance and \(Z_0\) is the reference impedance, usually 50 ohms. The voltage standing-wave ratio is

\[

VSWR=\frac{1+|\Gamma|}{1-|\Gamma|},

\]

provided \(|\Gamma|<1\). A VSWR requirement is a matching requirement, not a complete antenna-performance requirement.

1.2 Electrical size

Let \(a\) be the radius of the smallest sphere enclosing the antenna and \(k=2\pi/\lambda\) the free-space wavenumber. The dimensionless quantity \(ka\) measures electrical size. An antenna is conventionally called electrically small when \(ka\ll1\), although practical literature sometimes uses \(ka<1\) as a broader category. The exact enclosing sphere matters: a long feed, counterpoise, or matching structure can increase the effective size.

An electrically small antenna stores substantial reactive near-field energy relative to its radiated power. This produces high quality factor, narrow impedance bandwidth, sensitivity to loss, and difficult matching. These are physical consequences of Maxwell’s equations, not merely limitations of a particular geometry.

2. Broadband and Frequency-Independent Design Principles

Broadband behavior can be obtained by reducing the rapid reactance variation associated with a single resonance, by combining multiple resonances, or by using a traveling-wave structure in which the active radiating region moves with frequency.

A structure is approximately frequency-independent when its shape is specified mainly by angles and ratios of dimensions. Rumsey’s principle states that antennas whose geometry is defined only by angles, with no fixed characteristic length, tend toward frequency-independent behavior. Real antennas must be truncated, fed, and manufactured, so their bandwidth is finite. Truncation introduces lower- and upper-frequency limits.

The principal mechanisms are:

• frequency scaling: at a higher frequency, a smaller portion of a scale-invariant structure becomes electromagnetically active;
• traveling-wave radiation: energy propagates along the antenna and radiates gradually rather than being confined to one resonance;
• self-complementarity: certain planar geometries exhibit relatively stable impedance properties;
• multiple resonances: appropriately coupled resonant elements overlap their impedance bands.

A broadband design must also control common-mode currents, feed transitions, baluns, dielectric dispersion, and enclosure effects. The antenna itself may be broadband while the complete system is not.

3. Helical Antennas

A helix is formed by winding a conducting wire around a cylindrical support. Important geometrical parameters are turn circumference \(C=2\pi R\), turn spacing \(S\), pitch angle \(\alpha\), number of turns \(N\), and wire radius. The pitch angle is

\[

\alpha=\tan^{-1}\left(\frac{S}{C}\right).

\]

Two principal modes are used.

3.1 Normal mode

When the helix circumference and spacing are small compared with wavelength, the helix behaves approximately as a combination of a short dipole along the axis and a small loop in the transverse plane. Radiation is relatively broadside, gain is modest, and the input impedance can be reactive. Normal-mode helices are useful when compactness and moderate bandwidth are more important than high gain.

3.2 Axial mode

When the circumference is approximately one wavelength and the pitch is selected appropriately, fields from successive turns add constructively along the helix axis. The antenna produces end-fire radiation, circular polarization, and moderate-to-high gain. Approximate design guidance for axial-mode helices is

\[

0.8\lambda\lesssim C\lesssim1.2\lambda,

\qquad 0.2\lambda\lesssim S\lesssim0.3\lambda,

\]

with pitch angle often in the range of roughly 12°–14°. These are starting values, not universal laws; finite ground planes, conductor diameter, feed geometry, and the desired axial-ratio bandwidth require simulation and measurement.

A commonly used empirical gain estimate is

\[

G\approx 15N\left(\frac{C}{\lambda}\right)^2\left(\frac{S}{\lambda}\right),

\]

where gain is expressed as a dimensionless power ratio and the formula is valid only as an approximate axial-mode estimate for a sufficiently long helix with suitable termination and spacing. It should not be used for normal-mode helices or very small values of \(N\) without validation.

The helix supports circular polarization because the orthogonal field components have nearly equal magnitudes and approximately 90° phase difference. Reversing the winding sense reverses the polarization handedness. A helix is attractive for satellite links and telemetry, but its axial length, windings, and feed transition may be inconvenient at low frequency.

