Interferometric Residual Phase Noise Measurement System

Pakpoom BuabthongUniversity of Illinois at Urbana-Champaign

buabtho2@illinois.edu

Tim BerencArgonne National Laboratory

berenc@aps.anl.gov

Abstract

This paper presents a prototype of an interferometric residual phase noise measurementsystem operating at 2.815 GHz. The system is an improvement over a traditional saturatedmixer system by including carrier suppression before detection to overcome dynamic range issues.By using suppression followed by rf amplification, the sensitivity of the interferometric systemis increased to 15.6 V/rad compared to 0.385 V/rad for the saturated mixer system, a 32 dBimprovement. The experimental results show a ∼15 dB improvement in the 1/f noise and ∼4 dBimprovement in the white noise floor. The cumulative integrated phase noise of the interferometricand saturated mixer systems was measured to be ∼32µdegrms and ∼65µdegrms respectively overa 0.1Hz-100kHz bandwidth. At 2.815 GHz, this corresponds to a residual jitter noise floor of ∼32attosecondsrms and ∼65 attosecondsrms respectively. Measurements of the various contributionsto the interferometric system reveal that it is the rf amplifier which limits the white noise floor,while the carrier suppression section limits the low frequency 1/fn type noise, especially due tomicrophonics. Also a novel technique of properly aligning the measurement plane is described.

1 Introduction

Stability of the differential phase noise betweenradio frequency (rf) cavities plays a crucial rolein many rf systems. To measure the performanceof a system, a noise measurement system with asufficiently low noise floor is needed.

In polar coordinates, the noise of an rf car-rier can be represented as amplitude modulation(AM) and phase modulation (PM). Let α(t) andϕ(t) be amplitude and phase noise. Then, thecarrier with noise can be represented as

v(t) = V0(1 + α(t))cos(ω0t+ ϕ(t)) . (1)

The carrier plus noise can also be expressed inCartesian coordinates as

v(t) = V0cos(ω0t) + nIcos(ω0t)− nQsin(ω0t).

In the case when amplitude and phase noise arevery small (α(t), ϕ(t) � 1) Eq. (1) can be well

Figure 1: Phasor representation of noise.

approximated as

v(t) 'V0cos(ω0t)+ V0α(t)cos(ω0t)− V0ϕ(t)sin(ω0t) .

Thus the polar and Cartesian coordinates are re-lated by

nI(t) ' α(t)V0nQ(t) ' ϕ(t)V0 .

The terminology of polar and Cartesian coor-dinates stems from phasor concepts in which asinusoid is represented by a complex exponentialand the phasor is the vector as seen in the frame

1

rotating at the carrier frequency. The phasorrepresentation is depicted in Fig.1 and is writtenin both polar and Cartesian coordinates as:

v(t) = Re{[V0(1 + α(t))ejϕ(t)] · ejω0t}

v(t) = Re{[V0 + nI(t) + jnQ(t)] · ejω0t} .

While performance of an rf system is the ul-timate interest, this project focuses on develop-ment and characterization of a measurement sys-tem that could be used as an out-of-loop mea-sure of an rf system’s performance. Furthermore,since phase noise specifications are usually muchlower than amplitude specifications, this projectfocused on residual phase noise as opposed toabsolute phase noise or amplitude noise.

2 Noise Measurement Methods

The simplest approach to measure residual phasenoise uses the technique of a saturated mixer,which mixes a device under test’s (DUT) outputwith a 90◦ phase shifted version of a commonsource signal as depicted in Fig. 2. The noisefloor of the saturated mixer system is typicallylimited by the noise floor of the baseband lownoise amplifier (LNA) as well as the mixer andcable vibrations. The interferometric techniqueon the other hand cancels the common carrierusing an interferometer and then amplifies theresidual noise before detection with a mixer asdepicted in Fig. 3. The result is an increasein the sensitivity and in overcoming noise floorlimitations of the baseband section including theLNA.

The measurement systems presented here weredesigned for S-band operating at 2.815GHz.They were built in an unshielded laboratory, lo-cated at the Advanced Photon Source of Ar-gonne National Laboratory. Therefore, distur-bances from conducted power line interferencefrom accelerator operations or other nearby labspaces, electromagnetic interference, and me-chanical vibrations are expected in the results.The two measurement systems are described inthe following sections including detailed experi-mental setup and results.

