Q: Microwaves and the ionosphere — typical behavior How do microwave-frequency signals interact with the Earth’s ionosphere under normal conditions?

Introduction / Context: The ionosphere significantly affects HF and some VHF communications by refracting or reflecting radio waves back to Earth. However, the behavior at microwave frequencies is very different. Understanding this is vital for satellite links, radar, and terrestrial microwave relays. Given Data / Assumptions: Frequency regime: microwaves (approximately > 1 GHz). Typical mid-latitude ionospheric electron densities and collision rates. Normal propagation conditions (no extreme events). Concept / Approach: The ionosphere's refractive index depends on plasma frequency f_p, which scales with electron density. For reflection to occur, the radio frequency f must be less than or comparable to f_p. Microwave frequencies are far above typical ionospheric plasma frequencies, so they pass through with little refraction and minimal absorption. This is why satellite communications (GHz bands) operate reliably through the ionosphere, suffering mainly from tropospheric, not ionospheric, effects. Step-by-Step Solution: Compare f_mw (GHz) with f_p (a few to tens of MHz): f_mw ≫ f_p → no reflection.Assess absorption: at GHz, electron-neutral collision losses are small → minimal absorption.Conclude: microwaves are essentially transmitted through the ionosphere. Verification / Alternative check: Satellite downlinks (e.g., L-, S-, X-, Ku-, Ka-bands) demonstrate negligible ionospheric reflection/absorption compared to lower-frequency HF skywave behavior. Why Other Options Are Wrong: Reflected: true for HF/VHF under certain conditions, not for microwaves. Absorbed: ionospheric absorption at GHz is minor. Both reflected and absorbed: contradicts plasma-frequency scaling. Common Pitfalls: Generalizing HF skywave concepts to microwaves; ignoring that troposphere, rain, and clouds dominate microwave propagation impairments (e.g., rain fade). Final Answer: are neither reflected nor absorbed by ionosphere

Question 1

When Is Reflection Significant? Wavelength vs. Object Size  The strength of EM reflection from a target depends on the relation between wavelength and object dimensions. Reflection from the object is significant only when the wavelength is:

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Introduction / Context: Target detectability in radar and general scattering problems depends on the ratio of object size to wavelength. This question asks which relationship makes reflections strong enough to be significant for measurement. Given Data / Assumptions: Simple monostatic reflection from an object in free space. No resonant cavity effects; we are focused on size vs. wavelength scaling. “Significant” means the scattered field is large compared with background/noise. Concept / Approach: Scattering theory distinguishes three regimes: Rayleigh (object ≪ wavelength), resonance (object ≈ wavelength), and optical (object ≫ wavelength). For a given object, as the wavelength becomes much smaller than the object’s size, geometric optics applies and reflections are strong (large radar cross section). When the wavelength is much larger than the object (Rayleigh), scattering is weak and falls rapidly with decreasing size relative to wavelength. Step-by-Step Solution: 1) Consider the Rayleigh case (λ ≫ size): scattered power is very low → not significant.2) Consider resonance/transition (λ ≈ size): reflections can be moderate but often sensitive to geometry and frequency.3) Consider optical regime (λ ≪ size): strong specular reflection and shadowing → significant reflections. Verification / Alternative check: Radar cross-section approximations grow with physical cross-section as λ decreases relative to dimensions, supporting the “much smaller than the object” condition. Why Other Options Are Wrong: (A) leads to Rayleigh weak scattering; (C) can produce noticeable effects but “only when” is too restrictive compared with strong, reliable reflection in the λ ≪ size regime; (D) includes (A) which is incorrect; (E) is an arbitrary ratio without general validity. Common Pitfalls: Assuming resonance is required for detectability; large objects at high frequency can be easily detected without resonance. Final Answer: much smaller than the size of the object

Question 2

Total Radiated Power and the Radiation Sphere Concept  To compute the total power radiated by an antenna, one conceptually encloses it with a very large closed surface and integrates the outward power flow. What is this surface taken to be in standa…

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Introduction / Context: Total radiated power is found by integrating the time-average Poynting vector over a closed surface enclosing the source in the far field. The choice of surface simplifies calculation and interpretation of radiation intensity and directivity. Given Data / Assumptions: Far-field region such that fields locally approximate outward spherical waves. Steady-state sinusoidal excitation. Lossless surrounding space for the conceptual integration. Concept / Approach: In the far field, radiation from any antenna approximates a spherical wave with power density decreasing as 1/r^2. Because of this, a sphere centered on the antenna is the natural Gaussian surface for integration. The radiation intensity U(θ, φ) relates to total power Prad via Prad = ∮ S · dA over the sphere, commonly expressed as Prad = ∫∫ U(θ, φ) dΩ. Step-by-Step Solution: 1) Choose a large radius r so all observations lie in the far field.2) Use a spherical surface area element dA = r^2 sinθ dθ dφ.3) Integrate the radial Poynting component over the sphere to obtain total radiated power. Verification / Alternative check: Directivity, gain, and effective aperture are all derived using spherical integration, reinforcing the standard choice. Why Other Options Are Wrong: Rectangles, squares, ellipses, or cylinders complicate integration and are not aligned with the spherical symmetry of far-field radiation. Common Pitfalls: Confusing near-field reactive energy with radiated power; only the far-field outward flux contributes to total radiated power. Final Answer: sphere

Question 3

Understanding TE01 vs. TE10 in a Rectangular Waveguide  Which statement best describes the TE01 mode in a rectangular waveguide relative to the dominant TE10 mode?

