low noise oscillator design and performance - m.m.driscoll

Low Noise Oscillator Design and PerformanceLow Noise Oscillator Design and Performance

Michael M. DriscollMichael M. DriscollPresented at the 2002 IEEE Frequency Control SymposiumPresented at the 2002 IEEE Frequency Control SymposiumJune 1, 2002 New Orleans, LA, USAJune 1, 2002 New Orleans, LA, USA

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ContentsContents

uu ShortShort--Term Frequency/Phase/Amplitude StabilityTerm Frequency/Phase/Amplitude Stabilityuu Basic Oscillator OperationBasic Oscillator Operationuu Types of Resonators and Delay LinesTypes of Resonators and Delay Linesuu Useful Network/Impedance TransformationsUseful Network/Impedance Transformationsuu Sustaining Stage Design and PerformanceSustaining Stage Design and Performanceuu Oscillator Frequency Adjustment/Voltage TuningOscillator Frequency Adjustment/Voltage Tuninguu Environmental Stress EffectsEnvironmental Stress Effectsuu Oscillator Circuit Simulation & Noise ModelingOscillator Circuit Simulation & Noise Modelinguu Oscillator Noise DeOscillator Noise De--correlation/Noise Reduction Techniquescorrelation/Noise Reduction Techniquesuu Oscillator Test/TroubleshootingOscillator Test/Troubleshootinguu SummarySummaryuu List of ReferencesList of References

1. Short-term Frequency/Phase/Amplitude Stability1. Short-term Frequency/Phase/Amplitude Stability

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SignalSignalSpectralSpectral

AmplitudeAmplitude(dB)(dB)

Signal Frequency (Hz)Signal Frequency (Hz)

Carrier SignalsCarrier Signals

fofo fo’fo’

AdditiveAdditive

Baseband flickerBaseband flicker(1/f) noise(1/f) noise

MultiplicativeMultiplicative(i.e., 1/f AM & 1/f PM)(i.e., 1/f AM & 1/f PM)

Types of Phase and Amplitude NoiseTypes of Phase and Amplitude Noise

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Additive Noise [noise power Additive Noise [noise power independentindependent of signal]of signal]

Types of Phase and Amplitude Noise (cont.)Types of Phase and Amplitude Noise (cont.)

Thermal noise:Thermal noise: enen22=4KTRB=4KTRB K = Boltzman’s constantK = Boltzman’s constant= 1.374X10= 1.374X10--2222

T = temp in KelvinT = temp in Kelvin= 300K at room temp.= 300K at room temp.

R = resistance in ohmsR = resistance in ohmsB = bandwidthB = bandwidth

Shot noise:Shot noise: inin22=2qIB=2qIB q=1.59X10q=1.59X10--1919

I=current in amperesI=current in amperes

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How to Calculate Additive NoiseHow to Calculate Additive Noise

Amplifier additive noise Amplifier additive noise powerpower

KTBF (Rg=50 ohms, T=300K, B=1Hz), KTBF (Rg=50 ohms, T=300K, B=1Hz), referred to input = referred to input = --174dBm/Hz + NF(dB)174dBm/Hz + NF(dB)

Carrier SignalCarrier Signal--toto--Noise Noise RatioRatio

in dBc/Hz = in dBc/Hz = --174 + NF(dB) 174 + NF(dB) -- input signal input signal power (dBm)power (dBm)

OneOne--half noise power is half noise power is AM, OneAM, One--half PMhalf PM

in dBc/Hz = in dBc/Hz = --177 + NF(dB) 177 + NF(dB) -- input signal input signal power (dBm)power (dBm)

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Characteristics of Multiplicative Noise Characteristics of Multiplicative Noise

uu An example of multiplicative noise is a noise component in the An example of multiplicative noise is a noise component in the transmission gain magnitude (AM noise) and phase (PM noise) transmission gain magnitude (AM noise) and phase (PM noise) in an amplifierin an amplifier

uu The noise component can equivalently occur in a transistor, for The noise component can equivalently occur in a transistor, for example, as noiseexample, as noise--like variation in the transconductance (gm) or like variation in the transconductance (gm) or junction capacitancejunction capacitance

uu Device multiplicative AM and PM noise levels usually are nonDevice multiplicative AM and PM noise levels usually are non--identicalidentical

uu Multiplicative noise level can be affected by nonMultiplicative noise level can be affected by non--linearity (i.e., inlinearity (i.e., in--compression amplifier operation)compression amplifier operation)

uu Multiplicative noise most often occurs as flickerMultiplicative noise most often occurs as flicker--ofof--amplitude amplitude and flickerand flicker--ofof--phase modulation, or 1/f AM and 1/f PMphase modulation, or 1/f AM and 1/f PM

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Characteristics of Multiplicative Noise Characteristics of Multiplicative Noise (continued)(continued)

uu The spectral level of the 1/f AM and PM noise decreases at a The spectral level of the 1/f AM and PM noise decreases at a rate of 10dB/decade with increasing carrier offset (modulation) rate of 10dB/decade with increasing carrier offset (modulation) frequencyfrequency

uu In (oscillator sustaining stage) transistor amplifiers:In (oscillator sustaining stage) transistor amplifiers:

ll Relatively low1/f AM and PM noise is observed in Relatively low1/f AM and PM noise is observed in silicon bipolar and HBT transistor amplifiers operating silicon bipolar and HBT transistor amplifiers operating at and below Lat and below L--bandbandll Highest 1/f AM and PM noise is observed in microwave Highest 1/f AM and PM noise is observed in microwave

GaAs FET amplifiersGaAs FET amplifiersuu 1/f AM and PM noise is also observed in passive devices. 1/f AM and PM noise is also observed in passive devices.

1/f variation in quartz crystal and SAW resonator impedance(s) 1/f variation in quartz crystal and SAW resonator impedance(s) is often the main source of nearis often the main source of near--carrier noise in oscillators using carrier noise in oscillators using these resonators these resonators

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Characteristics of Multiplicative Noise Characteristics of Multiplicative Noise (continued)(continued)

uu Other mechanisms resulting in carrier signal noiseOther mechanisms resulting in carrier signal noise--modulation modulation include:include:ll Noise on device DC power suppliesNoise on device DC power suppliesll NoiseNoise--like environmental stress (especially vibration)like environmental stress (especially vibration)

uu 1/f AM and 1/f PM noise levels vary (widely) from vendor1/f AM and 1/f PM noise levels vary (widely) from vendor--toto--vendor for similar performance devices and can vary vendor for similar performance devices and can vary significantly for the same component on a devicesignificantly for the same component on a device--toto--device device basisbasis

uu It is necessary to evaluate noise performance via measurement It is necessary to evaluate noise performance via measurement of purchased/sample devicesof purchased/sample devices

uu In an oscillator, amplifier 1/f PM noise is converted to higher In an oscillator, amplifier 1/f PM noise is converted to higher level 1/f FM at carrier offset frequencies within the resonator level 1/f FM at carrier offset frequencies within the resonator halfhalf--bandwidthbandwidth

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1 10 100 1K 10K 100K 1M

-110

-120

-130

-140

-150

-160

-170

Carrier Offset Frequency (Hz)

PhaseNoiseSidebandLevel(dBc/Hz)

““Typical” Component 1/f PM Multiplicative Typical” Component 1/f PM Multiplicative Noise LevelsNoise Levels

X-band GaAs Amp.

X-band Schottky Mixer& X-band HBT amp.

HF-VHF Bipolar Amp. &HF-UHF Schottky Mixer

L-band Bipolar and HBTAmp.

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Component 1/f InstabilityComponent 1/f Instability

uu The nonThe non--semiconductor components in the oscillator circuit also semiconductor components in the oscillator circuit also exhibit shortexhibit short--term instabilityterm instability

uu “Passive” components (resistors, capacitors, inductors, reverse“Passive” components (resistors, capacitors, inductors, reverse--biased, varactor diodes) exhibit varying levels of flickerbiased, varactor diodes) exhibit varying levels of flicker--ofof--impedance instability whose effects can be comparable to or impedance instability whose effects can be comparable to or higher than to that of the sustaining stage amplifier 1/f AM andhigher than to that of the sustaining stage amplifier 1/f AM andPM noise in the oscillator circuitPM noise in the oscillator circuit

uu The oscillator frequency control element (i.e., resonator) can The oscillator frequency control element (i.e., resonator) can exhibit dominant levels of flickerexhibit dominant levels of flicker--ofof--resonant frequency resonant frequency instability, especially acoustic resonatorsinstability, especially acoustic resonators

uu In an open loop sense, the resonator instability can be plotted In an open loop sense, the resonator instability can be plotted as flickeras flicker--ofof--phase noise (induced on a carrier signal passing phase noise (induced on a carrier signal passing through the resonator)through the resonator)

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1 10 100 1K 10K 100K 1M

-110

-120

-130

-140

-150

-160

-170


Passive Component 1/f Impedance Passive Component 1/f Impedance InstabilityInstability

PSD(DX/X)2

in dB

HF Varactor diodes, Ceram. Capacitors, Powedered Iron Inductors

VHF Varactor & PIN diodes, Ceram. Capacitors, Powdered Iron InductorsHF-VHF Bipolar Amp. &

HF-UHF Schottky Mixer



X-band GaAs Amp.

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1 10 100 1K 10K 100K 1M

-110

-120

-130

-140

-150

-160

-170


PhaseNoiseSidebandLevel(dBc/Hz)

Resonator Open Loop Phase InstabilityResonator Open Loop Phase Instability

Low Noise HF/VHF BAW

Low Noise UHF SAWR/STWR

X-band GaAs Amp.


HF-VHF Bipolar Amp. &HF-UHF Schottky Mixer


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PhasePhaseNoiseNoise

SidebandSidebandLevelLevel

(dBc/Hz)(dBc/Hz)

Carrier Offset Frequency (Hz)Carrier Offset Frequency (Hz)

ττ = oscillator closed loop group delay= oscillator closed loop group delay1/21/2ππττ = BW/2 for a single (1 pole) resonator= BW/2 for a single (1 pole) resonator

PMPM--toto--FM Noise Conversion in an OscillatorFM Noise Conversion in an Oscillator

Additional signal noise degradationAdditional signal noise degradationdue to resonator FM noisedue to resonator FM noise

1/f FM1/f FM

Oscillator closed loop signal FM noiseOscillator closed loop signal FM noisedue to sustaining stage open loop PM due to sustaining stage open loop PM noisenoise

white FMwhite FM1/f PM1/f PM

1/21/2ππττ

white PMwhite PM

Oscillator sustaining stage open Oscillator sustaining stage open loop PM noiseloop PM noise

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Commonly Used Measures of Oscillator Commonly Used Measures of Oscillator Signal ShortSignal Short--Term Frequency StabilityTerm Frequency Stability

(f) = Single sideband phase noise(f) = Single sideband phase noise--toto--carrier power ratiocarrier power ratioin a 1Hz bandwidth at a offset frequency f from thein a 1Hz bandwidth at a offset frequency f from thecarrier (dBc/Hz)carrier (dBc/Hz)

SSφφ(f) = Spectral density of the phase fluctuations (rad(f) = Spectral density of the phase fluctuations (rad22/Hz)./Hz).SSyy(f) = Spectral Density of the fractional frequency(f) = Spectral Density of the fractional frequency

fluctuations (1/Hz).fluctuations (1/Hz).SSyy(f) = (f/(f) = (f/ννoo))22SSφφ(f), (f), (f) = 10LOG(S(f) = 10LOG(Sφφ(f)/2)(f)/2)ννo o = carrier frequency= carrier frequency

Frequency Domain:Frequency Domain:

Time Domain: Time Domain: σσyy(τ)(τ) = Two= Two sample deviation (square root sample deviation (square root Allan Variance)Allan Variance)

σσyy((ττ) = ½ () = ½ (yyk+1k+1--yyk)k)22>>

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(f)(dBc/Hz)

σσyy((ττ))

White phaseWhite phase0dB/decade0dB/decade

τ τ --11

Flicker of phaseFlicker of phase10dB/decade10dB/decade

τ τ --11

τ τ --1/21/2

White frequencyWhite frequency20dB/decade20dB/decade

Flicker of frequencyFlicker of frequency30dB/decade30dB/decade

τ τ 00

Random walkRandom walk40dB/decade40dB/decade

τ τ 1/21/2

Frequency DomainFrequency Domain

Time DomainTime Domain

1Hz1Hz

1sec1sec

Types of Frequency/Phase Noise SpectraTypes of Frequency/Phase Noise Spectra

TimeTime

FrequencyFrequency

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Conversion from Frequency to Time DomainConversion from Frequency to Time Domain

uu If the nature of the noise spectra is known to If the nature of the noise spectra is known to dominate over a large carrier offset region, the Allan dominate over a large carrier offset region, the Allan Variance can be calculated from the frequency Variance can be calculated from the frequency domain data using the appropriate conversion domain data using the appropriate conversion equations. The equations differ, depending on the equations. The equations differ, depending on the type of noise (random walk, etc.)type of noise (random walk, etc.)