3 Saturated Mixer System

To measure the noise added to the carrier by thedevice under test (DUT), a mixer is used to formthe product of the two signals at the RF and Lo-cal Oscillator (LO) ports of Fig.2. Ensuring thatthe input signal levels saturate the mixer makesthe output insensitive to amplitude modulationsof the input signals [1]. With the nominal phasedifference between the RF and LO ports set to90◦, the mixer ideally detects phase modulation.The intermediate frequency (IF) output of themixer is given as

vIF (t) = V1cos(ω0at+ ϕ(t)) · V2sin(ω0t)

=V1V2

2[sin(ϕ(t)) + sin(2ω0t+ ϕ(t)]

The low-pass filter (LPF) then eliminates thedouble frequency term. The noise at the outputto the Fast Fourier Transform (FFT) analyzer isthen simply

R(t) = −V1V2ϕ(t)

2= kϕϕ(t)

where kϕ is a scaling factor [V/rad] used toconvert the readout of the FFT analyzer fromdBV2/Hz to dBrad2/Hz. Since the mixer is sat-urated, amplitude fluctuations of V1 and V2 areideally suppressed and kϕ is independent of V1and V2. To measure the noise floor of the satu-rated mixer setup, the DUT is replaced with asimple piece of coaxial cable.

3.1 Calibration, Scaling Factor

Since the carrier’s phase at the LO and IF portsof the mixer need to be 90◦ out of phase, a simplepiece of cable along with a variable phase shiftercan be used to establish the phase difference.The length difference of the two paths can beapproximated with the assumption that the sig-nal is traveling in the cable at 0.8 times the speedof light. In this experiment, the frequency of thecarrier is 2.815GHz with a wavelength (λ) of ap-proximately v/f = (0.8·2.99·108)/(2.815·109) =0.0850m. Therefore, for a 90◦ phase difference,

2

DUT

Fast Fourier Transform (FFT) Analyzer

FFT

φ

R(t)V1RF

LOV2

Source

Low PassFilter(LPF)

IF

Arra L9428AManual Phase Shifter

Stanford Research SystemsSR785

MarkiM1-0204MP

Low NoiseAmplifier

(BPAA-1000)

Figure 2: Saturated mixer technique for phase noise measurements.

ϕ

DUT

φ

FFTAnalyzer

RF Amp

Source

Phase Shifter

Attenuator 180 degHybrid

Low PassFilter

Low NoiseAmplifier

LO Phase Adjust Baseband Section

Figure 3: Interferometeric technique for phase noise measurements.

the length should be about 2.13 cm. After set-ting the cable with a rough calculation, the phasedifference is precisely adjusted using the manualphase shifter while monitoring the voltage at theoutput of the mixer. The phase shifter is ad-justed until the nominal DC voltage at the mixeroutput reaches zero.

The FFT analyzer displays a power spectraldensity measurement in units of [V2/Hz]. Thusthe scaling factor kϕ in V/rad is needed to con-vert between voltage units and phase units. Tomeasure the scaling factor, a phase shift is ap-plied via the adjustable phase shifter and the re-sultant voltage change is measured. Thus an in-termediate scaling is needed relating the phaseshift at 2.815 GHz per unit turn of the phaseshifter. The ratio of V/rad can then be deter-mined by measuring the change in voltage at theoutput of the mixer for a given adjustment ofthe phase shifter’s micrometer drive. The phasenoise in dBrad2/Hz can then be calculated bysubtracting the scaling factor in dB from theraw data reported as dBV2/Hz from the FFTanalyzer.

For this experiment, a network analyzershowed that the phase shifter (an ARRAL9428A) changes the phase at 2.815GHz by 0.3rad per unit (1/10 inch). The corresponding DCvoltage at the output of the mixer for a unit

0.1 1 10 100 1k 10k 100k1

10

100

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100k

1m

Frequency [Hz]

nVrm

s /

Hz

Noise Referred to the Output of the Audio Amp

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1k

10k

100k

1m

Frequency [Hz]

nVrm

s /

Hz

Noise Referred to the Output of the Audio Amp

G =60dB

FFT Analyzer

LNA

Total, 11dBm RF/LO

Figure 4: Voltage Noise Spectral Density Re-ferred to the Output of the LNA.

change was 115 mV. Hence the mixer scaling iscalculated to be

kϕ = 0.383 V/rad .