Accepted Answer

Introduction / Context: Rectangular waveguides support TE and TM modes indexed by two integers corresponding to standing-wave variations along the broad (a) and narrow (b) walls. Understanding how TE01 relates to TE10 helps with cutoff and field-pattern intuition. Given Data / Assumptions: Uniform rectangular waveguide with dimensions a (broad) and b (narrow). Standard boundary conditions for perfect electric conductors. Air-filled guide for simplicity. Concept / Approach: TE10 has one half-sine variation across the a-dimension and none across b. TE01 has the complementary pattern: one half-sine across the b-dimension and none across a. If one physically rotates the guide by 90°, the axes swap and the field pattern of TE01 corresponds to TE10 in the rotated frame. Thus, TE01 is effectively TE10 rotated by 90°, although cutoffs differ if a ≠ b. Step-by-Step Solution: 1) Recall TE10: variation along a; no variation along b.2) TE01: variation along b; no variation along a.3) A 90° rotation exchanges a and b, mapping TE10 to TE01. Verification / Alternative check: Cutoff frequencies fc(mn) = (c/2) * sqrt((m/a)^2 + (n/b)^2). Swapping a and b interchanges (m, n) = (1, 0) and (0, 1), consistent with a 90° rotation. Why Other Options Are Wrong: 180° rotation (B) leaves the same mode unchanged; (C) “the same” ignores the axis swap; (D) cannot be right since (B) is wrong; (E) confuses rectangular-guide TE01 with circular-guide TE11. Common Pitfalls: Assuming TE01 is another higher-order version of TE10 without considering geometry; forgetting that if a ≠ b, the cutoff frequencies differ even though patterns are rotationally related. Final Answer: is merely the TE10 mode rotated 90°

Question 4

Single-Mode Upper Frequency for a 1 cm × 2 cm Air-Filled Rectangular Waveguide  For an air-filled rectangular waveguide with internal dimensions 1 cm (height b) × 2 cm (width a), estimate the practical maximum operating frequency for single-mode (TE…

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Introduction / Context: To maintain single-mode operation in a rectangular waveguide, we operate above the TE10 cutoff but below the cutoff of the next higher mode (usually TE20 or TE01). Estimating the upper frequency limit ensures stable patterns and predictable impedance. Given Data / Assumptions: Dimensions: a = 2 cm = 0.02 m (broad wall), b = 1 cm = 0.01 m (narrow wall). Air fill: wave speed c ≈ 3 * 10^8 m/s. Single-mode band bounded above by the lowest of fc(TE20) and fc(TE01). Concept / Approach: Cutoff frequency formula: fc(mn) = (c / 2) * sqrt((m / a)^2 + (n / b)^2). For TE10: fc10 = c / (2a). For TE20: fc20 = c / a. For TE01: fc01 = c / (2b). With a = 2 cm and b = 1 cm, fc20 = c / 0.02 = 15 GHz and fc01 = c / 0.02 = 15 GHz, both equal. A practical upper edge is set slightly below these, often ~95% of the next-mode cutoff, giving about 14–14.25 GHz. Step-by-Step Solution: 1) Compute fc10 = c / (2a) = 3e8 / 0.04 = 7.5 GHz.2) Compute fc20 = c / a = 3e8 / 0.02 = 15 GHz.3) Compute fc01 = c / (2b) = 3e8 / 0.02 = 15 GHz (same).4) Choose practical max ≈ 0.95 * 15 GHz ≈ 14.25 GHz → nearest option ≈ 14,000 MHz. Verification / Alternative check: Standard waveguide single-mode recommendations place the upper limit a few percent below next-mode cutoff to avoid excitation due to tolerances or bends, consistent with ~14 GHz. Why Other Options Are Wrong: 1000 MHz and 5000 MHz are well below TE10 cutoff; 140,000 MHz is far above multi-mode onset; 7500 MHz equals TE10 cutoff and is not an upper limit. Common Pitfalls: Confusing cutoff frequencies with operating band edges; ignoring that both TE20 and TE01 can define the upper bound depending on a and b. Final Answer: 14000 MHz

Question 5

PIN diode applications in RF/microwave switching A PIN (p–i–n) diode can be used in which switching topologies within RF and microwave circuits?

