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

A method for primary calibration of AM and PM noise measurements TimeNav ’ 07 – May 31, 2007 Enrico Rubiola FEMTO-ST Institute, Besançon, France CNRS and Université de Franche Comté Outline Introduction Power measurements I-Q modulators and detectors Method and error budget Perspectives and conclusions home page http:/ /rubiola.org

The SI 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 unit) Electrical circuits => Phasors In low-noise conditions t) l a n g i s 0 modulation d e t a ω l u α ( t ) = x ϕ ( t ) = y d o m ysin( and carrier V 0 V 0 − V cos( ω t) 0 0 | x/V 0 | ≪ 1 and | y/V 0 | ≪ 1 ω x cos( t) thus, arctan( y/x ) → y/x 0 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

State of the art 3 However accurate in practice, A - B are incorrect because of the simultaneous presence of AM and PM. A B synthes. rf noise P 0 P 0 ν s on on output P s output N ν 0 ν s ν 0 off off freq. | ν s − ν 0 | << ν 0 ref. P 0 P 0 ref. ref. ν ν 0 0 ν s ν 0 ν 0 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 C - D are correct because only PM (or AM) is present C D P 0 P 0 synthes. near−dc ν s output output N noise α or ϕ modulat. on ν 0 ν s ν 0 freq. | ν s − ν 0 | << ν 0 ref. off P P 0 0 ref. ref. ν 0 ν 0 ν 0 ν s ν 0 The calibrators are still to be referred to the SI unit rad Primary laboratories declare 1–2 dB accuracy in PM noise measurements

Reference AM - PM modulator 4 RF input RF output V cos( ω t) + x cos( ω t) − ysin( ω t) V cos( ω t) 0 0 0 0 carrier 0 0 LO I−Q modulator RF I−Q modulation sidebands LO pump modul ω ω x cos( t) − ysin( t) 0 0 I Q 90° RF output x y modul. input I Q This scheme is similar to the single-mixer scheme (NIST) The novelty is in the calibration process • 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

Power detector 5 rf in video out Herotek DT8012 s.no. 232028 -20 -40 output voltage, dBV 10 k Ω external ~60 50 Ω to 3.2 k Ω 10−200 -60 Ω 100 k Ω 1 k Ω pF 320 Ω -80 100 Ω ≥ 30 A –1 Schottky law: v = k d P -100 ≥ 300 A –1 Tunnel -60 -50 -40 -30 -20 -10 0 10 input power, dBm 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, “The measurement of AM noise of oscillators,” arXiv:physics/0512082, dec 2005 E. Rubiola, F. Lardet-Vieudrin “Low flicker-noise amplifier ...” Rev. Sci. Instr 75 5 p.1323–26,

Power meter and calibrated attenuator 6 Power meter ◆ We have two similar power meters and some probes ◆ The RF probe goes up to 2 GHz, the μ wave 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 μ wave 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 0.05 dB Accuracy: angle 0.05º ... 0.5º, 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 –40 ... –60 dB

I-Q detector and modulator 7 RF input DC output I s(t) = v I = V cos( ϕ ) I-Q detector Im V 2 cos( ω t + ϕ ) 0 remove Gets the I and Q components of V sin( ϕ ) 2 ω 0 terms V the input phasor vs. the Cartesian Q v = V sin( ϕ ) Q frame defined by the LO pump r (t) = r (t) = Q I ω t ) ω t ) − 2 sin( 2 cos( Ve j ϕ 0 0 90° ϕ Re r(t) = LO ω t ) V cos( ϕ ) pump 2 cos( O 0 DC input RF output I I-Q modulator v I = V cos( ϕ ) s(t) = Im V 2 cos( ω t + ϕ ) 0 Combines the I and Q inputs into RF V sin( ϕ ) V block a phasor referred to a Cartesian Q ϕ ) v = V sin( Q frame is defined by the LO pump r (t) = r (t) = Q I − 2 sin( ω t ) 2 cos( ω t ) Ve j ϕ 0 0 90° ϕ Re r(t) = LO pump 2 cos( ω t ) O V cos( ϕ ) 0 E. Rubiola, “Tutorial on the double-balanced mixer,” arXiv/physics/0608211, aug 2006