4. Spiral Antennas

Spiral antennas are planar frequency-independent structures. Common forms include equiangular, Archimedean, and logarithmic spirals. A two-arm spiral is usually fed differentially at its center; a balanced-to-unbalanced transition is necessary when connecting it to coaxial cable.

The active-region principle states that, at a given frequency, radiation is concentrated near the portion of the spiral whose local circumference is comparable with one wavelength. As frequency increases, this region moves inward; as frequency decreases, it moves outward. The outer and inner truncations therefore establish the approximate low- and high-frequency limits.

Spirals commonly provide:

• very wide impedance bandwidth;
• frequency-independent or slowly varying patterns;
• broadband circular polarization;
• relatively low or moderate gain;
• bidirectional radiation unless backed by a cavity or absorber.

A two-arm spiral can support two counter-rotating modal waves. Termination is important: an abrupt open end can create reflections and pattern ripple, while resistive loading or an absorber can improve performance at the cost of efficiency. Cavity-backed spirals provide unidirectional radiation but add depth and may narrow or perturb the bandwidth.

The central feed region is electrically small at the lower frequencies and can dominate impedance behavior. Balun design, arm-width variation, substrate properties, and truncation must therefore be included in the electromagnetic model.

5. Log-Periodic Antennas

A log-periodic antenna consists of a sequence of elements whose dimensions and spacings scale by a constant factor \(\tau\), with \(0<\tau<1\). If successive element lengths satisfy

\[

\frac{L_{n+1}}{L_n}=\tau,

\]

and corresponding spacings scale similarly, the geometry repeats under logarithmic frequency scaling. The active region shifts along the array as frequency changes.

The classic log-periodic dipole array uses alternately connected dipole elements. Its operation depends on the active region containing elements whose lengths are near resonance. Elements much longer than the active region behave largely as reflectors, while shorter elements behave as directors or weakly participating elements, depending on the design and phase progression.

Performance is controlled by scale factor, spacing factor, number of elements, boom geometry, element diameter, and feed arrangement. Increasing the number of elements generally extends the frequency range and improves pattern stability, but increases size, weight, cost, and wind loading. A log-periodic array offers broadband directional gain but does not usually achieve the peak gain of a narrowband array of comparable maximum aperture.

The array is not truly infinite or exactly frequency-independent. End effects determine the usable band, and the feed line must preserve the intended phase and balance over the entire range. Log-periodic structures are widely used for EMC measurements, signal interception, direction finding, and broadband communications.

6. Vivaldi and Other Tapered-Slot Antennas

A Vivaldi antenna is a traveling-wave, exponentially tapered slot antenna, usually fabricated in a planar conductor on a dielectric substrate. A representative taper can be written as

\[

y(x)=\pm A e^{rx},

\]

where \(A\) sets the initial slot scale and \(r\) controls the rate of opening. The exact coordinate origin and taper convention vary among authors; the physical requirement is a smooth flare that transforms a guided wave into a radiated wave.

At lower frequencies, the available aperture length and flare width determine whether the antenna can support efficient radiation. At higher frequencies, the feed transition, slot width near the throat, conductor loss, dielectric loss, and fabrication accuracy become increasingly important. The antenna is commonly end-fire and can provide wide impedance bandwidth, moderate-to-high gain, and relatively stable phase center.

Variants include antipodal Vivaldi antennas, balanced antipodal Vivaldis, dielectric-loaded Vivaldis, and cavity-backed tapered slots. Antipodal arrangements improve broadband transition from a planar feed to the slot but require careful control of overlap, substrate thickness, and mode conversion.

Vivaldi antennas are used in ultra-wideband radar, ground-penetrating radar, microwave imaging, near-field scanning, and broadband phased arrays. Their limitations include substrate dispersion, cross-polarization caused by asymmetry, phase-center movement, and the need for a broadband balun or transition.

7. Electrically Small Antennas: Fundamental Limits

7.1 Quality factor and bandwidth

For a narrowband resonant antenna, a useful definition is

\[

Q=\omega\frac{W_{stored}}{P_{loss}+P_{rad}},

\]

where \(W_{stored}\) is an appropriately defined cycle-averaged stored energy, \(P_{loss}\) is dissipated power, \(P_{rad}\) is radiated power, and \(\omega=2\pi f\). Stored-energy definitions become subtle for radiating systems because the field energy is not spatially localized in the same way as in a lumped circuit. Consequently, reported Q values should state the adopted definition.

