Oscillators, Mixers and Frequency Synthesis

Introduction

Microwave systems require stable sources at frequencies ranging from approximately 1 GHz to the millimetre-wave and submillimetre-wave regions. These sources must generate signals with adequate output power, low phase noise, high spectral purity, and precise frequency control. Three functional blocks are central to this requirement: the oscillator, which generates a periodic microwave signal; the mixer, which translates signals from one frequency to another; and the frequency synthesizer, which produces selected frequencies from a stable reference.

At microwave frequencies, conventional low-frequency circuit intuition becomes inadequate. Distributed effects, transmission-line discontinuities, resonator losses, device parasitics, and negative-resistance phenomena strongly influence performance. Consequently, oscillator and mixer design combines network theory, nonlinear circuit analysis, semiconductor-device physics, feedback concepts, and frequency-domain measurement.

This chapter develops the operating principles, analytical models, design equations, practical implementation issues, and contemporary applications of these circuits.

Learning Objectives

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

1. Explain the conditions required for microwave oscillation.
2. Analyse oscillator stability using impedance, admittance, and scattering-parameter concepts.
3. Compare transistor, Gunn, IMPATT, dielectric-resonator, and voltage-controlled oscillators.
4. Explain frequency conversion, image frequencies, conversion loss, and mixer noise.
5. Analyse fundamental frequency synthesizer architectures, including PLL, integer-N, fractional-N, and direct digital synthesis.
6. Select appropriate oscillator, mixer, and synthesizer architectures for communication and radar systems.
7. Evaluate phase noise, spurious responses, tuning range, output power, and frequency accuracy.

1. Microwave Oscillation Fundamentals

An oscillator converts dc power into an approximately periodic ac signal without an externally applied periodic input. In a feedback description, oscillation occurs when the loop gain has the appropriate magnitude and phase. For a linear feedback loop, the Barkhausen conditions are

and

where A is the forward gain, β is the feedback factor, ω is angular frequency in radians per second, and n is an integer. These conditions describe the onset of oscillation. In a practical oscillator, nonlinear device behaviour reduces the effective gain as amplitude increases, producing a stable limiting amplitude. Thus, the small-signal loop condition alone does not determine the final output power or waveform.

At microwave frequencies, oscillators are often analysed as an active one-port connected to a passive resonator or load. The active device is designed to present a negative resistance over a suitable frequency range. If the negative resistance magnitude exceeds the positive loss resistance of the resonator, small disturbances grow into oscillation.

For a parallel-resonant representation, the start-up condition may be written as

where G_a is the active-device conductance and G_r is the resonator conductance. Equivalently, using resistance magnitudes,

where R_a is the negative resistance of the active device and R_r is the positive loss resistance of the resonator. These expressions are valid for a locally linearized small-signal model near the intended oscillation frequency.

1.1 Reflection-coefficient interpretation

For a one-port device with reflection coefficient Γ, oscillation is possible when the active device and terminating network satisfy a magnitude and phase relationship. A useful design method is to plot the device negative-resistance region on a Smith chart and superimpose the resonator or load reflection coefficient. The oscillation frequency is determined by the frequency at which the phase condition is satisfied and the magnitude condition provides sufficient start-up margin.

If a device is characterized by S-parameters with reference impedance Z₀, its input impedance is

where Z₀ is usually 50 Ω and Γ_in is the input reflection coefficient. The real part of Z_in must be negative over a suitable frequency interval for a negative-resistance oscillator. S-parameters are small-signal quantities; therefore, large-signal effects must subsequently be checked using nonlinear simulation or measurement.

1.2 Resonators and quality factor

The quality factor of a resonator is defined by

where ω₀ is resonant angular frequency, W_stored is the maximum stored energy, and P_loss is the average power dissipated per cycle-related time interval. A high-Q resonator generally provides better frequency selectivity and lower close-in phase noise, but it may reduce tuning range and increase physical size.

For a narrowband resonator, the approximate fractional 3 dB bandwidth is

where B is bandwidth in hertz and f₀ is resonant frequency in hertz. This approximation applies to a lightly loaded, high-Q resonator.

