Question 1

Assertion–Reason on PIN Diodes: Applications and Structure  Assertion (A): A PIN diode can be used as an RF/microwave attenuator and as a power limiter in receiver front-ends. Reason (R): A PIN diode has a thin intrinsic (i) layer between the p and …

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Introduction / Context: PIN diodes are widely used in RF and microwave systems as current-controlled resistors. Their unique structure allows applications such as variable attenuators, T/R switches, and power limiters that protect low-noise amplifiers from large incident signals. Given Data / Assumptions: We are evaluating an Assertion–Reason pair about a PIN diode's applications and the nature of its intrinsic layer. No numerical computation is required; conceptual understanding is key. Concept / Approach: In a PIN diode, a deliberately thick intrinsic (i) region separates the p and n regions. Under forward bias at RF, the diode exhibits a resistance that depends on carrier lifetime and stored charge. Under reverse bias, it behaves like a small capacitor with low conductance. These behaviors enable attenuation control and RF limiting. Step-by-Step Solution: 1) Check Assertion: PIN diodes are used as attenuators and limiters. This is true because biasing controls their RF resistance and they can shunt or series-attenuate signals, while carrier storage enables power limiting action.2) Check Reason: It claims the intrinsic layer is thin. In reality, the i-region is intentionally thick to reduce junction capacitance and increase carrier lifetime, which is essential to the RF behavior.3) Relate R to A: Since the i-layer is not thin, the Reason is false and cannot explain the Assertion. Verification / Alternative check: Standard PIN diode datasheets and RF textbooks describe the i-layer thickness (often several micrometers or more) and its role in RF resistance control and limiting behavior. Why Other Options Are Wrong: Option A: Wrong because R is false. Option B: Wrong since R is not even correct. Option D: Wrong because A is true. Option E: Wrong since A is true. Common Pitfalls: Confusing PIN with a regular pn diode; assuming the i-layer is always thin like in small-signal diodes; ignoring carrier lifetime effects at RF. Final Answer: A is correct but R is wrong.

Question 2

Magnetron Structure and Cavities: True/False with Context  A magnetron employs a cylindrical (thermionic) cathode at the center and an anode block containing resonant cavities. These cavities are coupled to the interaction space via slots, enabling …

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Introduction / Context: The cavity magnetron is a high-power microwave oscillator used in radar and microwave heating. Its operation relies on resonant cavities in the anode block and the interaction of electrons with RF fields in a crossed E–B field region. Given Data / Assumptions: Cylindrical cathode at center; anode with cavities around it. Slots couple cavities to the interaction space. We judge correctness of the structural description. Concept / Approach: In a magnetron, the anode block contains resonant cavities. Electrons emitted by the central cathode are influenced by radial electric fields and axial magnetic fields, forming spokes that interact with the RF fields through coupling slots between cavities and the interaction space. Step-by-Step Solution: 1) Identify device type: The described device with an anode cavity block and central cathode is a cavity magnetron.2) Check elements: Cavities reside in the anode; coupling occurs via slots to the interaction space, which is correct.3) Conclude truth value: The statement matches standard magnetron construction, so it is true. Verification / Alternative check: Any introductory microwave engineering text shows exploded drawings of magnetrons with anode cavities and coupling slots. Why Other Options Are Wrong: Option B: Contradicts standard construction. Option C: Describes a different device (reflex klystron) that uses a repeller, not an anode cavity block like a magnetron. Option D: A magnetron requires a magnetic field for normal operation. Option E: Cavities are not in the cathode. Common Pitfalls: Confusing magnetron with klystron or traveling-wave tube; misplacing cavities in the cathode instead of the anode. Final Answer: True.