For a simple high-Q series or parallel resonance, fractional impedance bandwidth is approximately proportional to \(1/Q\), with the exact relation depending on the matching criterion and the resistance or reactance model. This approximation should not be applied indiscriminately to multiresonant or strongly broadband antennas.

7.2 Chu–Harrington limit

For a passive antenna contained in a sphere of radius \(a\), the fundamental spherical-mode analysis gives a lower bound on Q. For the dominant electric and magnetic dipole modes, a commonly quoted small-\(ka\) behavior is

\[

Q\gtrsim \frac{1}{(ka)^3}+\frac{1}{ka},

\]

with the precise bound depending on the allowed modes, polarization, and definition of Q. The expression demonstrates the dominant \((ka)^{-3}\) growth as the antenna becomes electrically smaller. It is a lower bound, not a prediction for a particular antenna. Practical antennas often have higher Q because of geometry, loss, nonoptimal current distribution, and matching networks.

The Harrington extension relates maximum directivity to spherical mode order and electrical size. It emphasizes that arbitrary improvements in gain, bandwidth, and compactness cannot be obtained simultaneously within a fixed enclosing volume.

7.3 Bode–Fano matching limit

The Bode–Fano criterion limits how well a reactive, high-Q load can be matched over a prescribed bandwidth using a passive, lossless network. For a parallel RC load, one form is

\[

\int_0^\infty \ln\left(\frac{1}{|\Gamma(\omega)|}\right)d\omega

\leq \frac{\pi}{RC},

\]

under the idealized assumptions of a rational passive load and a lossless, stable matching network. Related forms apply to series RL and other canonical loads. The principle is more important than memorizing one form: reducing reflection over a wider bandwidth requires a price in matching quality, load Q, or network complexity. A matching network cannot remove the underlying energy-storage constraint; it can redistribute mismatch across frequency.

8. Matching, Loss, and Miniaturization

A small antenna often has a low radiation resistance and substantial reactance. An L-, T-, or pi-network can cancel reactance and transform resistance to the transmitter impedance. However, the network has finite quality factor and introduces conductor, dielectric, and switching losses.

The total radiation efficiency is

\[

\eta_{rad}=\frac{P_{rad}}{P_{rad}+P_{loss}},

\]

and the realized gain includes mismatch effects. If mismatch efficiency is \(\eta_m=1-|\Gamma|^2\), then, under a consistent reference impedance and neglecting other system losses,

\[

G_{realized}=D\,\eta_{rad}\,\eta_m,

\]

where \(D\) is directivity. This expression makes clear why a small antenna with an excellent VSWR can still have poor realized gain: matching loss and ohmic loss may be hidden if only return loss is reported.

Miniaturization methods include meandering, folding, top loading, dielectric loading, magnetic or magnetodielectric loading, shorting pins, reactive parasitic elements, and high-impedance surfaces. These techniques reduce physical resonance length but generally increase stored energy, conductor current, dielectric loss, sensitivity to tolerances, or narrowness of bandwidth. High-permittivity loading can be effective in compact devices, but it may concentrate electric fields and reduce radiation efficiency.

A responsible design workflow is therefore:

1. define the minimum usable bandwidth, efficiency, pattern, polarization, and volume;

2. estimate the electrical size and fundamental limitations;

3. choose the radiation mechanism and current topology;

4. optimize the radiator before adding a matching network;

5. co-design the feed, ground plane, enclosure, and user platform;

6. evaluate realized gain and total efficiency, not return loss alone;

7. verify performance with calibrated measurement and uncertainty analysis.

9. Multiband and Wideband Operation

Multiband operation can be achieved through multiple resonant paths, slots of different electrical lengths, parasitic elements, reconfigurable switches, tunable capacitors, or broadband radiators followed by frequency-selective filtering. A multiband antenna is not necessarily wideband: separated narrow bands may satisfy a multistandard product requirement while leaving large gaps between bands.