The LNA in the Wenzel Test Set has a gain of60dB or 10

6020 = 1000 in voltage. Thus the phase

noise in dBrad2/Hz can be calculated by sub-tracting (60dB+20 log10(kϕ))=51.7 dB from theraw dBV2/Hz FFT data.

3.2 Saturated Mixer Noise Floor

A low-noise amplifier is inserted after the mixerphase detector in order to overcome the noise

3

0.1 1 10 100 1k 10k 100k

1

10

100

1k

10k

Frequency [Hz]

nVrm

s /

Hz

Noise Referred to the Input (RTI) of the Audio Amp

0.1 1 10 100 1k 10k 100k

1

10

100

1k

10k

Frequency [Hz]

nVrm

s /

Hz

Noise Referred to the Input (RTI) of the Audio Amp

LNA

Total

FFT Analyzer

Figure 5: Voltage Noise Spectral Density Re-ferred to the Input of the LNA compared to theFFT Analyzer Noise.

floor of the analyzer. Figure 4 shows raw mea-surements at the FFT analyzer for (1) the to-tal noise floor of the measurement system, (2)the LNA with a 50Ω load at its input, and (3)the FFT analyzer alone with a 50Ω input termi-nation. The actual noise floor of the measure-ment system and the LNA as referred to the in-put of the LNA (which is the output of the sys-tem’s phase detector) can be obtained by sub-tracting the amplifier gain of 60 dB, resultingin Fig.5. This shows that the LNA provides fora lower system noise floor than if the FFT an-alyzer was used alone. For example, the totalwhite noise floor of the system referred to theinput of the LNA is only 1-2 nVrms/

√Hz, while

the noise floor of the FFT analyzer is around 5nVrms/

√Hz. Without the LNA, the noise floor

of the system would be limited by the FFT ana-lyzer.

Using the system’s scaling factor the noisefloor in phase units can be obtained. The re-sults are shown in Fig. 6. The white noise floorof the total system is ∼ -172 dBrad2/Hz, andthe noise at 1Hz offset from the carrier is ∼ -139dBrad2/Hz. The white noise from the amplifieris about the same level at ∼ -172 dBrad2/Hz.While its flicker noise at 1 Hz offset is almost10dB lower. Lastly, the white noise floor contri-bution of the FFT analyzer is negligible at aneffective ∼ -215 dBrad2/Hz.

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Frequency [Hz]

dBra

d2 /

Hz

FFT Analyzer LNA

Total

Figure 6: Contributions to Saturated Mixer testset Phase Noise Spectral Density.

4 Interferometric System

In an attempt to better detect the residual noiseand obtain a lower noise floor, carrier suppres-sion is introduced with the interferometric tech-nique. From Fig.7, the carrier and its inherentnoise from the source is suppressed, leaving be-hind the residual noise from the DUT which canthen be amplified before detection in the mixer.This overcomes dynamic range issues if one wasto try to amplify the DUT’s noise in the presenceof the large carrier. With the carrier suppressed,only the residual noise is amplified. This greatlyincreases the sensitivity of the measurement sys-tem.

A block diagram of the interferometric sys-tem setup is shown in Fig.8. The innermostinterferometer coarsely adjusts the carrier sup-pression using a step attenuator while the outerinterferometer provides a fine adjust using acontinuously variable attenuator. The carrier-suppressed signal goes into a bandpass filter be-fore being amplified by a high gain rf amplifier.The bandpass filter eliminates any out-of-bandnoise that could saturate the amplifier and causea higher noise floor [2]. The output of the rf am-plifier then goes to a mixer whose LO is adjustedto detect the quadrature noise component. Thusthe interferometer inherently works in Cartesiancoordinates. The mixer is followed by a LPFand a LNA before measurement with a FFT an-alyzer. Not shown are two additional directionalcouplers that are used to monitor for carrier sup-

4

DUT

JFW1dB (0.1dB step)Step Attenuator

ArraL9428A

ArraL4428D

Arra4194-20

20dB

RF AmpMiteq

LCN0204

K&L Microwave 3C45

Source

ϕ

ϕ

ϕ

PasternackPE7065-2

ArraL9428A

(e)

(R)(a)

(b)

Wenzel Test Set

(S)

MarkiM1-0204MP

LNA(BPAA-1000)

LPF

FFTAnalyzer

SRS SR785LO

RFIF

Figure 8: Block Diagram of the interferometric noise measurement system with fine adjust.