Common microwave resonators include cavity resonators, dielectric resonators, microstrip or coplanar-waveguide resonators, ceramic resonators, YIG resonators, and transmission-line resonators. Selection depends on frequency, required Q, tuning range, size, cost, and environmental stability.

2. Microwave Oscillator Devices and Architectures

2.1 Transistor oscillators

Gunn, IMPATT, HEMT, HBT, and silicon-germanium devices may be used in microwave oscillators. A transistor oscillator can be implemented in common-source, common-emitter, common-gate, common-base, or reflection-type form. The active device supplies gain or negative resistance, while a resonator establishes frequency selectivity.

A practical oscillator normally includes:

• a bias network that provides stable dc operating conditions;
• an active device with adequate gain or negative resistance;
• a resonator or frequency-selective feedback network;
• an output coupling network;
• stabilizing elements, such as resistors, attenuators, isolators, or buffer amplifiers;
• thermal and mechanical provisions that limit frequency drift.

The output coupling must be chosen carefully. Excessive loading lowers the loaded Q and may suppress oscillation; insufficient coupling produces poor power transfer and may allow the oscillator to be disturbed by the following circuit.

2.2 Gunn oscillators

A Gunn diode is a transferred-electron device, commonly fabricated from materials such as GaAs or InP. Under suitable electric fields, the electron distribution shifts to a higher-energy valley with lower mobility. The resulting current decrease with increasing voltage produces a region of negative differential resistance. Gunn oscillators are relatively simple and can provide useful microwave power, although their efficiency and spectral purity are generally inferior to those of high-quality transistor-resonator oscillators.

2.3 IMPATT oscillators

An IMPATT diode uses avalanche multiplication and carrier transit-time delay. The avalanche process introduces a phase delay, and the transit of carriers through the drift region contributes an additional delay. Together these effects can produce negative dynamic resistance at microwave frequencies. IMPATT devices can generate comparatively high power, but they exhibit substantial noise because avalanche multiplication is a stochastic process. They are therefore less attractive where low phase noise is essential.

2.4 Dielectric-resonator oscillators

A dielectric-resonator oscillator, or DRO, couples a high-permittivity dielectric resonator to a transistor or other active device. The resonator can provide high Q, low loss, and good frequency stability in a compact package. DROs are widely used as local oscillators, radar sources, and reference oscillators. Their principal limitations include restricted tuning range and sensitivity to coupling, temperature, and mechanical construction.

2.5 Voltage-controlled oscillators

A voltage-controlled oscillator, or VCO, changes its oscillation frequency in response to a control voltage. A varactor diode changes the effective capacitance of a resonant circuit, thereby changing resonant frequency. For an ideal LC resonator,

where L is inductance in henries and C is capacitance in farads. If the capacitance is voltage-dependent, C = C(V_c), then the frequency becomes a function of control voltage, f₀ = f₀(V_c). The tuning sensitivity is

with units of hertz per volt, over the specified operating range. In practice, the response is nonlinear and must be calibrated or linearized when accurate tuning is required.

2.6 Frequency stability and phase noise

Frequency stability describes how the average frequency changes with time, temperature, supply voltage, mechanical vibration, and ageing. Phase noise describes short-term random phase fluctuations around the carrier. A common single-sideband phase-noise specification is L(f_m), expressed in dBc/Hz at an offset frequency f_m from the carrier.

For a resonator-limited oscillator, the Leeson model provides a useful, though approximate, interpretation:

where F is the effective noise factor, k is Boltzmann’s constant in joules per kelvin, T is absolute temperature in kelvin, P_s is signal power in watts, Q_L is loaded quality factor, f₀ is carrier frequency, and ∆f is offset frequency in hertz. The expression assumes a linearized oscillator, a resonator-dominated close-in noise region, and a simplified white-noise model. Real oscillators may exhibit flicker noise, discrete spurs, resonator noise, supply pushing, and environmental modulation not captured by this equation.