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Introduction / Context: PIN diodes are the workhorse devices for RF and microwave switching, attenuation, and phase control. Thanks to their intrinsic region, they behave like current-controlled resistors at high frequencies. Designers routinely place them either in series with the signal path or in shunt to ground to realize Single-Pole Single-Throw (SPST) and Single-Pole Double-Throw (SPDT) switches across a wide frequency range. Given Data / Assumptions: PIN diode structure: p+ – i – n+. RF behavior approximated as a resistance R_pi that depends on bias current. Goal: identify feasible switching topologies. Concept / Approach: Under forward bias, stored charge in the intrinsic region lowers the RF resistance, enabling low-loss conduction. Under reverse bias, depletion produces a high impedance with small junction capacitance, yielding isolation. In a series switch, the diode sits in the signal path; low R_pi means low insertion loss in the ON state. In a shunt switch, the diode connects the line to ground; low R_pi in the OFF path (for the main line) means the shunt leg is reverse-biased and presents high impedance, while the ON state of the shunt leg shorts RF to ground for isolation. Often, designers combine both series and shunt diodes to maximize isolation and minimize insertion loss. Step-by-Step Solution: Identify series topology → diode in line; ON: low R_pi gives low insertion loss; OFF: high impedance blocks signal.Identify shunt topology → diode to ground; ON: low R_pi dumps signal to ground (isolation); OFF: high impedance minimally loads the line.Recognize hybrid topologies (series + shunt) used for broadband, high-isolation switches. Verification / Alternative check: Typical datasheets specify insertion loss (ON) and isolation (OFF) for series, shunt, and series–shunt configurations, confirming all are valid placements for PIN switches. Why Other Options Are Wrong: Only shunt or only series ignores the versatility of PIN diodes. None of the above contradicts standard RF practice. Common Pitfalls: Ignoring bias networks; forgetting that isolation depends on both diode resistance and residual junction capacitance; overlooking the benefit of adding a shunt path to a series-only design. Final Answer: both as series or shunt mounted switch

Question 6

Skin effect with frequency — qualitative trend As signal frequency is increased in a conductor, how does the skin effect change?

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Introduction / Context: Skin effect describes the tendency of alternating current to concentrate near the surface of a conductor. It is a central concept in RF design, affecting resistance, loss, and heating. Understanding its frequency dependence helps in choosing conductor size, plating, litz wire, and surface finishes for RF/microwave hardware and high-speed interconnects. Given Data / Assumptions: Good conductor with conductivity sigma and permeability mu. Angular frequency ω = 2 * pi * f. Skin depth δ is the characteristic penetration depth. Concept / Approach: The standard relation is δ = sqrt(2 / (ω * mu * sigma)). As frequency f increases, ω increases, causing δ to decrease. A smaller skin depth means current is confined to a thinner surface region, effectively reducing the cross-sectional area available to carry current. The effective AC resistance R_ac therefore increases with frequency. Consequently, we say the skin effect “increases” with frequency because its impact on current crowding and losses becomes more pronounced. Step-by-Step Solution: Start with δ = sqrt(2 / (ω * mu * sigma)).Increase f → ω increases → denominator larger → δ smaller.Smaller δ → more current crowding at the surface → higher effective R_ac and greater loss. Verification / Alternative check: Measured insertion loss of copper microstrip increases with frequency chiefly due to skin effect and dielectric loss; plating with silver (lower surface resistance) improves high-frequency performance, consistent with stronger skin effect at higher f. Why Other Options Are Wrong: Decreases: contradicts δ shrinking with frequency. Remains the same / either (b) or (c): skin effect is frequency-dependent; it does not stay constant. Common Pitfalls: Mixing skin effect with proximity effect; assuming DC behavior applies at RF; ignoring magnetic materials which further reduce δ through higher mu. Final Answer: increases

Question 7

Circular waveguide at millimetre wavelengths — favoured low-loss propagation mode At millimetre wavelengths, which mode in a circular waveguide is typically preferred for long, low-loss transmission?

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Introduction / Context: In circular waveguides, different modes exhibit different attenuation, power handling, and field symmetry. At millimetre wavelengths, long low-loss links and high-power transport often prioritize a mode with particularly low wall-current losses and minimal mode conversion. This question asks which mode is favoured for such purposes. Given Data / Assumptions: Metal circular waveguide, smooth inner wall. Millimetre-wave operation (approximately 30–300 GHz). Interest in low attenuation over distance, not just lowest cutoff. Concept / Approach: While TE11 is the dominant (lowest-cutoff) mode in circular waveguide, the TE01 mode is often preferred for long-haul millimetre-wave power transmission because it has very low conductor loss due to circumferential surface current distribution and no longitudinal electric field at the wall, reducing ohmic loss and breakdown risk. TE01 also offers improved power-handling and reduced susceptibility to bends, provided suitable mode converters are used at interfaces. Step-by-Step Solution: Recognize dominance vs preference: dominant ≠ always preferred.Evaluate attenuation constants of candidate modes: TE01 typically exhibits lower attenuation than TE11 at mm-wave.Account for practical implementations: TE01 lines with mode converters are common in high-power/mm-wave systems. Verification / Alternative check: Millimetre-wave literature and handbooks document TE01 lines for low-loss transmission and high-power gyro-device outputs, confirming its favored status for these specific applications. Why Other Options Are Wrong: TE11: dominant, but not lowest loss for long transport. TE20, TE21: higher-order modes with higher cutoffs and typically higher attenuation. Common Pitfalls: Equating “dominant” with “preferred for long-haul.” The engineering preference may differ when loss and power handling dominate the design criteria. Final Answer: TE01

Question 8

Traveling-Wave Tube (TWT) synchronism condition In a TWT, the phase velocity of the axial field on the slow-wave structure is kept how, relative to the electron beam velocity, for effective energy transfer?