Lee Teng Internship 2013, Final Presentation1

Signal Level

Frequency

Carrier

DUT Noise

Suppress Carrier

Signal Level

Frequency

Amplify residual noise

Figure 7: Interferometric System Principle.

pression. One is inserted between point (S) andthe rf amplifier. The other is inserted betweenthe rf amplifier and the mixer.

While the interferometer-based system ex-hibits a lower noise floor, the result dependsheavily on the stability of the system. Anysubtle mechanical perturbation can cause an in-crease in the noise floor level. Hence, the set-upof an interferometric system should be properlymounted. To minimize mechanical vibrationsof the system the prototype, shown in Fig.9, ismounted to a metal plate. All the semi-rigid ca-bles are secured by adhesive tape.

4.1 Carrier Suppression

To suppress the carrier before the amplifier,manual attenuators and phase shifters are usedto properly orient the signal at (a), (b), and (e)in Fig. 8. Both attenuation and phase have to becarefully adjusted to achieve maximum suppres-sion. From Fig.10, small amplitude error andphase error can introduce a great loss in carriersuppression.

4.1.1 Coarse adjust

In the coarse adjust path, path (b) in Fig.8, aby-step attenuator is used because it is less sen-sitive to mechanical fluctuations of contacts [3].Neglecting accuracy of the attenuator, using a0.1 dB step attenuator will lead to at most a0.05 dB error in amplitude difference. The sig-nals at (a) and (b) could thus be considered to

5

Figure 9: Interferometric System Prototype.

30

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35

35

35

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45

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50 60

Phase Error [deg]

Am

plitu

de E

rror

[dB

]

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

Figure 10: Carrier Suppression contours in dBvs. Amplitude and Phase Errors.

be related as

20 log(b

a) = −0.05

b = a(10−0.0520 )

Neglecting any phase errors, this would result in

R = a− b

= a(1− 10−0.0520 )

= 0.0057a

This corresponds to a suppression of

20 log(a

R) = 44.8 dB

If one is lucky in adjusting (b), better sup-pression can be achieved. However we found thattypical coarse adjustment rarely gave better than50 dB suppression and usually less than this.

4.1.2 Fine Adjust

A carrier suppression of 45 dB could still causethe rf amplifier to saturate either from the cw

6

Lee Teng Internship 2013, Final Presentation1

Carrier

(R)(S)

DUT signal

Correctmeasurement plane

Wrongmeasurement plane

Figure 11: Vector Representation of Coarse andFine Adjust.

output carrier approaching the 1 dB compres-sion point and/or from instantaneous noise peaksalong with the carrier. It also allows the rf am-plifier to cause flicker noise around the carrierwhich can limit the low frequency noise floorof the measurement system [4]. Therefore, afine adjust is incorporated. Ideally, it cancelsthe residual carrier left over from the coarse ad-just. From Fig.11, the fine adjust signal is muchsmaller compared to the coarse adjust signal. Asa result, the path is less sensitive to mechanicalfluctuations of the attenuator contacts. There-fore, a continuous attenuator can be used in thispath. The fine adjust should ideally have thesame magnitude and opposite phase of the resid-ual vector left from the coarse adjust. A properamount of fixed attenuation is included to getthe fine adjust signal level at the same order ofthe residual vector while having adequate adjust-ment range with the variable attentuator.

As an example of how the fine adjust is desen-sitized to variable attenuator errors/fluctuations,let the signal in the fine path ideally be e =−R = −a(1 − 10

−0.0520 ) where R is considered

the residual carrier left over from a 0.05 dB er-ror in the coarse adjust. Then, if a similar 0.05dB error is introduced into the fine adjust, thecombined signal at the output of the directionalcoupler, S would be

S = R+ e(1− 10−0.05

20 )

= a(1− 10−0.05

20 )2

= (3.29 · 10−5)a

which, corresponds to a suppression of

20 log(a

S) = 89.6 dB

4.2 Scaling factor

To calculate the scaling factor of an interferomet-ric system, an additional RF generator is used togenerate a signal at a small frequency offset fromthe system’s carrier frequency. Referring to Fig.8, the connection at point (a) is broken. Theoffset signal generator is connected to drive theinput of the combiner while the DUT output sideof the break is properly terminated in 50Ω. Theconnections at points (b) and (e) are also brokenwith each side of the break terminated in 50Ω.