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Relationships between Relationships between SSyy(f) and (f) and σσyy(t):(t):

S y (f) = Hα f α

α =Sy(f) = a σy(t)a =

(white phase)

(flicker noise)

(white frequency)

(flicker frequency)

(random walk frequency)

((2π )2 τ2f 2)/(3fh)

2τ

1/((2f) (2))

6/(2π)2τf2

2

1

0

-1

-2

((2π )2τ2f2)/(1.038+3 (ωτ ))

νν00 = carrier frequency= carrier frequencyf = fourier frequencyf = fourier frequency

νν00LL(f) in (f) in dBc/Hz = 10LOG(SdBc/Hz = 10LOG(Sϕϕ(f)/2) = 10LOG[((f)/2) = 10LOG[( ff ))22Sy(f)/2Sy(f)/2

ShortShort--Term Frequency/Phase/Time Stability Term Frequency/Phase/Time Stability RelationshipsRelationships

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Example: Conversion from Frequency to Example: Conversion from Frequency to Time DomainTime Domain

Suppose a 100MHz Crystal Oscillator signal spectrum Suppose a 100MHz Crystal Oscillator signal spectrum in the region around f=100Hz is flickerin the region around f=100Hz is flicker--ofof--frequency frequency with:with:

(f=100Hz) = (f=100Hz) = --120dBc/Hz120dBc/Hz

Then Sy(f) in the same regionThen Sy(f) in the same region= (10= (10 (f)/10(f)/10)2f/)2f/ννoo = (10= (10--1212)(200/10)(200/1088)=2X10)=2X10--2222/f/f

And (from the conversion formula for flickerAnd (from the conversion formula for flicker--ofof--frequency noise):frequency noise):

σσyy22((ττ) in the region) in the region

ττ = 1/f = 1sec = (2)(ln(2))(Sy(f))(f) = 2.77X10= 1/f = 1sec = (2)(ln(2))(Sy(f))(f) = 2.77X10--2222therefore,therefore, σσyy((ττ) = 1.66X10) = 1.66X10--1111

2. Basic Oscillator Operation2. Basic Oscillator Operation

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ResonatorResonator

InputInputMatchingMatching

& Frequency& FrequencyTuningTuningCircuitsCircuits

NegativeNegativeResistanceResistance

(Gain) Stage(Gain) StageIncludingIncludingAGC/ALCAGC/ALC

OutputOutputMatchingMatching

CircuitCircuitLoadLoad

Zin at fo = jXin + Rin (Rin is negative)Zin at fo = jXin + Rin (Rin is negative)

Zin at fo = jXr + RrZin at fo = jXr + Rr

Conditions for startConditions for start--up: Xr = up: Xr = --Xin, Rr + RinXin, Rr + Rin<< 00Steady State: Xr = Steady State: Xr = --Xin, Rr + Rin = 0Xin, Rr + Rin = 0

Oscillator Viewed as a Two Terminal Oscillator Viewed as a Two Terminal Negative Resistance GeneratorNegative Resistance Generator

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ResonatorResonatorMatchingMatching& Tuning& TuningCircuitsCircuits

ResonatorResonatorMatchingMatching

and and TuningTuningCircuitsCircuits

LoadLoad

ResonatorResonatororor

Delay LineDelay Line

AmplifierAmplifier(Gain) Stage(Gain) Stage

IncludingIncludingAGC/ALCAGC/ALC

GGM1M1,, φφM1M1 OutputOutputMatchingMatching

CircuitCircuit

GGAA,, φφAA

GGM2M2,, φφM2M2

GGM3M3,, φφM3M3GGRR,, φφRR

Conditions for startConditions for start--up: Gup: GM1M1GGAAGGM2M2GGM3M3GGRR>>1,1, φφM1M1++φφAA++φφM2M2++φφM3M3++φφRR = = 2N2Nππ radiansradians

Steady State: GSteady State: GM1M1GGAAGGM2M2GGM3M3GGRR= 1,= 1, φφM1M1++φφAA++φφM2M2++φφM3M3++φφRR = = 2N2Nππ radiansradians

Oscillator Viewed as a Feedforward Oscillator Viewed as a Feedforward Amplifier with Positive FeedbackAmplifier with Positive Feedback

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*Symmetrical diode waveform clipping provides better (harder) *Symmetrical diode waveform clipping provides better (harder) limiting, compared to singlelimiting, compared to single--ended clipping, and appears to ended clipping, and appears to provide more immunity from the effects of diode noise. The leasprovide more immunity from the effects of diode noise. The least t noisy form of transistor amplifier gain compression is singlenoisy form of transistor amplifier gain compression is single--ended current limiting, rather than voltage limiting (saturationended current limiting, rather than voltage limiting (saturation). ). SingleSingle--ended limiting is soft limiting.ended limiting is soft limiting.

(1) Instantaneous signal amplitude limiting/waveform (1) Instantaneous signal amplitude limiting/waveform clipping via sustaining stage amplifier gain clipping via sustaining stage amplifier gain compression or separate diode waveform clipping.*compression or separate diode waveform clipping.*

(2) Gain reduction using a feedback control loop. The (2) Gain reduction using a feedback control loop. The oscillator RF signal is DCoscillator RF signal is DC--detected, and the amplified detected, and the amplified detector output fed to a variable gain control element detector output fed to a variable gain control element (i.e., PIN attenuator) in the oscillator.(i.e., PIN attenuator) in the oscillator.

ALC / AGC Must OccurALC / AGC Must Occur

uu Types of automatic level control (ALC) and/or Types of automatic level control (ALC) and/or automatic gain control (AGC):automatic gain control (AGC):

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Oscillator TurnOscillator Turn--On BehaviorOn Behavior

uu Oscillation is initiated by spectral components of Oscillation is initiated by spectral components of circuit noise and/or DC turncircuit noise and/or DC turn--on transients occurring at on transients occurring at the frequency where the small signal conditions for the frequency where the small signal conditions for oscillation are satisfiedoscillation are satisfied

uu TurnTurn--on time is determined by the: on time is determined by the: ll initial noise/transient spectral signal level, initial noise/transient spectral signal level, ll steadysteady--state signal level, state signal level, ll oscillator loop (resonator loaded Q) delay, oscillator loop (resonator loaded Q) delay, ll and small signal excess gainand small signal excess gain

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Resonator,Resonator,MultiMulti--pole Filter,pole Filter,

or Delay Lineor Delay Line

AA

uu This conversion results in significant signal spectral degradatiThis conversion results in significant signal spectral degradation at on at carrier offset frequencies withincarrier offset frequencies within f=1/2f=1/2πτ πτ wherewhere ττ is the loop group delayis the loop group delay(1/2(1/2πτπτ = = BW/2 for a single resonator)BW/2 for a single resonator)

τ = δφ/2πδτ = δφ/2πδff

δδf = f = δφ/2πτδφ/2πτ

uu The amount of signal frequency change caused by the phase The amount of signal frequency change caused by the phase perturbation is related to the oscillator loop group delay (i.e.perturbation is related to the oscillator loop group delay (i.e., resonator , resonator loaded Q)loaded Q)

--δφδφ

uu If a phase perturbation,If a phase perturbation, δφδφ occurs in an oscillator component (i.e., occurs in an oscillator component (i.e., sustaining stage amplifier phase noise), the oscillator signal fsustaining stage amplifier phase noise), the oscillator signal frequency requency must change in order to maintain constantmust change in order to maintain constant (2(2nnππ radians) loop phase radians) loop phase shiftshift

Conversion of Phase to Frequency Conversion of Phase to Frequency Instability in an OscillatorInstability in an Oscillator

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Conversion of OpenConversion of Open--Loop Noise to ClosedLoop Noise to Closed--Loop Noise (cont.)Loop Noise (cont.)

uu The conversion process can be described by:The conversion process can be described by:ll ClosedClosed--loop Sloop Sφφ(f) = open(f) = open--loop Sloop Sφφ(f)(1/2(f)(1/2πτπτf)f)22

ll Noise sideband level = Noise sideband level = (f) = 10LOG(S(f) = 10LOG(Sφφ(f)/2)(f)/2)

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PhasePhaseNoiseNoise

SidebandSidebandLevelLevel

(dBc/Hz)(dBc/Hz)

Carrier Offset Frequency (Hz)Carrier Offset Frequency (Hz)1/21/2πτπτ

ττ = oscillator closed loop group delay= oscillator closed loop group delay1/21/2πτπτ = BW/2 for a single (1 pole) resonator= BW/2 for a single (1 pole) resonator

PMPM--toto--FM Noise Conversion in an OscillatorFM Noise Conversion in an Oscillator

1/f PM1/f PM

Additional signal noise degradationAdditional signal noise degradationdue to resonator FM noisedue to resonator FM noise

1/f FM1/f FM

Oscillator closed loop signal FM noiseOscillator closed loop signal FM noisedue to sustaining stage open loop PM due to sustaining stage open loop PM noisenoise

white FMwhite FMwhite PMwhite PM

Oscillator sustaining stage open Oscillator sustaining stage open loop PM noiseloop PM noise

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Characteristics of Ideal ResonatorCharacteristics of Ideal Resonator

uu High group delay (high resonator loaded Q)High group delay (high resonator loaded Q)uu High operating frequency High operating frequency uu Low LossLow Lossuu Moderate Drive CapabilityModerate Drive Capabilityuu Low frequency sensitivity to environmental stress (vibration, Low frequency sensitivity to environmental stress (vibration,

temperature, etc.)temperature, etc.)uu Good shortGood short--term and longterm and long--term frequency stabilityterm frequency stabilityuu Accurate frequency setAccurate frequency set--on capabilityon capabilityuu External frequency tuning capabilityExternal frequency tuning capabilityuu No undesired resonant modes or higher loss in undesired No undesired resonant modes or higher loss in undesired

resonant modes or undesired resonant mode frequencies far resonant modes or undesired resonant mode frequencies far from desired operating frequencyfrom desired operating frequency

uu High manufacturing yield of acceptable devicesHigh manufacturing yield of acceptable devices

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Characteristics of Ideal Characteristics of Ideal Oscillator Sustaining StageOscillator Sustaining Stage

uu Low multiplicative (1/f AM and especially 1/f PM) noiseLow multiplicative (1/f AM and especially 1/f PM) noiseuu Low additive noise (good noise figure)Low additive noise (good noise figure)uu Drive capability consistent with resonator drive level and lossDrive capability consistent with resonator drive level and lossuu Low noise in ALC/AGC circuits and/or inLow noise in ALC/AGC circuits and/or in--compression amplifier compression amplifier

operationoperationuu Low gain and phase sensitivity to DC supply and circuit Low gain and phase sensitivity to DC supply and circuit

temperature variationstemperature variationsuu Low group delay (wide bandwidth)Low group delay (wide bandwidth)uu High load circuit isolationHigh load circuit isolationuu High MTBF; minimal number of adjustable componentsHigh MTBF; minimal number of adjustable componentsuu Ease of alignment and testEase of alignment and testuu Good DC efficiencyGood DC efficiencyuu Low costLow cost

3. Types of Resonators and Delay Lines3. Types of Resonators and Delay Lines

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5. Cavity, Waveguide5. Cavity, Waveguide1. Lumped Element (L1. Lumped Element (L--C)C)2. Acoustic2. Acoustic

Bulk Acoustic Wave (BAW)Bulk Acoustic Wave (BAW)Surface Acoustic Wave (SAW)Surface Acoustic Wave (SAW)Surface Transverse WaveSurface Transverse Wave(STW)(STW)

3. Distributed Element 3. Distributed Element (transmission line)(transmission line)

HelicalHelicalMicrostrip and StriplineMicrostrip and StriplineDielectric Loaded CoaxialDielectric Loaded Coaxial

4. Dielectric4. Dielectric

6. Optical Fiber6. Optical Fiber7. Whispering Gallery 7. Whispering Gallery Mode, Sapphire DielectricMode, Sapphire Dielectric

Highlighted types used in Highlighted types used in lower noise oscillatorslower noise oscillators

2. AcousticBulk Acoustic Wave (BAW)Surface Acoustic Wave (SAW)Surface Transverse Wave(STW)

4. Dielectric

6. Optical Fiber7. Whispering Gallery Mode, Sapphire Dielectric

Types of Resonators and Delay LinesTypes of Resonators and Delay Lines

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Quartz Acoustic ResonatorsQuartz Acoustic Resonators

Desirable PropertiesDesirable Propertiesuu Very high QVery high Quu Controllable (selectable) Controllable (selectable)

frequency temperature frequency temperature coefficientcoefficient

uu Excellent longExcellent long--term and term and shortshort--term frequency stabilityterm frequency stability

uu Relatively low costRelatively low costuu Moderately small volume Moderately small volume

(especially SAW, STW)(especially SAW, STW)uu Well defined, mature Well defined, mature

technologytechnology

Undesirable PropertiesUndesirable Propertiesuu 1/f FM noise that often 1/f FM noise that often

exceed effects of sustaining exceed effects of sustaining stage 1/f PM noisestage 1/f PM noise

uu UnitUnit--toto--unit 1/f FM noise unit 1/f FM noise level. variation; high cost level. variation; high cost associated with low yield of associated with low yield of very low noise resonatorsvery low noise resonators

uu BAW resonator drive level BAW resonator drive level limitations: 1limitations: 1--2mW for AT2mW for AT--cut, 5cut, 5--7mW for SC7mW for SC--cut, even cut, even lower drive for low drift/aginglower drive for low drift/aging

uu NonNon--uniform vibration uniform vibration sensitivitysensitivity

uu FOM (loaded Q) decreases FOM (loaded Q) decreases with increasing frequencywith increasing frequency

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Fundamental resonance, Fundamental resonance, ffss=1/(2=1/(2ππ(LmCm)(LmCm)0.50.5))

Third overtone resonance, fThird overtone resonance, f =3f=3fss

Fifth overtone resonance, fFifth overtone resonance, f =5f=5fss

Quartz Crystal Electrical Equivalent CircuitQuartz Crystal Electrical Equivalent Circuit(for widely used AT(for widely used AT--cut and SCcut and SC--cut crystals)cut crystals)

Co = Static capacitance

uu LLmm = motional (series) inductance= motional (series) inductance

uu CCmm = motional capacitance= motional capacitance

uu RRss = series resistance 2= series resistance 2ππffss/R/Rs s = unloaded Q= unloaded Q

Anharmonic and higher oddAnharmonic and higher odd--overtone overtone resonance(s)resonance(s)

Lm Cm Rs

Quartz Acoustic Resonators, continuedQuartz Acoustic Resonators, continued

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YearYear Resonator TypeResonator Type FrequencyFrequency Noise Level, Sy(f=100Hz)Noise Level, Sy(f=100Hz) PmaxPmax VirbrationVirbration(mW)(mW) SensitivitySensitivity

NominalNominal BestBest (parts in 10(parts in 10--1010/g)/g)

19851985 22 5 to 205 to 205th OT AT5th OT AT--cutcut 80MHz80MHz 1X101X10--2424 2X102X10--2525

19851985 Raytheon SAWRaytheon SAW 500MHz500MHz 2X102X10--2424 4X104X10--2525 5050 5 to 505 to 50

19951995 SAWTEK STWSAWTEK STW 1000MHz1000MHz 5X105X10--2424 1X101X10--2424 100100 1 to 31 to 3

19991999 FEI OT S CFEI OT S C--cutcut 100MHz100MHz ?????? ≤≤1.6X101.6X10--2626 ?????? ??????

80MHz80MHz100MHz100MHz19891989 3rd OT S C3rd OT S C--cutcut 2X102X10--2525 4X104X10--2626 77 3 to 103 to 10

19891989 5th OT AT5th OT AT--cutcut 40MHz40MHz 5X105X10--2626 1X101X10--2626 22 10 to 3010 to 30

19951995 5th OT S C5th OT S C--cutcut 160MHz160MHz 1X101X10--2525 2X102X10--2626 77 3 to 103 to 10

Improvements in Acoustic Resonator Improvements in Acoustic Resonator Performance Performance -- 1985 to 19991985 to 1999

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metal tabmetal tab

metalmetal--plated, dielectric rodplated, dielectric rodwith platedwith plated--thru holethru hole

DielectricDielectric--Filled Coaxial ResonatorsFilled Coaxial Resonators

uu Very popular in wireless hardwareVery popular in wireless hardwareuu High drive capabilityHigh drive capabilityuu One piece, plated construction results in low vibration sensitivOne piece, plated construction results in low vibration sensitivityityuu Unloaded Q is only moderate (proportional to volume)Unloaded Q is only moderate (proportional to volume)uu LL(100Hz)=(100Hz)=--100dBc/Hz, with 100dBc/Hz, with --178dBc/Hz noise floor achieved at 640MHz 178dBc/Hz noise floor achieved at 640MHz

using large volume resonators as multiusing large volume resonators as multi--pole filter oscillator stabilization pole filter oscillator stabilization elementselements

uu Even though resonators are “passive”, excess 1/f noise has beenEven though resonators are “passive”, excess 1/f noise has beenmeasured in large volume, high delay devices with variations in measured in large volume, high delay devices with variations in 1/f noise 1/f noise level of up to 20dBlevel of up to 20dB