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Introduction / Context: A Traveling-Wave Tube (TWT) achieves amplification by continuous interaction between an electron beam and an RF wave slowed down by a slow-wave structure (e.g., helix). Proper synchronism between beam velocity and wave phase velocity is essential for net transfer of kinetic energy from electrons to the RF field. Given Data / Assumptions: Electron beam with average velocity v_e. Axial RF wave with phase velocity v_p along the slow-wave structure. Goal: set relation between v_p and v_e for gain. Concept / Approach: For sustained energy transfer, electrons must “overtake” the RF phase such that they see a retarding electric field on average, giving up kinetic energy to the wave. This requires v_e to be slightly greater than v_p, which equivalently means the phase velocity is kept slightly less than the electron velocity. Exact tuning is adjusted via beam voltage and circuit parameters to maintain synchronism over the device length. Step-by-Step Solution: Set desired inequality: v_e > v_p for net energy flow from electrons to wave.Implement via slow-wave structure so v_p << c and slightly below v_e.Bias beam voltage to maintain near-synchronism as space-charge and circuit loading alter velocities. Verification / Alternative check: Small-signal TWT theory shows growth when the beam line intersects the circuit dispersion just above the wave's phase velocity, yielding a negative beam power change and positive RF power growth. Why Other Options Are Wrong: Equal to v_e: narrow interaction; practical operation prefers a slight margin for consistent gain. Slightly more than v_e: electrons would gain energy from the wave. Equal to c: impossible in a slow-wave helix and not conducive to interaction. Common Pitfalls: Confusing group and phase velocities; assuming maximum gain at exact equality rather than slightly less v_p than v_e. Final Answer: slightly less than velocity of electron

Question 9

Microwaves and the ionosphere — typical behavior How do microwave-frequency signals interact with the Earth’s ionosphere under normal conditions?

Accepted Answer

Introduction / Context: The ionosphere significantly affects HF and some VHF communications by refracting or reflecting radio waves back to Earth. However, the behavior at microwave frequencies is very different. Understanding this is vital for satellite links, radar, and terrestrial microwave relays. Given Data / Assumptions: Frequency regime: microwaves (approximately > 1 GHz). Typical mid-latitude ionospheric electron densities and collision rates. Normal propagation conditions (no extreme events). Concept / Approach: The ionosphere's refractive index depends on plasma frequency f_p, which scales with electron density. For reflection to occur, the radio frequency f must be less than or comparable to f_p. Microwave frequencies are far above typical ionospheric plasma frequencies, so they pass through with little refraction and minimal absorption. This is why satellite communications (GHz bands) operate reliably through the ionosphere, suffering mainly from tropospheric, not ionospheric, effects. Step-by-Step Solution: Compare f_mw (GHz) with f_p (a few to tens of MHz): f_mw ≫ f_p → no reflection.Assess absorption: at GHz, electron-neutral collision losses are small → minimal absorption.Conclude: microwaves are essentially transmitted through the ionosphere. Verification / Alternative check: Satellite downlinks (e.g., L-, S-, X-, Ku-, Ka-bands) demonstrate negligible ionospheric reflection/absorption compared to lower-frequency HF skywave behavior. Why Other Options Are Wrong: Reflected: true for HF/VHF under certain conditions, not for microwaves. Absorbed: ionospheric absorption at GHz is minor. Both reflected and absorbed: contradicts plasma-frequency scaling. Common Pitfalls: Generalizing HF skywave concepts to microwaves; ignoring that troposphere, rain, and clouds dominate microwave propagation impairments (e.g., rain fade). Final Answer: are neither reflected nor absorbed by ionosphere

Question 10

PIN diode switch figures of merit — ON vs OFF performance Which pair best represents the standard performance metrics for a PIN-diode RF switch?