A single-tone of amplitude Vs at a frequencyoffset of ∆ω from the carrier can be representedas

vSSB(t) = Vs cos (ωo + ∆ω)t= Vs cos ∆ωt cosωot− Vs sin ∆ωt sinωot

This can be considered a single-sideband modu-lation of the carrier for which the in-phase andquadrature noise are sinusoidal modulations inquadrature with each other, each with magni-tude Vs. In the small signal approximation, for agiven carrier level of Vo the corresponding phasenoise is

ϕ(t) =VsVo

sin ∆ωt =√PsPosin∆ωt

The scaling factor for the measurement systemcan thus be found by applying a signal from theoffset generator and measuring the peak voltage,Vpk, at the modulation frequency on the FFTanalyzer. The scaling factor for the system isthus given as

kϕ =Vpk sin ∆ωt

ϕ(t)=

√P0Ps· Vpk

The measurement requires a power ratio of theoffset generator’s power and the nominal carrierpower at point (a). It is important to keep thepower level of the offset generator very low in or-der to prevent the system from saturating. Weused a Rhode & Schwarz FSU26 spectrum ana-lyzer to measure the offset generator and nomi-nal carrier powers at point (a). For this experi-ment the power of the carrier and the offset gen-erator were measured to be +8.32 dBm and -93.2

7

Lee Teng Internship 2013, Final Presentation1

Carrier

(R)(S)

DUT signal

Correctmeasurement plane

Wrongmeasurement plane

Figure 12: Principle of the LO Calibration.

dBm respectively at point (a) using a Rhode &Schwarz FSU26 spectrum analyzer. The peakvoltage measured on the FFT analyzer was 131.2mV with the LNA gain of 60dB. Hence the scal-ing factor without the LNA is calculated to be

kϕ =10+8.32/20

10−93.2/20· 131.2 · 10−6

= 15.63 V/rad

This is a factor of 40 or a 32 dB improve-ment over the 0.385 V/rad scaling of the sat-urated mixer system. The overall scaling factorof the interferometric system with the LNA gainof 60dB is 15,630 V/rad.

4.3 LO Phase Calibration

Unlike the saturated mixer system, a voltagemeasurement at the output of the mixer cannotbe used to calibrate the LO in an interferomet-ric system because the carrier at the RF port hasalready been suppressed. Furthermore, the mea-surement plane axes have to match the axes ofthe DUT signal. If the two do not match as de-picted in Fig.12, both in-phase and quadraturemodulations of the DUT would each be projectedonto both axes of the measurement plane.

To adjust the LO phase, previous literaturesuggested replacing the DUT with a voltage con-trolled phase shifter [3],[4] and that the inser-tion phase of the phase shifter does not matter.On the contrary, such a scheme would set up anincorrect orientation of the measurement planeif the DUT and the phase shifter do not havethe same insertion phase. What matters is forthe LO to have the proper phase relationship to

the DUT signal at point (a) of Fig. 8 to detectthe in-phase and quadrature components of theDUT signal. The signals at point (a) and themixer LO input are derived from the rf source.If the insertion phase from the source to point (a)is changed, then the phase relationship betweenthe mixer LO input and point (a) is changed andhence the measurement plane is incorrectly ro-tated.

Thus a scheme to properly orient the measure-ment plane is desired. A solution is now brieflydiscussed. The fine adjust is removed from thesystem by breaking the connection at point (e)of Fig. 8 and properly terminating both sides ofthe break in 50Ω. A voltage controlled attenua-tor (VCA) is inserted into the nulling arm, path(b), of the innermost interferometer. With nomodulation to the VCA control voltage, the stepattenuator and the variable phase shifter in path(b) are adjusted to achieve minimum carrier sup-pression. A DC offset on the VCA control volt-age can be used to aid in the carrier suppression.

Since the fine adjust is removed, only two ofthe vectors in Fig. 11 are present, the carrier andthe coarse adjust signal. When maximum carriersuppression is achieved the coarse adjust vectoris parallel to the carrier vector. A modulatingvoltage applied to the VCA will now be equiva-lent to an in-phase modulation of the DUT sig-nal. The LO phase adjust in Fig. 8 can now beadjusted until a null at the modulating frequencyis measured by the FFT; thus implying that theLO is adjusted to detect quadrature componentmodulations.