36

Dielectric ResonatorsDielectric Resonators

AdvantagesAdvantagesuu High Q at high High Q at high

(microwave) (microwave) frequencyfrequency

uu No measurable resonator 1/f No measurable resonator 1/f noisenoise

uu High drive capabilityHigh drive capabilityuu NearNear--zero temperature zero temperature

coefficient for some ceramic coefficient for some ceramic dielectric materialsdielectric materials

uu Amenable to mechanical Amenable to mechanical adjustment and electronic adjustment and electronic frequency tuningfrequency tuning

DisadvantagesDisadvantagesuu Substantial Q degradation Substantial Q degradation

unless cavity volume is large unless cavity volume is large compared to that of dielectric compared to that of dielectric (low order mode resonances)(low order mode resonances)

uu Highest Q with modest volume Highest Q with modest volume occurs above Coccurs above C--band where band where sustaining stage amplifiers are sustaining stage amplifiers are primarily GaAs sustaining stage primarily GaAs sustaining stage amplifiers exhibiting relatively amplifiers exhibiting relatively high 1/f AM and PM noisehigh 1/f AM and PM noise

uu Resonator frequency sensitivity Resonator frequency sensitivity to vibration is typically 10 to 100 to vibration is typically 10 to 100 times higher, compared to BAW, times higher, compared to BAW, SAW resonatorsSAW resonators

37

Multiple Resonators Can Provide Lower NoiseMultiple Resonators Can Provide Lower Noise

uu Multiple resonators can be cascaded (isolated by amplifiers) or Multiple resonators can be cascaded (isolated by amplifiers) or used in multiused in multi--pole filters in order to increase the oscillator open pole filters in order to increase the oscillator open loop signal path group delayloop signal path group delay

uu Analysis shows that for a given net insertion loss, increasing tAnalysis shows that for a given net insertion loss, increasing the he filter order beyond 2filter order beyond 2--pole does not result in significant increase pole does not result in significant increase in group delayin group delay

uu The group delay increase (going from 1 pole to 2 poles) for net The group delay increase (going from 1 pole to 2 poles) for net loss in the range 3dB to 15dB is 17% to 60%loss in the range 3dB to 15dB is 17% to 60%ll Increasing the number of poles does result in an increase in theIncreasing the number of poles does result in an increase in the

bandwidth over which the group delay is maximumbandwidth over which the group delay is maximumll Use of a single, multiUse of a single, multi--pole filter at a given, net insertion loss results pole filter at a given, net insertion loss results

in approximately the same delay as a cascade of resonators havinin approximately the same delay as a cascade of resonators having g the same overall insertion lossthe same overall insertion loss

38

Optical Fiber Delay LinesOptical Fiber Delay Lines

AdvantagesAdvantagesuu High delay possible: tens of High delay possible: tens of

microsecondsmicrosecondsuu Low optical signal strength Low optical signal strength

loss in fiberloss in fiberuu OptoOpto--electronic Oscillator electronic Oscillator

(OEO) signal generation (OEO) signal generation directly at microwavedirectly at microwave

uu Noise level (i.e., delay) Noise level (i.e., delay) theoretically independent of theoretically independent of carrier frequencycarrier frequency

uu Possible generation of Possible generation of multiple, selectable multiple, selectable frequency signals (spaced at frequency signals (spaced at the reciprocal of the delay the reciprocal of the delay timetime

DisadvantagesDisadvantagesuu Detector and/or microwave Detector and/or microwave

amplifier noise may limit amplifier noise may limit attainable performanceattainable performance

uu For low noise signal For low noise signal generation, long fiber length generation, long fiber length results in conditions for results in conditions for oscillation being satisfied at oscillation being satisfied at multiple, closelymultiple, closely--spaced spaced frequenciesfrequencies

uu Selectable (reciprocal of Selectable (reciprocal of delay) frequencies are nondelay) frequencies are non--coherentcoherent

39

LaserLaser

Optical fiberOptical fiber

ModulatorModulator

delay = delay = ττ

DetectorDetector

BandpassBandpassFilterFilter Possible operating frequencies separated by 1/Possible operating frequencies separated by 1/ττ

Bandpass filter selectivityBandpass filter selectivity

uWaveuWaveAmpAmp

Reference: JPL:1995Reference: JPL:1995--1999 Freq. Contr. Symp.1999 Freq. Contr. Symp.

OptoOpto--Electronic Oscillator (OEO)Electronic Oscillator (OEO)

uu Other refinements include use of a second, shorter length Other refinements include use of a second, shorter length optical fiber for selection (inoptical fiber for selection (in--phase reinforcement) of a specific phase reinforcement) of a specific frequency signal and use of carrier suppression for additional frequency signal and use of carrier suppression for additional noise reductionnoise reduction

uu Approximately Approximately --84dBc/Hz at fm=100Hz demonstrated at 10GHz 84dBc/Hz at fm=100Hz demonstrated at 10GHz using carrier suppression. This level of nearusing carrier suppression. This level of near--carrier PM noise is carrier PM noise is comparable to that obtainable using frequencycomparable to that obtainable using frequency--multiplied, quartz multiplied, quartz crystal oscillator or SAW oscillatorcrystal oscillator or SAW oscillator--derived, Xderived, X--band signalband signal

40

(f)(f)(dBc/Hz)(dBc/Hz)


10dB typ.10dB typ.

10dB typ.10dB typ.

15dB typ.15dB typ.

10dB typ.10dB typ.

SS--Band Dielectric Resonator OscillatorBand Dielectric Resonator OscillatorSignal Multiplied to XSignal Multiplied to X--BandBand

100MHz Quartz Crystal Oscillator100MHz Quartz Crystal OscillatorSignal Multiplied to XSignal Multiplied to X--BandBand

1GHz Quartz SAW or STW Oscillator1GHz Quartz SAW or STW OscillatorSignal Multiplied to XSignal Multiplied to X--BandBand

Spectral Tradeoff: NearSpectral Tradeoff: Near--Carrier vs Noise Carrier vs Noise Floor PerformanceFloor Performance

41

Whispering Gallery Mode, Sapphire Whispering Gallery Mode, Sapphire Dielectric ResonatorsDielectric Resonators

uu Dielectric loss in sapphire is low at room temperature Dielectric loss in sapphire is low at room temperature and rapidly decreases with decreasing temperatureand rapidly decreases with decreasing temperature

uu HighHigh--order “whispering gallery” mode ring and solid order “whispering gallery” mode ring and solid cylindrical resonators have been built that exhibit cylindrical resonators have been built that exhibit unloaded Q values, at Xunloaded Q values, at X--band, of 200,000 at room band, of 200,000 at room temperature and 5 to 10million at 80Ktemperature and 5 to 10million at 80K

uu This ultraThis ultra--high resonator Q results in oscillators high resonator Q results in oscillators whose Xwhose X--band output signal spectra are significantly band output signal spectra are significantly superior to that attainable using any other resonator superior to that attainable using any other resonator technology technology

42

Whispering Gallery Mode, Sapphire Whispering Gallery Mode, Sapphire Dielectric Resonators: IssuesDielectric Resonators: Issues

uu Resonator volume (including hermetic, cooled enclosure) is Resonator volume (including hermetic, cooled enclosure) is relatively largerelatively large

uu The ultraThe ultra--low phase noise spectrum exhibited by the oscillator low phase noise spectrum exhibited by the oscillator is degraded by correspondingly low levels of vibration is degraded by correspondingly low levels of vibration

uu For cryoFor cryo--cooled resonators, cryocooled resonators, cryo--cooler vibration, MTBF, cost, cooler vibration, MTBF, cost, etc. constitute overall hardware performance issues. etc. constitute overall hardware performance issues. VibrationVibration--free, TEfree, TE--coolers are inefficient with limited cooling coolers are inefficient with limited cooling capability. Resonant frequency temperature coefficient is capability. Resonant frequency temperature coefficient is large at elevated (i.e., TElarge at elevated (i.e., TE--cooler) temperaturescooler) temperatures

uu Addition of temperature compensating materials usually Addition of temperature compensating materials usually degrades resonator Qdegrades resonator Q

uu GaAs sustaining stage amplifiers exhibit high 1/f PM noise GaAs sustaining stage amplifiers exhibit high 1/f PM noise that degrades oscillator nearthat degrades oscillator near--carrier signal spectral carrier signal spectral performance. Noise reduction feedback circuitry adds performance. Noise reduction feedback circuitry adds cost/volume/complexity to the oscillator circuitcost/volume/complexity to the oscillator circuit

43

Measured Performance: TEMeasured Performance: TE--Cooled, Cooled, Sapphire DROSapphire DRO

Poseidon Scientific Instruments (PSI) Sapphire DRO Phase Noise at 9GHz

-180.0

-160.0

-140.0

-120.0

-100.0

-80.0

-60.0

10.0 100.0 1000.0 10000.0 100000.0Frequency (Hz)

Phas

e N

oise

Sid

eban

d Le

vel

(dB

c/H

z)

4. Useful Network/Impedance Transformations4. Useful Network/Impedance Transformations

45

Impedance Matching and TransformationsImpedance Matching and Transformations

uu Useful for matching nonUseful for matching non--50 ohm devices to 50 ohms 50 ohm devices to 50 ohms or to each otheror to each other

uu A standard tool used extensively in the design of A standard tool used extensively in the design of bandband--pass or bandpass or band--reject filters allowing use of reject filters allowing use of practical component element valuespractical component element values

uu Very useful in oscillator design, both within the Very useful in oscillator design, both within the sustaining circuit stage itself and also for matching sustaining circuit stage itself and also for matching between oscillator functional elements (i.e., resonator between oscillator functional elements (i.e., resonator and resonator tuning circuitry)and resonator tuning circuitry)

46

RpRp XpXp

Let “Q” = Rp/Xp = Xs/RsLet “Q” = Rp/Xp = Xs/Rs

RsRs

XsXs

Rs = Rp/(QRs = Rp/(Q22+1)+1)Xs = Xp(QXs = Xp(Q2) 2) /(Q/(Q22+1)+1)

Example: If Rp = 300 ohms and Xp = j100 ohms at frequency fo, thExample: If Rp = 300 ohms and Xp = j100 ohms at frequency fo, then en “Q” = 3 at (and only at fo), this is equivalent to Rs + jXs = 3“Q” = 3 at (and only at fo), this is equivalent to Rs + jXs = 30 + j900 + j90The “Q” is an approximate measure of the bandwidth of the The “Q” is an approximate measure of the bandwidth of the transformation (i.e., BW=fo/Q) transformation (i.e., BW=fo/Q)

Series Series -- Parallel Reactance/Parallel Reactance/Resistance ConversionsResistance Conversions

47

ZZ = ZaZb + ZaZc + ZbZcZZ = ZaZb + ZaZc + ZbZc

Zx = Zx = ZZZZ

ZbZb

Zy = Zy = ZZZZ

ZcZc

Zz = Zz = ZZZZ

ZaZa

Zc

Za Zb

ZzZx

Zy

DeltaDelta--Star TransformationStar Transformation

uu Often results in being able to obtain more realistic Often results in being able to obtain more realistic element values (component impedance levels)element values (component impedance levels)

48

ZZK:1K:1

ZZ

ZZ

K(KK(K--1)1)ZZ

11--KK

KK

ZZ

K:1K:1

Z(KZ(K--1)1)KK22

ZZ

KK

KKZ(1Z(1--K)K)

Norton’s TransformationNorton’s Transformationuu Very powerful and useful Very powerful and useful uu Not a single frequency approximation, a true transformationNot a single frequency approximation, a true transformationuu Negative value, reactive element can usually be absorbed into Negative value, reactive element can usually be absorbed into

existing, adjacent positive value similar reactive elementexisting, adjacent positive value similar reactive element

49

R’R’00=g=g00=1=1

C’C’11=g=g11

L’L’22=g=g22 L’L’nn=g=gnn

C’C’nn--11=g=gnn--11 G’G’n+1n+1=g=gn+1n+1

ωω

AA

[1] G. L. Matthaei, “Tables of Chebyshev Impedance[1] G. L. Matthaei, “Tables of Chebyshev Impedance--Transforming Networks of Transforming Networks of LowLow--Pass Filter Form”, Proc. IEEE, Vol. 52, No. 8, August 1988, pp. Pass Filter Form”, Proc. IEEE, Vol. 52, No. 8, August 1988, pp. 939939--963.963.

Chebyshev Impedance Transforming Chebyshev Impedance Transforming Networks Networks [1][1]

uu Tabulated impedance ratios from 1.5:1 to 50:1 and bandwidths Tabulated impedance ratios from 1.5:1 to 50:1 and bandwidths from 10% to 100%from 10% to 100%

uu Can be lumped or distributed elementCan be lumped or distributed element

50

Lumped element approximations for a quarterLumped element approximations for a quarter--wavelength lineswavelength lines

RRLL

quarterquarter--wavelength at fowavelength at fo

Zin = ZZin = Z0022/R/RLL characteristic impedancecharacteristic impedance

= Z= Z00

RRLL


Zin = (ZZin = (Z010122/ Z/ Z0202

22)R)RLL characteristic impedancecharacteristic impedance= Z= Z0202


characteristic impedancecharacteristic impedance= Z= Z0101

QuarterQuarter--wavelength Impedance Inverters, Impedance wavelength Impedance Inverters, Impedance Transformers, and Delay Lines (phase shift)Transformers, and Delay Lines (phase shift)

51

Transmission Lines: Lumped Element Transmission Lines: Lumped Element ApproximationsApproximations

LLtotal total = (= ( //λ λ )(Z)(Z0 0 /f/f00), C), Ctotal total = (= ( //λλ)(1/ (Z)(1/ (Z00 ff00)), L)), Ltotaltotal/C/Ctotaltotal = Z= Z0022

If the line is considered a series of pi networks, the inner capIf the line is considered a series of pi networks, the inner capacitor acitor values are twice that of the end capacitors (i.e., C2=2C1)values are twice that of the end capacitors (i.e., C2=2C1)

SingleSingle--ended linesended lines(coaxial, microstrip, stripline)(coaxial, microstrip, stripline)

Balanced linesBalanced lines(twin(twin--lead, twisted pair)lead, twisted pair)

L1/2L1/2 L1/2L1/2

C1C1 C2C2 C1C1

L1/2L1/2 L1/2L1/2

L1L1 L1L1

C1C1 C2C2 C1C1

52

Useful Aspects of Lumped or Distributed Useful Aspects of Lumped or Distributed Element Transmission LinesElement Transmission Linesuu Impedance inversion/transformation (can transform a resonator seImpedance inversion/transformation (can transform a resonator seriesries--

resonance impedance to a parallel resonance)resonance impedance to a parallel resonance)

uu Relatively broadband impedance transformation, compared to bandRelatively broadband impedance transformation, compared to band--pass pass structures (lower sensitivity to element value tolerance, temperstructures (lower sensitivity to element value tolerance, temperature ature coefficient, etc.)coefficient, etc.)