A practical design should therefore distinguish:

3. Mixers and Frequency Conversion

A mixer is a nonlinear or time-varying circuit that combines two signals to produce sum and difference frequencies. Let the RF and local-oscillator signals be

and

An ideal multiplier produces

where K is a conversion constant. Using the product identity,

there are components at angular frequencies ω_RF + ω_LO and |ω_RF − ω_LO|. A filter selects the desired output, normally the intermediate frequency or RF signal.

Real mixers are commonly based on diode rings, FETs, bipolar transistors, Gilbert cells, resistive switching networks, or subharmonic structures. A switching mixer approximates multiplication by rapidly changing the sign or conduction state of the RF path under LO control. It is efficient over a wide frequency range but generates many harmonics and requires filtering.

3.1 Mixer terminology

The ports of a conventional down-converting mixer are:

• RF port: the received or higher-frequency signal;
• LO port: the large, usually periodic local-oscillator drive;
• IF port: the translated output.

For down-conversion,

For up-conversion, the output may be

depending on the selected sideband and filtering arrangement.

Conversion loss is defined for a passive or switching mixer as

where P_RF is the available RF input power and P_IF is the delivered desired IF power. A mixer with conversion gain has P_IF greater than the appropriately referenced input power and is normally implemented with an active device. Conversion loss does not include unrelated mismatch or external filter loss unless explicitly stated.

3.2 Single-ended, balanced, and image-reject mixers

A single-ended mixer offers simplicity but usually has poor suppression of LO feedthrough and RF-to-IF isolation. A single-balanced mixer suppresses some even-order products or one class of feedthrough. A double-balanced mixer can provide improved isolation and suppression of carrier leakage, but it generally requires more complex circuitry and adequate LO drive.

In a superheterodyne receiver, two RF frequencies can produce the same IF. If the desired signal is above the LO, then

The image frequency is the other solution,

assuming positive frequencies and an appropriate high-side or low-side injection arrangement. An RF preselector, image-reject mixer, or quadrature architecture is required to suppress the image.

For a first-order tuned circuit with centre frequency f_RF and quality factor Q, the approximate attenuation at an image frequency separated by ∆f may be estimated from the filter response. Exact image rejection depends on filter order, topology, source and load impedance, and the frequency ratio; therefore, a single-Q approximation should not be treated as a universal design formula.

3.3 Mixer nonlinearity and intermodulation

A nonlinear device can be represented locally by a polynomial,

where a₁, a₂, and a₃ are nonlinear coefficients. With multiple tones, second- and third-order terms generate intermodulation products. Third-order products are particularly important in receivers because they can fall close to the desired channel. The input third-order intercept point, IIP3, is a standardized extrapolated measure rather than a physically reached operating point. Higher IIP3 generally indicates better large-signal linearity, but it may require greater dc power or reduce conversion gain.

3.4 Noise in mixers

Mixer noise is commonly represented by a noise figure, defined as

where SNR denotes signal-to-noise ratio and F is dimensionless. Noise figure in decibels is

The definition requires consistent signal and noise bandwidths and a specified source impedance. For a receiver cascade, the Friis formula is

where F_i is the linear noise factor of stage i and G_i is the available linear power gain of the preceding stage. For a passive mixer, conversion loss often contributes directly to the first-stage noise factor, making the RF preamplifier and mixer interface especially important.

4. Frequency Synthesis

Frequency synthesis is the generation of one or more precisely controlled output frequencies from a stable reference. A synthesizer is evaluated by frequency resolution, accuracy, phase noise, spurious output, switching speed, tuning range, output power, and implementation complexity.

A stable reference oscillator, often a crystal oscillator or atomic reference, supplies the timebase. The synthesis architecture then multiplies, divides, mixes, or numerically processes this reference to produce the required frequency.

4.1 Direct analogue synthesis

Direct analogue synthesis uses frequency multipliers, dividers, mixers, filters, and switched sources. It can achieve rapid switching and very low phase noise when high-quality components are used. However, it may require many filters and produces numerous unwanted mixing products. Calibration and hardware complexity increase rapidly as the number of output frequencies grows.