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Introduction / Context: Two headline specifications define the usefulness of an RF switch in front-ends, test systems, and phased arrays: how little loss it introduces when conducting, and how well it blocks signals when nonconducting. PIN-diode switches are no exception—these two metrics capture most application trade-offs. Given Data / Assumptions: Switch types: series, shunt, or series–shunt. Bias states: ON (forward-biased conduction) and OFF (reverse-biased isolation). Concept / Approach: Insertion loss is measured in the ON state and should be as low as possible. It captures conductor loss, finite R_pi, and layout parasitics. Isolation is measured in the OFF state and should be as high as possible; it reflects the residual coupling via diode capacitance and circuit paths. Together they describe the signal-handling extremes of the switch, while other specs (P1dB, IP3, switching speed) refine selection for a project. Step-by-Step Solution: Define ON metrics → insertion loss (dB) in the through path.Define OFF metrics → isolation (dB) between ports.Match the pair to options → “insertion loss when switch is on and isolation loss when switch is off.” Verification / Alternative check: Any RF switch datasheet tabulates “Insertion Loss (ON)” and “Isolation (OFF)” across frequency, confirming these as standard metrics. Why Other Options Are Wrong: Insertion loss when OFF or isolation when ON mixes states and has no standard meaning. Only insertion loss or only isolation omits a critical half of performance. Common Pitfalls: Confusing isolation with return loss; overlooking that isolation is frequency-dependent and may need a shunt element to improve broadband blocking. Final Answer: insertion loss when switch is on and isolation loss when switch is off

Question 11

Manufacturing method for strip-type transmission lines (e.g., microstrip) Which fabrication technique is commonly used to manufacture strip-type transmission lines on dielectric substrates?

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Introduction / Context: Strip-type transmission lines (microstrip, stripline, coplanar waveguide) are realized on printed circuit boards or ceramic substrates. Their geometry must be precisely defined to control impedance and coupling. The mainstream process in both PCB and thin-film MIC technology is photolithography followed by etching—colloquially referred to as photoetching. Given Data / Assumptions: Substrate: FR-4, Rogers laminates, alumina, or similar. Metallization: copper, gold, or other conductor films. Goal: identify the standard patterning method. Concept / Approach: Photoetching uses a photoresist patterned via UV exposure through a mask (or via direct imaging). The developed photoresist protects the desired metal traces while unwanted metal is chemically etched away. The resulting lines, grounds, and pads form accurate transmission-line structures. Alternative semiconductor processes—oxidation and epitaxy—pertain to forming dielectric and crystalline layers in ICs, not to defining RF conductor patterns. Cladding refers to bonding metal foils or layers to substrates, not the patterning step itself. Step-by-Step Solution: Coat metalized substrate with photoresist.Expose and develop to create the line pattern in resist.Etch unprotected metal to leave precise strip geometries. Verification / Alternative check: Standard PCB fabrication houses and thin-film MIC processes list photolithography + etch as the core methodology for microstrip and CPW lines. Why Other Options Are Wrong: Oxidation: creates oxides (e.g., SiO2) in semiconductor processing, not the conductor pattern. Epitaxial: grows single-crystal layers for active devices. Cladding: attaches metal foil but does not pattern it into lines. Common Pitfalls: Confusing substrate preparation or metallization with line patterning; assuming semiconductor front-end steps apply directly to PCB/MIC metallization. Final Answer: photoetching technique

Question 12

Microstrip line materials — common dielectric choice In a typical microstrip line used for RF printed-circuit designs, which dielectric material is most commonly used?

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Introduction / Context: Microstrip lines are fabricated on dielectric substrates with a metal trace on top and a ground plane beneath. The dielectric choice impacts loss tangent, dielectric constant, manufacturability, and cost. In commercial and consumer RF PCBs, the most common dielectrics are plastics or plastic-based laminates (e.g., FR-4 epoxy glass, PTFE-based composites). Given Data / Assumptions: Focus on common, mass-produced RF PCB technology. Option set is generic rather than brand-specific. Concept / Approach: Silicon is a semiconductor wafer used in ICs, not a typical PCB dielectric. Rubber is lossy and mechanically unsuitable. Bakelite is an old thermoset historically used but uncommon in modern RF PCB microstrip. By contrast, plastics—especially epoxy-glass (FR-4) and PTFE-based materials—dominate. High-performance RF uses PTFE or low-loss plastics; cost-sensitive designs use FR-4. Therefore, among the provided choices, “plastic” is the correct generalized answer. Step-by-Step Solution: Recognize microstrip is a PCB technology.Match to mainstream PCB dielectrics: plastic-based laminates.Exclude specialty/incorrect materials (Si, rubber, bakelite) per typical RF practice. Verification / Alternative check: Fabrication standards and vendor catalogs list FR-4 and PTFE composites (both plastic-derived) as ubiquitous microstrip substrates across frequencies from HF to microwave. Why Other Options Are Wrong: Silicon: used for ICs and MMICs, not for ordinary microstrip PCBs. Rubber: high loss, poor dimensional stability. Bakelite: obsolete for precision RF, inferior electrical properties compared to modern plastics. Common Pitfalls: Confusing MMIC-on-silicon with PCB microstrip; assuming any insulator is suitable regardless of loss tangent and mechanical constraints. Final Answer: plastic

Question 13

VSWR from power readings — directional coupler example In the setup shown (forward power meter at point A reads 1 mW; reflected power meter at point B reads 110 μW), determine the Voltage Standing Wave Ratio (VSWR) on the line.