Question 3

Directivity of a Receiving Antenna: Effects on Intercept Area, Noise, and Signal Discrimination  Consider the statements: 1) Increasing directivity increases the effective intercept area in the forward direction. 2) Increasing directivity reduces no…

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Introduction / Context: Directivity describes how concentrated an antenna's radiation or reception pattern is in a preferred direction. For receiving antennas, higher directivity effectively increases sensitivity from the look direction while suppressing energy from elsewhere. Given Data / Assumptions: Three qualitative statements relate directivity to effective area, noise pickup, and discrimination. Broadband/system noise is often dominated by off-axis interference and environmental sources. Concept / Approach: Effective aperture A_e is related to gain G by A_e = (lambda^2 * G) / (4 * pi). For a given wavelength, increasing gain (and thus directivity for lossless antennas) increases A_e in the main lobe. A narrower beam also rejects off-axis noise and interference. Step-by-Step Solution: 1) Statement 1: True. Higher directivity implies larger effective area in the main lobe, improving desired signal capture.2) Statement 2: True. A narrower pattern reduces energy received from other directions, lowering off-axis noise/interference.3) Statement 3: True. With a tighter beam, the antenna can discriminate against undesired directions. Verification / Alternative check: Standard antenna theory links directivity, gain, and effective aperture; pattern plots show how beam narrowing reduces reception from unwanted angles. Why Other Options Are Wrong: Options A, B, D, and E omit at least one correct statement, so they are incorrect. Common Pitfalls: Confusing directivity with efficiency; assuming higher directivity always raises received SNR without considering pointing accuracy and bandwidth. Final Answer: 1, 2 and 3.

Question 4

Cutoff Wavelength in a Circular Waveguide: Dependence on Physical Size  For a given propagation mode (for example, the dominant TE11 mode), how does the cutoff wavelength vary with the circular waveguide's inside diameter?

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Introduction / Context: Waveguides support propagation only above cutoff. In circular waveguides, each mode has a specific cutoff wavelength set by the boundary conditions and the diameter. Given Data / Assumptions: We consider qualitative dependence of cutoff wavelength on diameter. Mode constants are fixed (e.g., TE11). Concept / Approach: For a circular waveguide, lambda_c = k * D for a given mode, where k is a constant determined by the root of a Bessel function equation. For the dominant TE11 mode, lambda_c ≈ 1.706 * D. Thus, cutoff wavelength scales linearly with diameter. Step-by-Step Solution: 1) Recognize that cutoff is set by boundary conditions leading to characteristic equations with Bessel function roots.2) For a fixed mode, the root is a constant, so lambda_c must scale directly with D.3) Therefore, doubling D doubles lambda_c; halving D halves lambda_c. Verification / Alternative check: Design charts or tables for circular waveguides list lambda_c as a constant times D for each mode. Why Other Options Are Wrong: Quadratic, cubic, square-root, or diameter-independent relations contradict the linear dependence defined by the modal eigenvalue. Common Pitfalls: Confusing cutoff wavelength with cutoff frequency (f_c ∝ 1/D). Remember f_c and lambda_c have inverse trends. Final Answer: Directly proportional to guide diameter.

Question 5

TWT Slow-Wave Structure: Axial RF Phase Velocity along the Tube  In a traveling-wave tube (TWT), the axial component of the RF electric field progresses along the slow-wave structure with what approximate velocity relative to the speed of light?

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Introduction / Context: TWTs use slow-wave structures (e.g., helix) to reduce the RF phase velocity so that it can synchronize with the electron beam's velocity, enabling continuous interaction and amplification. Given Data / Assumptions: The question asks for a qualitative comparison of axial RF phase velocity with c. We consider a typical helix TWT designed for beam-wave synchronism. Concept / Approach: Without a slow-wave structure, the phase velocity in a waveguide is comparable to or greater than c. The helix introduces a long path for the wave, reducing axial phase velocity to a small fraction of c, closer to typical electron beam speeds. Step-by-Step Solution: 1) Purpose of slow-wave: Reduce axial phase velocity so beam can interact over long distance.2) Typical operating condition: Beam velocities are often a small fraction of c, hence the RF axial velocity is engineered to be similar.3) Conclusion: The correct qualitative choice is a small fraction of c. Verification / Alternative check: Representative TWT designs show phase velocities well below c to maintain synchronism. Why Other Options Are Wrong: Option A and E: Too fast for interaction. Option C: 50% of c is typically high for many helix designs. Option D: Phase velocity can exceed c in some media, but axial slow-wave velocity in a helix is deliberately reduced below c for amplification. Common Pitfalls: Confusing group and phase velocity; forgetting that synchronism requires comparable velocities. Final Answer: A small fraction of the speed of light.

