Q: Assertion–Reason (Impedance Matching with Stubs): Impedance matching on a transmission line can be achieved using reactive stubs. Reason: A double-stub tuner is specifically used for impedance matching when the signal frequency varies widely.

Introduction: Single- and double-stub tuners are classic tools for impedance matching on RF transmission lines. This question asks whether stubs accomplish matching and whether double-stub tuners are the solution for signals with varying frequency. Given Data / Assumptions: Lossless or low-loss lines for conceptual clarity. Reactive stubs (short- or open-circuited) provide controllable susceptance/ reactance. Double-stub tuners allow position-fixed matching using two adjustable stubs at specified spacings. Concept / Approach: Stubs can transform impedances by adding a controlled reactive element that cancels the load’s reactive part and transforms the resistive part to match Z0. A double-stub arrangement is helpful when the load position is not adjustable or unknown; however, like most lumped/distributed matching networks, a double-stub solution is inherently narrowband. It is not “specifically for varying frequency”; instead, it enables matching at a chosen frequency (or narrow band) when the stub locations are constrained. Step-by-Step Solution: 1) Confirm A: Reactive stubs introduce susceptance to cancel load reactance and transform resistance → matching is achievable.2) Evaluate R: Double-stub tuning addresses positional constraints and realizability, not wide frequency variation.3) Conclude: A is true; R is false. Verification / Alternative check: Smith-chart constructions show single-stub solutions at specific positions; adding a second stub relaxes position constraints while remaining frequency-sensitive. Why Other Options Are Wrong: Options a, b: misstate the explanatory role of R. Option d: claims A is wrong, contradicting standard practice. Option e: both are not wrong; A is correct. Common Pitfalls: Assuming “more stubs = broadband.” Broadband behavior requires multi-section transformers or wideband networks, not simply adding a second narrowband stub. Final Answer: A is correct but R is wrong

Q: A waveguide field with nonzero axial magnetic field component Hz described by Hz = C * cos(Bx) * cos(Ay) indicates which class of modes? (Assume standard rectangular waveguide mode definitions and boundary conditions.)

Introduction: In rectangular waveguides, modes are categorized as TE (transverse electric) or TM (transverse magnetic) depending on whether the axial electric field Ez or the axial magnetic field Hz is zero. Recognizing which axial component exists identifies the mode family. Given Data / Assumptions: Rectangular waveguide with conducting walls and standard boundary conditions. Field expression includes a nonzero Hz = C * cos(Bx) * cos(Ay). No claim that Ez is present; only Hz is explicitly nonzero. Concept / Approach: By definition: TE modes have Ez = 0 and generally Hz ≠ 0; TM modes have Hz = 0 and Ez ≠ 0. Therefore, the presence of a nonzero axial magnetic field (Hz) directly indicates a TE mode. The specific cosine dependence in x and y (with separation constants A and B) is consistent with standing field patterns that satisfy wall boundary conditions for a TEmn mode. Step-by-Step Solution: 1) Examine axial components: Hz is explicitly nonzero.2) Apply mode definitions: TE ⇒ Ez = 0, Hz may be nonzero; TM ⇒ Hz = 0.3) Conclude the field belongs to the TE family. Verification / Alternative check: Solving Maxwell’s equations with conducting boundary conditions yields families TEmn and TMmn. For TE, the scalar potential solution is typically cast in terms of Hz; for TM, it is cast in terms of Ez. The given form matches the TE formulation. Why Other Options Are Wrong: TM waves: would require Hz = 0, contradicting the given. Both / Some of each: a single field solution cannot simultaneously satisfy both Ez = 0 and Hz = 0 unless trivial; mode families are distinct. TEM in rectangular guides: not supported below cutoff because waveguides do not sustain a true TEM mode without a return path like in coax. Common Pitfalls: Confusing which component is zero for TE vs TM. Remember: “TE → Transverse Electric → Ez = 0.” Final Answer: TE waves

Q: Assertion–Reason (Klystron Bandwidth Enhancement): Klystron amplifiers often include one or more intermediate cavities in addition to the buncher and catcher. Reason: Adding intermediate cavities can increase the achievable bandwidth (and gain flatn…

Introduction: Multi-cavity klystron amplifiers use additional resonators beyond the basic buncher and catcher to tailor gain, efficiency, and bandwidth. This item checks whether you know the purpose of intermediate cavities. Given Data / Assumptions: Bunched electron beam interacts with multiple tuned cavities. Intermediate cavities can be tuned at or staggered around the center frequency. Design target includes bandwidth and gain flatness over a specified range. Concept / Approach: Intermediate cavities manipulate the phasing and amplitude of the beam’s RF current harmonics as the bunching evolves, thereby shaping the overall transfer function. By judicious tuning (including stagger-tuning), designers can broaden the 3 dB bandwidth and smooth the gain response compared to a simple two-cavity configuration. Step-by-Step Solution: 1) Start with two-cavity operation: limited bandwidth caused by the sharp resonance of the catcher and buncher.2) Insert one or more intermediate cavities with appropriate coupling and Q.3) Tune these cavities (possibly stagger-tuned) to extend the composite passband.4) Result: improved bandwidth and gain flatness, often at some cost in peak gain or efficiency trade-offs. Verification / Alternative check: Small-signal models show the amplifier’s gain proportional to the RF beam current at the catcher; intermediate cavities adjust the beam current spectrum across frequency, broadening the response. Why Other Options Are Wrong: Options b–e deny either the assertion or the causal explanation, contradicting standard multi-cavity design practice. Common Pitfalls: Assuming more cavities always increase gain without trade-offs. Practical designs balance Q, coupling, stability, and efficiency. Final Answer: Both A and R are correct and R is the correct explanation of A

Question 1

Which microwave device employs internal positive feedback to sustain oscillations through electron bunching and reflection? (Assume standard device configurations and biasing.)

