A method for primary calibration of AM and PM noise measurements

Transcription

1 A method for primary calibration of AM and PM noise measurements TimeNav 07 May 31, 2007 Enrico Rubiola FEMTO-ST nstitute, Besançon, France CNRS and Université de Franche Comté Outline ntroduction Power measurements - modulators and detectors Method and error budget Perspectives and conclusions home page

2 The S unit of angle 2 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 uni Electrical circuits => Phasors modulated signal carrier V0 cos( ω 0 modulation ysin(ω 0 n low-noise conditions α( = x and ϕ( = y V 0 V 0 x/v 0 1 and y/v 0 1 xcos( ω 0 thus, arctan(y/x) y/x 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 other primary measurement OK unused significantly more precise measurement tolerated needed

3 State of the art 3 synthes. ν s However accurate in practice, A - B are incorrect because of the simultaneous presence of AM and PM. A on P 0 P s rf noise on B P 0 N freq. ref. ν 0 off ν s << ref. P 0 ν s off ref. P 0 ν s The problem is that the phase detector (saturated-mixer) is sensitive to AM E. Rubiola, R. Boudot, EEE Trans. UFFC 54 5 p , may 2007 synthes. ν s C - D are correct because only PM (or AM) is present C P 0 ν s near dc noise on D α or ϕ modulat. P 0 N freq. ref. ν s << ref. P 0 off ref. P 0 ν s The calibrators are still to be referred to the S unit rad Primary laboratories declare 1 2 db accuracy in PM noise measurements

4 Reference AM - PM modulator 4 input V0 cos( ω 0 carrier V cos( ω xcos( ω 0 y sin(ω 0 x modul y modulation sidebands xcos( ω 0 ysin(ω 0 modul. input modulator pump 9 This scheme is similar to the single-mixer scheme (NST) The novelty is in the calibration process fix the defects of the - modulator (quadrature and symmetry) fix the arbitrary phase that derives from the layout calibrate the modulation index

5 Power detector 5 rf in video out -20 Herotek DT8012 s.no ~60 Ω pf external 50 Ω to 100 kω voltage, dbv kω 3.2 kω 1 kω 320 Ω Ω law: v = kd P 30 A 1 Schottky 300 A 1 Tunnel input power, dbm Large video bandwidth: 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, The measurement of AM noise of oscillators, arxiv:physics/ , dec 2005 E. Rubiola, F. Lardet-Vieudrin Low flicker-noise amplifier... Rev. Sci. nstr 75 5 p ,

6 Power meter and calibrated attenuator 6 Power meter We have two similar power meters and some probes The probe goes up to 2 GHz, the μwave probe starts at 50 MHz (overlap in the 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 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 angle 0.05º º, accuracy 6x10 3 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 db

7 - detector and modulator 7 input DC s( = V 2 cos( ω0t+ϕ) 9 remove 2ω 0 terms r ( = r ( = 2 sin( ω0 2 cos( ω0 v = V cos(ϕ) v = V sin( ϕ) V sin(ϕ) m Ve jϕ V - detector Gets the and components of the input phasor vs. the Cartesian frame defined by the pump r( = pump 2 cos( ω0 O ϕ Re V cos(ϕ) DC input v = V cos(ϕ) v = V sin( ϕ) block r ( = 2 sin( ω0 9 r ( = 2 cos( ω0 s( = V 2 cos( ω0t+ϕ) V sin(ϕ) m Ve jϕ V - modulator Combines the and inputs into a phasor referred to a Cartesian frame is defined by the pump pump r( = 2 cos( ω0 O ϕ Re V cos(ϕ) E. Rubiola, Tutorial on the double-balanced mixer, arxiv/physics/ , aug 2006

8 Real - detector 8 input v r = cos( ωs)t detector under test F v = 1 2 cos(ω b matrix osc in MHz - = cos( ω + ω )t 0 = cos(ω 0 cos(ω b sin( ω0 sin(ωb b 1+ε sin(ω 0t+ψ) 9+ψ remove 2ω 0 terms v = 1 2 = (1+ε) 1 lock in amplifier in sin( ωb cos(ψ) cos(ω b (1+ε) sin(ω t ψ) 2 b a11 a12 a21 a22 sin(ψ) 8 12 GHz - pump cos( ω 0 synthes. freq. reference ω 0 matrix Problems & solutions quadrature error ψ amplitude asymmetry ε fix the errors with a matrix use the Gram Schmidt process the phase is still arbitrary ψ ε m m Re Re