The VCA is then removed from the systemand the fine adjust is restored. The nullingarm path and fine adjust are then readjustedfor proper carrier suppression. During the en-tire process the DUT path is undisturbed. Addi-tionally when restoring the system, the adjustedLO phase to the mixer is preserved. Hence thecalibrated phase relationship between the DUToutput signal and the LO is preserved.

A voltage controlled phase shifter (VCPS)could be used instead of a VCA while adjust-ing for a maximum on the FFT. However, betteraccuracy can be achieved when tuning for a nullthan tuning for a maximum. When tuning for

8

0 2 4 6 8 10 12-80

-60

-40

-20

0

Modulation Frequency [kHz]

dB

V pk

Phase Noise, Modulation at 10kHz

Phase modulation

Amplitude modulation

Figure 13: LO Adjust Using Voltage ControlledAttenuator (VCA) and Voltage Controlled PhaseShifter (VCPS).

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dBra

d2 /

Hz

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Frequency [Hz]

dBra

d2 /

Hz

Total

LNA

RF Section

Figure 14: Contributions to Test Set NoiseFloor.

a null with the VCA, the detected voltage atthe FFT is proportional to the sine of the LOphase adjust error and hence the local derivativeis maximum. On the otherhand, if a VCPS isused the detected voltage is proportional to thecosine of the LO phase adjust error and hencethe local derivative is zero. Fig.13 shows the re-sults the FFT measurements using a VCA and aVCPS to adjust the LO. When using the VCA,the detected signal can be reduced down to thenoise floor of the system.

4.4 Interferometric Noise Floor

The noise floor of the interferometric system wasmeasured by using a simple cable in place of theDUT. The total noise floor along with measure-

ments of contributions from the rf section andthe LNA section are shown in Fig. 14. The LNAsection contribution is made by terminating theinput of the LNA in 50Ω, measuring the noisevoltage spectral density on the FFT with theLNA gain set to 60dB, and then converting tophase noise spectral density units using the in-terferometric system’s scaling factor. Comparingback to Fig. 6 note that due to the increased sen-sitivity of the interferometric system, the noisefrom the LNA section is much less than in thesaturated mixer system.

The noise of the rf section was measured bybreaking points (R) and (e) of Fig. 8 and prop-erly terminating the connections on each sideof the break in 50Ω. Thus the rf section in-cludes the rf amplifier, the mixer, and the base-band LNA and FFT. This noise is dominatedby the rf amplifier. Thus the rf amplifier is acrucial component of the system. It should pro-vide high enough gain to achieve good sensitivitywhile having a low noise figure to achieve a lowwhite noise floor for the system. It should alsohave low flicker noise to deal with imperfect car-rier suppression. The amplifier used here was aMiteq LCN0204.

The additional noise seen in the total noisefloor is then from the interferometer section. Thewhite noise floor is limited by the rf amplifieras is discussed in [4]. The slight increase seennear 100kHz could be from the source’s phasenoise beginning to constructively as opposed todestructively interfere at the carrier suppressionpoint (S) of Fig. 8. This could be due to differ-ences in path lengths of the two arms of the in-terferometer. The additional low frequency noiseseen below a few 100Hz is thought to be due tomechanical vibrations affecting the interferom-eter while that below a 2Hz is also thought tobe due to long-term mechanical stability of theinterferometer.

5 Comparison

Fig. 15 shows the phase noise spectral densityof both the interferometric system and the sat-urated mixer system for comparison. Also in-

9

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Interferometer

Saturated mixer

Figure 15: Phase Noise Density Comparison

Interferometer [0.1Hz-100kHz]Interferometer [1Hz-100kHz]Sat. Mixer [0.1Hz-100kHz]Sat. Mixer [1Hz-100kHz]

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degr

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rms

x 10

-6

Interferometer [0.1Hz-100kHz]Interferometer [1Hz-100kHz]Sat. Mixer [0.1Hz-100kHz]Sat. Mixer [1Hz-100kHz]

Figure 16: Forward Cumulative Integral Com-parison

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InterferometerSaturated Mixer

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InterferometerSaturated Mixer

Figure 17: Reverse Cumulative Integral Com-parison

Coefficient Interferometer Sat. Mixerbo dBrad2/Hz -176.5 -172.3b−1 dBrad2 -155 -139b−2 dBrad2Hz -156 N/Ab−3 dBrad2Hz2 -150 N/A

Table 1: Power Law Coefficients in dB

cluded on the graph are estimates of the coeffi-cients of a power law fit to each system of theform

Sϕ(f) = bo +b−1f

+b−2f2

+b−3f3

rad2/Hz .