Accepted Answer

Introduction: Positive feedback is a defining feature of oscillators: part of the output is fed back in phase to sustain a self-excited RF signal. In microwave tubes, different mechanisms produce or avoid feedback. This item asks you to identify which device uses internal positive feedback by design. Given Data / Assumptions: Standard two-cavity and multi-cavity klystrons are configured as amplifiers with external input drive. A reflex klystron uses a single resonant cavity and a repeller electrode. We consider normal bias and operating modes. Concept / Approach: The reflex klystron is an oscillator. Electrons are accelerated toward a cavity, pass through its gap, and are then turned back by a negatively biased repeller. Proper repeller voltage and transit time cause bunched electrons to return to the cavity gap in phase with the RF field, reinforcing it. This constitutes internal positive feedback. By contrast, two-cavity and multi-cavity klystrons are amplifiers; they rely on an external RF input and do not intentionally create the regenerative loop necessary for self-oscillation. Step-by-Step Solution: 1) Identify devices that are oscillators versus amplifiers.2) Note that the reflex klystron’s repeller establishes an internal feedback path via electron transit timing.3) Conclude that only the reflex klystron employs inherent positive feedback for sustained oscillation. Verification / Alternative check: Operationally, the reflex klystron can start from noise and build RF amplitude without an external signal, a hallmark of regenerative feedback oscillators. Why Other Options Are Wrong: Two-cavity and multi-cavity klystron amplifiers: designed for gain with external drive; feedback is minimized to avoid oscillation. TWT with helix: distributed interaction amplifier; typically not a self-oscillator without additional feedback. “All of the above”: incorrect because only the reflex klystron is inherently regenerative. Common Pitfalls: Assuming any device with bunching “has feedback.” Bunching alone does not imply the regenerative loop required for oscillation. Final Answer: Reflex klystron (oscillator)

Question 2

Assertion–Reason (Transmission/Guided Waves): The phase velocity of electromagnetic waves on overhead lines and on coaxial cables is the same. Reason: Free space has an intrinsic impedance of 377 Ω.

Accepted Answer

Introduction: Assertion–Reason questions test conceptual linkage. Here, we compare phase velocity on different transmission media and evaluate a statement about the free-space intrinsic impedance to see whether it explains the assertion. Given Data / Assumptions: Overhead lines are largely surrounded by air (effective relative permittivity εr ≈ 1), so v ≈ c / sqrt(εeff) ≈ c. Coaxial cables use a dielectric (e.g., polyethylene with εr ≈ 2.25 to 2.3), so v ≈ c / sqrt(εr) < c. Free space intrinsic impedance η0 ≈ 377 Ω is a material property defined by sqrt(μ0 / ε0). Concept / Approach: Phase velocity on a transmission line is determined by effective permittivity and permeability of the medium guiding the fields: v = 1 / sqrt(L′C′) = c / sqrt(εeff μeff). Overhead lines mainly see air, while coax fields reside within a dielectric. Therefore, velocities are generally not equal. The reason statement about η0 = 377 Ω is true but unrelated to whether two guided structures have the same phase velocity. Step-by-Step Solution: 1) Evaluate Assertion A: v_overhead ≈ c; v_coax ≈ c / sqrt(εr) → smaller; hence A is false.2) Evaluate Reason R: η0 = 377 Ω is a correct constant of free space.3) Check explanation link: R does not explain A, since η0 does not enforce equal velocities on different dielectrics. Verification / Alternative check: Typical coaxial velocity factor ≈ 0.66 for solid polyethylene and ≈ 0.8–0.9 for foam dielectrics; overhead line velocity factor ≈ 1. Why Other Options Are Wrong: Options a, b, c: all assume A is correct, which it is not. Option e: R is true; thus “both wrong” is incorrect. Common Pitfalls: Confusing impedance with velocity: η and v involve ε and μ differently; equal impedances or a known η0 value do not imply equal phase velocities in dielectrics. Final Answer: A is wrong but R is correct

Question 3

Assertion–Reason (Impedance Matching with Stubs): Impedance matching on a transmission line can be achieved using reactive stubs. Reason: A double-stub tuner is specifically used for impedance matching when the signal frequency varies widely.