Question 6

Directive Gain versus Wavelength for a Fixed-Size Transmitting Antenna  How does the directive gain of a transmitting antenna vary with the operating wavelength (assuming physical aperture/size is fixed)?

Accepted Answer

Introduction / Context: The directive gain of an antenna relates to how concentrated its radiation is. For a physically fixed aperture, gain is strongly tied to wavelength. Given Data / Assumptions: Physical aperture is held constant. We are varying wavelength only. Concept / Approach: For an aperture antenna, gain G ≈ (4 * pi * A_e) / lambda^2. If physical aperture (and thus effective aperture A_e in the high-efficiency case) is fixed, gain varies as 1 / lambda^2. Step-by-Step Solution: 1) Start with G ≈ (4 * pi * A_e) / lambda^2.2) Hold A_e constant. Then G ∝ 1 / lambda^2.3) Hence, halving lambda increases gain by about 4×, and doubling lambda reduces gain by about 4×. Verification / Alternative check: Aperture theory and antenna textbooks consistently show the inverse-square dependence with wavelength for fixed apertures. Why Other Options Are Wrong: Options A, B, C, and E contradict the aperture-gain relationship when physical size is fixed. Common Pitfalls: Confusing physical aperture with electrical size; neglecting efficiency factors which change the constant but not the lambda^2 dependence. Final Answer: Inversely proportional to square of wavelength.

Question 7

Transmission Line with Complex Load: Compute the Voltage Transmission Coefficient  A lossless line has Z0 = 300 Ω and is terminated with ZL = 300 − j300 Ω. Find the voltage transmission coefficient T at the load (magnitude and angle).

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Introduction / Context: On a transmission line with characteristic impedance Z0 and load ZL, the reflection coefficient Γ and transmission coefficient T describe how waves reflect from and transmit into the load. Here we compute T for a complex load. Given Data / Assumptions: Z0 = 300 Ω ZL = 300 − j300 Ω Lossless line; standard voltage-wave definitions. Concept / Approach: For voltage waves at the load: Γ = (ZL − Z0) / (ZL + Z0). The transmission coefficient for voltage at the load is T = 1 + Γ. Step-by-Step Solution: 1) Compute Γ: ZL − Z0 = (300 − j300) − 300 = − j300.2) ZL + Z0 = (300 − j300) + 300 = 600 − j300.3) Γ = (− j300) / (600 − j300) = (0.2 − j0.4). Magnitude |Γ| ≈ 0.447, angle ≈ −63.43°.4) Transmission coefficient T = 1 + Γ = (1.2 − j0.4). |T| = sqrt(1.2^2 + (−0.4)^2) ≈ 1.265, angle ≈ arctan(−0.4/1.2) ≈ −18.43°. Verification / Alternative check: Compute Γ on a Smith chart at ZL / Z0 = 1 − j1 and then add 1 vectorially to obtain T; the numerical result matches. Why Other Options Are Wrong: Option B and D: Magnitude/angle do not match T. Option C: Wrong quadrant/angle. Option E: That is |Γ|∠∠ for the reflection coefficient, not the transmission coefficient. Common Pitfalls: Confusing Γ with T; forgetting that T = 1 + Γ for voltage at the load; mixing degrees and radians. Final Answer: 1.265 ∠ -18.43°.

Question 8

Characteristic Impedance from Per-Unit-Length L and C for a Coaxial Line  A coaxial line has per-unit-length parameters L = 500 nH/m and C = 50 pF/m. Compute the characteristic impedance Z0.