uu All or some of the line can be realized using actual transmissioAll or some of the line can be realized using actual transmission line (coaxial n line (coaxial cable)cable)

ll Thermal isolation of ovenized componentsThermal isolation of ovenized components

ll Vibration isolation of acceleration sensitive componentsVibration isolation of acceleration sensitive components

uu At HF and Low VHF, transmission line transformers can be realizeAt HF and Low VHF, transmission line transformers can be realized with d with values for characteristic impedance not obtainable using conventvalues for characteristic impedance not obtainable using conventional coaxial ional coaxial or twin lead cableor twin lead cable

uu Positive or negative phase shifts may be obtained using highPositive or negative phase shifts may be obtained using high--pass or lowpass or low--pass lumped element approximations pass lumped element approximations

53

LmLm

CmCm

RsRs

CoCoLoLo

CvCv LpLp

Quartz CrystalQuartz Crystalwith Parallelwith ParallelCapacitanceCapacitance

AntiAnti--resonatedresonated

VaractorVaractorInductorInductorTuningTuningCircuitCircuit

LmLm

CmCm

RsRs

CoCo

CvCv Lp’ = LpLo/(Lp+Lo)Lp’ = LpLo/(Lp+Lo)

The series resonant frequency of a high Q dipole is unaffected bThe series resonant frequency of a high Q dipole is unaffected by y movement of parallel elements from one portion of the dipole to movement of parallel elements from one portion of the dipole to the the

other as long as series and parallel resonant frequencies do notother as long as series and parallel resonant frequencies do notapproach one anotherapproach one another

Dipole TransformationDipole Transformation

5. Sustaining Stage Design and Performance5. Sustaining Stage Design and Performance

55

Zin (ideal voltageZin (ideal voltage--controlled current source)controlled current source)= Z1 + Z2 + gm(Z1)(Z2)= Z1 + Z2 + gm(Z1)(Z2)If Z1 and Z2 are reactances, Z1=jX1, Z2=jX2, andIf Z1 and Z2 are reactances, Z1=jX1, Z2=jX2, andZin = j(X1+X2) Zin = j(X1+X2) --gm(X1)(X2)gm(X1)(X2)where where --gm(X1)(X2) is the negative resistance termgm(X1)(X2) is the negative resistance term

Z1Z1

Z2Z2

The Transistor Viewed as a ReactanceThe Transistor Viewed as a Reactance--plusplus--Negative Resistance GeneratorNegative Resistance Generator

uu Normally, capacitors are used for the reactances X1 Normally, capacitors are used for the reactances X1 and X2and X2

uu At microwave frequencies, transistor junction At microwave frequencies, transistor junction capacitance may comprise a significant part or all of capacitance may comprise a significant part or all of the reactancethe reactance

56

Z1Z1 Z2Z2

Z3Z3

Zin (ideal voltageZin (ideal voltage--controlled current source)controlled current source)= (Z1)(Z2)/(Z1+Z2+Z3) + 1/gm= (Z1)(Z2)/(Z1+Z2+Z3) + 1/gmIf Z1=1/jIf Z1=1/jωωC1, Z2=1/jC1, Z2=1/jωωC2, and Z3=jC2, and Z3=jωωLs+RsLs+Rsand if, at and if, at ωω= = ωωoo, Z1/Z2/Z3 are resonant , Z1/Z2/Z3 are resonant (Z1+Z2+Z3 = Rs),(Z1+Z2+Z3 = Rs),then Zin at then Zin at ωω= = ωωoo = = --1/(1/(ωωoo

22C1C2Rs) +1/gmC1C2Rs) +1/gm

The Transistor Viewed as a Negative The Transistor Viewed as a Negative Resistance Generator (at Resistance Generator (at ωωo)o)

uu Normally, capacitors are used as the impedances Z1 Normally, capacitors are used as the impedances Z1 and Z2and Z2

uu Z3 is normally an inductor, and the net resonant Z3 is normally an inductor, and the net resonant resistance of the series combination, Rs, includes resistance of the series combination, Rs, includes that due to the circuit external load resistance as well that due to the circuit external load resistance as well as the loss in the inductoras the loss in the inductor

57

Zin = j(X1+X2) Zin = j(X1+X2) -- (X1)(X2)/(RE+1/gm)(X1)(X2)/(RE+1/gm)

where where --(X1)(X2)/(RE+1/gm) is the (X1)(X2)/(RE+1/gm) is the negative resistance term negative resistance term

X1X1

X2X2RERE

Use of Unbypassed Emitter Resistance for Use of Unbypassed Emitter Resistance for Gain (Negative Resistance) StabilizationGain (Negative Resistance) Stabilization

uu The addition of RE stabilizes the negative resistance The addition of RE stabilizes the negative resistance (makes it more dependent on RE then on gm(makes it more dependent on RE then on gm

uu In addition, unIn addition, un--bypassed emitter resistance bypassed emitter resistance constitutes one method for reducing transistor 1/f PM constitutes one method for reducing transistor 1/f PM noise levelsnoise levels

58

RERE

C1C1

C2C2

LsLs

RsRs

Q1Q1

basic oscillator circuitbasic oscillator circuitC1C1

C2C2

LsLs

RsRs

Q1Q1

crystal operation at fscrystal operation at fswhere Zwhere ZY1Y1 = Rs (i.e., Z=RE)= Rs (i.e., Z=RE)

RERE

C1C1

C2C2

Q1Q1

crystal operation above fscrystal operation above fswhere Zwhere ZY1Y1 = j= jωωLs + RsLs + Rs

Y1Y1

Crystal Oscillators with Crystal Placement in Crystal Oscillators with Crystal Placement in Different Portions of the CircuitDifferent Portions of the Circuit

59* From* From the NIST Tutorial on 1/f AM and PM Noise in Amplifiersthe NIST Tutorial on 1/f AM and PM Noise in Amplifiers

Methods for Reducing Discrete Transistor Methods for Reducing Discrete Transistor Sustaining Stage 1/f PM NoiseSustaining Stage 1/f PM Noise

uu Use unUse un--bypassed emitter resistance (a resistor or the bypassed emitter resistance (a resistor or the resonator itself connected in series with the emitter resonator itself connected in series with the emitter

uu Use high frequency transistors having small junction Use high frequency transistors having small junction capacitance and operate at moderately high bias voltage to capacitance and operate at moderately high bias voltage to reduce phase modulation due to junction capacitance noise reduce phase modulation due to junction capacitance noise modulation*modulation*

uu Use heavily bypassed DC bias circuitry and regulated DC Use heavily bypassed DC bias circuitry and regulated DC supplies*supplies*

uu Consider the use of a baseConsider the use of a base--band noise reduction feedback band noise reduction feedback loop*loop*

uu Extract the signal through the resonator to the load, thereby Extract the signal through the resonator to the load, thereby using the resonator transmission response selectivity to filter using the resonator transmission response selectivity to filter the carrier noise spectrumthe carrier noise spectrum

60

C1C1

LsLsRsRs

Q1Q1C2C2

Q2Q2 MatchingMatchingNetworkNetwork

RRLLY1Y1

IIY1Y1 NN22(I(IY1Y1))

NN22:1:1

Transformer sometimes usedTransformer sometimes usedto step up current into Q1,Q2to step up current into Q1,Q2

NN11(I(IY1Y1))

1:N1:N11

Extraction of the Oscillator Signal Through Extraction of the Oscillator Signal Through the Resonatorthe Resonator

61

RLRL

Cascode transistorCascode transistorconfigurationconfiguration

(large ratio of Po/P(large ratio of Po/PY1Y1))

+VDC+VDC

Y1Y1Symmetric diodeSymmetric diode

clippingclipping

Ref. bias (RF level adjust)Ref. bias (RF level adjust)

Ferrite beadsFerrite beadsto prevent UHFto prevent UHF

oscillationoscillation

Discrete Transistor Oscillator Example:Discrete Transistor Oscillator Example:Low Noise, VHF Crystal OscillatorLow Noise, VHF Crystal Oscillator

62

Discrete Transistor Sustaining StagesDiscrete Transistor Sustaining Stages

AdvantagesAdvantagesuu Low CostLow Costuu PrePre--fabrication and postfabrication and post--

fabrication design and fabrication design and design change flexibilitydesign change flexibility

uu Biasing flexibilityBiasing flexibilityuu Efficiency (DC power Efficiency (DC power

consumption)consumption)

DisadvantagesDisadvantagesuu For low noise, transistors For low noise, transistors

with high ft should be used; with high ft should be used; circuit is then susceptible to circuit is then susceptible to high frequency instability due high frequency instability due to layout parasitics and lossto layout parasitics and loss--less resonator outless resonator out--ofof--band band impedanceimpedance

uu Difficulty in predicting or Difficulty in predicting or measuring 1/f AM and PM measuring 1/f AM and PM noise using 50 ohm test noise using 50 ohm test equipment since actual equipment since actual sustaining stagesustaining stage--toto--resonator circuit interface resonator circuit interface impedances are not usually impedances are not usually 50 ohms.50 ohms.

63

Advantages of Modular Amplifier Advantages of Modular Amplifier Sustaining StagesSustaining Stages

uu Easily characterized using 50 ohm test equipment (amplifier sEasily characterized using 50 ohm test equipment (amplifier s--parameters, 1/f AM , 1/f PM, and KTBF noise)parameters, 1/f AM , 1/f PM, and KTBF noise)

uu Availability of unconditionally stable amplifiers eliminates posAvailability of unconditionally stable amplifiers eliminates possibility sibility of parasitic oscillationsof parasitic oscillations

uu Amplifiers available (especially silicon bipolar and GaAs HBT tyAmplifiers available (especially silicon bipolar and GaAs HBT types) pes) exhibiting low 1/f AM and PM noiseexhibiting low 1/f AM and PM noise

uu Certain models maintain low noise performance when operated in Certain models maintain low noise performance when operated in gain compression thereby eliminating a requirement for separate gain compression thereby eliminating a requirement for separate ALC/AGC circuitry in the oscillatorALC/AGC circuitry in the oscillator

uu Amplifier use allows a building block approach to be used for alAmplifier use allows a building block approach to be used for all of l of the oscillator functional subthe oscillator functional sub--circuits: amplifier, resonator, resonator circuits: amplifier, resonator, resonator tuning, resonator mode selection filter, etctuning, resonator mode selection filter, etc

uu Relatively low cost amplifiers (plastic, COTS, HBT darlington paRelatively low cost amplifiers (plastic, COTS, HBT darlington pair ir configuration) are now available with multiconfiguration) are now available with multi--decade bandwidths decade bandwidths operating from HF to microwave frequencies operating from HF to microwave frequencies

64

Silicon Bipolar Modular Amplifier: Silicon Bipolar Modular Amplifier: Measured 1/f PM NoiseMeasured 1/f PM Noise

1/f PM noise (10dB/decade)1/f PM noise (10dB/decade)

White PM noise (floor)White PM noise (floor)

65

1 10 100 1K 1 10 100 1K 10K10K 100K 1M100K 1M

--110110

--120120

--130130

--140140

--150150

--160160

--170170


PhasePhaseNoiseNoiseSidebandSidebandLevelLevel(dBc/Hz)(dBc/Hz)

XX--band GaAs Amp.band GaAs Amp.

XX--band Schottky Mixerband Schottky Mixer& X& X--band HBT amp.band HBT amp.

HFHF--VHF Bipolar Amp. &VHF Bipolar Amp. &HFHF--UHF Schottky MixerUHF Schottky Mixer

LL--band Bipolar and HBTband Bipolar and HBTAmp.Amp.

““Typical” Component 1/f PM Multiplicative Typical” Component 1/f PM Multiplicative Noise LevelsNoise Levels

66

Modular Amplifiers: General CommentsModular Amplifiers: General Comments

uu Generally, amplifier vendors do not design for, specify, or Generally, amplifier vendors do not design for, specify, or measure device 1/f AM and PM noisemeasure device 1/f AM and PM noise

uu It is usually necessary to evaluate candidate sustaining stage It is usually necessary to evaluate candidate sustaining stage amplifiers in terms of measured 1/f AM and PM noise at amplifiers in terms of measured 1/f AM and PM noise at intended drive level (i.e., in gain compression when the intended drive level (i.e., in gain compression when the oscillator will not employ separate ALC/AGC)oscillator will not employ separate ALC/AGC)

uu Amplifier S21 phase angle sensitivity to gain compression, as Amplifier S21 phase angle sensitivity to gain compression, as well as gain magnitude and phase sensitivity to DC supply well as gain magnitude and phase sensitivity to DC supply variation (noise) must be consideredvariation (noise) must be considered

uu Silicon bipolar amplifiers and HBT amplifiers operating below Silicon bipolar amplifiers and HBT amplifiers operating below LL--band normally exhibit lower levels of 1/f AM and PM noise, band normally exhibit lower levels of 1/f AM and PM noise, compared to microwave amplifierscompared to microwave amplifiers

67

SAWRSAWRSAWRSAWR

SAWRSAWR XsXs SAWRSAWR

looploopphasephaseadjustadjust

XsXs

XsXs XsXs

Modular Amplifier Oscillator Design Modular Amplifier Oscillator Design Example: Low Noise, SAWR OscillatorExample: Low Noise, SAWR Oscillator

uu Xs = SelectXs = Select--inin--test inductor or capacitor to align SAWR center test inductor or capacitor to align SAWR center frequency frequency

uu Four, cascaded combinations of SAWRs and amplifiers used to Four, cascaded combinations of SAWRs and amplifiers used to increase loop group delayincrease loop group delay

uu Achieved Achieved --124dBc/Hz at fm=100Hz at fo=320MHz124dBc/Hz at fm=100Hz at fo=320MHzuu Requires accurate tracking between resonators over time and Requires accurate tracking between resonators over time and

temperaturetemperature

68

Zs = Rs at foZs = Rs at fo

RpRp RpRpGGAA = 14dB,= 14dB,φφAA = 180= 180oo

Lumped element, quarterLumped element, quarterwavelength lineswavelength lines

ZoZo22 = 50Zx= 50ZxAA

Tune inputTune input

Modular Amplifier Oscillator Design Modular Amplifier Oscillator Design Example: Low Noise, HF OscillatorExample: Low Noise, HF Oscillator

uu QuarterQuarter--wavelength lines yield 90wavelength lines yield 90oo phase shift and match 50 ohms to phase shift and match 50 ohms to Zx at fo, provide improper phase shift below fo and attenuation Zx at fo, provide improper phase shift below fo and attenuation above above fo preventing oscillation at other crystal resonant modes fo preventing oscillation at other crystal resonant modes (previous (previous exercise)exercise)

uu Demonstrated Demonstrated --156dBc/Hz at fm=100Hz at fo=10MHz using third 156dBc/Hz at fm=100Hz at fo=10MHz using third overtone ATovertone AT--cut crystalscut crystals

6. Oscillator Frequency Adjustment/Voltage Tuning6. Oscillator Frequency Adjustment/Voltage Tuning

70

Methods for Providing Oscillator Methods for Providing Oscillator Frequency TuningFrequency Tuning

XsXs ResonatorResonator

sustaining stagesustaining stage

AA

uuXs = variable reactance in series with the resonator used Xs = variable reactance in series with the resonator used to vary the overall resonant frequency of the resonatorto vary the overall resonant frequency of the resonator--reactance combinationreactance combination