Accepted Answer

Introduction: Single- and double-stub tuners are classic tools for impedance matching on RF transmission lines. This question asks whether stubs accomplish matching and whether double-stub tuners are the solution for signals with varying frequency. Given Data / Assumptions: Lossless or low-loss lines for conceptual clarity. Reactive stubs (short- or open-circuited) provide controllable susceptance/ reactance. Double-stub tuners allow position-fixed matching using two adjustable stubs at specified spacings. Concept / Approach: Stubs can transform impedances by adding a controlled reactive element that cancels the load’s reactive part and transforms the resistive part to match Z0. A double-stub arrangement is helpful when the load position is not adjustable or unknown; however, like most lumped/distributed matching networks, a double-stub solution is inherently narrowband. It is not “specifically for varying frequency”; instead, it enables matching at a chosen frequency (or narrow band) when the stub locations are constrained. Step-by-Step Solution: 1) Confirm A: Reactive stubs introduce susceptance to cancel load reactance and transform resistance → matching is achievable.2) Evaluate R: Double-stub tuning addresses positional constraints and realizability, not wide frequency variation.3) Conclude: A is true; R is false. Verification / Alternative check: Smith-chart constructions show single-stub solutions at specific positions; adding a second stub relaxes position constraints while remaining frequency-sensitive. Why Other Options Are Wrong: Options a, b: misstate the explanatory role of R. Option d: claims A is wrong, contradicting standard practice. Option e: both are not wrong; A is correct. Common Pitfalls: Assuming “more stubs = broadband.” Broadband behavior requires multi-section transformers or wideband networks, not simply adding a second narrowband stub. Final Answer: A is correct but R is wrong

Question 4

Atomic and molecular resonance absorption occurs predominantly at which part of the electromagnetic spectrum? (Think of rotational and some vibrational transitions in matter.)

Accepted Answer

Introduction: Different materials exhibit resonant absorption at specific electromagnetic frequencies corresponding to physical processes such as electronic transitions, molecular rotations, and vibrations. This question focuses on where atomic and molecular resonances commonly appear for rotational modes and some vibrational modes relevant to matter–radiation interaction. Given Data / Assumptions: Matter exhibits quantized energy levels for rotation and vibration. Rotational transitions typically lie in the microwave region; certain vibrational overtones extend into millimeter-wave/infrared. Macroscopic conductors at audio/AM frequencies primarily exhibit conduction and polarization losses, not discrete quantum resonances. Concept / Approach: Rotational energy levels of many molecules (e.g., water vapor, oxygen) have spacings corresponding to microwave wavelengths. Thus, microwave radiation efficiently couples to these transitions, producing strong resonance absorption and dispersion. While electronic transitions dominate the visible/UV and fundamental vibrational transitions lie in the infrared, the signature molecular rotational spectra are characteristic of the microwave band. Step-by-Step Solution: 1) Identify the physical mechanism: rotational transitions in molecules.2) Map energy spacings to frequency: rotational spectra → microwave; vibrational fundamentals → infrared (with some interaction near mm-wave).3) Conclude that pronounced atomic/molecular resonance of this type is observed at microwave frequencies. Verification / Alternative check: Atmospheric attenuation peaks near 22 GHz (water vapor) and 60 GHz (oxygen) are practical demonstrations of molecular resonance effects in the microwave/mm-wave region. Why Other Options Are Wrong: Very low or AM broadcast frequencies: energies are too small for discrete rotational/vibrational transitions. Visible band only: primarily electronic transitions, not rotational spectra. Common Pitfalls: Assuming all resonances are optical. In RF planning, microwave molecular resonances drive link budgeting due to atmospheric absorption not present at LF/MF. Final Answer: at microwave frequencies

Question 5

A waveguide field with nonzero axial magnetic field component Hz described by Hz = C * cos(Bx) * cos(Ay) indicates which class of modes? (Assume standard rectangular waveguide mode definitions and boundary conditions.)

Accepted Answer

Introduction: In rectangular waveguides, modes are categorized as TE (transverse electric) or TM (transverse magnetic) depending on whether the axial electric field Ez or the axial magnetic field Hz is zero. Recognizing which axial component exists identifies the mode family. Given Data / Assumptions: Rectangular waveguide with conducting walls and standard boundary conditions. Field expression includes a nonzero Hz = C * cos(Bx) * cos(Ay). No claim that Ez is present; only Hz is explicitly nonzero. Concept / Approach: By definition: TE modes have Ez = 0 and generally Hz ≠ 0; TM modes have Hz = 0 and Ez ≠ 0. Therefore, the presence of a nonzero axial magnetic field (Hz) directly indicates a TE mode. The specific cosine dependence in x and y (with separation constants A and B) is consistent with standing field patterns that satisfy wall boundary conditions for a TEmn mode. Step-by-Step Solution: 1) Examine axial components: Hz is explicitly nonzero.2) Apply mode definitions: TE ⇒ Ez = 0, Hz may be nonzero; TM ⇒ Hz = 0.3) Conclude the field belongs to the TE family. Verification / Alternative check: Solving Maxwell’s equations with conducting boundary conditions yields families TEmn and TMmn. For TE, the scalar potential solution is typically cast in terms of Hz; for TM, it is cast in terms of Ez. The given form matches the TE formulation. Why Other Options Are Wrong: TM waves: would require Hz = 0, contradicting the given. Both / Some of each: a single field solution cannot simultaneously satisfy both Ez = 0 and Hz = 0 unless trivial; mode families are distinct. TEM in rectangular guides: not supported below cutoff because waveguides do not sustain a true TEM mode without a return path like in coax. Common Pitfalls: Confusing which component is zero for TE vs TM. Remember: “TE → Transverse Electric → Ez = 0.” Final Answer: TE waves

Question 6

Assertion–Reason (Klystron Bandwidth Enhancement): Klystron amplifiers often include one or more intermediate cavities in addition to the buncher and catcher. Reason: Adding intermediate cavities can increase the achievable bandwidth (and gain flatn…