Useful strategies include:

• combining a monopole with quarter-wave branches for separated resonances;
• using nested slots or complementary resonators in planar antennas;
• applying varactors, RF MEMS, PIN diodes, or tunable materials;
• using a wideband element with a reconfigurable matching network;
• employing diversity or multiple-input multiple-output architectures.

Reconfigurability introduces bias-line radiation, nonlinear distortion, switching loss, control complexity, and reliability concerns. The antenna must be evaluated in every state, including transition states where relevant.

10. Measurement and System-Level Evaluation

Broadband antennas require broadband measurement methods. A vector network analyzer provides reflection and transmission data, but calibration planes, cable movement, connector repeatability, and time gating must be controlled. Far-field gain and pattern measurements require a sufficiently quiet environment and attention to chamber frequency range, polarization alignment, and absorber performance.

Important reported quantities include:

• impedance bandwidth under a stated VSWR or \(|\Gamma|\) criterion;
• realized gain and total efficiency versus frequency;
• radiation-pattern stability and beam squint;
• axial ratio for circular polarization;
• cross-polarization discrimination;
• group delay or phase-center variation for impulse and UWB systems;
• sensitivity to installation, housing, nearby objects, and user interaction.

For ultra-wideband systems, a smooth group-delay response can be as important as a good return loss. Strong frequency-dependent phase distortion can stretch pulses and cause intersymbol interference even when the magnitude response appears acceptable.

11. Worked Example: Axial-Mode Helix

Design a preliminary four-turn axial-mode helix for a center frequency of 1.5 GHz. Assume free-space operation, pitch spacing \(S=0.23\lambda\), circumference \(C=\lambda\), and neglect the finite ground plane during the first estimate.

The wavelength is

\[

\lambda=\frac{c}{f}=\frac{3.00\times10^8}{1.50\times10^9}=0.200\text{ m}.

\]

Thus,

\[

C=0.200\text{ m},\qquad S=0.23(0.200)=0.046\text{ m}.

\]

The helix radius is

\[

R=\frac{C}{2\pi}=\frac{0.200}{2\pi}=0.0318\text{ m},

\]

and the approximate axial length for four turns is

\[

L=NS=4(0.046)=0.184\text{ m}.

\]

The pitch angle is

\[

\alpha=\tan^{-1}(S/C)=\tan^{-1}(0.23)\approx13.0^\circ.

\]

Using the empirical gain estimate,

\[

G\approx15N(C/\lambda)^2(S/\lambda)=15(4)(1)^2(0.23)=13.8,

\]

or approximately 11.4 dBi if interpreted as a power ratio. This is only a preliminary estimate. A final design must include conductor diameter, ground-plane size, feed transition, axial ratio, impedance, and measured gain.

12. Illustrative Case Study: Broadband Antenna for Ground-Penetrating Radar

Background

A survey instrument requires a compact antenna covering approximately 0.8–3.0 GHz. It must operate close to the ground, retain a reasonably stable phase center, and produce short pulses with limited dispersion.

Problem

A conventional patch antenna provides adequate gain near its design frequency but cannot cover the required ratio of 3.75:1 without severe impedance variation. A log-periodic antenna offers bandwidth but is mechanically large and has a frequency-dependent phase center. A spiral offers excellent bandwidth but produces undesired polarization and insufficiently directional radiation in the proposed installation.

Analysis and approach

A tapered-slot Vivaldi antenna is selected because it supports end-fire radiation, planar fabrication, and a broad frequency range. The lower-frequency limit is addressed by extending the flare and increasing the effective aperture. The upper-frequency limit is addressed through a broadband microstrip-to-slotline transition, careful control of substrate thickness, and low-loss material.

Two antennas are mounted symmetrically to improve common-mode behavior and pulse coupling. The design is optimized using both frequency-domain S-parameters and time-domain impulse response. The metal housing is included in simulation because it changes the current distribution and phase center.

Outcome

The final design meets the reflection-coefficient target over most of the intended band, but the lowest frequencies show reduced gain because the finite aperture is electrically short. The measured pulse response is improved after suppressing a feed-transition resonance. A small decrease in peak gain is accepted in exchange for smoother group delay and better subsurface image fidelity.