4.2 Direct digital synthesis

A direct digital synthesizer, or DDS, uses a reference clock, phase accumulator, phase-to-amplitude conversion, digital-to-analogue conversion, and output filtering. If the phase accumulator has N bits and the frequency control word is M, the ideal output frequency is

where f_clk is the clock frequency, 0 ≤ M < 2^N for the fundamental Nyquist-zone output, and f_out is the unaliased output frequency. The frequency resolution is

This equation assumes an ideal accumulator and clock. In practice, DAC quantization, clock jitter, truncation, images, and reconstruction-filter limitations determine spectral performance. DDS offers extremely fine frequency resolution and fast switching, but its highest output frequency is limited relative to the clock and its spurious spectrum requires careful filtering.

4.3 Phase-locked-loop synthesis

A PLL synthesizer compares the phase of a reference-derived signal with a divided version of the VCO output. A charge pump and loop filter produce a control voltage that drives the VCO. In lock, the average phase error is bounded and the frequency relationship is established.

For an integer-N PLL,

where N is the feedback-divider ratio, R is the reference-divider ratio, f_ref is the reference frequency, and f_out is the VCO output frequency. If R = 1, the output frequency is an integer multiple of the reference frequency.

A fractional-N PLL allows the effective division ratio to be N + α, where 0 ≤ α < 1. Ideally,

Fractional-N operation provides finer channel spacing without reducing the phase-detector frequency. Delta-sigma modulation is commonly used to control the sequence of integer division ratios and shape quantization noise outside the loop bandwidth. Fractional spurs, reference spurs, modulator noise, charge-pump mismatch, leakage, and VCO phase noise must be managed.

4.4 PLL dynamics and loop bandwidth

A PLL is a feedback control system. Its loop bandwidth represents a compromise. A wider bandwidth can reduce the time required to settle and can suppress some VCO noise within the loop, but it may pass more reference and charge-pump noise. A narrower bandwidth can suppress reference-related disturbances but increases settling time and may allow more VCO noise to appear at the output.

The exact transfer function depends on phase-detector gain, charge-pump current, loop-filter impedance, VCO gain, divider ratio, and the selected loop-filter order. A second-order approximation is useful for understanding damping and natural frequency, but practical synthesizers often use third-order or higher filters to control stability, spurs, and out-of-band attenuation.

4.5 Phase noise in frequency synthesis

The output phase noise of a PLL is the combined result of reference noise, divider noise, phase-detector and charge-pump noise, loop-filter noise, VCO noise, and fractional-modulator noise. Within the loop bandwidth, reference-related noise is transferred according to the closed-loop response. Outside the bandwidth, VCO noise commonly dominates.

Reference multiplication increases phase fluctuations expressed in radians. Ideally, frequency multiplication by N increases single-sideband phase noise by approximately

because phase deviation is multiplied by N. This approximation assumes the multiplier itself adds negligible noise and that the comparison is made at corresponding offset frequencies.

5. Worked Examples

Example 1: Down-conversion and image frequency

A receiver uses a 10.7 GHz local oscillator and an IF of 1.2 GHz. With high-side injection, the desired RF frequency is

The image is the other frequency that gives the same IF:

Thus, an RF filter must pass approximately 11.9 GHz while rejecting 9.5 GHz. The frequency separation is 2.4 GHz.

Example 2: DDS frequency resolution

A DDS operates with a 1 GHz clock and a 32-bit phase accumulator. Its ideal frequency resolution is

For a control word M = 429,496,730,

The result is an ideal numerical value. Clock jitter and DAC spurs may dominate the practical error and spectral impurity.

Example 3: PLL output frequency

An integer-N synthesizer uses f_ref = 20 MHz, R = 1, and N = 450. Then

If the desired channel spacing is 20 MHz, this architecture is suitable. For 1 MHz spacing without reducing the phase-detector frequency, a fractional-N architecture or an alternative synthesis arrangement is preferable.

6. Applied Case: Local-Oscillator Synthesizer for a Ka-Band Radar

Background

Consider an illustrative Ka-band radar requiring a tunable local oscillator from 33.0 to 35.0 GHz. The radar demands 1 MHz frequency resolution, low phase noise at 100 kHz offset, rapid frequency changes between pulses, and adequate isolation from the receiver input.