Accepted Answer

Introduction: Multi-cavity klystron amplifiers use additional resonators beyond the basic buncher and catcher to tailor gain, efficiency, and bandwidth. This item checks whether you know the purpose of intermediate cavities. Given Data / Assumptions: Bunched electron beam interacts with multiple tuned cavities. Intermediate cavities can be tuned at or staggered around the center frequency. Design target includes bandwidth and gain flatness over a specified range. Concept / Approach: Intermediate cavities manipulate the phasing and amplitude of the beam’s RF current harmonics as the bunching evolves, thereby shaping the overall transfer function. By judicious tuning (including stagger-tuning), designers can broaden the 3 dB bandwidth and smooth the gain response compared to a simple two-cavity configuration. Step-by-Step Solution: 1) Start with two-cavity operation: limited bandwidth caused by the sharp resonance of the catcher and buncher.2) Insert one or more intermediate cavities with appropriate coupling and Q.3) Tune these cavities (possibly stagger-tuned) to extend the composite passband.4) Result: improved bandwidth and gain flatness, often at some cost in peak gain or efficiency trade-offs. Verification / Alternative check: Small-signal models show the amplifier’s gain proportional to the RF beam current at the catcher; intermediate cavities adjust the beam current spectrum across frequency, broadening the response. Why Other Options Are Wrong: Options b–e deny either the assertion or the causal explanation, contradicting standard multi-cavity design practice. Common Pitfalls: Assuming more cavities always increase gain without trade-offs. Practical designs balance Q, coupling, stability, and efficiency. Final Answer: Both A and R are correct and R is the correct explanation of A

Question 7

In microwave and RF switching applications, which semiconductor diode type is most commonly used as a high-isolation, low-loss switch (controlled by bias current) over a broad GHz range?

Accepted Answer

Introduction / Context: Pulsed radar front ends, T/R modules, and microwave test equipment often require electronically controlled RF switches with low insertion loss, high isolation, and wide bandwidth. The device most widely used for this function is the PIN diode, thanks to its current-controlled RF resistance behavior. Given Data / Assumptions: Frequency of interest: microwave (GHz) range. Need: reliable switching (on/off) of RF signals. Bias control available (forward and reverse bias currents/voltages). Concept / Approach: A PIN diode has a wide intrinsic region between the p and n layers. Under forward bias, injected carriers flood the I-region and dramatically lower the RF resistance (on-state). Under reverse bias (or zero bias), carrier density drops and the RF resistance rises to a very large value (off-state). Its junction capacitance is small and nearly voltage independent over useful ranges, giving broadband performance. Step-by-Step Solution: 1) Identify the need: low-loss ON state, high-isolation OFF state at GHz.2) Map device physics to RF behavior: PIN diode's RF resistance varies strongly with DC current.3) Choose bias networks (chokes, DC blocks) to realize series or shunt switch topologies.4) Verify wideband performance due to small, stable capacitance and resistive control law. Verification / Alternative check: Measured S-parameters of PIN-diode SPST/SPDT switches show insertion loss often < 1 dB and isolation > 30–50 dB over octave bands when correctly biased and matched. Why Other Options Are Wrong: Varactor diode: Used for voltage-controlled capacitance (tuning/phase), not primary switching. Tunnel diode: Negative-resistance device used in oscillators/amplifiers, not typical RF switch. Gunn diode: Microwave oscillator in transferred-electron materials, not a switch. Schottky diode: Excellent detector/mixer/limiter, but not the standard broadband RF switch. Common Pitfalls: Confusing PIN with varactor; forgetting bias networks that isolate DC while passing RF; overlooking thermal limits at high RF power. Final Answer: PIN diode

Question 8

A transmission line has an attenuation constant of 0.054 Np/m. What is the corresponding attenuation in decibels per meter (dB/m)?

Accepted Answer

Introduction / Context: Attenuation constants for transmission lines may be reported either in nepers per unit length or decibels per unit length. Converting correctly between these units is essential for link budgets and cable length planning. Given Data / Assumptions: Attenuation α = 0.054 Np/m. Need to express attenuation in dB/m. Standard conversion: 1 Np = 8.686 dB. Concept / Approach: The conversion relies on the identity: amplitude ratio in dB = 20 * log10(e) * nepers. Since 20 * log10(e) ≈ 8.686, multiply α (in Np/m) by 8.686 to obtain dB/m. Step-by-Step Solution: 1) Note conversion factor: 1 Np = 8.686 dB.2) Compute: 0.054 Np/m * 8.686 dB/Np = 0.469044 dB/m.3) Round to two significant digits suitable for engineering use: ≈ 0.47 dB/m. Verification / Alternative check: Reverse check: 0.47 dB/m ÷ 8.686 ≈ 0.0541 Np/m, consistent with the original value. Why Other Options Are Wrong: 4.7 dB/m and 5.4 dB/m: Off by a factor of 10 or 100 relative to 0.47 dB/m. 0.54 dB/m: Not the correct product of 0.054 and 8.686. 0.0054 dB/m: Incorrect by a factor of ~100. Common Pitfalls: Using 10 * log10 instead of 20 * log10 for amplitude ratios; mixing power and field conversions; rounding too early. Final Answer: 0.47 dB/m

Question 9

In microwave engineering, what is a typical power gain of a multicavity klystron amplifier (order-of-magnitude selection)?