9 Real - modulator 9 input modulator under test input reference detector MHz - x y matrix a11 a12 a21 a22 dc offset 1+ε v x V y 9+ψ 9 freq. reference ω 0 pump VLcos( ω 0 t+θ) arbitrary length pump VLcos( ω GHz - V m cos( ω m osc out lock in amplifier in matrix Problems & solutions quadrature error ψ amplitude asymmetry ε fix the errors with a matrix use the Gram Schmidt process the phase is still arbitrary ψ ε m m Re Re

10 Setting up the reference modulator 10 V0 cos( ω 0 arbitrary phase θ v i power detector cv 2 v d dc voltm. V dc = c V V 2 m cos( ω0t +θ) ideal (corrected for ψ and ε) modul v a11 a12 a21 a22 matrix cos( ω0t +θ) v sin( ω 0 t +θ) PM AM V m cos( ω m osc lock in in amplifier : :,: V ω = fundamental c V m V 0 cos( θ) cos( ω m V ω = c V 0 sin( θ) cos( ω m V m 2nd harmonics 1 V 2ω = c 2V 4 2 m cos(2ω m Problems & solutions the 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 guarantees the pure AM

11 Assessing the modulation depth 11 carrier input V0 cos( ω 0 SW1 A G SW2 A G modulated narrowband ampli power meter arbitrary phase O the DUT can be inserted here O ideal (corrected for θ, ψ and ε) modul v y v x PM G AM SW3 ω m operation pass through (modulation OFF) calibrate (modulation ON) self calibration meas. P 0 /l 2 1/2 self calibration 2/2 meas. P s SW1 O SW1 O SW1 G O O AM/PM A A G G G AM/PM Problems & solutions 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

12 Modulator linearity 12 v = a 1 tanh(a 2 i F ) v = a 1 tanh(a 2 i F ) + a 3 i F pure tanh(x) model tanh(x) model with dissipation, Vrms MiniCircuits ZFM 2 (modulator) file 922 zfm2 modulh E. Rubiola, 4 apr 2007 black points: measured green: a*tanh(bx) red: a*tanh(bx)+cx dashed: tangent measured values F current, Adc expected error, if non-linearity is ignored i F v /v v P ma (dimensionless) mv rms µw dbm

13 Error budget 13 parameter and conditions value power ratio measurement (0.1 db) (commercial power meter) path (0.2 db) (couplers, cables etc.) reference 40 db attenuator (0.05 db) mixer and detector linearity null measurements (commercial lock-in, 10 bi signal-to-noise ratio worst case total (0.37 db) rms total (0.23 db) Using off-the-shelf instruments and parts, an accuracy of db is feasible

14 from AM out 20 db Bridge (interferometric) instrument 14 power meter AM out 9 9 inner interferometer CP1 CP2 DUT γ 9 9 Δ virtual gnd Δ" CP3 CP4 18 channel b ampli & detector readout 1b g v 2b matrix detect v w 1b R w 2b fine carrier control by pass channel a ampli & det. readout detect g v 2a matrix v 1a w 1a R w 2a dual channel FFT analyzer 18 automatic carrier control to AM/PM modul input modul Σ Σ u 1 u z ( dt 2 z 1 z 2 D matrix osc lock in in amplifier AM matrix PM modulation input The dual-bridge contains almost all the blocks needed to calibrate the measurement n light blue: the parts to be added (future work) E. Rubiola, V. Giordano, Rev. Sci. nstrum 73 6 p , jun Also arxiv:physics/

15 Conclusions 15 The S phase is a derived quantity, which can be obtained as φ = arctan(y/x) n principle, the application of primarymetrology methods to the AM-PM noise measurements is surprisingly simple FEMTO-ST has not primary-metrology facilities on site, which limits our possibility of a real test Using off-the-shelf instruments and parts, an accuracy of db is feasible The commercial parts are shown only for reproducibility The bridge (interferometric) instrument is suitable to the proposed method with a minimum added complexity home page Free downloads (texts and slides)