Phase noise limitation in CW

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noise/sensors Friedt& al.

RADAR basics:

CW RADAR basics:

FMCW Passive wireless sensors Phase noise Resonators as passive wireless sensors Conclusion

On the need for low phase noise oscillators for wireless passive sensor probing

N. Chr´etien, J.-M Friedt, B. Fran¸cois, G. Martin, S. Ballandras

http://jmfriedt.free.fr

April 6, 2012

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RADAR basics:

CW RADAR basics:

CW basics

It all started with ... 9 GHz CW RADAR ¹

~cos(f(t)−f(t+ ))τ LNA

PA I

target

τ/2 τ/2

frequence (coef. de Fourier)

temps (u.a.) 0

5

10

15

20

25

30

0 200 400 600 800 1000

-0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3

0 0.2 0.4 0.6 0.8 1

tension (V)

temps (s)

1http://www.lextronic.fr/P1455-tete-hf-hyperfrequence-mdu1130.html&

http://www.microwave-solutions.com/

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RADAR basics:

CW RADAR basics:

CW basics

It all started with ... 9 GHz CW RADAR ¹

Target velocity induces frequency shiftfD = 2×^f⁰_c^v when vc Contribution of the LO fluctuations duringτ ?

1http://www.lextronic.fr/P1455-tete-hf-hyperfrequence-mdu1130.html&

http://www.microwave-solutions.com/

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RADAR basics:

CW RADAR basics:

Phase noise limitation in CW

RADAR equation: Precv

P_xmit = G1G2λ²σ (4π)³d⁴

-100 -80 -60 -40 -20 0 20

10 100 1000 10000 100000

puissance (dBc/Hz)

écart à la porteuse (Hz)

τ = 2d/c so d∈[0.15−150] m⇒τ∈[1−1000] ns,i.e.

f ∈[1−1000] MHz whereL<−100 dBc/Hz⇒d= 560 cm

(G1=G2= 8 dBi,λ= 3 cm,σ'1000 cm²for 10×10 cm²metal plate, 16 Hz FFT)

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RADAR basics:

CW RADAR basics:

Outline

1 pulsed CW RADAR as SAW delay line reader

2 FMCW RADAR as SAW resonator reader

3 ADC jitter effect on delay line measurement

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RADAR basics:

CW RADAR basics:

From CW to FMCW

• Static target = no returned signal

• Linear passive sensors⇒returned freq. = emitted freq.

• How to recover delay information ? frequency sweep

• Spatial resolution is defined bybandwidth∆f only f

t df

dt

1 ∆f is swept during ∆t so after a time delay dt: df = ∆f ×_∆t^τ

2 Application: 100 MHz during 1 ms⇒1 µs target (150 m) = 100 kHz beat

3 FFT(output)=distance (delay)

4 range cellr =c/(2∆f) (since df >1/∆T & df = ^∆f_∆t ×^2d_c ) Bistatic configuration only requires a VCO and a mixer (+amplifiers)²

2Build a Small Radar System Capable of Sensing Range, Doppler, and Synthetic Aperture Radar Imaging, at http://ocw.mit.edu/resources/

res- ll- 003- build- a- small- radar- system- capable- of- sensing- range- doppler- and- synthetic- aperture- radar- imaging- january- iap- 2011/

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RADAR basics:

CW RADAR basics:

From CW to FMCW

• Spatial resolution is defined bybandwidth∆f only f

t dt

dt df

df’

df’!=df

1 ∆f is swept during ∆t so after a time delay dt: df = ∆f ×_∆t^τ

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RADAR basics:

CW RADAR basics:

From CW to FMCW

• Spatial resolution is defined bybandwidth∆f only

période 1 ms +4 dBm

VCO PA

−8 dBm I/Q

G=16 dB *2 NF=6.8

NF=2.5

+2dBm +16dBm

G=14 dB oscilloscope

FFT & avg

PA ZX60−V82−S+

AD8347 I/Q demod émission

réception

LNA HMC478 ZFDC−10−5 VCO

ROS2625 splitter

tag CTR

tag CTR 2.37−2.43 GHz

<30 cm

1 ms 1 ∆f is swept during ∆t so after a time delay dt: df = ∆f ×_∆t^τ

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RADAR basics:

CW RADAR basics:

Pulse mode SAW delay line reader

90

τ2 τ1 LO τ

RF IF

t

Q I

ADC (HMCAD1511) dual−channel

e.g 2.45 GHz

e.g 100 MHz

emitted

pulse echos

-1 -0.5

signal (V)

0 0.5 1

-1e-06

time (s)

I component Q component

0 1e-06 2e-06 3e-06 4e-06

• ∆ϕ= 2πdSAW/λ= 2πdSAWf/v= 2πfτ (τ propagation duration of the pulse,i.e.) ⇒ ∂∆ϕ= 2πf∂τ ⇔∂τ = 1/(2πf)∂∆ϕ

• Information of interest: |I +jQ|for coarse measurement, arg(I+jQ) for accurate delay measurement

• τ ∈[1−5]µs, pulse width∼30-40 ns

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RADAR basics:

CW RADAR basics:

Phase noise definition

Mixer outputm:

m= cos (2π(f(t) +δf))×cos (2π(f(t+τ)))

∝cos (2π(f(t) +δf ±f(t+τ))) (1) Ifδf negligible: m'cos (2π(f(t)−f(t+τ))).

should vanish when the target is not moving, butf(t+τ) andf(t) differ the phase noise spectrum of an oscillator is defined as the Fourier transform of the autocorrelation function of the oscillator output frequency ³ or⁴ phase fluctuation density in a 1 Hz-wide bandwidth

S∆ϕ= ∆ϕ²_RMS

measurement bandwidth rad²/Hz and the classical representation of the noise spectrum is given by L(f) =¹₂S∆ϕ(f) = 10×log₁₀

PSSB

P_S

dBc/Hz.

3E. Rubiola,Phase Noise and Frequency Stability in Oscillators, Cambridge Univ. Press (2010)

4Phase noise characterization of microwave oscillators – phase detector method, Agilent Product Note, vol. 11729B-1.

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RADAR basics:

CW RADAR basics:

Influence on RADAR detection limit

• So we have local oscillator noise spectraL(f), how to analyze these results for delay line measurement resolution ?

• Assumptions: -130 dBc/Hz and -170 dBc/Hz atf_carrier = 1/τ.

• Phase measurement within a 30 ns long pulse (bw=30 MHz):

∆ϕ_RMS =√

2×10−(130..170)/10×30×10⁶rad i.e. 0.14ô to 0.0014ô (and 14.0ô for -90 dBc/Hz)

2.45 GHz source generated by an Analog Devices ADF4360-0 Phase Locked Loop (poorly controlled), & Rohde & Schwartz SMA 100 A tabletop frequency synthesizer.

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RADAR basics:

CW RADAR basics:

Influence on RADAR detection limit

• So we have local oscillator noise spectraL(f), how to analyze these results for delay line measurement resolution ?

• Assumptions: -130 dBc/Hz and -170 dBc/Hz atf_carrier = 1/τ.

• Phase measurement within a 30 ns long pulse (bw=30 MHz):

∆ϕRMS =√

2×10−(130..170)/10×30×10⁶rad i.e. 0.14ô to 0.0014ô (and 14.0ô for -90 dBc/Hz)

dBc/Hz

−174

−154

−134

−114 dBc/Hz dBc/Hz dBc/Hz L(floor) P (dBm)

−20

−40

−60 0

sensor 35 dB 35 dB

Fp Fl L(f)

f

L(f)

f +Fp+Fl

kT*Fl/P

+10 dBm P>−62 dBm

Returned power P induced noise floor elevation:

P∈[−70..0] dBm range, and noise floor is the highest of either initial noise floor+F_p +F_l or LNA noise floorkT/P=−198.6+10 log₁₀(P)

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RADAR basics:

CW RADAR basics:

Influence on delay line resolution

∆ϕ= 2π×d_SAW/λ= 2π×d_SAW×f/v

The variation with temperatureT of this phase difference is associated with the velocity variation, so that

∂∆ϕ

∆ϕ _T

= ∂v v

_T

⇔∂∆ϕ(T) = 2πd_SAW ×f

v × ∂v

v _T

For a LiNbO3substrate,v'3000 m/s,∂v/v '60 ppm/K. If dSAW = 10 mm andf = 100 MHz, then

2π×60×10⁻⁶×10⁻²×10⁸/3000 = 0.13 rad/K= 7.2 ^o/K.

Phase noise half distance between reflectors resolution

-170 dBc/Hz 10 mm 2×10⁻⁴K

-170 dBc/Hz 1 mm 2×10⁻³K

-130 dBc/Hz 10 mm 0.02 K

-130 dBc/Hz 1 mm 0.2 K

-90 dBc/Hz 10 mm 2 K

-90 dBc/Hz 1 mm 20 K

Temperature measurement resolution, assuming a 60 ppm/K temperature drift of the delay-line sensor, as a function of various local oscillator parameters.

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RADAR basics:

CW RADAR basics:

Resulting design rules

Design rules for SAW delay lines:

• minimize phase noise of LO ! poor phase noise might become limiting factor in resolution

• keep maximum delay below inverse of Leeson frequency

f_L=f_LO/(2Q_LO) (abovef_L, noise floor is only defined byF andP of feedback amplifier)

• resolution increases withτ ⇒ τ≤1/f_L

• Q= 2000,f_LO = 2.45 GHz⇒f_L= 600 kHz⇒τ ≤1.6µs

• Q= 20000 (HBAR),fLO = 2.45 GHz⇒fL= 60 kHz⇒τ≤16µs (24 mm-long propagation path)

• electromagnetic clutter fades within 700 ns (100 m range) and typical pulse length 40 ns spaced by at least 100 ns, 1.5µs⇒ 5 reflections formulti-parameter-sensing

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RADAR basics:

CW RADAR basics:

Application to SAW resonator sensors

2Q/( f)π

|S11|

f

• resonator load and unload time constant: τ =Q/(πf₀)

• typical measurement duration:

256τ

• minimum measurement duration: 8τ (2 resonators, 2 measurements/resonance) ^a

aJ.-M Friedt, C. Droit, S. Ballandras, S. Alzuaga, G. Martin, P. Sandoz,Remote vibration measurement: a wireless passive surface acoustic wave resonator fast probing strategy, accepted Rev.

Sci. Instrum. (accepted March 2012)

Q = 10000,f0= 434 MHz⇒τ= 7 µs

⇒measurement duration ∈[60−1900]µs⇒f ∈[500−17000] Hz

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RADAR basics:

CW RADAR basics:

Phase noise to frequency noise conversion

Phase noiseS∆ϕand frequency fluctuationsS∆f atf from the carrier are related (f =dϕ/dt) through

S_∆f =f²×S_∆ϕ=∆f_RMS² BW

⇒for a measurement bandwidthBW of 2f, frequency fluctuations are given by

∆f_RMS² =BW ×f²×S_∆ϕ and

∆fRMS =p

BW ×f²×2L(f)

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RADAR basics:

CW RADAR basics:

Resonator measurement limitations

• 2.5 kHz/K temperature sensitivity (170 K measurement range within the 1.7 MHz wide 434 MHz ISM band)

• 25 Hz frequency resolution (10 mK resolution) requires -105 dBc/Hz.

• consistent with the phase noise spectra provided in⁵

(L(f) =−105 dBc/Hz atf ∈[500−5000] Hz at 434 MHz, DDS).