Problem

A free-running VCO can cover the required range, but its frequency accuracy and long-term stability are inadequate. A simple integer-N PLL would require a low comparison frequency to obtain 1 MHz channel spacing, which would increase in-band phase noise and lengthen settling time.

Analysis

A practical architecture uses a low-noise reference, a fractional-N PLL, a wideband Ka-band VCO, and a buffer or frequency doubler as required. The fractional divider permits approximately 1 MHz channel spacing while retaining a higher phase-comparison frequency. The loop bandwidth is selected by balancing VCO noise against reference and fractional-modulator noise.

The output chain includes an isolator or buffer amplifier to reduce load pulling. A band-pass filter suppresses harmonics and fractional spurs. The synthesizer is housed in a thermally controlled enclosure because VCO gain and resonator characteristics vary with temperature.

Approach and solution

1. Use a 100 MHz oven-controlled crystal oscillator as the reference.
2. Apply reference division and fractional feedback division to establish the required output frequency.
3. Select a loop bandwidth after phase-noise modelling rather than by tuning speed alone.
4. Use a calibrated VCO tuning curve to ensure that the control voltage remains inside its reliable range.
5. Add output buffering, filtering, and power monitoring.
6. Measure phase noise, reference spurs, fractional spurs, switching time, frequency error, and output power over temperature.

Outcome

The fractional-N architecture provides fine frequency resolution without the severe comparison-frequency penalty of a narrow-channel integer-N design. Buffering reduces load pulling, while filtering improves spectral purity. The remaining engineering trade-off is between rapid settling and close-in phase noise; it cannot be removed by selecting a divider ratio alone.

Learning points

The case illustrates that synthesizer selection is a system-level decision. Frequency resolution, phase noise, switching speed, thermal behaviour, spur control, and output isolation must be considered together. A theoretically correct frequency relationship does not guarantee an acceptable radar waveform.

7. Practical Design, Measurement, and Limitations

Oscillator design should begin with a clear specification for frequency, power, phase noise, tuning range, stability, load impedance, start-up time, and environmental conditions. Stability analysis must include all possible modes, because a circuit may oscillate at an unintended frequency or harmonic. Large-signal harmonic-balance simulation is useful, but prototype measurement remains essential.

Important measurements include output spectrum, phase noise, frequency drift, pulling, pushing, output power, harmonic distortion, conversion loss, isolation, noise figure, and intermodulation. A spectrum analyser alone is insufficient for accurate close-in phase-noise characterization; dedicated phase-noise analysers or cross-correlation techniques may be needed.

Mixer measurements must specify LO power, RF frequency, IF frequency, impedance, conversion-loss reference plane, and filter bandwidth. Ambiguous measurement conditions can lead to apparently contradictory data sheets.

Common limitations include:

• device and resonator loss;
• temperature-dependent frequency drift;
• supply pushing and load pulling;
• phase noise and flicker noise;
• unwanted harmonics and spurs;
• mixer image responses;
• intermodulation under strong signals;
• PLL reference leakage and fractional spurs;
• finite DDS clock rate and DAC quantization;
• electromagnetic coupling between source, control, and output paths.

8. Contemporary Developments and Professional Practice

Modern microwave sources increasingly integrate VCOs, dividers, phase detectors, charge pumps, calibration engines, and digital control on a single silicon or compound-semiconductor die. Wideband fractional-N synthesizers, digitally controlled oscillators, digitally assisted calibration, and multi-core PLLs support agile radios and radar systems.

Silicon-germanium and advanced CMOS technologies enable millimetre-wave integration, while III–V devices remain valuable for high output power and high-frequency operation. Photonic frequency synthesis can provide exceptionally low phase noise and wide tunability by transferring stability from optical references to microwave carriers. Quantum and cryogenic systems also motivate ultra-low-noise microwave generation.

Artificial intelligence can assist oscillator calibration, phase-noise prediction, fault detection, and adaptive spur cancellation. Nevertheless, machine-learning results must be validated against physical constraints, calibrated measurements, and reproducible test conditions. AI should support—not replace—device modelling, safety analysis, and engineering verification.