Only the white noise and flicker noise terms, boand b−1 respectively, are overlaid on the graph.Also, only the interferometer model includes theb−2 random walk phase and the b−3 term. Thetotal phase noise model, Sϕ(f) of each is alsooverlaid on the graph; the saturated mixer sys-tem in magenta and the interferometric systemin cyan. The specific noise coefficients in dBunits, 10 · log10(bx), are given in Table 1.

The interferometric system shows an ∼4 dBimprovement in white noise and a substantial∼15 dB improvement in flicker, or 1/f , noise. Asmentioned previously the increase in the interfer-ometric system’s noise near 100kHz is likely dueto path length differences which may be able tobe corrected. The interferometric system how-ever shows a large amount of 1/f2 and 1/f3

noise. This is thought to be due to mechanicalstability of the interferometer. Careful mechan-ical construction improvements could help here.

Figures 16 and 17 show the forward andreverse cumulative integrals of the short-termphase noise from both the interferometric andsaturated mixer systems. The results are shownin micro-degrees rms where the conversion fromradians to degrees is given as deg = 180/π. Thecumulative integral is defined as follows

180π

√∫ f2f1

Sϕ(f) df

The forward graph shows the results for two dif-ferent lower limits of the integral, 0.1 Hz and 1

10

0 1 2-200

-100

0

100

200de

gree

s x

10-6

Time [sec]

Sat. Mixer

0 1 2-200

-100

0

100

200

Time [sec]

Interferometer

Figure 18: Time Domain, No Disturbance Ap-plied

0 1 2-200

-100

0

100

200

degr

ees

x 10

-6

Time [sec]

Sat. Mixer

0 1 2-200

-100

0

100

200

Time [sec]

Interferometer

Figure 19: Time Domain, Walking Nearby

Hz. The total integrated phase noise over 0.1Hz-100kHz is seen to be ∼32µdegrms for the inter-ferometric system compared to ∼65µdegrms forthe saturated mixer system. Conversion to resid-ual jitter is easily made by jitter=ϕ/(2πf). At2.815 GHz, 1µdeg, is equivalent to 1 attosec-ond. Thus the total equivalent residual jitter ofthe interferometric and saturated mixer systemsare ∼32 attosecondsrms and ∼65 attosecondsrmsrespectively.

0 1 2

-500

0

500

degr

ees

x 10

-6

Time [sec]

Sat. Mixer

0 1 2

-500

0

500

Time [sec]

Interferometer

Figure 20: Time Domain, Knock on Table

0 1 2-200

-100

0

100

200

degr

ees

x 10

-6

Time [sec]

Sat. Mixer

0 1 2-200

-100

0

100

200

Time [sec]

Interferometer

Figure 21: Time Domain, Waving Hand OverTest Set

Measurements were also made in the time do-main using the FFT analyzer. Figures 18, 20,19, and 21 show time domain results for fourdifferent cases respectively: (1) no purposely ap-plied disturbance, (2) walking nearby the mea-surement table, (3) a single impulse applied bya knock on the measurement table, and (4) wav-ing a hand above the measurement setup. Allmeasurements were taken with a 400 Hz band-width. Note that the saturated mixer systemnoise is dominated by a 60 Hz component. Theinterferometric system appears more sensitive toa knock on the measurement table which indi-cates that it is more susceptible to mechanicalvibrations. However, the knock was manuallyapplied and therefore uncalibrated. The inter-ferometric system can also detect heavy walk-ing by a passerby and even a hand waving overthe test setup. Obviously the first is due tomechanical vibrations while the second is mostlikely due to a disturbance in electromagneticcoupling/shielding. Due to the 60 Hz noise com-ponent of the saturated mixer system, it is hardto determine whether it can detect similar dis-turbances.

6 Conclusion

An interferometric system with two levels of car-rier suppression was built for 2.815 GHz. Itssensitivity was measured to be 15.63 V/rad com-pared to 0.385 V/rad for the saturated mixer sys-tem, an improvement by a factor of 40.6, or 32dB. It showed a ∼4 dB improvement in white

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noise and a ∼15 dB improvement in flicker, or1/f , noise. However both 1/f3 and randomwalk, 1/f2, type noise was higher, most likelydue to mechanical stability of the system withthe increased number of components all of whichcontribute to carefully achieving carrier suppres-sion.