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Introduction / Context: For a lossless (or low-loss) transmission line, the characteristic impedance Z0 depends on its per-unit-length inductance L and capacitance C. Given Data / Assumptions: L = 500 nH/m = 500 × 10^-9 H/m C = 50 pF/m = 50 × 10^-12 F/m Line is treated as lossless for Z0 calculation. Concept / Approach: For a lossless line, Z0 = sqrt(L / C). We will compute this directly using the given values. Step-by-Step Solution: 1) Form the ratio L / C = (500 × 10^-9) / (50 × 10^-12) = (500/50) × 10^3 = 10 × 10^3 = 10^4.2) Take square root: Z0 = sqrt(10^4) = 100 Ω.3) Therefore, the characteristic impedance is 100 ohms. Verification / Alternative check: Dimensional check: sqrt(H/F) has units of ohms. Numerical value agrees with typical coax impedances when L/C ratio is 10^4. Why Other Options Are Wrong: 500 Ω, 250 Ω, 50 Ω, and 75 Ω do not satisfy Z0 = sqrt(L/C) for the supplied numbers. Common Pitfalls: Arithmetic slips with scientific notation; forgetting that Z0 depends on the ratio L/C, not on frequency for the ideal lossless case. Final Answer: 100 Ω.

Question 9

Assertion (A): A half-wavelength (λ/2) transmission line section can be used as a 1:1 transformer to present the load directly at the input. Reason (R): For a lossless line, the input impedance of a half-wavelength section equals the load impedance …

Accepted Answer

Introduction: Transmission-line sections are often used as impedance transformers. A special case is a half-wavelength (λ/2) section, which repeats impedances seen at its load end. This question checks whether λ/2 can act as a 1:1 transformer and why. Given Data / Assumptions: Lossless or low-loss uniform line Electrical length = λ/2 at the frequency of interest Characteristic impedance Z0 is real Concept / Approach: The general input impedance of a line is Z_in = Z0 * (Z_L + j Z0 tan(βl)) / (Z0 + j Z_L tan(βl)). For l = λ/2, βl = π, and tan(π) = 0, simplifying Z_in to Z_L. Hence, a λ/2 line repeats the load impedance at its input, acting as a 1:1 transformer. Step-by-Step Solution: 1) Start from Z_in formula with l = λ/2 → tan(βl) = 0.2) Substitute to get Z_in = Z0 * (Z_L + 0) / (Z0 + 0) = Z_L.3) Therefore, the line presents the load directly: it behaves as a 1:1 transformer.4) Assertion (A) is true; Reason (R) correctly states the mechanism (impedance repetition every λ/2). Verification / Alternative check: On a Smith chart, a λ/2 rotation returns any impedance point to itself, confirming Z_in = Z_L at λ/2. Why Other Options Are Wrong: B: R is the correct causal explanation, not incidental. C: R is not wrong; it is the core principle. D: A is not wrong; λ/2 repetition is standard theory. Common Pitfalls: Applying λ/2 behavior off-frequency (where electrical length ≠ λ/2); ignoring losses which slightly perturb equality in real lines. Final Answer: Both A and R are correct and R is correct explanation of A

Question 10

Consider the following statements about RF/microwave attenuators: 1) A dissipative attenuator has a fixed value of attenuation. 2) A reflective attenuator has a fixed value of attenuation. 3) Both dissipative and reflective attenuators are available…

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Introduction: Attenuators reduce signal power by a known amount. They can be dissipative (absorptive) or reflective (using controlled reflection). The question tests knowledge of whether these attenuators are limited to fixed attenuation or may be variable. Given Data / Assumptions: Dissipative attenuators use resistive networks or PIN-diode/RFIC absorptive elements. Reflective attenuators vary mismatch to control returned vs delivered power. Commercial parts exist in fixed pads and variable/step forms. Concept / Approach: Dissipative attenuators are available as fixed pads (e.g., 3 dB, 6 dB) and as variable/step attenuators using PIN/FET elements. Reflective attenuators (e.g., shunt PIN diode bridges) can also provide continuously variable or step attenuation by changing bias, not just fixed values. Step-by-Step Solution: 1) Statement 1 claims dissipative is fixed: incorrect—variable and step types exist.2) Statement 2 claims reflective is fixed: incorrect—bias-tunable reflection enables variable attenuation.3) Statement 3 generalizes both as only fixed: incorrect.4) Statement 4 correctly states both come in fixed or variable versions → correct. Verification / Alternative check: Catalogs show fixed pads (X dB) and step/continuous attenuators in both absorptive and reflective designs. Why Other Options Are Wrong: A/B/C: Each includes false claims that attenuation must be fixed. Common Pitfalls: Confusing reflective attenuators with isolators; assuming only pad-style attenuators exist. Final Answer: 4 only