Professional practice also requires compliance with electromagnetic-compatibility regulations, spectrum-allocation rules, spurious-emission limits, and laboratory safety procedures. High-power microwave sources can create exposure hazards, while PLL control software may affect spectrum occupancy and should be protected against unauthorized changes.

Best-Practice Checklist

• Define frequency, power, phase-noise, spur, tuning, and stability requirements before selecting an architecture.
• Use negative-resistance and loop-stability analyses for start-up prediction.
• Treat S-parameters as small-signal data and verify large-signal operation separately.
• Isolate oscillators from variable loads with buffers or isolators.
• Specify mixer conversion loss and noise figure with complete test conditions.
• Analyse image frequencies before selecting the IF and LO plan.
• Model PLL noise contributions and settling time together.
• Measure temperature, supply, load, and vibration sensitivities.
• Filter harmonics and reference-related spurs at the appropriate reference planes.
• Maintain traceable calibration and document all assumptions.

Chapter Summary

Microwave oscillators generate periodic signals by combining active-device gain or negative resistance with a frequency-selective network. Start-up requires both magnitude and phase conditions, while the final amplitude is determined by nonlinear limiting. Resonator Q, device noise, thermal effects, load pulling, and supply pushing determine practical frequency quality. Gunn and IMPATT devices offer useful microwave power, whereas transistor, dielectric-resonator, and VCO architectures provide alternatives for stability, integration, and tuning.

Mixers exploit nonlinear or switching behaviour to translate frequencies. The desired sum or difference component must be selected by filtering. Conversion loss, isolation, image response, noise figure, intermodulation, and LO drive are central design parameters. Receiver architecture and preselection strongly influence image rejection and dynamic range.

Frequency synthesizers derive accurate, tunable outputs from stable references. Direct analogue synthesis offers speed and potentially excellent phase noise but can be complex. DDS provides fine resolution and rapid control, subject to clock, DAC, and spur limitations. PLL synthesis provides accurate frequency relationships; integer-N systems are simple, while fractional-N systems provide fine spacing at higher comparison frequencies but require careful spur and noise management.

Successful microwave source design is a system problem involving circuit theory, device physics, control dynamics, thermal engineering, measurement, electromagnetic compatibility, and regulatory responsibility.

Key Terms

Oscillator: A circuit that generates a periodic signal from dc power.

Barkhausen condition: Magnitude and phase conditions describing the onset of feedback oscillation.

Negative resistance: An active-device impedance region in which increasing voltage produces decreasing current in the local small-signal model.

Resonator: A frequency-selective network that stores electromagnetic energy.

Quality factor: Ratio of stored energy-related power to dissipated power at resonance.

DRO: Dielectric-resonator oscillator.

VCO: Voltage-controlled oscillator.

Phase noise: Random short-term phase fluctuation represented spectrally around a carrier.

Mixer: A circuit that translates frequency through nonlinear or time-varying operation.

Conversion loss: Ratio, in decibels, of input available power to desired output delivered power.

Image frequency: An unwanted frequency that produces the same IF as the desired signal.

Noise figure: Degradation of signal-to-noise ratio expressed as a linear factor or decibels.

Intermodulation: Generation of new frequencies by nonlinear interaction among signals.

PLL: Phase-locked loop.

Integer-N synthesis: PLL synthesis using an integer feedback-divider ratio.

Fractional-N synthesis: PLL synthesis using a fractional effective divider ratio.

DDS: Direct digital synthesis using a phase accumulator and digital waveform generation.

Reference spur: A discrete unwanted spectral component associated with periodic reference operation.

Load pulling: Oscillator frequency variation caused by changes in the connected load.

Supply pushing: Oscillator frequency variation caused by changes in supply voltage.

Review Questions

Short Answer Questions

1. State the magnitude and phase conditions for the onset of feedback oscillation.
2. Why is a high-Q resonator useful in a microwave oscillator?
3. Define mixer conversion loss.
4. What is the image frequency in a superheterodyne receiver?
5. State the ideal output-frequency equation for a DDS.

