A method for primary calibration of AM and PM noise measurements - - PowerPoint PPT Presentation

FEMTO-ST Institute, Besançon, France CNRS and Université de Franche Comté

home page http:/ /rubiola.org

A method for primary calibration of AM and PM noise measurements

Introduction Power measurements I-Q modulators and detectors Method and error budget Perspectives and conclusions

TimeNav’07 – May 31, 2007

Outline

Enrico Rubiola

2

The SI unit of angle

The radian is now considered a derived unit because an angle can always be defined in terms of the ratio of two homogeneous quantities

(formerly, it was considered an auxiliary unit)

Electrical circuits => Phasors

x t) ω ysin( − V cos( t) ω m

• d

u l a t e d s i g n a l carrier cos( modulation t) ω

requirements for a derived measurement to be primary

type of partial measurement allowed? this work null measurement always OK needed ratio measurement always OK needed

• ther primary measurement

OK unused significantly more precise measurement tolerated needed

In low-noise conditions α(t) = x V0 and ϕ(t) = y V0

|x/V0| ≪ 1 and |y/V0| ≪ 1

thus, arctan(y/x) → y/x

3

State of the art

rf noise

νs

νs ν0 ν0 − | << | P0 ν0 νs Ps ν0 νs P0

• n
• ff

synthes. ref.

• utput

freq. ref.

A

ν0 P0 N ν0 P0

ν0

B

• n
• ff

ref.

• utput

ν

D

ν0 νs ν0 νs P0

ν0 νs

νs ν0 ν0 − | << |

C

synthes. ref. freq. ref.

• utput

ν0 P0 ν0 P0 N

ν0

• r ϕ

α modulat. near−dc noise

• n
• ff

ref.

• utput

P

However accurate in practice, A - B are incorrect because of the simultaneous presence of AM and PM. C - D are correct because only PM (or AM) is present The calibrators are still to be referred to the SI unit rad

The problem is that the phase detector (saturated-mixer) is sensitive to AM

• E. Rubiola, R. Boudot, IEEE Trans. UFFC 54 5 p.926–932, may 2007

Primary laboratories declare 1–2 dB accuracy in PM noise measurements

4

Reference AM - PM modulator

I−Q modulator V cos( t) ω cos( t) ω x t) ω ysin( − V cos( t) ω + LO I Q RF I−Q modul

y x

• modul. input

cos( t) ω x t) ω ysin( − RF output RF input carrier modulation sidebands 90°

• utput

RF I Q LO pump

• fix the defects of the I-Q modulator (quadrature and

symmetry)

• fix the arbitrary LO phase that derives from the layout
• calibrate the modulation index

This scheme is similar to the single-mixer scheme (NIST) The novelty is in the calibration process

5

Power detector

• E. Rubiola, “The measurement of AM noise of oscillators,” arXiv:physics/0512082, dec 2005
• 50
• 40
• 20
• 60

10

• 10
• 20
• 30
• 40
• 60
• 80
• 100

kΩ 3.2 kΩ 320 Ω 100 Ω 1 kΩ input power, dBm

• utput voltage, dBV

10 Herotek DT8012 s.no. 232028

10−200 Ω k 100 50 Ω to external

video out rf in

Ω ~60 pF

law: v = kd P

≥30 A–1 Schottky ≥300 A–1 Tunnel

Large video bandwidth: 10–100 MHz Short storage time => Virtually no discriminator effect A detected null of AM validates a phase modulator For best accuracy, use a lock-in amplifier Need a low-noise dc amplifier

• E. Rubiola, F. Lardet-Vieudrin “Low flicker-noise amplifier ...” Rev. Sci. Instr 75 5 p.1323–26,

6

Power meter and calibrated attenuator

Power meter

◆ We have two similar power meters and some probes ◆ The RF probe goes up to 2 GHz, the μwave probe starts at 50 MHz (overlap in the 50-2000 MHz region) ◆ Reproducibility within 0.01 dB, max 0.02 (observed)

• changing the mainframe
• replacing the probe with another of the same type
• interchanging the RF probe with μwave one

◆ Similar accuracy is expected in differential meas.