Question 11

Consider the following statements about electron bunching in klystron devices: 1) Bunching of electrons occurs in a two-cavity klystron amplifier. 2) Bunching of electrons occurs in a multi-cavity klystron amplifier. 3) Bunching of electrons occurs …

Accepted Answer

Introduction: Electron bunching, the grouping of electrons into density-modulated packets, is central to klystron operation. The question asks in which klystron types bunching occurs. Given Data / Assumptions: Devices considered: two-cavity klystron amplifier, multi-cavity klystron amplifier, reflex klystron oscillator. Bunching forms after initial velocity modulation by an RF gap. Concept / Approach: In two-cavity and multi-cavity klystron amplifiers, the buncher gap imposes velocity modulation; in the drift region, faster electrons catch slower ones, creating bunches that deliver energy to the catcher/output cavities. In reflex klystrons, a single cavity and a negatively biased repeller create a round-trip path that sets the transit time for electrons to return bunched and reinforce oscillations. Step-by-Step Solution: 1) Two-cavity amplifier: buncher → drift → bunching → catcher (true).2) Multi-cavity amplifier: same principle with added intermediate cavities for higher gain (true).3) Reflex klystron: repeller timing causes bunching before electrons re-enter the gap (true).4) Therefore, all three statements are correct. Verification / Alternative check: Standard klystron block diagrams and reflex-klystron timing diagrams show density modulation and bunch formation explicitly. Why Other Options Are Wrong: A/C/D: Each omits at least one true case where bunching occurs, contradicting device physics. Common Pitfalls: Confusing velocity modulation with current modulation; assuming oscillators do not use bunching. Final Answer: 1, 2 and 3 only

Question 12

A coaxial RF cable has characteristic impedance Z0 = 50 Ω and capacitance per unit length C = 40 pF/m. Calculate the inductance per unit length L (in μH/m).

Accepted Answer

Introduction: In a lossless transmission line, the characteristic impedance relates inductance and capacitance per unit length. This problem applies the fundamental formula to compute L given Z0 and C for a coaxial cable. Given Data / Assumptions: Z0 = 50 Ω C = 40 pF/m = 40 * 10^-12 F/m Assume lossless line so Z0 = sqrt(L / C) Concept / Approach: For a lossless line, Z0 = sqrt(L / C). Rearranging gives L = Z0^2 * C. Convert units carefully so the final L is expressed in μH/m. Step-by-Step Solution: 1) Use L = Z0^2 * C.2) Compute Z0^2 = 50^2 = 2500.3) Multiply by C: 2500 * 40 * 10^-12 = 100000 * 10^-12 H/m.4) Simplify: 100000 * 10^-12 H/m = 1 * 10^-7 H/m.5) Convert to μH/m: 1 * 10^-7 H/m = 0.1 μH/m. Verification / Alternative check: Dimensional check: Ω = sqrt(H/F); squaring Ω gives H/F; multiplying by F returns H, confirming unit consistency. Why Other Options Are Wrong: A (1 μH/m): 10 times larger than the correct computed value. B (10 μH/m): off by two orders of magnitude. D (0.01 μH/m): ten times smaller than correct. Common Pitfalls: Forgetting to square Z0; mishandling pico to base unit conversions; mixing nH and μH scales. Final Answer: 0.1 μH/m

Question 13

Statement: The noise figure of a multi-cavity klystron amplifier is very low. Choose the correct truth value.