φφ ResonatorResonator


AA

uu φφ = variable phase shifter used to force the oscillator signal = variable phase shifter used to force the oscillator signal frequency to change to a (new, 360frequency to change to a (new, 360oo loop phase shift) loop phase shift) frequency that varies within the resonator passfrequency that varies within the resonator pass--bandband

71

Oscillator Frequency TuningOscillator Frequency TuningReactance TuningReactance Tuning Phase Shift TuningPhase Shift Tuning

Carrier signal is maintained at Carrier signal is maintained at center of the transmission center of the transmission response of the resonatorresponse of the resonator--reactance combinationreactance combination

Carrier signal moves within the Carrier signal moves within the resonator transmission resonator transmission response passresponse pass--band; tuning band; tuning range is restricted to less than range is restricted to less than the passband widththe passband width

Impedance transformation is Impedance transformation is often required between the often required between the resonator and the tuning circuitresonator and the tuning circuit

Phase shift circuit can be Phase shift circuit can be implemented as a 50 ohm implemented as a 50 ohm devicedeviceFor electronic (voltage) tuning, For electronic (voltage) tuning, the placement of the phase shift the placement of the phase shift tuning circuit in the oscillator tuning circuit in the oscillator effects the sideband response effects the sideband response of the oscillator, and must be of the oscillator, and must be taken into account in phasetaken into account in phase--locked oscillator applicationslocked oscillator applications

72

Tuning voltageTuning voltage

VCO GainVCO Gain

modulationmodulationfrequencyfrequency

desired gain constant = Ko/sdesired gain constant = Ko/sactual gain constantactual gain constant

1/21/2πτπτ

delay = delay = ττφφ ResonatorResonator


AA

Phase Shift TuningPhase Shift Tuning

uu Modulation frequency response affected by Modulation frequency response affected by placement of phase shifterplacement of phase shifter

73

Methodology of Linear Frequency Tuning Methodology of Linear Frequency Tuning Using Abrupt Junction Varactor DiodesUsing Abrupt Junction Varactor Diodes

uu A resonator operated at/near series resonance exhibits a nearA resonator operated at/near series resonance exhibits a near--linear reactance vs frequency characteristiclinear reactance vs frequency characteristic

uu Connection of a linear reactance vs voltage network in series wiConnection of a linear reactance vs voltage network in series with th the resonator will then result in a circuit whose overall resonathe resonator will then result in a circuit whose overall resonant nt frequency vs voltage characteristic is nearfrequency vs voltage characteristic is near--linearlinear

uu The same holds true for a parallel connection of a parallel resoThe same holds true for a parallel connection of a parallel resonant nant resonator and a linear susceptance vs voltage circuitresonator and a linear susceptance vs voltage circuit

uu Impedance transformation between the resonator and the tuning Impedance transformation between the resonator and the tuning circuit is often required to increase tuning range using practiccircuit is often required to increase tuning range using practical al value components in the tuning circuitvalue components in the tuning circuit

uu Use of backUse of back--toto--back varactor diodes in the tuning circuits has been back varactor diodes in the tuning circuits has been found to eliminate effects of tuning circuit diode noise n oscilfound to eliminate effects of tuning circuit diode noise n oscillator lator signal spectral performance signal spectral performance

74

LLpp

CCvv

LLss

Obtaining Linear Reactance vs VoltageObtaining Linear Reactance vs Voltage

uu For abrupt junction varactor diodes, C = K/(V+For abrupt junction varactor diodes, C = K/(V+φφ))γγ where where φ φ = = contact potential = 0.6 volts at room temp, and contact potential = 0.6 volts at room temp, and γγ = 0.5= 0.5

uu To achieve nearTo achieve near--linear reactance vs voltage using abrupt linear reactance vs voltage using abrupt junction varactor diodes, 1/(LpCvo) = junction varactor diodes, 1/(LpCvo) = ωωoo

22/3 where Cvo is the /3 where Cvo is the varactor diode capacitance at the band center voltage = Vovaractor diode capacitance at the band center voltage = Vo

uu For zero reactance at the band center tuning voltage, Ls=Lp/2For zero reactance at the band center tuning voltage, Ls=Lp/2uu The reactance vs voltage slope at the band center voltage is The reactance vs voltage slope at the band center voltage is

0.3750.375ωωooLp/(vo+Lp/(vo+φφ) )

75

CCpp

CCvv

LLss

Linear Susceptance vs VoltageLinear Susceptance vs Voltage

uu For nearFor near--linear susceptance vs voltage using abrupt junction linear susceptance vs voltage using abrupt junction varactor diode, 1/(LsCvo) = varactor diode, 1/(LsCvo) = ωωoo

22/3 where Cvo is the varactor /3 where Cvo is the varactor diode capacitance at the band center voltage = Vodiode capacitance at the band center voltage = Vo

uu For zero susceptance at the band center tuning voltage, For zero susceptance at the band center tuning voltage, Cp = Cvo/2Cp = Cvo/2

76

Linear Tunable Low Noise Oscillators: Linear Tunable Low Noise Oscillators: Typical ResultsTypical Results

Resonator TypeResonator Type

ATAT--Cut FundamentalCut FundamentalQuartz CrystalQuartz Crystal

ATAT--Cut FundamentalCut FundamentalQuartz CrystalQuartz Crystal

SCSC--Cut OvertoneCut OvertoneQuartz CrystalQuartz Crystal

SAWRSAWR

STWSTW

Coaxial ResonatorCoaxial ResonatorBand pass FilterBand pass Filter

Tuning Range Tuning Range (ppm)(ppm)

20002000

250250

1010

500500

500500

150150

Error from LinearError from Linear(ppm)(ppm)

55

11

0.50.5

55

100100

5050

Tuning Circuit TypeTuning Circuit Type

ReactanceReactance

ReactanceReactance

ReactanceReactance

ReactanceReactance

Phase ShiftPhase Shift

Phase ShiftPhase Shift

7. Environmental Stress Effects7. Environmental Stress Effects

78

EnvironmentallyEnvironmentally--Induced Oscillator Signal Induced Oscillator Signal Frequency ChangeFrequency Change

uu Resonator/Oscillator signal frequency change can be Resonator/Oscillator signal frequency change can be induced by changes in:induced by changes in:ll TemperatureTemperaturell PressurePressurell Acceleration (vibration)Acceleration (vibration)ll Other (radiation, etc)Other (radiation, etc)

79

VibrationVibration

uu Vibration constitutes the primary environmental Vibration constitutes the primary environmental stress affecting oscillator signal shortstress affecting oscillator signal short--term frequency term frequency stability (phase noise)stability (phase noise)

uu Although resonator sensitivity to vibration is often the Although resonator sensitivity to vibration is often the primary contributor, vibration primary contributor, vibration --induced changes in the induced changes in the nonnon--resonator portion of the oscillator circuit can be resonator portion of the oscillator circuit can be significantsignificant

uu High Q mechanical resonances in the resonator High Q mechanical resonances in the resonator and/or nonand/or non--resonator oscillator circuitry and resonator oscillator circuitry and enclosure can cause severe signal spectral enclosure can cause severe signal spectral degradation under vibrationdegradation under vibration

80

Vibration: An ExampleVibration: An Example

uu A 100MHz crystal oscillator can exhibit a phase noise sideband A 100MHz crystal oscillator can exhibit a phase noise sideband level at 1KHz carrier offset frequency of level at 1KHz carrier offset frequency of --163dBc/Hz.163dBc/Hz.

uu The fractional frequency instability is Sy(f=1000Hz) = 1X10The fractional frequency instability is Sy(f=1000Hz) = 1X10--2626/Hz./Hz.uu The corresponding phase instability, SThe corresponding phase instability, Sφφ(f), is 1X10(f), is 1X10--1616 radrad22/Hz./Hz.uu The crystal vibration level that would degrade the atThe crystal vibration level that would degrade the at--rest oscillator rest oscillator

signal spectrum, based a crystal frequency vibration sensitivitysignal spectrum, based a crystal frequency vibration sensitivityvalue value ΓΓf f = 5X10= 5X10--1010/g is quite small: Sg(f) = Sy(f)//g is quite small: Sg(f) = Sy(f)/ΓΓff

22 = 4X10= 4X10--88 gg22/Hz./Hz.uu The corresponding allowable signal path dimensional change, The corresponding allowable signal path dimensional change,

based on a wavelength of 300cm is: 48 angstroms/Hzbased on a wavelength of 300cm is: 48 angstroms/Hz1/21/2..uu In the 50In the 50--ohm circuit, a capacitance variation (due to vibrationohm circuit, a capacitance variation (due to vibration--

induced printed board or enclosure cover movement) of: 6X10induced printed board or enclosure cover movement) of: 6X10--77

pF/HzpF/Hz1/21/2 would degrade the atwould degrade the at--rest signal spectrum.rest signal spectrum.

81

Methods for Attenuating Effects of VibrationMethods for Attenuating Effects of Vibration

uu Vibration isolation of resonators or of entire oscillatorVibration isolation of resonators or of entire oscillatoruu Cancellation vie feedback of accelerometerCancellation vie feedback of accelerometer--sensed sensed

signals to oscillator frequency tuning circuitrysignals to oscillator frequency tuning circuitryuu Measurement of individual (crystal) resonator vibration Measurement of individual (crystal) resonator vibration

sensitivity magnitude and direction and use of matched, sensitivity magnitude and direction and use of matched, oppositelyoppositely--oriented devicesoriented devicesll Use of multiple, unmatched oppositelyUse of multiple, unmatched oppositely--oriented devicesoriented devices

uu Reduction of resonator vibration sensitivity via resonator Reduction of resonator vibration sensitivity via resonator design (geometry, mounting, mass loading, etc.)design (geometry, mounting, mass loading, etc.)

82

yy xx

zz

aa bb

cc dd

““Poor Mans” Method for Reducing Quartz Poor Mans” Method for Reducing Quartz Crystal Vibration SensitivityCrystal Vibration Sensitivity

uu Two Crystals: partial Two Crystals: partial cancellation in z and x cancellation in z and x directions, no cancellation in y directions, no cancellation in y directiondirection

uu Four Crystals: partial Four Crystals: partial cancellation in x, y, and z cancellation in x, y, and z directionsdirections

uu Crystals connected electrically in seriesCrystals connected electrically in series

uu 5:1 reduction in vibration sensitivity magnitude has been 5:1 reduction in vibration sensitivity magnitude has been achieved using four crystalsachieved using four crystals

83

Measurement of Oscillator/Resonator Measurement of Oscillator/Resonator Vibration SensitivityVibration Sensitivity

uu Entire oscillator or resonator alone can be mounted on a Entire oscillator or resonator alone can be mounted on a shaker for determination of vibration sensitivity.shaker for determination of vibration sensitivity.ll Resonator vibration sensitivity measurements can be made with Resonator vibration sensitivity measurements can be made with

the resonator connected to the oscillator sustaining stage or the resonator connected to the oscillator sustaining stage or connected in a passive phase bridge.connected in a passive phase bridge.

uu The effects of coaxial cable vibration must be taken into The effects of coaxial cable vibration must be taken into account, especially for measurement of devices having very account, especially for measurement of devices having very small values of vibration sensitivity.small values of vibration sensitivity.ll The effects of cable vibration can be determined by reThe effects of cable vibration can be determined by re--orienting orienting

the DUT on the shake table 180 degrees while not rethe DUT on the shake table 180 degrees while not re--orienting orienting the connecting coaxial cable and measuring the relative change the connecting coaxial cable and measuring the relative change in the magnitude and phase of the recovered, vibrationin the magnitude and phase of the recovered, vibration--induced induced carrier signal sideband, relative to that of the shake table carrier signal sideband, relative to that of the shake table accelerometer.accelerometer.

84

shake tableshake table

D.U.T.D.U.T.

vibration directionvibration direction

shake tableshake table

D.U.T. D.U.T.

vibration directionvibration direction

Measurement #1Measurement #1Overall vibration sensitivityOverall vibration sensitivity

= = ΓΓCOAXCOAX + + ΓΓDUTDUT

Measurement #2Measurement #2Overall vibration sensitivityOverall vibration sensitivity

= = ΓΓCOAXCOAX -- ΓΓDUTDUT

Measurement of Oscillator/Resonator Measurement of Oscillator/Resonator Coaxial Cable AffectsCoaxial Cable Affects

85

Test Results for 40MHz Oscillator Sustaining Test Results for 40MHz Oscillator Sustaining Stage and Coaxial CablesStage and Coaxial Cables

(vibration(vibration--induced phase shift increases with carrierinduced phase shift increases with carrier frequency)frequency)

50 ohm flexible coaxial 50 ohm flexible coaxial cablecable

approx 15 microapprox 15 micro--radians radians per gper g

50 ohm semi50 ohm semi--rigid coaxialrigid coaxialcablecable

approx 5 microapprox 5 micro--radians radians per gper g

Coaxial cableCoaxial cable

Open loop measurements Open loop measurements for a 2.5X2.5 inch PWB for a 2.5X2.5 inch PWB mounted on corners with mounted on corners with no adjustable componentsno adjustable components

approx 1.5 microapprox 1.5 micro--radians radians per gper g

Sustaining StageSustaining Stage

8. Oscillator Circuit Simulation and Noise Modeling8. Oscillator Circuit Simulation and Noise Modeling

87

CAD Small Signal Analysis/Simulation of CAD Small Signal Analysis/Simulation of Oscillator CircuitsOscillator Circuits

uu Small signal analysis is useful for simulating linear Small signal analysis is useful for simulating linear (start(start--up) conditionsup) conditions

uu Simulation of steadySimulation of steady--state condition is possible state condition is possible if/when large signal (i.e., inif/when large signal (i.e., in--compression) device scompression) device s--parameters or ALC diode steadyparameters or ALC diode steady--state impedance state impedance values are knownvalues are known

uu Circuit analysis/simulation should include component Circuit analysis/simulation should include component parasitic reactance (inductor distributed capacitance parasitic reactance (inductor distributed capacitance and loss, component lead inductance, etc). For and loss, component lead inductance, etc). For circuits operating at and above VHF, printed circuits operating at and above VHF, printed board/substrate artwork (printed tracks, etc) should board/substrate artwork (printed tracks, etc) should also be included in the circuit model.also be included in the circuit model.

88

CAD Small Signal Analysis of Oscillator CAD Small Signal Analysis of Oscillator CircuitsCircuits

uu Two port analysis is most appropriate for oscillator Two port analysis is most appropriate for oscillator circuits employing modular amplifier sustaining stages. circuits employing modular amplifier sustaining stages. Open loop simulation in a 50 ohm system is valid for Open loop simulation in a 50 ohm system is valid for simulation of closed loop performance only when the simulation of closed loop performance only when the loop is “broken” at a point where either the generator or loop is “broken” at a point where either the generator or load impedance is 50 ohms (i.e., at the amplifier input load impedance is 50 ohms (i.e., at the amplifier input or output if the amplifier has good input or output or output if the amplifier has good input or output VSWR).VSWR).

uu One port (negative resistance generator) analysis is One port (negative resistance generator) analysis is useful when simulating discrete oscillators employing useful when simulating discrete oscillators employing transistor sustaining stage circuitry.transistor sustaining stage circuitry.