Phase noise frequency Q ∆fRMS(Hz) resolution -170 dBc/Hz 434 MHz 10000 0.01 4.10⁻⁷K

-130 dBc/Hz 434 MHz 10000 1 4.10⁻⁵K

-90 dBc/Hz 434 MHz 10000 140 5 mK

-170 dBc/Hz 2.450 GHz 1500 2 10⁻⁵K

-130 dBc/Hz 2.450 GHz 1500 230 1 mK

-90 dBc/Hz 2.450 GHz 1500 23000 0.1 K

assuming a 60 ppm/K sensitivity. For 5.7 ppm/K sensitivity, the values in the last column are multiplied by 10.

5J.-M Friedt, C. Droit, G. Martin, and S. Ballandras A wireless interrogation system exploiting narrowband acoustic resonator for remote physical quantity measurement Rev. Sci. Instrum. vol. 81, 014701 (2010)

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RADAR basics:

CW RADAR basics:

Resonator measurement limitations

• 2.5 kHz/K temperature sensitivity (170 K measurement range within the 1.7 MHz wide 434 MHz ISM band)

• 25 Hz frequency resolution (10 mK resolution) requires -105 dBc/Hz.

• consistent with the phase noise spectra provided in⁵

(L(f) =−105 dBc/Hz atf ∈[500−5000] Hz at 434 MHz, DDS).

5J.-M Friedt, C. Droit, G. Martin, and S. Ballandras A wireless interrogation system exploiting narrowband acoustic resonator for remote physical quantity measurement Rev. Sci. Instrum. vol. 81, 014701 (2010)

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RADAR basics:

CW RADAR basics:

ADC jitter influence on SAW delay line measurements

Delay line seems favorable since oscillator has less time to drift,butfast sampling of the returned signal is needed.

Phase noise to jitter conversion⁶: σ_t=

Rf2 f1 2L(f)df

2πfc '

√

2×10^−S^{ϕ /}¹⁰×BW (2π×BW)

Jitterσt yields ⁷resolution loss ofSNR= (2πfsσt)

• 0.13 rad/K ⇒0.13 rad over 2πrad range requires 6 bit resolution

• 40 ns pulse⇒BW '100 MHz, and duration of A/D <5 µs

• ifL(f) =−130 dBc/Hz inf ∈[0.2−200 MHz range⇒σt = 7 ps,

• 1 K resolution: σ_t must not exceed 42 ps (6 bit at 100 MS/s),

• 0.1 K resolution requires a 9 bit ADC and a maximum jitter of 5 ps.

Digital PLL of an iMX27 CPU is specified at a maximum jitter of 200 ps

6_{W. Kester,}Converting oscillator phase noise to time jitter, Analog Devices MT-008 Tutorial, 2008

7D. Redmayne, E. Trelewicz, and A. Smith,Understanding the effect of clock jitter on high speed ADCs, Linear Technology Design Note 1013, 2006

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RADAR basics:

CW RADAR basics:

Conclusion (& perspectives)

• delay line provide short delay response (floor since far from carrier)

⇒low phase noisebuthigh losses (IL) and fast sampling rate at receiver⇒moves requirements on LO from emission to ADC clocking circuit

• pulse-mode (UWB) delay line reader doesnotrequire tunable LO

⇒improved stability ?

• resonator seems to be LO limited (25 Hz for -105 dBc/Hztunable (DDS) LO)

• design rule for delay lines: keep 1/τ >fL

→need to experimentally demonstrate all these concepts !

→low phase noise LO by avoiding PLL and using high Q/high frequency resonators ?

→∂∆ϕ∝∂τ×f ⇒does increased phase slope with frequency com- pensate for increased phase noise of

oscillator ? -200

-150 -100 -50 0

100 101 102 103 104 105 106 107 108

200 kHz 1 M Hz -165 dBc/Hz

Sφ (dBc/Hz)

f (Hz)

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