Accepted Answer

Introduction: Noise figure (NF) describes how much an amplifier degrades the signal-to-noise ratio. Understanding typical NF values for vacuum-electronic RF power devices such as klystrons is important in receiver front-end design and link budgets. Given Data / Assumptions: Device: multi-cavity klystron amplifier Operating region: RF/microwave power amplification Comparison: low-noise front-end devices vs high-power devices Concept / Approach: Klystron amplifiers are primarily power devices with high gain and efficiency for transmit chains. They are not used as low-noise front ends; their noise figures are comparatively high (often many dB above specialized LNAs). Thus the statement claiming “very low” NF is incorrect. Step-by-Step Discussion: 1) Low-noise applications typically use LNAs (e.g., GaAs/HEMT) or cryogenic devices, not klystrons.2) Multi-cavity klystrons deliver power/gain but introduce significant noise relative to state-of-the-art LNAs.3) Therefore, asserting a “very low” NF is false. Verification / Alternative check: Transmitter line-ups place klystrons after the exciter; receivers avoid klystrons in the first stage precisely due to noise. Why Other Options Are Wrong: True: contradicts common usage and measured NF performance of klystron power amplifiers. Common Pitfalls: Confusing high gain/efficiency with low noise; assuming all vacuum devices have inherently low noise. Final Answer: False

Question 14

Which one of the following is NOT a negative-resistance microwave device?

Accepted Answer

Introduction: Negative-resistance devices can sustain oscillations or provide gain by exhibiting a region where current decreases as voltage increases. Identifying which devices exhibit negative resistance is foundational in microwave electronics. Given Data / Assumptions: Candidate devices: Gunn, Tunnel, IMPATT, Varactor diodes Context: microwave generation/amplification vs reactive tuning Concept / Approach: Gunn and IMPATT diodes are classic negative-resistance sources for microwave oscillators and amplifiers. Tunnel diodes exhibit negative differential resistance due to quantum tunneling in their I–V curve. Varactors, by contrast, are voltage-dependent capacitors used for tuning and frequency multiplication; they do not operate via negative resistance in normal use. Step-by-Step Reasoning: 1) Gunn diode: transferred-electron effect → negative resistance (true).2) Tunnel diode: tunneling peak and valley currents → negative differential resistance (true).3) IMPATT diode: impact ionization and transit-time effects → negative resistance at microwave frequencies (true).4) Varactor diode: provides nonlinear capacitance, not negative resistance (not a negative-resistance device). Verification / Alternative check: Small-signal models: varactor shows C(V) with series R but no negative-resistance region; others have negative differential resistance ranges. Why Other Options Are Wrong: A/B/C: Each is a well-known negative-resistance device used for oscillation/amplification. Common Pitfalls: Equating nonlinearity with negative resistance; assuming all “special diodes” share the same property. Final Answer: Varactor diode

Question 15

If a finite (short) transmission line is terminated in its characteristic impedance Z0, it behaves as if it were infinitely long (no reflections are observed). Choose the correct truth value.

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Introduction: A key matching condition in transmission-line theory is Z_L = Z0. When this condition holds, reflections vanish and the line appears to the source as if it continued indefinitely. This item tests understanding of that principle. Given Data / Assumptions: Uniform line with characteristic impedance Z0 Load Z_L = Z0 (perfect match) Finite physical length Concept / Approach: The load reflection coefficient Γ_L = (Z_L − Z0) / (Z_L + Z0). For Z_L = Z0, Γ_L = 0, so no reflected wave exists. Without reflections, standing waves do not form and the input impedance equals Z0 regardless of line length, mimicking an infinite line extension. Step-by-Step Reasoning: 1) Set Z_L = Z0 → Γ_L = 0.2) With no reflected wave, voltage/current are purely traveling waves.3) The input impedance Z_in = Z0 for any length.4) The source cannot distinguish between a matched finite section and an infinitely long matched line. Verification / Alternative check: On the Smith chart, the match point is the chart center; rotation (changing length) keeps you at center (Z0). Why Other Options Are Wrong: False: Contradicts the definition of perfect matching (Γ = 0). Common Pitfalls: Assuming physical length must be infinite; confusing loss-induced damping with reflection-free matching. Final Answer: True

Question 16

Determine whether the traveling wave v(x, t) = E_m cos(βx − ωt) represents a backward wave or not. Statement: The wave E_m cos(βx − ωt) is a backward wave.