Long Answer Questions

1. Explain negative-resistance oscillator analysis using impedance and reflection-coefficient concepts.
2. Compare Gunn, IMPATT, DRO, transistor, and VCO microwave oscillators.
3. Explain mixer operation, including sum and difference frequencies, image response, isolation, and intermodulation.
4. Derive and discuss the frequency relationships of integer-N and fractional-N PLL synthesizers.
5. Discuss the major contributors to phase noise in microwave oscillators and PLL frequency synthesizers.

Analytical / Application Questions

1. A receiver uses an LO at 8.8 GHz and an IF of 900 MHz with high-side injection. Determine the desired RF frequency and image frequency, and explain what filtering is required.
2. A DDS uses a 2.4 GHz clock and a 40-bit phase accumulator. Calculate its ideal frequency resolution and discuss two practical limitations that may prevent this resolution from appearing in the measured spectrum.
3. Design a conceptual frequency-synthesizer architecture for a 24 GHz radar requiring 500 kHz channel spacing, fast switching, and low phase noise. Justify the reference, PLL or DDS choice, loop bandwidth, buffering, filtering, and measurement plan.

Multiple Choice Questions with Answers

Question 1

Which condition is associated with the onset of feedback oscillation?

A. Loop-gain magnitude is zero and phase is π

B. Loop-gain magnitude is unity and phase is an integer multiple of 2π

C. Loop-gain magnitude is infinite and phase is π/2

D. Loop-gain magnitude is less than unity and phase is zero

Correct Answer: B. Loop-gain magnitude is unity and phase is an integer multiple of 2π

Question 2

A mixer receives an RF signal at 11.9 GHz and an LO signal at 10.7 GHz. What is the difference-frequency IF output?

A. 0.8 GHz

B. 1.0 GHz

C. 1.2 GHz

D. 22.6 GHz

Correct Answer: C. 1.2 GHz

Question 3

For the high-side injection case with f_LO = 10.7 GHz and f_IF = 1.2 GHz, which is the image frequency?

A. 9.5 GHz

B. 10.7 GHz

C. 11.9 GHz

D. 12.1 GHz

Correct Answer: A. 9.5 GHz

Question 4

The ideal output frequency of a DDS with a 1 GHz clock, 32-bit accumulator, and frequency-control word 2^31 is:

A. 125 MHz

B. 250 MHz

C. 500 MHz

D. 1 GHz

Correct Answer: C. 500 MHz

Question 5

An integer-N PLL has f_ref = 20 MHz, R = 1, and N = 450. What is its output frequency?

A. 900 MHz

B. 4.5 GHz

C. 9 GHz

D. 90 GHz

Correct Answer: C. 9 GHz

Question 6

Which device mechanism is primarily associated with IMPATT-diode noise?

A. Avalanche multiplication

B. Optical pumping

C. Thermionic emission only

D. Digital quantization

Correct Answer: A. Avalanche multiplication

Question 7

Which parameter directly describes random spectral spreading around an oscillator carrier?

A. Conversion gain

B. Phase noise

C. Image rejection ratio

D. Divider modulus

Correct Answer: B. Phase noise

Question 8

For an ideal LC resonator, increasing capacitance while holding inductance constant causes resonant frequency to:

A. Increase

B. Decrease

C. Remain unchanged

D. Become independent of inductance

Correct Answer: B. Decrease

Question 9

A principal advantage of fractional-N synthesis over simple integer-N synthesis is:

A. It eliminates the need for a reference oscillator

B. It provides fine frequency spacing while retaining a relatively high comparison frequency

C. It guarantees zero phase noise

D. It removes all harmonic filtering requirements

Correct Answer: B. It provides fine frequency spacing while retaining a relatively high comparison frequency

Question 10

In a receiver cascade, the first stage is especially important because its noise contribution is:

A. Multiplied by all later gains

B. Reduced by the gain of preceding stages

C. Not affected by system gain

D. Usually divided by the LO frequency

Correct Answer: A. Multiplied by all later gains