Accepted Answer

Introduction / Context: A multicavity klystron amplifier is a velocity-modulated vacuum device used to obtain high gain and significant output power at microwave frequencies. Understanding its typical gain helps in system cascade design and noise budgeting. Given Data / Assumptions: Device: multicavity klystron amplifier (not oscillator). Question asks for a representative power-gain magnitude. Single RF stage under proper beam voltage and drive level. Concept / Approach: Multicavity klystrons use multiple resonators (buncher, catcher, and intermediate cavities) to enhance electron bunching and energy transfer to the RF field, yielding high gain. Practical values commonly exceed 30 dB per amplifier stage. Step-by-Step Solution: 1) Recognize that each additional intermediate cavity increases bunching efficiency.2) Typical catalog data show gains ≳ 30 dB for many communications and radar-band klystron amplifiers.3) Extreme gains (≫ 60 dB) are uncommon for a single stage and usually require cascading or additional IF stages. Verification / Alternative check: System handbooks and vendor datasheets frequently list klystron amplifier gains in the 30–60 dB range depending on design; thus “more than 30 dB” is the best generic choice. Why Other Options Are Wrong: Around 3 dB / Less than 1 dB: Far too low for an active high-power microwave amplifier. Causes acceleration of some electrons and retardation of others: That describes velocity modulation physics, not a gain figure. More than 100 dB in a single stage: Unrealistic for one microwave power stage. Common Pitfalls: Confusing amplifier gain with bunching mechanism statements; assuming oscillator characteristics apply to amplifiers. Final Answer: More than 30 dB

Question 10

In microwave practice, a cavity resonator is best described as which of the following?

Accepted Answer

Introduction / Context: Cavity resonators are foundational building blocks in microwave engineering, used for filters, oscillators, frequency meters, and high-Q references. Given Data / Assumptions: Context: microwave resonators. Materials: good conductors for walls to achieve high Q. Fields: standing electromagnetic fields at discrete resonant frequencies. Concept / Approach: Metal-walled cavities trap electromagnetic energy by reflecting fields at the boundaries. Boundary conditions quantize field distributions, leading to discrete resonant modes with high quality factors when conductor and dielectric losses are low. Step-by-Step Solution: 1) Recognize the need for low loss at microwave frequencies to sustain resonance.2) Metal walls approximate perfect conductors, confining fields effectively.3) The cavity dimensions set resonant frequencies; coupling loops or irises extract energy. Verification / Alternative check: Measured S-parameters reveal sharp resonant peaks with narrow bandwidth, characterizing high-Q metal cavities. Why Other Options Are Wrong: Magnetic or purely dielectric walls alone: Not the standard high-Q microwave cavity construction. Either (b) or (c): Overgeneralization; typical cavities are metallic. Acoustic chamber: Not an RF/microwave device. Common Pitfalls: Confusing dielectric resonators (which do exist) with the definition of a metal cavity; mixing acoustic and electromagnetic resonance concepts. Final Answer: A hollow metallic enclosure that confines and resonates electromagnetic fields

Question 11

To interconnect an unbalanced coaxial line with a balanced parallel two-wire line while minimizing common-mode currents and preserving impedance, which device should be used?

Accepted Answer

Introduction / Context: Connecting coaxial (unbalanced) feeds to balanced lines or antennas requires mode conversion to prevent radiation and pattern distortion. Given Data / Assumptions: One port: coaxial line (unbalanced). Other port: parallel two-wire line (balanced). Goal: proper impedance transfer and suppression of common-mode currents. Concept / Approach: A balun converts between balanced and unbalanced modes and can also perform impedance transformation (e.g., 1:1, 4:1). It enforces equal and opposite currents on the balanced conductors, thereby mitigating feedline radiation. Step-by-Step Solution: 1) Identify mode mismatch (unbalanced vs balanced).2) Select a device that performs mode and impedance conversion: the balun.3) Implement an appropriate balun topology (transformer, transmission-line, or ferrite choke). Verification / Alternative check: Common TV twin-lead adapters and many antenna feeds use baluns to achieve clean patterns and low VSWR. Why Other Options Are Wrong: Slotted line: Measurement tool. Directional coupler: Samples power; not a mode converter. Quarter-wave transformer only: Matches impedances but does not enforce balance. Wilkinson divider: Power division with isolation resistors; not a balun. Common Pitfalls: Assuming impedance matching alone is sufficient; ignoring mode balance leads to unwanted radiation. Final Answer: Balun (balanced-to-unbalanced transformer)

Question 12

A transmission line is open-circuited at its load end. For a general (possibly lossy) line with propagation constant γ and characteristic impedance Z0, is the input impedance Z_in = Z0 * tanh(γ l)?

Accepted Answer

Introduction / Context: Transmission-line input impedances depend on termination. Knowing the correct expressions for open and short circuits prevents design mistakes in matching networks and stubs. Given Data / Assumptions: Characteristic impedance Z0. Propagation constant γ = α + jβ. Open-circuited termination (Z_L → ∞). Concept / Approach: The general input-impedance formula is Z_in = Z0 * (Z_L + Z0 tanh(γ l)) / (Z0 + Z_L tanh(γ l)). Taking the limit Z_L → ∞ gives Z_in(open) = Z0 * coth(γ l). For a short circuit (Z_L = 0), Z_in(short) = Z0 * tanh(γ l). Thus the statement equating the open-circuit input impedance to Z0 tanh(γ l) is incorrect. Step-by-Step Solution: 1) Start from Z_in = Z0 * (Z_L + Z0 tanh(γ l)) / (Z0 + Z_L tanh(γ l)).2) Let Z_L → ∞ (open circuit): numerator ≈ Z_L, denominator ≈ Z_L tanh(γ l), ratio → 1 / tanh(γ l) = coth(γ l).3) Therefore Z_in(open) = Z0 * coth(γ l), not Z0 * tanh(γ l).4) For completeness, Z_in(short) = Z0 * tanh(γ l). Verification / Alternative check: In the lossless limit (α → 0), coth(jβl) = −j cot(βl), which matches the well-known result Z_in(open) = −j Z0 cot(βl). Why Other Options Are Wrong: True / length-specific claims: Confuse open- and short-circuit formulas. Only true for lossless lines: Still wrong; even lossless case gives −j Z0 cot(βl). Common Pitfalls: Memorizing tanh for both terminations; forgetting to apply limiting forms for Z_L → ∞ and Z_L → 0. Final Answer: False