Learning points

The case illustrates that the best antenna is selected from system requirements rather than bandwidth alone. Aperture size determines low-frequency performance, the feed transition can dominate the upper band, and time-domain distortion must be measured when short pulses are transmitted.

13. Limitations, Regulation, and Contemporary Developments

Broadband systems may radiate into licensed services and must satisfy national emission masks, electromagnetic compatibility requirements, and exposure limits. A broadband antenna does not authorize broadband transmission. Laboratory measurements should distinguish conducted emissions, common-mode cable radiation, and true far-field radiation.

Current research includes electrically small antennas using characteristic-mode engineering, non-Foster active matching, metamaterial-inspired loading, additive manufacturing, flexible substrates, and machine-learning-assisted optimization. Non-Foster circuits can theoretically compensate reactance over bandwidths unavailable to passive networks, but they introduce noise, instability, nonlinear behavior, power consumption, and difficult certification issues. Machine learning can accelerate geometry searches, yet it does not replace electromagnetic verification or physical insight; training data, objective functions, and manufacturability constraints strongly influence the result.

Best practice is to use optimization as a controlled design aid, retain physically interpretable parameters, test sensitivity to tolerances, and report uncertainty. Claims of bandwidth or miniaturization should always state the reference impedance, matching criterion, efficiency, physical volume, ground-plane assumptions, and measurement conditions.

Chapter Summary

Broadband antennas achieve useful operation over a continuous frequency range, whereas frequency-independent antennas rely on scale-invariant geometry and active-region behavior. Helices provide normal-mode compact radiation or axial-mode end-fire circular polarization. Spirals use a moving active region and offer very wide bandwidth, often with circular polarization. Log-periodic antennas use geometrically scaled elements to maintain a broadband directional response. Vivaldi antennas use tapered traveling-wave slots and are especially useful for planar ultrawideband and impulse systems.

Electrically small antennas are constrained by stored energy, high Q, narrow bandwidth, low radiation resistance, and efficiency loss. The Chu–Harrington framework expresses fundamental size–Q–directivity trade-offs, while the Bode–Fano criterion limits passive broadband matching of reactive loads. Matching networks can improve impedance transfer but cannot eliminate the underlying energy-storage and loss constraints. Miniaturization generally trades size for bandwidth, efficiency, tolerance sensitivity, or complexity.

Professional evaluation must include realized gain, total efficiency, pattern, polarization, group delay, phase center, enclosure effects, and regulatory compliance. The correct design is therefore a system-level compromise rather than the geometry with the lowest return loss or the largest nominal bandwidth.

Key Terms

Electrically small antenna: An antenna whose enclosing-sphere parameter \(ka\) is much less than unity.

Broadband antenna: An antenna meeting specified performance criteria over a wide continuous frequency range.

Frequency-independent antenna: An antenna whose ideal behavior depends mainly on angles and scale ratios.

Fractional bandwidth: Frequency span divided by a selected center frequency.

Active region: The portion of a frequency-scaled antenna that contributes most strongly to radiation at a given frequency.

Axial-mode helix: A helix radiating primarily along its axis, usually with circular polarization.

Normal-mode helix: A compact helix operating as a combination of dipole-like and loop-like radiators.

Spiral antenna: A planar frequency-independent antenna using one or more spiral arms.

Log-periodic antenna: A geometrically scaled antenna whose characteristics repeat approximately with logarithmic frequency.

Vivaldi antenna: A tapered-slot traveling-wave antenna with broadband end-fire radiation.

Quality factor: A measure of stored energy relative to power dissipated and radiated.

Chu–Harrington limit: Fundamental size-related bounds on antenna Q and directivity.

Bode–Fano limit: A passive matching bound for reactive loads over bandwidth.

Radiation efficiency: Radiated power divided by accepted power before mismatch effects.

Realized gain: Gain including mismatch and other relevant efficiency factors.

Miniaturization: Reduction of physical size, usually with bandwidth or efficiency penalties.

Group delay: Negative frequency derivative of transmission phase, important in pulse fidelity.