89

CAD Small Signal Simulation of Oscillator CAD Small Signal Simulation of Oscillator CircuitsCircuits

uu CAD circuit simulation can (and should) include circuit CAD circuit simulation can (and should) include circuit analysis at outanalysis at out--ofof--band frequency regions to make sure band frequency regions to make sure conditions for oscillation are only satisfied at the desired conditions for oscillation are only satisfied at the desired frequency. frequency.

uu Frequency bands where undesired resonator resonant Frequency bands where undesired resonator resonant responses occur (i.e., unwanted crystal overtone responses occur (i.e., unwanted crystal overtone resonances) should be analyzed.resonances) should be analyzed.

uu CAD circuit simulation results can be experimentally CAD circuit simulation results can be experimentally checked using an Automatic Network Analyzer (ANA).checked using an Automatic Network Analyzer (ANA).

uu Simulation also allows optimization of element values to Simulation also allows optimization of element values to tune the oscillator, as well as statistical analyses to be tune the oscillator, as well as statistical analyses to be performed for determination of the effects of component performed for determination of the effects of component tolerance. tolerance.

90

RLRL

+VDC+VDC

Y1Y1

VbiasVbias

Zin = impedance (negative Zin = impedance (negative resistance)resistance)

‘seen’ by the crystal ‘seen’ by the crystal resonatorresonator

CxCx CyCy

ZZALCALC

RcRc

Simulation of the Sustaining Stage Portion Simulation of the Sustaining Stage Portion of a Crystal Oscillatorof a Crystal Oscillator

uu Cx and Cy values optimized to Cx and Cy values optimized to provide Zin = provide Zin = --70 + j0 at 70 + j0 at 100MHz100MHz

uu Zin calculated from 50MHz to Zin calculated from 50MHz to 1GHz to insure negative 1GHz to insure negative resistance is only generated resistance is only generated over a small band centered at over a small band centered at 100MHz (note use of Rc)100MHz (note use of Rc)

uu Large signal condition (where Large signal condition (where the negative resistance the negative resistance portion of Zin drops to 50 portion of Zin drops to 50 ohms = crystal resistance) ohms = crystal resistance) simulated by reducing the simulated by reducing the ALC impedance valueALC impedance value

91

++

+

+

+

+

+

+

+

+

+

++

+

+

**

**

* *

*

*

**

*

*

**

*

100MHz Oscillator Sustaining Stage Circuit 100MHz Oscillator Sustaining Stage Circuit Simulation: 80MHz to 120MHzSimulation: 80MHz to 120MHz

uu Zin = Zin = -- 70 + j0 at 70 + j0 at 100MHz100MHz

92

++

++

+ + + + + +

++

++

+

+

*

*

*

*

*

*

**

*

*

*

*

*

*

*

*

100MHz Oscillator Sustaining Stage Circuit 100MHz Oscillator Sustaining Stage Circuit Simulation: 50MHz to 1.5GHzSimulation: 50MHz to 1.5GHz

uu 33 ohm collector resistor 33 ohm collector resistor installed in the circuitinstalled in the circuit

uu Note that the real part of Note that the real part of the impedance remains the impedance remains positive everywhere positive everywhere except at the desired except at the desired frequency band at frequency band at 100MHz100MHz

uu This fact indicates the This fact indicates the circuit will only oscillate circuit will only oscillate at the desired frequencyat the desired frequency

93

+ + ++ + + + + + +

+

+

++ +

+

*

* * **

* * **

*

*

*

*

*

*

*

Results of 100MHz Oscillator Sustaining Results of 100MHz Oscillator Sustaining Stage Circuit SimulationStage Circuit Simulation

uu 50MHz to 1.5GHz; 50MHz to 1.5GHz; collector resistor (Rc) collector resistor (Rc) removedremoved

uu Note that the real part of Note that the real part of the impedance becomes the impedance becomes highly negative1.15GHzhighly negative1.15GHz

uu This fact points to a This fact points to a probable circuit probable circuit oscillation at/near oscillation at/near 1.1GHz1.1GHz

94

RFRFAmplifierAmplifier

+VDC+VDC

PowerPowerDividerDivider

RF OutputRF Output

RF Level set viaRF Level set viaZener diode voltageZener diode voltage

value selectionvalue selection

loop phase shift set and SCloop phase shift set and SC--cutcutcrystal b mode suppression circuitcrystal b mode suppression circuit

TP1TP1 TP2TP2

80MHz Crystal Oscillator Using Modular 80MHz Crystal Oscillator Using Modular Amplifier Sustaining Stage and Diode ALCAmplifier Sustaining Stage and Diode ALC

uu Output signal nearOutput signal near--carrier (1/f FM) noise primarily determined by carrier (1/f FM) noise primarily determined by crystal self noisecrystal self noise

uu TP1TP1--toto--TP2 voltage is maximized via trimmer capacitor TP2 voltage is maximized via trimmer capacitor adjustment. The voltage level is a measure (verification) of adjustment. The voltage level is a measure (verification) of requisite loop excess gain.requisite loop excess gain.

95

80MHz Modular Amplifier Oscillator Circuit 80MHz Modular Amplifier Oscillator Circuit SimulationSimulation

uu Open Loop Transmission Open Loop Transmission Response: 79.998MHz to Response: 79.998MHz to 80.002MHz80.002MHz

uu Note that the excess gain Note that the excess gain is approximately 3dBis approximately 3dB

uu The loaded Q of the The loaded Q of the crystal in the circuit is crystal in the circuit is approximately 50,000approximately 50,000

++

+

+

+

+

+

+

++

+

+

*

*

*

*

*

*

*

*

*

*

*

*

96

+ + ++

++

+

+ +

+

++

+

+

+

+

+

++ +

80MHz Oscillator Circuit Simulation80MHz Oscillator Circuit SimulationEffect of 5% tolerance in inductors and capacitorsEffect of 5% tolerance in inductors and capacitors

uu 99% of the time, the 99% of the time, the effect on open loop effect on open loop response is a phase response is a phase shift off of nominal of shift off of nominal of less than 15 degrees less than 15 degrees (2.5ppm frequency (2.5ppm frequency error without circuit error without circuit frequency frequency adjustment)adjustment)

uu 90% of the time, the 90% of the time, the phase shift error is phase shift error is less than 10 degreesless than 10 degrees

97

1.Express the open loop noise of each component as a Sf(f)/2 noiseExpress the open loop noise of each component as a Sf(f)/2 noisepower spectral density function of the form:power spectral density function of the form:

1010K1/10K1/10/f+10/f+10K2/10K2/10

K1 = 1Hz 1/f PM noise level, in dBc/HzK1 = 1Hz 1/f PM noise level, in dBc/Hz

K2 = white PM noise “floor” level, in dBc/Hz K2 = white PM noise “floor” level, in dBc/Hz

Reference: Mourey, Galliou, and Besson, “ A Phase Noise Model to Improve the Frequency Stability of Ultra Stable Oscillator”, Proc. 1997 IEEE Freq. Contr. Symp.

Simple Oscillator Noise Modeling*Simple Oscillator Noise Modeling*(Open loop(Open loop--toto--closed loop method)closed loop method)

uu Model the open loop noise of each functional subModel the open loop noise of each functional sub--circuit circuit (i.e., sustaining stage amplifier, tuning circuit, ALC/AGC (i.e., sustaining stage amplifier, tuning circuit, ALC/AGC circuit, and the resonator), usually as having a flickercircuit, and the resonator), usually as having a flicker--ofof--phase and a white phase noise component.phase and a white phase noise component.

Steps:Steps:

98

Simple Oscillator Noise Modeling (cont.)Simple Oscillator Noise Modeling (cont.)

Steps, continued:Steps, continued:2.2. Add each of the noise power numeric values for the Add each of the noise power numeric values for the

cascaded devices together. cascaded devices together.

2a.2a. Also, apply the appropriate, normalized frequencyAlso, apply the appropriate, normalized frequency--selective transmission responses (as a function of selective transmission responses (as a function of frequency offset from the carrier), including that of the frequency offset from the carrier), including that of the frequencyfrequency--determining element (i.e., resonator) to determining element (i.e., resonator) to those component noises that are “filtered” by the those component noises that are “filtered” by the responses along the signal path. In most cases, the responses along the signal path. In most cases, the transmission responses of the nontransmission responses of the non--resonator circuits resonator circuits are broadband and are not included in modeling.are broadband and are not included in modeling.

99

Simple Oscillator Noise Modeling (cont.)Simple Oscillator Noise Modeling (cont.)

3.3. Calculate the oscillator Calculate the oscillator closedclosed loop signal PM noise sideband level as loop signal PM noise sideband level as (for example): (for example):

(f) = 10LOG[(((S(f) = 10LOG[(((Sφφ11(f)/2)+(S(f)/2)+(Sφφ22(f)/2))(H(f)/2))(Haa(f)))+(S(f)))+(Sφφ22(f)/2))(H(f)/2))(Hbb(f))+ (f))+ SSφφ33(f)/2...)((1/2(f)/2...)((1/2πτπτ))22+1)]+1)]llH(f) terms are the normalized transmission responses of frequencH(f) terms are the normalized transmission responses of frequency y selective circuitry as a function of carrier offset (modulation)selective circuitry as a function of carrier offset (modulation) frequency, frequency, and and ττ is the open loop group delay. The primary selectivity functionis the open loop group delay. The primary selectivity functionand delay are those of the frequency determining element (resonaand delay are those of the frequency determining element (resonator, tor, multimulti--pole filter, delay line, etc). pole filter, delay line, etc). llThe((1/2The((1/2πτπτ))22+1) term accounts for the conversion of open loop phase +1) term accounts for the conversion of open loop phase fluctuations to closed loop frequency fluctuations in the oscillfluctuations to closed loop frequency fluctuations in the oscillator.ator.

100

Helpful Hints for Simple Oscillator Noise Helpful Hints for Simple Oscillator Noise ModelingModeling

uu The shortThe short--term frequency instability of the frequencyterm frequency instability of the frequency--determining element can be modeled either as:determining element can be modeled either as:(a) having a open loop (normally flicker(a) having a open loop (normally flicker--ofof--phase) phase phase) phase fluctuation spectrum that is then also “filtered” by the fluctuation spectrum that is then also “filtered” by the resonator transmission response, orresonator transmission response, or(b) a flicker(b) a flicker--ofof--frequency fluctuation spectrum that is added frequency fluctuation spectrum that is added separately to the calculated oscillator signal noise separately to the calculated oscillator signal noise spectrum (not subject to the ((1/2spectrum (not subject to the ((1/2πτπτ))22+1) term).+1) term).

101

Helpful Hints for Simple Oscillator Noise Helpful Hints for Simple Oscillator Noise ModelingModeling

uu The advantage of modeling the frequencyThe advantage of modeling the frequency--determining element instability as an open loop, determining element instability as an open loop, phase fluctuation spectrum is that the spectrum used phase fluctuation spectrum is that the spectrum used can be data collected from separate, phase bridge can be data collected from separate, phase bridge measurements of the phase instability induced onto a measurements of the phase instability induced onto a carrier signal by the device with corrections made for carrier signal by the device with corrections made for any differences in inany differences in in--bridge vs inbridge vs in--oscillator circuit oscillator circuit loadingloading

102

Oscillator Noise Modeling Oscillator Noise Modeling -- VibrationVibration

uu The vibrationThe vibration--induced noise can be modeled similarly by entering induced noise can be modeled similarly by entering the vibration power spectral density function (including the the vibration power spectral density function (including the transmission responses of vibration isolation systems used, transmission responses of vibration isolation systems used, unintentional mechanical resonances, etc), together with the unintentional mechanical resonances, etc), together with the frequency and/or phase sensitivities of the oscillator functionafrequency and/or phase sensitivities of the oscillator functional subl sub--circuits to vibrationcircuits to vibration

uu Normally, the most sensitive element is the resonatorNormally, the most sensitive element is the resonatoruu The vibrationThe vibration--induced PM noise is then simply added to the noise induced PM noise is then simply added to the noise

power numeric in the spreadsheet…either as vibrationpower numeric in the spreadsheet…either as vibration--induced, induced, open loop phase instability spectrum (then converted with the otopen loop phase instability spectrum (then converted with the other her open loop noises to the closed loop noise) or as vibrationopen loop noises to the closed loop noise) or as vibration--induced, induced, resonator frequency instability spectrum added to the calculatedresonator frequency instability spectrum added to the calculatedoscillator closed loop noiseoscillator closed loop noise

103

--180.0180.0

--160.0160.0

--140.0140.0

--120.0120.0

--100.0100.0

--80.080.0

--60.060.0

1010 100100 10001000 1000010000 100000100000Carrier Offset Frequency (Hz)Carrier Offset Frequency (Hz)

PM

Noi

se S

ideb

and

Leve

l (dB

c/H

z)P

M N

oise

Sid

eban

d Le

vel (

dBc/

Hz)

Sustaining Stage AmplifierOpen Loop NoiseQuartz Crystal CircuitOpen Loop NoiseXtal M.O. Static PM Noise IndBbc/HzOscillator Closed LoopNoise Under Vibration

mechanicalmechanicalresonanceresonance

isolatorisolatorresonanceresonance

Typical Plotted Result with Effects of Typical Plotted Result with Effects of Mechanical Resonance(s)Mechanical Resonance(s)

VHF Crystal OscillatorVHF Crystal Oscillator

9. Oscillator Noise De-correlation/Noise Reduction Techniques

9. Oscillator Noise De-correlation/Noise Reduction Techniques

105

matchingmatchingcircuitcircuit

RL’RL’

Y1Y1

RLRL

ResonatorResonator

AmpAmp

PwrPwrDivDiv..

Output AmpOutput Amp

AA

AA

Methods to Reduce Noise Internal to the Methods to Reduce Noise Internal to the Oscillator CircuitOscillator Circuit

uu OutOut--ofof--band noise band noise suppression via:suppression via:ll Resonator transmission Resonator transmission

selectivity (RL) orselectivity (RL) orll Resonator (high outResonator (high out--ofof--

band) impedance band) impedance selectivity (RL’)selectivity (RL’)

uu The technique shown above is not The technique shown above is not very useful for suppressing noise very useful for suppressing noise unless the output amplifier 1/f PM unless the output amplifier 1/f PM noise and noise figure are better noise and noise figure are better than that of the sustaining stage than that of the sustaining stage amplifieramplifier

Use the resonator impedance or transmission response selectivityUse the resonator impedance or transmission response selectivity to to reduce noise (i.e., extract the signal though the resonator to treduce noise (i.e., extract the signal though the resonator to the load).he load).