The cumulative integrated noise floor of theinterferometric system and the saturated mixersystem were ∼32µdegrms and ∼65µdegrms re-spectively over a [0.1Hz-100kHz] bandwidth. At2.815 GHz This corresponds to a residual jitterof ∼32 attosecondsrms and ∼65 attosecondsrmsrespectively.

A novel technique of aligning the measurementreference plane to the DUT signal was developed.Contrary to previous literature, it establishes thecorrect orientation. It also leaves the DUT pathundisturbed throughout the LO phase calibra-tion.

7 Future recommendations

Both the saturated mixer and the interferomet-ric system make use of amplifiers. While the sat-urated mixer system relies heavily on the noiseperformance of the LNA, the interferometric sys-tem relies heavily on the noise performance ofits rf amplifier. Thus using a rf amplifier witha lower noise figure should improve the whitenoise floor of the system. An increased carrierlevel can also improve the white noise floor sincethe noise floor is determined by the ratio of thecarrier power to the thermal noise of the system[4].

One of the main issues faced with the interfer-ometric system was mechanical vibration of thesystem. Any subtle movement around the exper-imental area could cause changes in the result.Therefore, mounting the system on an isolatedoptical table and using better shielded coaxialcables could provide more mechanical stabilityand better performance. The stability of thecontinuously variable attenuator used in the fineadjust path was also problematic. A better at-tenuator with a good locking mechanism couldprovide improvement. The step attenuator was

also a bit finicky in achieving repeatability andbeing sensitive to slight touches of the dial. Thusit too could be replaced with a better unit if onecan be found.

With regards to electromagnetic disturbances,better shielded coaxial cable could be used. Thecable used was of the hand flexible type whichessentially has a tin-dipped braided shield. Truehard-line or semi-rigid cable with a solid shieldcould be used.

Automatic carrier suppression [4] could alsobe pursued. This is likely to keep the measure-ment plane aligned and minimize any flicker ofthe rf amplifier. Also the cause for 1/f typenoise seen in the system without the interferom-eter should be explored since ideally the ampli-fier should know nothing about the location ofthe carrier and should not be the source of theflicker seen in that measurement configuration.

The measurement system is not limited tomeasuring only phase noise. It can be used tomeasure in-phase or amplitude noise as well bya simple adjustment of the LO phase. Simultane-ous measurement of both in-phase and quadra-ture noise can be achieved by using two mixerswith quadrature LO phases.

Finally, the noise floor of a digital low-levelrf (LLRF) system is limited by the analog-to-digital (ADC) converters in the receiver due tothe level of the carrier compared to the totalnoise of the ADC including quantization, aper-ture jitter, non-linearity, and other noise sourcesassociated with the ADC. White noise floors oftypical digital LLRF systems can range from -150 dBrad2/Hz to -140 dBrad2/Hz and around-120 dBrad2 for the 1/f noise coefficient. The in-terferometric technique shows promise for a 25-35dB improvement in both compared to a dig-ital receiver. A mixed analog/digital approachcould be used by incorporating digital detectionwhile using analog carrier suppression to amplifythe noise sidebands without the carrier saturat-ing the ADC. Since the noise sidebands are keptnear the rf signal, this still allows detection of thenoise at rf or intermediate frequencies, as is donein digital LLRF, as opposed to at baseband. Aseparate detector would still be needed to mea-sure the level of the carrier.

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References

[1] K. H. Sann, ”The Measurement of Near-Carrier Noise in Microwave Amplifiers,”IEEE Trans. Microw. Theory Techs., no. 9,pp. 761-766, 1968.

[2] R. Boudot, E. Rubiola, ”Phase Noisein RF and Microwave Amplifiers,”arXiv:1001.2047v1 [physics.ins-det], Jan.2010, submitted to IEEE Trans- act. MTT.

[3] E. Rubiola, V. Giordano, ”A Low-FlickerScheme for the Real-Time Measurementof Phase Noise,” Proc. 2001 Freq. ControlSymp., pp. 138-143, 2001.

[4] E. Rubiola, V. Giordano, ”Advanced Inter-ferometric Phase and Amplitude Noise Mea-surement,” Rev. Sci. Instrum., vol. 73 no.6pp. 2445-2457, 2002.

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