Reference attenuator

a reference attenuator with 40 dB attenuation and 0.05 dB accuracy is not difficult to obtain

Power-ratio: 40–60 dB

Accuracy:

0.05 dB

This should be achievable with off-the-shelf parts, at least at a set of frequencies. A pinch of good luck may be useful

0 dB –40 ... –60 dB

angle 0.05º ... 0.5º, accuracy 6x10–3

7

I-Q detector and modulator

90° 2ω0 remove terms r (t) =

Q

r (t) =

I

2 ω t sin( ) − s(t) = ω t 2 cos( ) LO pump ω t 2 cos( ) vI = V cos(ϕ) v = V sin(

Q

ϕ) 2 cos( V ω t+ϕ) V sin(ϕ) V cos(ϕ) Vejϕ I Q RF input DC output r(t) = ϕ Im Re V O LO pump 90° r (t) =

Q

2 ω t sin( ) − r (t) =

I

ω t 2 cos( ) 2 cos( V ω t+ϕ) s(t) = RF block ω t 2 cos( ) v = V sin(

Q

ϕ) vI = V cos(ϕ) V sin(ϕ) V cos(ϕ) Vejϕ I Q DC input RF output r(t) = Im Re V O ϕ

I-Q detector

Gets the I and Q components of the input phasor vs. the Cartesian frame defined by the LO pump

I-Q modulator

Combines the I and Q inputs into a phasor referred to a Cartesian frame is defined by the LO pump

• E. Rubiola, “Tutorial on the double-balanced mixer,” arXiv/physics/0608211, aug 2006

Problems & solutions

8

Real I-Q detector

2ω0 remove terms ω t+ψ) −sin( 90° +ψ lock−in amplifier

• sc

in in ω pump LO cos( 0 ω t) cos(ω t)

b

1 2 vI = 1 2 ω t)

b

sin( cos(ψ) cos(ω t)

b

sin(ψ) (1+ε) − vQ = 1 2

b

ω t −ψ) sin( (1+ε) = cos(ω t) cos(ω t)

b

= vr =

s

ω cos( )t ω

b

ω ω t) sin( sin(ω t)

b

− I Q

• freq. reference

synthes. RF input IF output I−Q detector under test = cos( )t + 1+ε

• quadrature error ψ
• amplitude asymmetry ε
• fix the errors with a matrix
• use the Gram Schmidt process
• the LO phase is still arbitrary

a11 a12 a21 a22

matrix

95–105 MHz I-Q 8–12 GHz I-Q matrix

ε

Re Im

ψ

Re Im

Problems & solutions

9

Real I-Q modulator

• quadrature error ψ
• amplitude asymmetry ε
• fix the errors with a matrix
• use the Gram Schmidt process
• the LO phase is still arbitrary

a11 a12 a21a22

matrix 95–105 MHz I-Q 8–12 GHz I-Q matrix

ε

Re Im

V cos( 0 ω

L

t+θ) 1+ε ω lock−in amplifier

• sc
• ut

in cos( t) Vm

m

ω under test I−Q modulator V cos( 0 ω

L

t)

Vy

vx I−Q detector reference 90° +ψ 90° dc offset RF I Q LO pump

• freq. reference

arbitrary length input x y

• utput

I Q LO pump

• utput

RF input

ψ

Re Im

10

Setting up the reference modulator

• the LO phase θ is still arbitrary
• this is fixed with a matrix that rotates the

Cartesian frame by –θ

• pure PM is guaranteed by a null of the

detected AM

• the corrected IQ guarantees the pure AM

AM PM

Problems & solutions

V cos( t) ω

θ

voltm. dc 2 1 V2 4 1 Vdc

m

V2 vd power detector

cv2

vi modul LO I−Q I Q RF lock−in amplifier

• sc

in Vm ωm cos( t) V

ω

V

ω

V

0 sin( )