Real I-Q detector 8 RF input IF output 95–105 MHz I-Q I−Q detector 1 under test v I = cos( ω t) b 2 matrix I v r = cos( ω )t osc s in amplifier a 11 a 12 lock−in remove 2 ω 0 terms a 21 a 22 = cos( ω + ω )t 0 b Q in 1+ ε = cos( ω t) cos( ω t) 0 b ω t) sin( ω t) − sin( 8–12 GHz I-Q b 0 −sin( ω t + ψ ) 1 0 (1+ ε ) sin( ω t) cos( ψ ) − cos( ω t) sin( ψ ) v Q = b b 2 90° + ψ 1 = (1+ ε ) sin( ω t −ψ ) b 2 LO pump cos( 0 ω t) synthes. ω freq. reference 0 matrix Problems & solutions Im ψ • quadrature error ψ Re • amplitude asymmetry ε ε • fix the errors with a matrix Im • use the Gram Schmidt process Re • the LO phase is still arbitrary

Real I-Q modulator 9 I−Q modulator reference 95–105 MHz I-Q input under test output input I−Q detector output matrix v x x I I RF RF a 11 a 12 dc offset y V y a 21 a 22 Q Q 1+ ε + ψ 90° 90° 8–12 GHz I-Q LO pump LO pump V cos( 0 ω t + θ ) V cos( 0 ω t) L L freq. reference ω 0 arbitrary length V m cos( ω t) m osc in lock−in out amplifier matrix Problems & solutions Im ψ • quadrature error ψ Re • amplitude asymmetry ε ε • fix the errors with a matrix Im • use the Gram Schmidt process Re • the LO phase is still arbitrary

Setting up the reference modulator 10 power v i detector v d ω V cos( t) 0 0 voltm. 1 1 V 2 V 2 dc V dc = c + 0 m 2 4 cv 2 arbitrary θ phase ω t + θ ) cos( 0 fundamental LO in ideal V θ ω m t) RF I: = c V V cos( ) cos( I−Q ω m 0 (corrected modul amplifier for ψ and ε ) v I cos( ω t + θ ) − v Q sin( ω t + θ ) lock−in Q: V = −c V V 0 sin( ) θ cos( ω m t) 0 0 ω m I Q PM 2nd harmonics V m cos( ω m t) a 11 a 12 osc 1 c 2 a 21 a 22 V 2 I,Q: V ω m t) = cos(2 2 ω m 4 AM matrix Problems & solutions • 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

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

Modulator linearity 12 v RF = a 1 tanh( a 2 i IF ) pure tanh( x ) model v RF = a 1 tanh( a 2 i IF ) + a 3 i IF tanh( x ) model with dissipation 0.25 MiniCircuits ZFM − 2 (modulator) file 922 − zfm2 − modulh E. Rubiola, 4 apr 2007 0.2 black points: measured green: a*tanh(bx) red: a*tanh(bx)+cx RF output, Vrms dashed: tangent 0.15 0.1 measured 0.05 values 0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01 IF current, Adc expected error, if non-linearity is ignored i IF ∆ v RF /v RF v RF P RF 10 − 4 0.1 3.91 0.305 − 35 . 2 10 − 3 0.316 12.4 3.05 − 25 . 2 10 − 2 1 39.1 30.5 − 15 . 2 mA (dimensionless) mV rms µ W dBm

Error budget 13 parameter and conditions value 11 . 6 × 10 − 3 power ratio measurement (0.1 dB) (commercial power meter) 23 × 10 − 3 RF path (0.2 dB) (couplers, cables etc.) 5 . 8 × 10 − 3 reference 40 dB attenuator (0.05 dB) 1 . 0 × 10 − 3 mixer and detector linearity 1 . 0 × 10 − 3 null measurements (commercial lock-in, 10 bit) 1 . 0 × 10 − 3 signal-to-noise ratio 43 . 6 × 10 − 3 worst case total (0.37 dB) 26 . 5 × 10 − 3 rms total (0.23 dB) Using off-the-shelf instruments and parts, an accuracy of 0.2–0.4 dB is feasible