Accepted Answer

Introduction / Context: VSWR quantifies mismatch on a transmission line. Using a directional coupler or dual-direction power meter, one can read forward power P_f and reflected power P_r, convert to the magnitude of the reflection coefficient |Γ|, and then compute VSWR. This is a standard test-bench task in RF labs. Given Data / Assumptions: Forward power P_f = 1 mW at point A. Reflected power P_r = 110 μW at point B. Meters and coupler are properly calibrated; same reference impedance. Concept / Approach: The power reflection coefficient is |Γ|^2 = P_r / P_f. Hence |Γ| = sqrt(P_r / P_f). VSWR is defined as (1 + |Γ|) / (1 − |Γ|) for 0 ≤ |Γ| < 1. After computing |Γ| from the given readings, plug into the VSWR formula to get the final ratio. Step-by-Step Solution: Compute ratio: P_r / P_f = 110 μW / 1 mW = 0.11.Find |Γ|: |Γ| = sqrt(0.11) ≈ 0.3317.Compute VSWR: VSWR = (1 + 0.3317) / (1 − 0.3317) ≈ 1.3317 / 0.6683 ≈ 1.992.Round to nearest listed value: approximately 2. Verification / Alternative check: Convert |Γ| to return loss: RL = −20 * log10(|Γ|) ≈ 9.58 dB. The VSWR corresponding to about 9.6 dB return loss is ~2:1, which corroborates the calculation. Why Other Options Are Wrong: 1.5: corresponds to |Γ| ≈ 0.2, not 0.332. 2.5: implies |Γ| ≈ 0.429, larger reflection than measured. 3: implies |Γ| ≈ 0.5, much larger reflection. Common Pitfalls: Using power ratios directly in VSWR without taking the square root for |Γ|; mixing dB and linear units; misreading μW vs mW. Final Answer: 2

Question 14

Earliest practical applications of electromagnetic waves Historically, what were among the earliest widespread uses of electromagnetic waves?

Accepted Answer

Introduction / Context: Understanding the chronology of electromagnetic (EM) technology helps frame how modern wireless systems evolved. The earliest practical deployments focused on sending information over distance without wires, long before the advent of sophisticated detection systems such as radar. Given Data / Assumptions: Late 19th to early 20th-century developments. Key figures: Hertz (experiments), Marconi (wireless telegraphy). Focus on “earliest uses” in real systems. Concept / Approach: Heinrich Hertz demonstrated EM wave propagation in the 1880s. Soon after, Guglielmo Marconi pioneered wireless telegraphy for point-to-point communication across increasing distances, culminating in transatlantic messages by the early 1900s. These point-to-point links—ships to shore, coastal stations, military—constituted the earliest large-scale use of radio waves. Radar, by contrast, emerged later (1930s–1940s), driven by the need for object detection and ranging, especially around World War II. Thus, communication predates radar as the earlier widespread application. Step-by-Step Solution: Identify initial demonstrations (Hertz) as proof-of-concept, not practical use.Note early commercialization: Marconi’s wireless telegraphy enabling point-to-point communications.Recognize radar's later development timeline in the 1930s–1940s.Conclude that point-to-point communication is the earliest widespread use. Verification / Alternative check: Historical timelines in communications engineering show wireless telegraphy and telephony deployments well before large-scale radar systems, confirming the ordering. Why Other Options Are Wrong: Radar: important but later in chronology. Both (a) and (b): overstates; only (a) qualifies as earliest widespread use. Neither: ignores the foundational role of early radio links. Common Pitfalls: Associating early experiments with practical deployment; confusing timelines influenced by wartime acceleration of radar development. Final Answer: point to point communication

Question 15

Dielectric guiding at microwaves: Can an electromagnetic wave be completely guided by a dielectric rod or a dielectric slab (without relying on metallic walls)?

Accepted Answer

Introduction: This conceptual question probes how electromagnetic waves are confined in dielectric waveguides such as rods and slabs, especially at microwave frequencies. It asks whether guidance can be “complete,” meaning perfectly confined with zero leakage, when only dielectric boundaries are used and no metallic enclosure is present. Given Data / Assumptions: Dielectric rod or slab in a lower-index surrounding (often air). Operation in the microwave regime where surface-wave behavior is significant. “Completely guided” is interpreted as no radiative leakage and perfect confinement. Concept / Approach: Dielectric guiding relies on total internal reflection (TIR) when a higher-index core is surrounded by a lower-index medium. While TIR can strongly confine light in optical fibers (which are long and uniform with a cladding), many microwave dielectric-rod waveguides primarily support surface or leaky modes. These modes exhibit finite radiation loss, bends cause additional radiation, and real materials have finite loss tangent. Therefore, although energy can be guided efficiently, it is not “completely” (perfectly) confined in practice. Step-by-Step Solution: Clarify guidance mechanism: dielectric discontinuity enables partial or strong confinement via TIR.Note that dielectric rods in air commonly support surface/leaky modes with finite attenuation.Real dielectrics have nonzero loss tangent; boundaries are not perfectly smooth; bends radiate power.Hence, the assertion of “complete” (ideal, lossless and nonradiative) guidance is not correct for practical microwave dielectric rods or slabs without cladding optimization. Verification / Alternative check: Textbook plots of attenuation constants for dielectric-rod waveguides show nonzero conductor/dielectric/radiation losses. Optical-fiber analogies approach very low loss but still are not strictly zero; and the question refers to microwave dielectric rods/slabs, which are more prone to radiation leakage than metal waveguides. Why Other Options Are Wrong: True: implies perfect confinement, which is not achieved in practice for dielectric rods/slabs at microwaves. Only for perfect dielectrics with zero loss: even with zero material loss, radiation leakage from open geometries can persist. Only if metal-coated: adding metal walls changes the device into a metallic waveguide, not a dielectric guide. Only at optical frequencies: optics can be very low loss, but not “completely” lossless. Common Pitfalls: Equating strong but finite confinement with “complete” guidance; overlooking radiation at discontinuities and bends; assuming an idealized zero-loss medium. Final Answer: False