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Introduction: The direction of travel of a sinusoidal wave is inferred from the sign convention in its phase. Recognizing forward versus backward waves is fundamental in electromagnetics and transmission-line analysis. Given Data / Assumptions: Waveform: v(x,t) = E_m cos(βx − ωt) β > 0, ω > 0 Medium is uniform Concept / Approach: For a phasor with phase ψ = βx − ωt, setting ψ = constant gives βx − ωt = constant → x = (ω/β) t + constant/β, which increases with time. Hence the phase front moves in +x direction: a forward wave. A backward wave traveling toward −x would have phase βx + ωt (or equivalently cos(ωt + φ + βx)). Step-by-Step Reasoning: 1) Take βx − ωt = C → x(t) = (ω/β) t + C/β.2) Since ω/β > 0, x increases with t → motion toward +x.3) Therefore, v(x,t) represents a forward wave, not a backward wave. Verification / Alternative check: Equivalently, write v(x,t) = Re{E_m e^{j(βx − ωt)}}; the sign convention with −ωt and +βx indicates +x propagation. Why Other Options Are Wrong: True: would require βx + ωt for backward travel in this convention. Common Pitfalls: Mixing time-domain and phasor sign conventions; assuming any “−ωt” implies backward propagation. Final Answer: False

Question 17

In circular waveguides, which mode has the lowest cutoff frequency (i.e., is the dominant mode)?

Accepted Answer

Introduction: Waveguides support discrete modes with specific cutoff frequencies. The mode with the lowest cutoff is called dominant and determines basic design and bandwidth considerations. This question asks for the dominant mode in a circular waveguide. Given Data / Assumptions: Geometry: circular metallic waveguide of radius a Mode families: TE_nm and TM_nm with Bessel-function roots determining cutoff Concept / Approach: The cutoff frequency f_c for TE_nm/TM_nm modes in a circular guide is proportional to the corresponding Bessel-function root divided by radius a. The smallest root among propagating modes corresponds to TE11, making it the dominant mode in circular waveguides (analogous to TE10 dominance in rectangular guides). Step-by-Step Reasoning: 1) Compare normalized roots: TE11 has the smallest cutoff parameter among common modes.2) Therefore, TE11 achieves the lowest f_c for a given radius.3) Hence TE11 is dominant in circular guides. Verification / Alternative check: Standard tables show TE11 cutoff parameter (approximately 1.841/a for k_c) lower than other TE/TM modes. Why Other Options Are Wrong: A/C/D: Their cutoff parameters are larger than that of TE11, so they require higher frequencies to propagate. Common Pitfalls: Confusing rectangular (TE10) dominance with circular; mixing TE01 (often used for low-loss bends) with dominant status. Final Answer: TE11

Question 18

A TV allocation has a total available spectrum of approximately 300 MHz. Assuming standard 6 MHz channel spacing, the number of TV channels that can be accommodated is approximately:

Accepted Answer

Introduction: Broadcast allocations divide spectrum into fixed-width channels. Estimating the number of channels from a total bandwidth is a straightforward bandwidth-division calculation used in spectrum planning. Given Data / Assumptions: Total spectrum ≈ 300 MHz Per-channel bandwidth ≈ 6 MHz Guard bands and practical constraints are neglected for a rough estimate Concept / Approach: The approximate number of channels equals total bandwidth divided by per-channel bandwidth. For rough planning and exam problems, guard bands are often ignored unless specified. Step-by-Step Solution: 1) Use count = Total_BW / Channel_BW.2) Substitute: 300 MHz / 6 MHz = 50.3) Therefore, about 50 TV channels can be accommodated. Verification / Alternative check: If small guard bands are included, the practical number may be slightly lower, but 50 remains the standard back-of-the-envelope figure for 300 MHz at 6 MHz spacing. Why Other Options Are Wrong: A/B: 5 or 10 would imply much larger channel bandwidths or very little spectrum. D: 200 would require channels of ~1.5 MHz, not typical for analog/ATSC-like allocations. Common Pitfalls: Mixing regional standards (e.g., 7/8 MHz in some countries) without being told; forgetting to keep units consistent. Final Answer: 50

Question 19

In a multi-cavity klystron amplifier, does the RF signal to be amplified create an alternating (AC) gap voltage at the signal frequency across the buncher cavity? (Assume standard klystron operation with input coupling into the buncher.)