Phase center: The effective point from which a radiated wave appears to originate.

Common-mode current: Unwanted current flowing along a feed or support structure relative to its intended differential mode.

Active matching: Matching using powered or potentially non-Foster circuitry.

Review Questions

Short Answer Questions

1. Define fractional bandwidth and explain why bandwidth criteria must include more than VSWR.

2. What is meant by the active region of a frequency-independent antenna?

3. Distinguish normal-mode and axial-mode operation of a helix.

4. Why does an electrically small antenna usually have high Q?

5. State the principal engineering meaning of the Bode–Fano limit.

Long Answer Questions

1. Explain the operating principles, advantages, and limitations of spiral and log-periodic antennas.

2. Discuss Vivaldi antenna design, including taper, feed transition, aperture, and phase-center behavior.

3. Derive the relationship between electrical size and the qualitative bandwidth limitations of an electrically small antenna.

4. Compare passive matching, miniaturization, and active matching for small antennas.

5. Develop a complete measurement plan for a broadband antenna intended for an impulse radar.

Analytical / Application Questions

1. A helix operates at 1.5 GHz with circumference equal to one wavelength and pitch spacing equal to 0.23 wavelengths. Calculate its radius and pitch angle, and explain which additional parameters must be optimized before fabrication.

2. An antenna has directivity 6, radiation efficiency 0.65, and reflection coefficient magnitude 0.30 at a frequency of interest. Calculate its realized gain under the assumptions used in this chapter and interpret the result.

3. Select between a spiral, log-periodic, and Vivaldi antenna for a compact ground-penetrating radar. Justify the choice using bandwidth, polarization, phase center, aperture, and installation constraints.

Multiple Choice Questions with Answers

Question 1

Which quantity directly measures the electrical size of an antenna enclosed by a sphere of radius a?

A. ka

B. VSWR

C. Q/ka

D. fH-fL

Correct Answer: A. ka

Question 2

In an axial-mode helix, the principal radiation direction is generally

A. broadside to the helix axis

B. along the helix axis

C. normal to the ground plane only

D. randomly oriented with frequency

Correct Answer: B. along the helix axis

Question 3

For a frequency-scaled spiral, the active region primarily

A. remains fixed at the feed for all frequencies

B. moves with frequency along the spiral

C. exists only at the outer termination

D. is determined only by the balun

Correct Answer: B. moves with frequency along the spiral

Question 4

A Vivaldi antenna is fundamentally a

A. tapered-slot traveling-wave antenna

B. short-circuited loop antenna

C. uniformly loaded monopole

D. resonant dielectric cavity only

Correct Answer: A. tapered-slot traveling-wave antenna

Question 5

The dominant small-ka behavior of the Chu-type lower bound on Q is proportional to

A. ka

B. 1/ka

C. 1/(ka)^3

D. (ka)^3

Correct Answer: C. 1/(ka)^3

Question 6

What does the Bode–Fano criterion limit?

A. The maximum conductor temperature

B. Passive broadband matching of reactive loads

C. The speed of light in a dielectric

D. The number of antenna elements in an array

Correct Answer: B. Passive broadband matching of reactive loads

Question 7

An antenna has directivity 4, radiation efficiency 0.50, and |Gamma|=0.20. Ignoring other losses, its realized gain is

A. 1.92

B. 2.00

C. 3.20

D. 4.80

Correct Answer: A. 1.92

Question 8

Which change commonly reduces antenna size but tends to increase stored energy and narrow bandwidth?

A. Increasing free-space wavelength only

B. Meandering the radiator

C. Removing all matching components

D. Eliminating the ground plane in every design

Correct Answer: B. Meandering the radiator

Question 9

For an axial-mode helix with C=lambda, S=0.23 lambda, and N=4, the approximate empirical gain formula in the chapter gives a linear gain of

A. 0.92

B. 4.00

C. 13.8

D. 60

Correct Answer: C. 13.8

Question 10

For an impulse radar antenna, which additional characteristic is especially important besides impedance bandwidth?

A. Group-delay smoothness

B. DC resistance only

C. Connector color

D. Element count independent of frequency

Correct Answer: A. Group-delay smoothness