Question 16

Foundations of fibre optics: In fibre-optic communications, thin glass (or plastic) fibres are used for efficient transmission of light over distance.

Accepted Answer

Introduction: The statement addresses the basic idea behind fibre-optic communication: using very pure, thin strands of glass or plastic to guide light signals with low attenuation and high bandwidth. Recognizing why fibres are efficient light guides is essential background for optical systems. Given Data / Assumptions: Fibre consists of a core with refractive index n1 and a cladding with slightly lower index n2. Guidance is by total internal reflection when light attempts to exit the higher-index core. Typical telecom wavelengths are near 850 nm, 1310 nm, and 1550 nm, where fibre loss is very small. Concept / Approach: Efficient transmission arises from two factors: very low material absorption/scattering in the selected wavelength windows, and waveguide confinement by total internal reflection. The numerical aperture determines the acceptance cone, while dispersion engineering (single-mode or graded-index) preserves pulse integrity for high data rates over long distances. Step-by-Step Solution: Understand waveguiding: core n1 > cladding n2 → internal reflections confine light.Low-loss windows: modern fibres exhibit attenuation ~0.2 dB/km at 1550 nm, enabling long spans with optical amplification.Bandwidth: single-mode fibres eliminate intermodal dispersion, supporting extremely high symbol rates.Result: thin glass/plastic fibres transmit light efficiently for communication, sensing, and imaging. Verification / Alternative check: Network deployments worldwide (long-haul, metro, FTTH) rely on fibre backbones, confirming practical efficiency and scalability compared with copper for high-capacity links. Why Other Options Are Wrong: False: contradicts the operational reality of global fibre networks. Only if the core is metallic: a metallic core would absorb light; optical fibres are dielectric. True only for infrared: fibres can guide both visible and infrared; telecom bands are chosen for loss/dispersion reasons. Hollow fibres only: hollow-core fibres exist but are specialized; standard fibres are solid glass. Common Pitfalls: Confusing guidance with lack of any loss; fibres are efficient, not perfectly lossless. Also, bandwidth is limited by dispersion and nonlinearity, not just by loss. Final Answer: True

Question 17

Klystron amplifier and weak-signal reception: Why is a klystron generally not chosen to amplify very weak microwave signals?

Accepted Answer

Introduction: Front-end amplifiers for very weak microwave signals must exhibit ultra-low noise figures. This question asks why a klystron is usually not the first choice for such applications, despite its usefulness as a high-power microwave amplifier at later stages. Given Data / Assumptions: Klystron is a vacuum-electron device using velocity modulation and bunching. Weak-signal preamplification in receivers demands minimum noise figure. Alternative devices include low-noise transistors, parametric amplifiers, and masers. Concept / Approach: The total system noise is dominated by the first active stage (Friis formula). Klystrons, while capable of significant gain and power, typically have higher noise figures compared to specialized low-noise devices. Therefore, they are not preferred as the first stage when the input signal is extremely weak; instead, low-noise solid-state LNAs or parametric/maser amplifiers are used up front, with klystrons possibly serving later power-amplifier roles. Step-by-Step Solution: Identify requirement: minimal noise figure in the first stage to preserve SNR.Assess device: klystron has higher inherent noise mechanisms (shot noise, partition noise, microphonics).Compare alternatives: GaAs pHEMT/HEMT LNAs or parametric/maser amplifiers achieve far lower noise.Conclude: klystron is not used for very weak signals primarily due to high noise, not lack of gain. Verification / Alternative check: Receiver design textbooks show first-stage noise figure targets well below what klystrons typically provide; historical deep-space and radio-astronomy systems favored cryogenic masers or HEMT LNAs. Why Other Options Are Wrong: Low gain: klystrons can deliver substantial gain; this is not the limiting factor. Low noise or both (a) and (b): contradict observed device characteristics. Bandwidth only: noise, not just bandwidth, is the key issue for preamps. Common Pitfalls: Assuming a high-power amplifier is automatically suitable as a low-noise preamplifier. The first stage requires different optimization. Final Answer: high noise

Question 18

Circular waveguides and symmetry: Which of the following circular waveguide modes are circularly symmetric (no azimuthal variation)?