Question 13

Assertion (A): A PIN diode is used as a fast RF/microwave switch. Reason (R): A PIN diode presents very high resistance when reverse biased and very low resistance when forward biased, enabling effective on/off control.

Accepted Answer

Introduction / Context: RF front ends frequently require rapidly controllable switches for routing, protection, and T/R operation. PIN diodes are preferred because they behave like current-controlled resistors at RF, toggling between low-loss conduction and high-isolation states. Given Data / Assumptions: Operation in the RF/microwave domain. Bias networks can forward or reverse bias the diode. Switching refers to RF path control, not logic-level digital gates. Concept / Approach: The intrinsic region of a PIN diode stores charge under forward bias, reducing RF resistance strongly; under reverse bias, the stored charge is removed and RF resistance becomes very high. With proper bias drivers, switching times from microseconds down to nanoseconds are achievable depending on device and power level. Step-by-Step Solution: 1) Forward bias ⇒ high carrier density in I-region ⇒ low R_RF ⇒ ON state.2) Reverse/zero bias ⇒ depleted I-region ⇒ high R_RF ⇒ OFF state.3) Use series or shunt topologies (or both) to meet isolation and insertion-loss targets. Verification / Alternative check: Datasheets for PIN-diode switches show low insertion loss and high isolation over wide bands, with specified switching speeds meeting typical RF system needs. Why Other Options Are Wrong: R not explanatory: It directly explains why the device works as a switch. A correct but R wrong / A wrong but R correct / Both wrong: Contradict practical RF switch design and measurements. Common Pitfalls: Equating “fast” with digital nanosecond logic without considering RF power; forgetting bias network design which limits practical speed. Final Answer: Both A and R are correct and R is the correct explanation of A

Question 14

A PIN diode can be used in which of the following microwave applications?  RF switch  Attenuator  Phase shifter  Oscillator

Accepted Answer

Introduction / Context: Passive, current-controlled components are invaluable in microwave front ends. The PIN diode is one such device used for reconfigurable RF functions without active oscillation. Given Data / Assumptions: Applications listed: switch, attenuator, phase shifter, oscillator. We must decide where a PIN diode is functionally appropriate. Concept / Approach: PIN diodes act as variable resistors at RF controlled by DC current. This property enables series/shunt switching, attenuator pads (e.g., Pi/T networks), and phase shifters (e.g., switched-line or loaded-line implementations). They do not provide negative resistance and therefore are not used as the active element in oscillators. Step-by-Step Solution: 1) Switch: use low R_RF (ON) and high R_RF (OFF) states ⇒ feasible.2) Attenuator: bias to intermediate R_RF values ⇒ controllable attenuation.3) Phase shifter: switch in/out delay lines or load reactances ⇒ phase control.4) Oscillator: requires an active device or negative resistance; a PIN diode alone cannot oscillate. Verification / Alternative check: Common catalog parts are marketed specifically as PIN-diode switches, step attenuators, and phase shifters; oscillators rely on devices like Gunn, IMPATT, BJT, FET, or tunnel diodes. Why Other Options Are Wrong: Including item 4 (oscillator): Mischaracterizes the role of a PIN diode. Omitting item 3: Phase control is a standard use case. Common Pitfalls: Assuming any diode can oscillate; overlooking biasing and linearity implications in attenuator design. Final Answer: 1, 2 and 3 only

Question 15

Compared with conventional oven cooking, the typical time required for microwave cooking is

Accepted Answer

Introduction / Context: Microwave ovens heat food primarily by exciting polar molecules (notably water) with electromagnetic energy at around 2.45 GHz. Because energy deposition occurs volumetrically (though still limited by penetration depth and standing-wave patterns), cooking is faster than in conventional ovens that rely on surface heating and conduction. Given Data / Assumptions: Typical home microwave frequency: about 2.45 GHz. Comparable dish, mass, and desired doneness. Proper container and microwave-safe materials used. Concept / Approach: Conventional ovens heat mainly by hot air convection and thermal radiation, producing slower internal heating since heat must conduct inward from the surface. Microwaves deposit energy deeper inside the food (penetration depth depends on composition), shortening the time to reach target internal temperatures. Step-by-Step Solution: 1) Identify heating mechanism: dielectric heating vs convective/conductive heating.2) Recognize that volumetric absorption accelerates temperature rise in the interior.3) Benchmark rule of thumb from culinary and engineering practice: microwave cooking often takes roughly one-fourth to one-third of the conventional time for many foods.4) Select the closest option reflecting typical reduction: about one-fourth. Verification / Alternative check: Recipe comparisons and appliance manuals commonly show substantial time reductions (e.g., 25–35%) for reheating and many cooking tasks, subject to mass, geometry, and water content. Why Other Options Are Wrong: About half: Underestimates typical speed-up. About the same: Ignores volumetric heating advantage. About one-tenth: Overly optimistic; rare outside thin or small items. Slightly longer: Opposite of observed practice. Common Pitfalls: Expecting uniformity without stirring/turning; disregarding container effects and cold spots; assuming all foods scale identically. Final Answer: about one-fourth

Question 16

Waveguide hybrids – Magic-Tee properties and what is not true For the four-port magic tee (E-plane port, H-plane port, and two co-linear ports), identify the statement that is incorrect about coupling, matching, and power division behavior.