106

Methods to Reduce Noise Internal to the Methods to Reduce Noise Internal to the Oscillator Circuit (continued)Oscillator Circuit (continued)

uu Multiple, parallel sustaining stage amplifiers (amplifier Multiple, parallel sustaining stage amplifiers (amplifier 1/1 PM noise de1/1 PM noise de--correlation)correlation)

uu Multiple, series connected resonators (resonator 1/f Multiple, series connected resonators (resonator 1/f FM noise deFM noise de--correlation)correlation)

uu Multiple resonators in an isolated cascade or multiMultiple resonators in an isolated cascade or multi--pole filter configuration (increased loop group delay)pole filter configuration (increased loop group delay)

107

Example: Example: Multiple Device Use for Noise ReductionMultiple Device Use for Noise Reduction

ResonatorResonator ResonatorResonator ResonatorResonator

PowerPowerDividerDivider PowerPower

CombinerCombinerPowerPowerDividerDivider ResonatorResonator PowerPower

DividerDivider

ResonatorResonator

uu Noise deNoise de--correlation in correlation in amplifiers and/or amplifiers and/or resonatorsresonators

AA

AA

AA

AA

AA

uu Cascaded amplifierCascaded amplifier--resonators to increase loop resonators to increase loop group delaygroup delay

108

Additional Methods for Reducing Noise Additional Methods for Reducing Noise Internal to the Oscillator CircuitInternal to the Oscillator Circuit

uu Consider sustaining stage amplifier noise reduction Consider sustaining stage amplifier noise reduction via: via: ll noise detection and basenoise detection and base--band noise feedback (to band noise feedback (to

phase and amplitude modulators) or phase and amplitude modulators) or ll feedfeed--forward noise cancellation forward noise cancellation

109

uWave localuWave localoscillatoroscillator

PowerPowerDividerDividerPowerPower

DividerDivider

PowerPowerDividerDivider

VoltageVoltagecontrolledcontrolled

phasephaseshiftershifter

ResonatorResonator

uWaveuWaveResonatorResonator

LoopLoopamp/filteramp/filter

downdownconverterconverter

upupconverterconverter

phasephasedetectordetector

τ

VHFVHFAmpAmp

Example: Noise Reduction Techniques Example: Noise Reduction Techniques

uu WideWide--band noise feedback band noise feedback to reduce sustaining stage to reduce sustaining stage amplifier 1/f PM noiseamplifier 1/f PM noise

uu VHF delay = VHF delay = ττuu Double frequency conversion:Double frequency conversion:

ll Sustaining stage implementation Sustaining stage implementation at VHF using a low 1.f PM noise at VHF using a low 1.f PM noise amplifieramplifier

110



ResonatorResonator

PwrPwrDivDiv



PwrPwrDiv.Div. ResonatorResonator




PwrPwrCombComb

carrier nullingcarrier nulling


postpost--nullingnullinguwave amplifieruwave amplifier

AmpAmp

AmpAmp

Example: Example: Additional Noise Reduction Techniques Additional Noise Reduction Techniques

Use of resonator response Use of resonator response to increase phase detector to increase phase detector sensitivity sensitivity

(JPL and Raytheon)(JPL and Raytheon)

Carrier nulling with postCarrier nulling with post--nulling uwave amplifier used nulling uwave amplifier used to increase phase detector to increase phase detector sensitivity sensitivity (Univ. Western Australia/Poseidon (Univ. Western Australia/Poseidon Scientific Instruments)Scientific Instruments)

111

PhasePhaseNoiseNoiseSidebandSidebandLevel,Level,dBc/HzdBc/Hz

Carrier Offset Frequency, HzCarrier Offset Frequency, Hz

--170170

--150150

--130130

--110110

--160160

--140140

--120120

--100100

100100 10001000 10K10K 100K100K 1M1M

Northrop Grumman Oscillator using double frequencyconversion sustaining stage and low order mode DR

at 77K, Q=350,000 (1995 IEEE FCS)

PSI Oscillator using high sensitivity noisefeedback and high order mode DR

at 300K, Q=200,000 (1996 IEEE FCS)

Hewlett Packard Oscillator using no noisefeedback and high order mode DR

at 28K, Q=20million (1993 IEEE FCS)

--180180

Advantages of Noise Feedback in XAdvantages of Noise Feedback in X--Band, Sapphire Band, Sapphire Dielectric Resonator (DR) OscillatorsDielectric Resonator (DR) Oscillators

uu Lower Noise with 60 times lower QLower Noise with 60 times lower Q

112

InputInputsignalsignal

powerpowerdividerdivider

ff

AA

fofo

ff

AA 1/f noise introduced1/f noise introducedby amplifierby amplifier

powerpowercombinercombiner(nuller)(nuller)

AA noise enhancement:noise enhancement:carrier nulled, butcarrier nulled, but

1/f noise not nulled1/f noise not nulled

fofo

fofo

postpost--nullnullamplifieramplifier

AA

fofoffff

ff

1/f noise cancelled1/f noise cancelled(subtracted out)(subtracted out)

fofo

AA

noisenoisesubtractionsubtraction

AmpAmp

AmpAmp

Amplifier Noise Reduction via FeedAmplifier Noise Reduction via Feed--forward forward Cancellation*Cancellation*

(no noise down(no noise down--conversion to baseconversion to base--band)band)*amplifier operated linearly*amplifier operated linearly

113

Methods to Reduce Noise External to the Methods to Reduce Noise External to the Oscillator CircuitOscillator Circuit

uu External active (phaseExternal active (phase--locked VCO) or passive, locked VCO) or passive, narrownarrow--band spectral cleanup filtersband spectral cleanup filters

uu Overall subsystem noise reduction via feedback or Overall subsystem noise reduction via feedback or feedfeed--forward noise reduction techniquesforward noise reduction techniques

114

UHF VCO Phaselocked To HF Crystal UHF VCO Phaselocked To HF Crystal Oscillator:Oscillator:uu Oscillator noise reduction can be accomplished via external filtOscillator noise reduction can be accomplished via external filters:ers:

ll passive filterpassive filterll phasephase--locked oscillatorlocked oscillator

uu Provides nearProvides near--carrier noise of HF crystal oscillator plus low noise carrier noise of HF crystal oscillator plus low noise floor of UHF VCO (PLL BW APPROX. 5KHz)floor of UHF VCO (PLL BW APPROX. 5KHz)

--180.0180.0

--160.0160.0

--140.0140.0

--120.0120.0

--100.0100.0

--80.080.0

--60.060.0

1.E+011.E+01 1.E+021.E+02 1.E+031.E+03 1.E+041.E+04 1.E+051.E+05 1.E+061.E+06Carrier Offset Freq (Hz)Carrier Offset Freq (Hz)

PM

Noi

se S

ideb

and

Leve

l (dB

c/H

z)P

M N

oise

Sid

eban

d Le

vel (

dBc/

Hz)

Crystal Oscillator-multiplier PM noise at PLL inputUHF Oscillator free-running PM noisePhaselocked UHF oscillator PM noise

115

““Noisy”Noisy”microwavemicrowaveinput signalinput signal

PowerPowerdividerdivider

Quadrature (phase)Quadrature (phase)detectordetector

Frequency DiscriminatorFrequency Discriminator

Video amp/filterVideo amp/filter

detected basedetected base--band noiseband noisefed back or fed forwardfed back or fed forwardto a voltageto a voltage--controlledcontrolled

phase shifter to cancel outphase shifter to cancel outcarrier signal phase noisecarrier signal phase noise

PowerPowerdividerdivider

OutputOutput

microwave delay linemicrowave delay lineor resonator, delay=tor resonator, delay=t

Overall Subsystem Noise Reduction using a Overall Subsystem Noise Reduction using a DiscriminatorDiscriminator

uu Large delay needed to obtain high detection sensitivityLarge delay needed to obtain high detection sensitivityuu Large delay implies high delay line loss and/or small Large delay implies high delay line loss and/or small

resonator bandwidthresonator bandwidthuu Can achieve similar noise levels by using the same, high Can achieve similar noise levels by using the same, high

delay device in a microwave oscillatordelay device in a microwave oscillator

10. Oscillator Test and Troubleshooting Methods10. Oscillator Test and Troubleshooting Methods

117

Trouble Shooting Methods for: Trouble Shooting Methods for: Discrete Transistor Sustaining StageDiscrete Transistor Sustaining Stage

Steps:Steps:1.1. Measure oneMeasure one--port negative resistance vs frequency using port negative resistance vs frequency using

Automated Network Analyzer (ANA) s11 measurements Automated Network Analyzer (ANA) s11 measurements (may need to use a series build(may need to use a series build--out resistor to keep the out resistor to keep the sustaining stage from oscillating).sustaining stage from oscillating).

2.2. For the closed loop (oscillating circuit), measure the circuit For the closed loop (oscillating circuit), measure the circuit nodal voltage amplitude and relative phase and view the nodal voltage amplitude and relative phase and view the amplitude waveforms to estimate the degree of limiting amplitude waveforms to estimate the degree of limiting (excess gain) using a vector voltmeter or similar test (excess gain) using a vector voltmeter or similar test equipment.equipment.

118

Trouble Shooting Methods for: Trouble Shooting Methods for: Discrete Transistor Sustaining StageDiscrete Transistor Sustaining Stage

Steps, continued:Steps, continued:3.3. If the circuit does not oscillate, break open the oscillator If the circuit does not oscillate, break open the oscillator

loop where accurate duplication of source and load loop where accurate duplication of source and load impedances is not critical (i.e., where Zimpedances is not critical (i.e., where ZSS is much smaller is much smaller than Zthan ZLL and drive the circuit with an external generator to and drive the circuit with an external generator to determine ‘faulty’ portion of the circuit from phase and determine ‘faulty’ portion of the circuit from phase and amplitude measurements made along the signal path.amplitude measurements made along the signal path.

4.4. As necessary, make circuit modifications to achieve As necessary, make circuit modifications to achieve desired circuit open loop phase and gain characteristics.desired circuit open loop phase and gain characteristics.

Note:Note:InIn--circuit resonator effective Q can be determined by intentionallycircuit resonator effective Q can be determined by intentionally altering altering the circuit phase shift by a known amount and measuring the resuthe circuit phase shift by a known amount and measuring the resultant ltant oscillator signal frequency shift.oscillator signal frequency shift.

119

Signal Signal GeneratorGenerator

Vector VoltmeterVector VoltmeterAABB

ScopeScope

20KHz sampled outputs20KHz sampled outputs

C1C1

C2C2

C3C3

L1L1

Q1Q1

ZZinin(Q1) > Z(C1)(Q1) > Z(C1)

Example: Test Set UpExample: Test Set Up

120

Modular Amplifier Sustaining Stage Modular Amplifier Sustaining Stage Oscillator Test and TroubleshootingOscillator Test and Troubleshooting

Steps:Steps:

1.1. Break open the oscillator loop at a point where the circuit Break open the oscillator loop at a point where the circuit impedance is close to 50 ohms (either on the generator or impedance is close to 50 ohms (either on the generator or load side).load side).

2.2. Using an Automated Network Analyzer (ANA), measure Using an Automated Network Analyzer (ANA), measure the transmission response (s21 phase and amplitude) to the transmission response (s21 phase and amplitude) to verify adequate excess gain and the response centered at verify adequate excess gain and the response centered at the zero degree phase frequency. the zero degree phase frequency.

2a.2a. Increase the ANA drive until steadyIncrease the ANA drive until steady--state drive state drive conditions are achieved (gain drops to unity). The conditions are achieved (gain drops to unity). The sustaining stage amplifier input is the recommended sustaining stage amplifier input is the recommended signal insertion point.signal insertion point.

121

Modular Amplifier Sustaining StageModular Amplifier Sustaining Stage

Steps, continued:Steps, continued:

3.3. As an alternative, the loop can be opened and driven from As an alternative, the loop can be opened and driven from a signal generator, and relative signal amplitude and a signal generator, and relative signal amplitude and phase measurements made along the circuit signal path phase measurements made along the circuit signal path using vector voltmeter probes.using vector voltmeter probes.

4.4. As necessary, make circuit modifications to achieve As necessary, make circuit modifications to achieve desired circuit open loop phase and gain characteristics.desired circuit open loop phase and gain characteristics.

122

Typical Display of Network Analyzer DataTypical Display of Network Analyzer Data

uu Example: ANA Measurement of 100MHz Crystal Oscillator Example: ANA Measurement of 100MHz Crystal Oscillator Small and Large Signal Open Loop Response: s21 magnitudeSmall and Large Signal Open Loop Response: s21 magnitude

Small Signal Gain Small Signal Gain -- +2.6dB+2.6dB(ANA Po=AMP 11dBm(ANA Po=AMP 11dBm--11dB11dB

=O dBm=O dBm

Large Signal (Steady State)Gain - 0 dB

(ANA Po=8 dBm)

Center 100,000 350 MHz SPAN Center 100,000 350 MHz SPAN .003 000.003 000 MHzMHz

123

Typical Display of Network Analyzer DataTypical Display of Network Analyzer Data

uu Example: ANA Measurement of 100MHz Crystal Oscillator Example: ANA Measurement of 100MHz Crystal Oscillator Small and Large Signal Open Loop Response: s21 angleSmall and Large Signal Open Loop Response: s21 angle

Large Signal (Unity Gain)

Phase Response

Small Signal Small Signal Phase Phase

ResponseResponse

Center 100,000 350 MHz Span .003 000 MHzCenter 100,000 350 MHz Span .003 000 MHz

11. Summary11. Summary

125

Designing the Optimal OscillatorDesigning the Optimal Oscillator

uu Identify the oscillator/resonator technology best Identify the oscillator/resonator technology best suited for the applicationsuited for the applicationll Operating frequencyOperating frequencyll Unloaded QUnloaded Qll Drive levelDrive levelll ShortShort--term stabilityterm stabilityll Environmental stress sensitivityEnvironmental stress sensitivity

126

Designing the Optimal OscillatorDesigning the Optimal Oscillator

uu Identify the optimum sustaining stage design to be Identify the optimum sustaining stage design to be usedusedll Discrete transistorDiscrete transistorllModular amplifierModular amplifierll Silicon bipolar, GaAs, HBT, etc.Silicon bipolar, GaAs, HBT, etc.ll ALC, AGC, or amplifier gain compressionALC, AGC, or amplifier gain compression

uu Determine if use of noise reduction techniques, Determine if use of noise reduction techniques, including multiple device use, noise feedback, feedincluding multiple device use, noise feedback, feed--forward noise cancellation, vibration isolation, etc is forward noise cancellation, vibration isolation, etc is neededneeded

127

Verify Oscillator DesignVerify Oscillator Design

uu Perform CAD circuit analysis/simulationPerform CAD circuit analysis/simulationuu Know or measure the resonator shortKnow or measure the resonator short--term frequency term frequency

stabilitystabilityuu Know or measure the sustainingKnow or measure the sustaining--stage 1/f PM noise stage 1/f PM noise

at operating drive levelat operating drive leveluu Know or measure the resonator and nonKnow or measure the resonator and non--resonator resonator

circuit vibration sensitivities and package mechanicalcircuit vibration sensitivities and package mechanical

128

The Optimal Oscillator: The Optimal Oscillator: ‘Wish List’ for Future Improvements‘Wish List’ for Future Improvements

uu Improvements in resonator performanceImprovements in resonator performancell New resonator types having higher Q, higher drive New resonator types having higher Q, higher drive

capability, higher frequency, smaller volume, better capability, higher frequency, smaller volume, better shortshort--term stability, and lower vibration sensitivityterm stability, and lower vibration sensitivity

uu Microwave (sustaining stage) transistors/amplifiers Microwave (sustaining stage) transistors/amplifiers with lower levels of 1/f AM and PM noise with lower levels of 1/f AM and PM noise ll New semiconductor designs, materials, processingNew semiconductor designs, materials, processingll Circuit noise reduction schemes (feedback, etc)Circuit noise reduction schemes (feedback, etc)

uu Improved vibration sensitivity reduction schemesImproved vibration sensitivity reduction schemesll Cancellation, feedback control, mechanical isolation, Cancellation, feedback control, mechanical isolation,

etc.etc.