θ ωmt) cos(

m

V θ cos( ) ωmt) cos( V

m

V V

2ω

4 1 c2

m

V2 ωm t) cos(2 vI +θ) cos( ω t vQ ω sin( t +θ) − 2nd harmonics fundamental = = −c c = I,Q: Q: I: +θ) cos( ω t for ψ and ε) ideal (corrected phase arbitrary + = c

a22 a21

matrix

a12 a11

11

Assessing the modulation depth

• measure the modulation depth as Psidebands / Pcarrier
• measure the carrier and the modulation separately
• need a reference attenuator for differential power

measurement

• need a narrowband amplifier to limit the thermal

noise of the power meter

Problems & solutions

modul LO I−Q I Q RF V cos( t) ω vx vy

m

ω

power meter

and ε) for θ, ψ (corrected ideal

• meas. P0/l 2
• meas. Ps

arbitrary phase SW3 input carrier SW1 SW2 modulated

• utput

narrowband ampli G G G PM AM O A A O

• peration

self calibration 1/2 self calibration 2/2 SW1 G SW1 A G SW1 G A AM/PM (modulation OFF) G O O (modulation ON) calibrate O O AM/PM pass through the DUT can be inserted here

12

Modulator linearity

expected error, if non-linearity is ignored iIF ∆vRF /vRF vRF PRF 0.1 10−4 3.91 0.305 −35.2 0.316 10−3 12.4 3.05 −25.2 1 10−2 39.1 30.5 −15.2 mA (dimensionless) mVrms µW dBm vRF = a1 tanh(a2iIF ) pure tanh(x) model vRF = a1 tanh(a2iIF ) + a3iIF tanh(x) model with dissipation

0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01 0.05 0.1 0.15 0.2 0.25

IF current, Adc RF output, Vrms

MiniCircuits ZFM−2 (modulator)

file 922−zfm2−modulh

• E. Rubiola, 4 apr 2007

black points: measured dashed: tangent green: a*tanh(bx) red: a*tanh(bx)+cx

measured values

13

Error budget

Using off-the-shelf instruments and parts, an accuracy of 0.2–0.4 dB is feasible

parameter and conditions value power ratio measurement 11.6×10−3 (0.1 dB) (commercial power meter) RF path 23×10−3 (0.2 dB) (couplers, cables etc.) reference 40 dB attenuator 5.8×10−3 (0.05 dB) mixer and detector linearity 1.0×10−3 null measurements 1.0×10−3 (commercial lock-in, 10 bit) signal-to-noise ratio 1.0×10−3 worst case total 43.6×10−3 (0.37 dB) rms total 26.5×10−3 (0.23 dB)

14

Bridge (interferometric) instrument

−90° − 9 ° −90° − 9 °

0° 0° 0° 1 8 ° −90° −90° 0° ° 0° 0° 180° °

Q I fine carrier control

0° 0° 0° 1 8 °

Q I I−Q detect

g

v2a matrix R v1a w1a w2a

LO RF

ampli & det. readout channel a Q I I−Q detect

g

v2b matrix R

1b

v w1b w2b

LO RF

ampli & detector readout channel b virtual gnd RF Δ" dual channel FFT analyzer ( ) DUT Δ’ γ inner interferometer

−20 dB by−pass CP1 CP2 CP3 CP4

Q I I−Q modul

1

u

2

u t dt z matrix D

2

z

1

z

LO RF

automatic carrier control matrix lock−in in

• sc

amplifier to AM/PM

Σ Σ

AM PM modulation input from AM out AM out power modul input meter

• E. Rubiola, V. Giordano, Rev. Sci. Instrum 73 6 p.2445–57, jun 2002. Also arXiv:physics/0503015

The dual-bridge contains almost all the blocks needed to calibrate the measurement In light blue: the parts to be added (future work)

15

Conclusions

The SI phase is a derived quantity, which can be

• btained as φ = arctan(Y/X)

In principle, the application of primary- metrology methods to the AM-PM noise measurements is surprisingly simple FEMTO-ST has not primary-metrology facilities

• n site, which limits our possibility of a real test

Using off-the-shelf instruments and parts, an accuracy of 0.2–0.4 dB is feasible The bridge (interferometric) instrument is suitable to the proposed method with a minimum added complexity

home page http:/ /rubiola.org

The commercial parts are shown only for reproducibility

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