Accepted Answer

Introduction: Modes in circular waveguides are labeled TEmn or TMmn, where the first index m corresponds to azimuthal variations and the second index n corresponds to radial order. Recognizing which modes are circularly symmetric helps in low-loss transmission and mode conversion design. Given Data / Assumptions: Circular metallic waveguide with air filling. TE0n modes have m = 0 (no dependence on azimuthal angle φ). We are considering TE01 and TE02 specifically. Concept / Approach: Azimuthal symmetry means the fields do not vary with φ. In circular guides, m = 0 satisfies this, so any TE0n or TM0n mode is circularly symmetric. Therefore, TE01 and TE02 are both circularly symmetric modes. Step-by-Step Solution: Identify the azimuthal index: m = 0 implies circular symmetry.Check modes: TE01 → m = 0, n = 1; TE02 → m = 0, n = 2.Conclude: both choices are circularly symmetric. Verification / Alternative check: Field patterns for TE01 and TE02 show concentric rings with no angular variation, confirming circular symmetry useful for certain low-loss TE01 long-haul systems. Why Other Options Are Wrong: Neither or a single mode only contradict m = 0 symmetry criterion. TM11 only: TM11 has m = 1, hence not circularly symmetric. Common Pitfalls: Confusing dominant mode (TE11) with symmetry; dominance relates to cutoff, not azimuthal variation. Final Answer: both (a) and (b)

Question 19

Rectangular waveguide construction: What is the electrical requirement for the wall thickness of the guide relative to the skin depth at the operating frequency?

Accepted Answer

Introduction: Skin effect confines RF currents to a thin layer at the conductor surface. Waveguide walls must be thick enough to carry these currents without excessive loss or structural compromise. This question asks how wall thickness relates to the skin depth δ. Given Data / Assumptions: Good conductor (e.g., copper or aluminum) waveguide at microwave frequency. Skin depth δ is the current penetration depth where fields decay to 1/e. Goal: low conductor loss and mechanical robustness. Concept / Approach: Conductor loss and heating decrease as the wall thickness exceeds several skin depths, ensuring the current is fully supported within the conductor without significant field leakage. A practical rule is that thickness should be several times δ; making it less than or equal to δ risks increased loss and potential deformation or RF leakage at seams. Step-by-Step Solution: Compute δ = sqrt(2 / (ω μ σ)) for the chosen material and frequency.Choose wall thickness t such that t ≫ δ (commonly > 3δ for low added loss).Validate that plating and surface finish minimize roughness-induced loss.Confirm mechanical integrity for pressure or pressurization if used. Verification / Alternative check: Manufacturer datasheets and microwave handbooks recommend thicknesses multiple times δ; plating with silver over base metal further lowers loss while retaining adequate thickness. Why Other Options Are Wrong: Less than or equal to δ: leads to higher loss and possible RF leakage. Either (b) or (c) or exact multiples (e.g., exactly 2δ) are arbitrary and not general requirements. Common Pitfalls: Assuming thicker walls beyond several δ always improve performance; after a few δ, returns diminish and surface conductivity/finish dominate. Final Answer: wall thickness is more than skin depth

Question 20

Dominant mode in rectangular waveguides: Which mode is the first to propagate (lowest cutoff) in a standard air-filled rectangular waveguide?

Accepted Answer

Introduction: Every rectangular waveguide has a dominant mode: the mode with the lowest cutoff frequency, which therefore propagates first as frequency increases. Identifying it is essential for single-mode operation and component design. Given Data / Assumptions: Air-filled rectangular waveguide of width a and height b (a > b). Standard boundary conditions on perfectly conducting walls. TE/TM cutoff relationships apply: fc ∝ sqrt((m/a)^2 + (n/b)^2). Concept / Approach: For TEmn and TMmn modes, the lowest combination is m = 1, n = 0 in TE family for a typical guide with a > b. This gives TE10 as the dominant mode. Its cutoff frequency is fc = c / (2a), which is lower than other combinations for the same geometry. Step-by-Step Solution: Write cutoff: fc(m, n) = (c/2) * sqrt((m/a)^2 + (n/b)^2).For TE10: fc = c / (2a) (no dependence on b).Compare with TE01: fc = c / (2b) which is higher because b < a.All other modes (e.g., TE20, TE11, TM11) include larger indices → higher fc. Verification / Alternative check: Waveguide charts and standards (WR series) are based on TE10 dominance, ensuring single-mode bandwidth between TE10 cutoff and the next higher-order mode cutoff. Why Other Options Are Wrong: TE01, TE20, TE11, TM11 have higher cutoff frequencies for a standard aspect ratio. Common Pitfalls: Confusing dominant with circular-guide dominance (TE11 is dominant in circular guides). In rectangular guides, TE10 is dominant. Final Answer: TE10

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