Accepted Answer

Introduction: The waveguide magic-tee (also called a hybrid tee) is a 4-port passive microwave component formed by combining an E-plane tee and an H-plane tee. It provides sum and difference behavior between the two co-linear ports and is widely used for power division/combining, mixer/antenna feeds, and bridge circuits. This question probes which commonly claimed property is not correct for a practical magic-tee. Given Data / Assumptions: Four ports: two co-linear (coplanar) main waveguide ports, one side E-arm, one side H-arm. Passive, reciprocal, lossless approximation with realistic tuning screws/irises for matching. Standard phase conventions: H-arm is the “sum” port; E-arm is the “difference” port for the two co-linear ports. Concept / Approach: In an ideal hybrid tee, the E-arm and H-arm are isolated (no coupling), while each co-linear port couples to both side arms. Exciting the H-arm yields equal-phase outputs at the co-linear ports; exciting the E-arm yields equal-magnitude outputs that are 180° out of phase. A signal entering a co-linear port divides equally into the E and H arms (with the other co-linear port isolated in the ideal S-matrix). However, due to network constraints and finite element tuning, all four ports cannot be made perfectly matched simultaneously over bandwidth; usually only a subset are critically matched and the others are near-matched with residual reflection. Step-by-Step Solution: 1) Use the hybrid tee S-matrix properties: isolation between E and H arms; symmetry between co-linear ports.2) Identify correct statements: isolation (E vs H) is true; co-linear ports couple via the hybrid; co-linear excitation splits into E/H arms; H-arm excitation gives equal-phase co-linear outputs.3) Conclude the “all ports perfectly matched” claim is not achievable in practice for broadband operation. Verification / Alternative check: Design texts show tuning elements to improve matches at selected ports; perfect 4-port broadband conjugate matching is not simultaneously realized in a passive, lossless hybrid tee. Why Other Options Are Wrong: Option A: True—E and H arms are designed to be isolated. Option B: True—co-linear ports are coupled via the junction. Option D: True in the ideal S-matrix sense for co-linear input. Option E: True—H-arm acts as the sum port producing in-phase outputs. Common Pitfalls: Assuming “perfect matching everywhere” because individual ports can be tuned near match; ignoring bandwidth and lossless reciprocity constraints. Final Answer: All four ports can be made perfectly matched simultaneously over a band.

Question 17

Radar timing – Compute the duty cycle from pulse width and PRF A pulsed radar transmits rectangular pulses of width 1 microsecond (1 μs) at a pulse repetition rate of 1000 pulses per second. What is the duty cycle (fraction of time the transmitter i…

Accepted Answer

Introduction: Duty cycle in pulsed radar quantifies how much of each second the transmitter actually radiates energy. It is vital for estimating average power, thermal loading, and receiver protection timing. The concept ties directly to pulse width and pulse repetition frequency (PRF). Given Data / Assumptions: Pulse width τ = 1 μs = 1 * 10^-6 s per pulse. PRF f_p = 1000 pulses per second. Rectangular pulses, negligible rise/fall for this calculation. Concept / Approach: Duty cycle D is the fraction of time the transmitter is on: D = τ * f_p. It is dimensionless and often expressed as a ratio or percentage. Average power equals peak power multiplied by D, so accurate D helps size power supplies and cooling systems. Step-by-Step Solution: 1) Convert units: τ = 1 μs = 1 × 10^-6 s.2) Multiply by PRF: D = 1 × 10^-6 s * 1000 s^-1 = 1 × 10^-3.3) Express as ratio or percent: D = 0.001 = 0.1%. Verification / Alternative check: Compute on a per-second basis: total “on” time per second = 1000 pulses * 1 μs = 1000 μs = 1 ms; 1 ms / 1 s = 0.001—consistent. Why Other Options Are Wrong: 0.01 and 0.1 imply 1% and 10%, which would require 10 μs or 100 μs pulses at 1 kHz. “1” would mean continuous wave (100% duty). 0.0001 corresponds to 0.01% (e.g., 0.1 μs at 1 kHz), not the given case. Common Pitfalls: Mixing μs and ms; forgetting that PRF is per second; confusing duty cycle with duty factor in decibels. Final Answer: 0.001.