12. List of References12. List of References

130

1. Short-term Frequency/Phase/Amplitude Stability1. Short1. Short--term Frequency/Phase/Amplitude Stabilityterm Frequency/Phase/Amplitude Stability

1-1. J. A. Barnes et. al., NBS Technical Note 394, "Characterization of Frequency Stability", U. S. Dept. of Commerce, National Bureau of Standards, Oct. 1970.

1-2. D. Halford et. al., "Special Density Analysis: Frequency Domain Specification and Measurement of Signal Stability" Proc. 27th Freq. Contr. Symp., June 1973, pp. 421-431.

1-3. T. R. Faukner et. al., "Residual Phase Noise and AM Noise Measurements and Techniques", Hewlett-Packard Application Note, HP Part No. 03048-90011.

1-4. F. Labaar, Infrared and Millimeter Waves, Vol. 11, 1984. 1-5. D. W. Allan et. al., "Standard Terminology for Fundamental Frequency and Time Metrology", Proc. 42nd Freq. Contr. Symp., June 1988,

pp. 419-425. 1-6. J. R. Vig, "Quartz Crystals Resonators and Oscillators: A Tutorial", U. S. Army Communications-Electronics Command Report SLCET-

TR-88-1 (Rev. 8.5.1.6), December 2002, AD-M001251, http://www.ieee-uffc.org/index.asp?page=freqcontrol/fc_reference.html&Part=5#tutor.

1-7. W. F. Walls, "Cross-Correlation Phase Noise Measurements", Proc. 1992 IEEE Freq. Contr. Symp., May 1992, pp. 257-261.

1-8. M. M. Driscoll, "Low Noise Signal Generation Using Bulk Acoustic Wave Resonators:, Tutorial Session, 1993 IEEE Ultrason, Symp., Oct. 1993.

1-9. W. Walls, "Your Signal - a Tutorial Guide to Signal Characterization and Spectral Purity" Femtosecond Systems, Golden, CO, 1996. 1-10. Penny Technologies, Inc., "Correction Modules for Feed-forward Applications", Microwave Journal, Aug. 1996, pp. 142-144.

1-11. F. G. Ascarrunz, et. al., "PM Noise Generated by Noisy Components", Proc. 1998 IEEE Freq. Contr. Symp., June 1998, pp. 210-217. 1-12. M. M. Driscoll, "Evaluation of Passive Component Short-Term Stability via Use in Low Loop Delay Oscillators", Proc. 1999 EFTF-IEEE

IFCS, April 1999, pp. 1146-1149. 1-13. D.A. Howe and T.K. Pepler, “Definitions of “Total” Estimators of Common Time Domain Variances”, Proc. 2001 IEEE Freq. Contr.

Symp., June 2001, pp. 127-132.

http://www.ieee-uffc.org/index.asp?page=freqcontrol/fc_reference.html&Part=5#tutor

131

2. Basic Oscillator Operation2. Basic Oscillator Operation2. Basic Oscillator Operation

2-1. D. B. Leeson, "A Simple Model of Feedback Oscillator Noise Spectrum", Proc. IEEE, Vol.54, No.2, Feb. 1966, pp. 329-330.

2-2. W. A. Edson, Vacuum Tube Oscillators, John Wiley and Sons, N.Y., 1953. 2-3. J. P. Buchanan, "Handbook of Piezoelectric Crystals for Radio Equipment Designers", Wright Air Development

Center Tech, Report No. 56-156, Oct. 1956. 2-4. B. Parzen, The Design of Crystal and Other Harmonic Oscillators, John Wiley and Sons, N.Y., 1983. 2-5. E. A. Gerber et. al., Precision Frequency Control, Vol.2: Oscillators and Standards, Academic Press, Inc., 1985.

132

3. Types of Resonators and Delay Lines3. Types of Resonators and Delay Lines3. Types of Resonators and Delay Lines3-1. J. P. Buchanan, "Handbook of Piezoelectric Crystals for Radio Equipment Designers", Wright Air Development Center Tech.

Report No. 56-156, Oct. 1956. 3-2. D. Kajfez et. al., Dielectric Resonators, Aertech House, Norwood, MA. 3-3. E. A. Gerber et. al., Precision Frequency Control, Vol. 1: Acoustic Resonators and Filters, Academic Press,

Inc., 1985. 3-4. A. J. Giles et. al., "A High Stability Microwave Oscillator Based on a Sapphire Loaded Superconducting

Cavity", Proc. 43rd Freq. Contr. Symp., May 1989, pp. 89-93. 3-5. J. Dick et. al., "Measurement and Analysis of Microwave Oscillator Stabilized by Sapphire Dielectric Ring

Resonator for Ultra-Low Noise", Proc. 43rd Freq. Contr. Symp., May 1989, pp. 107-114. 3-6. M. M. Driscoll, "Low Noise Microwave Signal Generation: Resonator/Oscillator Comparisons", Proc. 1989

IEEE MTT Digest, June 1989, pp. 261-264. 3-7. C. A. Harper, editor, Passive Component Handbook, Chapter 7: Filters, McGraw-Hill, Inc., N.Y., 1997. 3-8. M. J. Loboda, et. al., "Reduction of Close-to-Carrier Phase Noise in Surface Acoustic Wave Resonators",

Proc. 1987 IEEE Ultrason, Symp., Oct. 1987, pp. 43-46. 3-9. S. Yao and L. Maleki, "Characteristics and Performance of a Novel Photonic Oscillator, Proc. 1995 IEEE Freq.

Contr. Symp., June 1995, pp. 161-168. 3-10. M. S. Cavin and R. C. Almar, "An Oscillator Design Using Lowg-Sensitivity, Low phase Noise STW Devices",

Proc. 1995 IEEE Freq.Contr. Symp., June 1995, pp. 476-485. 3-11. S. Yao, et. al., "Dual -Loop Opto-Electronic Oscillator", Proc. 1998 IEEE Freq. Contr. Symp., June 1998, pp.

545-549. 3-12. S. Yao, et. al., "Opto-Electronic Oscillator Incorporating Carrier Suppression Noise Reduction Technique",

Proc. 1999 EFTF-IEEE IFCS Symp., April 1999, pp. 565-566. 3-13. T. McClelland, et. al., "100 MHz Crystal Oscillator with Extremely Low Phase Noise". Proc. 1999 EFTF-IEEE

IFCS Symp., April 1999, pp.331-333. 3-14. M. M. Driscoll, "The Use of Multi-Pole Filters and Other Multiple Resonator Circuitry as Oscillator Frequency

Stabilization Elements", Proc. 1996 IEEE Freq. Contr. Symp., June 1996, pp. 782-789.

133

4. Useful Network/Impedance Transformations4. Useful Network/Impedance Transformations4. Useful Network/Impedance Transformations

4-1. G. L. Matthaei et. al., Microwave Filters, Impedance Matching Networks, and Coupling Structures, McGraw-Hill, Inc., N.Y., 1964.

4-2. A. I. Zverev, handbook of Filter Synthesis, John Wiley and Sons, N.Y., 1967

134

5. Sustaining Stage Design and Performance5. Sustaining Stage Design and Performance5. Sustaining Stage Design and Performance

5-1. W. A. Edson, Vacuum Tube Oscillators, John Wiley and Sons, N.Y., 1953 5-2. J. P. Buchanan, "Handbook of Piezoelectric Crystals for Radio Equipment Designers", Wright Air Development

Center Tech. Report No. 56-156, Oct. 1956. 5-3. C. Halford et. al., "Flicker Noise of Phase in RF Amplifiers and Frequency Multiliers: Characterization, Cause,

and Cure", Proc. 22nd Freq. Contr. Symp., April 1968, pp. 340-341. 5-4. M.M. Driscoll, "Two-Stage Self-Limiting Series Mode Type Crystal Oscillator Exhibiting Improved Short-Term

Frequency Stability", Proc. 26th Freq. Contr. Symp., June 1972, pp. 43-49. 5-5. A. VanDerZiel, "Noise in Solid State Devices and Lasers", Proc. IEEE, Vol. 58, No.8, Aug. 1979, pp. 1178-

1206. 5-6. B. Parzen, The Design of Crystal and Other Harmonic Oscillators, John Wiley and Sons, N.Y., 1983. 5-7. E. A. Gerber et al., Precision Frequency Control, Vol. 2: Oscillators and Standards, Academic Press, Inc.,

1985. 5-8. M. M. Driscoll, "Low Noise Oscillators Using 50 - ohm Modular Amplifier Sustaining Stages", Proc. 40th Freq.

Contr. Symp., May 1986, pp. 329-335. 5-9. G. K. Montress et. al., "Extremely Low Phase Noise SAW Resonator Oscillator Design and Performance",

Proc. 1987 IEEE Ultras. Symp., Oct. 1987, pp. 47-52. 5-10. T. McClelland, et. al., "100 MHz Crystal Oscillator with Extremely Low Phase Noise", Proc. 1999 EFTF - IEEE

IFCS Symp., April 1999. pp. 331-333.

135

6. Oscillator Frequency Adjustment/Voltage Tuning6. Oscillator Frequency Adjustment/Voltage Tuning6. Oscillator Frequency Adjustment/Voltage Tuning

6-1. M. M. Driscoll et. al., "Voltage-Controlled Crystal Oscillators", IEEE Trans. On Elect. Devices, Vol. Ed-18, No. 8, Aug. 1971, pp. 528-535.

6-2. R. Arekelian et. Al., "Linear Crystal Controlled FM Source for Mobile Radio Application", IEEE Trans. On Vehic. Tech., Vol. VT-27, No. 2, May 1978, pp. 43-50.

6.3. M. M. Driscoll, "Linear Tuning of SAW Resonators", Proc. 1989 IEEE Ultras, Symp., Oct. 1989, pp. 191-194.

136

7. Environmental Stress Effects7. Environmental Stress Effects7. Environmental Stress Effects

7.1 R. A. Filler, "The Acceleration Sensitivity of Quartz Crystal Oscillators: A Review", IEEE Trans. UFFC, Vol. 35, No. 3, May 1988, pp. 297-305.

7-2. S. M. Sparagna, "L-Band Dielectric Resonator Oscillators with Low Vibration Sensitivity and Ultra-Low Noise", Proc. 43rd Freq. Contr. Symp., May 1989, pp. 94-106.

7-3. M. M. Driscoll, "Quartz Crystal Resonator G-Sensitivity Measurement Methods and Recent Results", IEEE Trans. UFFC, Vol. 37, pp. 386-392.

7-4. J. R. Vig, "Quartz Crystals Resonators and Oscillators: A Tutorial", U. S. Army Communications-Electronics Command Report SLCET-TR-88-1 (Rev. 8.5.1.6), December 2002, AD-M001251, http://www.ieee-uffc.org/index.asp?page=freqcontrol/fc_reference.html&Part=5#tutor.

7-5. M. M. Driscoll, "Reduction of Crystal Oscillator Flicker-of-Frequency and White Phase Noise (Floor) Levels and Acceleration Sensitivity via Use of Multiple Crystals", Proc. 1992 Freq. Contr. Symp., May 1992, pp. 334-339.

7-6. "Precision Time and Frequency Handbook", Ball Corp., Efratom Time and Frequency Products, 1993. 7-7. "IEEE Guide for Measurement of Environmental Sensitivities of Standard Frequency Generators", IEEE STD

1193-1994. 7-8. J. T. Stewart et. al., "Semi-Analytical Finite Element Analysis of Acceleration-Induced Frequency Changes in

SAW Resonators", Proc. 1995 Freq. Contr. Symp., May 1995, pp. 499-506.

http://www.ieee-uffc.org/index.asp?page=freqcontrol/fc_reference.html&Part=5#tutor

137

8. Oscillator Circuit Simulation and Noise Modeling8. Oscillator Circuit Simulation and Noise Modeling8. Oscillator Circuit Simulation and Noise Modeling

8-1. Super-Compact TM User Manual, Compact Software, Inc., Paterson, N. J. 8-2. M. M. Driscoll et. al., "VHF Film Resonator and Resonator-Controlled Oscillator Evaluation Using computer-

Aided Design Techniques", Proc. 1984- IEEE Ultras. Symp., Nov. 1984, pp. 411-416. 8-3. M. Mourey, et. al., "A Phase Noise Model to Improve the Frequency Stability of Ultra-Stable Oscillator", Proc.

1997 IEEE Freq. Contr. Symp., June 1997, pp. 502- 508. 8-4. G. Curtis, "The Relationship Between Resonator and Oscillator Noise, and Resonator Noise Measurement

Techniques", Proc. 41st Freq. Contr. Symp., may, 1987, pp. 420-428.

138

9. Oscillator Noise De-correlation/Reduction Techniques9. Oscillator Noise De9. Oscillator Noise De--correlation/Reduction Techniquescorrelation/Reduction Techniques

9-1. Penny Technologies, Inc., "correction Modules for Feed-forward applications", Microwave Journal, Aug. 1996, pp. 142-144.

9-2. F. L. Walls, et. al., "The Origin of 1/f PM and AM Noise in Bipolar Junction Transistors", Proc. 1995 IEEE Freq. Contr. Symp., May, 1995, pp. 294-304.

9-3. M. M. Driscoll, "Reduction of Quartz Crystal Oscillator Flicker-of-Frequency and White Phase Noise (Floor) Levels and Acceleration Sensitivity via Use of Multiple Resonators", Proc. 1992 IEEE Freq. Contr. Symp., May, 1992, pp. 334-339.

9-4. P. Stockwell, et. al., "Review of Feedback and Feed-forward Noise Reduction Techniques", Proc. 1998 IEEE Freq. Contr. Symp., May, 1998.

9-5. E. N. Ivanov, et. al., "Advanced Noise Suppression Technique for Next Generation of Ultra-Low Phase Noise Microwave Oscillators", Proc. 1995 IEEE Freq. Contr. Symp., May, 1995, pp. 314-320.

9-6. J. Dick et. al., "Measurement and Analysis of Microwave Oscillator Stabilized by a Sapphire Dielectric Ring Resonator for Ultra-Low Noise", proc. 43rd Freq. Contr. Symp., May 1989, pp. 107-114.

9-7 S. Yao, et. al., "Opto-Electronic Oscillator Incorporating Carrier Suppression Noise Reduction Technique", Proc. 1999 EFTF-IEEE IFCS Symp., April 1999, pp. 565-566.

low noise oscillator design and performance - m.m.driscoll

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