Accepted Answer

Introduction: Klystron amplifiers use velocity modulation and subsequent bunching of an electron beam to achieve RF amplification. The buncher cavity is where the incoming RF signal is coupled to the beam. This question checks whether you understand that the applied signal appears as an alternating gap voltage across the buncher cavity, initiating velocity modulation. Given Data / Assumptions: Multi-cavity klystron amplifier with at least a buncher and a catcher (output) cavity. Small-signal, steady-state RF excitation at the input port. Normal operating bias on the electron gun and beam transport through drift spaces. Concept / Approach: The incoming RF power is coupled into the buncher cavity so that an AC electric field exists across its gap. Electrons traversing this gap experience time-varying acceleration or deceleration, producing velocity modulation. In the subsequent drift region, faster electrons catch up with slower ones, forming density bunches. These bunches then excite RF fields in the output (catcher) cavity, transferring kinetic energy to the RF signal and providing gain. Step-by-Step Solution: 1) Apply RF drive to the buncher cavity input coupler.2) An AC gap voltage at the drive frequency is established across the buncher gap.3) Electrons crossing the gap are velocity-modulated by this AC field.4) In the drift region, velocity modulation converts to density modulation (bunching).5) Bunched beam induces RF power in the catcher cavity, yielding amplification. Verification / Alternative check: Small-signal klystron theory shows that the induced RF voltage in the buncher is proportional to the applied drive; without an AC gap voltage there is no velocity modulation and therefore no gain. Why Other Options Are Wrong: False (and variants): contradicts fundamental klystron operation where the buncher must have an RF electric field. “Only at very low frequencies” or “only when over-coupled”: coupling conditions and frequency affect efficiency/bandwidth, not the existence of the AC gap voltage itself. Common Pitfalls: Confusing DC focusing/beam acceleration with the RF gap field. The buncher has both: DC beam acceleration elsewhere and a superimposed RF field across its gap from the drive. Final Answer: True

Question 20

In a coaxial cable under TEM operation, which statement correctly describes the orientations of the electric (E) and magnetic (H) field lines? (Assume an ideal, uniform coax with inner conductor, dielectric, and outer conductor.)

Accepted Answer

Introduction: Coaxial cables support a transverse electromagnetic (TEM) mode in which the electric and magnetic fields are entirely transverse to the direction of propagation. Recognizing the geometry of E and H field lines in a coax is essential for understanding impedance, shielding, and power flow. Given Data / Assumptions: Ideal, uniform coaxial line with inner and outer conductors and homogeneous dielectric. Steady-state sinusoidal TEM propagation along the cable axis. No higher-order modes excited (below cutoff for non-TEM modes). Concept / Approach: In a coax, the electric field originates on the inner conductor and terminates on the inner surface of the outer conductor. Therefore, E lines are radial (pointing from inner to outer conductor). The magnetic field encircles the current flowing along the center conductor (and returns on the outer conductor’s inner surface), so H lines form concentric circles around the axis consistent with the right-hand rule. Power flows axially, with the Poynting vector S = E × H directed along the cable. Step-by-Step Solution: 1) Identify conductor geometry: cylindrical symmetry around the axis.2) Apply boundary conditions: tangential E is zero on perfect conductors; normal E terminates on charges → E is radial.3) Use Ampere’s law: magnetic field encircles current → H is circumferential (azimuthal).4) Confirm TEM: both E and H are transverse to the axis; no longitudinal components in the ideal case. Verification / Alternative check: Compute line impedance Z0 ≈ (60 / sqrt(εr)) * ln(b/a) for coax of inner radius a and outer radius b, derived from radial E and circular H distributions. Why Other Options Are Wrong: Option b: swaps the roles of E and H. Option c: contradicts TEM field structure in coax. Option d: current direction flips H circulation but not field geometry (still circular), and E remains radial. Option e: E is not circular in coax; it is radial. Common Pitfalls: Confusing the right-hand rule’s sense of H with its geometry; direction reverses with current but the circular shape remains. Final Answer: The radial lines are E lines and the circular lines are H lines

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