Question 18

Microwave measurements – Using SWR to determine impedance Assertion (A): At microwave frequencies, the load impedance is commonly determined by measuring the standing wave ratio (SWR). Reason (R): Both SWR and the reflection coefficient depend on th…

Accepted Answer

Introduction: Direct impedance bridges become impractical at microwave frequencies because distributed effects dominate and lumped standards are difficult to realize. Instead, engineers use standing-wave measurements (SWR, minima positions) on a slotted line or a network analyzer to infer the complex reflection coefficient and thus the load impedance. Given Data / Assumptions: Lossless/low-loss transmission line segment with known characteristic impedance Z0. Measurable SWR and position of minima or phase via detector/probe or VNA. Linear, time-invariant system and steady-state single-tone excitation. Concept / Approach: SWR is related to the magnitude of the reflection coefficient Γ by SWR = (1 + |Γ|) / (1 − |Γ|). The reflection coefficient depends on ZL and Z0 via Γ = (ZL − Z0) / (ZL + Z0). Knowing |Γ| (and often its phase from minima location) allows recovery of ZL using Smith Chart or analytic inversion. Hence R explains A: because SWR and Γ depend on ZL and Z0, measuring SWR lets us determine ZL. Step-by-Step Solution: 1) Measure SWR and, if needed, the distance to the first minimum from a reference.2) Compute |Γ| from SWR.3) Determine the angle of Γ from minima position or VNA phase.4) Convert Γ to ZL using ZL = Z0 * (1 + Γ) / (1 − Γ). Verification / Alternative check: Network analyzer readings of S11 magnitude/phase directly yield Γ; Smith Chart transformation confirms the same ZL derived from SWR/minima measurements. Why Other Options Are Wrong: Options B–E deny the causal link: since Γ (and thus SWR) explicitly depends on ZL and Z0, R clearly explains A. Common Pitfalls: Using SWR alone (without phase) gives two possible impedances mirrored across the resistance axis; phase or minima position resolves ambiguity. Final Answer: Both A and R are correct and R is the correct explanation of A.

Question 19

Electron guns in linear-beam microwave tubes – Pierce gun usage Is it correct that a multi-cavity klystron amplifier generally employs a Pierce-type electron gun to form a laminar, low-emittance beam?

Accepted Answer

Introduction: The electron gun defines the initial quality of the beam in linear-beam tubes such as multi-cavity klystron amplifiers and traveling-wave tubes. The Pierce gun geometry is a widely used solution that produces a laminar electron beam with controlled convergence and low transverse velocity spread, improving efficiency and gain. Given Data / Assumptions: Linear-beam (not crossed-field) devices. Requirement for small beam interception and good coupling to RF gaps. Use of focusing elements (electrostatic and/or magnetic) along the drift region. Concept / Approach: The Pierce gun employs specific electrode shaping (e.g., 67.5° Pierce angle in planar versions) to make the equipotentials parallel to the beam near the cathode, achieving laminar flow. This minimizes beam scalloping and emittance growth before velocity modulation in the input cavity and bunching in the drift spaces. Step-by-Step Solution: 1) Start with thermionic cathode emission with space-charge-limited current.2) Use Pierce shaping to set initial beam convergence and reduce transverse fields.3) Inject the beam through the input cavity for velocity modulation; maintain focusing through solenoids or periodic permanent magnets. Verification / Alternative check: Operational data from commercial klystrons show Pierce-type guns are standard; reflex klystrons (oscillators) are a different class and do not define “Pierce gun” usage. Why Other Options Are Wrong: “False” contradicts common practice; restricting to reflex oscillators or low voltages is incorrect; magnetic focusing presence does not negate Pierce geometry. Common Pitfalls: Confusing Pierce guns (linear-beam) with magnetron cathodes (crossed-field); assuming gun geometry is irrelevant to RF performance. Final Answer: True.

Question 20

Varactor diode applications – Where is voltage-dependent capacitance actually used? A varactor (varicap) diode provides a controllable junction capacitance versus reverse bias. In which of the following applications is a varactor commonly employed?

Accepted Answer

Introduction: Varactor diodes act as voltage-controlled capacitors. They are key to frequency-tunable resonators and frequency multipliers because the junction capacitance changes predictably with reverse bias. Understanding where this effect is practically exploited helps distinguish common RF/microwave circuitry from low-frequency active filter design. Given Data / Assumptions: Applications listed: (1) TV tuning, (2) Active filter, (3) Microwave frequency multiplication. Reverse-biased junction supplies a non-linear, voltage-dependent capacitance Cj(V). Focus on mainstream, established uses. Concept / Approach: In television and other tuners, varactors are embedded in LC resonators; changing the bias changes C, thereby tuning the local oscillator and front-end filters across channels. In microwave multipliers, varactors exploit C(V) nonlinearity to generate harmonics efficiently, with appropriate matching networks selecting the desired multiple of the input frequency. By contrast, “active filters” in analog baseband commonly use op-amps with resistors/capacitors; while tunable RF filters can use varactors, the textbook association of “active filters” refers to op-amp topologies that do not require varactors. Step-by-Step Solution: 1) Map TV tuning to varactor-tuned LC tanks → applicable.2) Map microwave multiplication to non-linear C(V) device → applicable.3) Map “active filter” to op-amp based R-C networks → generally not varactor-based in classical definitions. Verification / Alternative check: Consumer tuner schematics and microwave multiplier modules routinely show varactors; baseband Sallen-Key/biquad filters do not. Why Other Options Are Wrong: Options A, B, D, E include “active filter” alone or exclude TV tuning; these do not reflect the standard, widely taught use cases. Common Pitfalls: Assuming any tunable filter is an “active filter”; confusing parametric amplifiers/multipliers with op-amp filters. Final Answer: 1 and 3 only (TV tuning; Microwave frequency multiplication).

Microwave Communication Questions