Fast and Accurate Simultaneous Characterization of Signal Generator Source Match and Absolute Power Using X-Parameters.

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1 Fast and Accurate Simultaneous Characterization of Signal Generator Source Match and Absolute Power Using X-Parameters. April 15, 2015 Istanbul, Turkey R&D Principal Engineer, Component Test Division Keysight Technologies

2 Agenda Keysight Restricted Page 2 Review Current Signal Generator Source Match and Absolute Power Measurement Methods Why we need the new method? How does the X-parameter method work? Measurement Results

3 Signal Generator Output Power Measurement Power Meter Spectrum Analyzer Power Meter Spectrum Analyzer P b ; P a 2 2 s s m b s b g 1 a l P m P s 1 1 g 2 g a g 1 b l l Γ g is not known. Keysight Restricted Page 3

4 Signal Generator Source Match Measurements Keysight Restricted 4 Passive Methods, Ripple Techniques Fixed Delay Variable Delay Variable Load Active Methods Signal Injection Hot S11 X-parameter formulation

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6 Ripple Technique Variable Delay b 2 a g *Γ g V max a g b 2 k variable delay line a 1 b 1 Mismatch Load b s Phasor Diagram delay V min b s g a g e -l a l l e -l b l b kb 1 e 2 l 2 s g Assume S11, S22 and loss of delay line 0 Length of delay line can change to allow V max and V min values to be capture at each frequency point. b2 1 (max) g b 1 2 (min) g Keysight Restricted Page 6

7 Ripple Technique Sliding Mismatch Load b 2 a g *Γ g V max a g b1 a 1 b 2 k b s Phasor Diagram V min Load phase rotation b s e -l a l Assume S11 and S22 of delay line 0 g a g e -l b l b kb 1 e 2 l 2 s g l b2 1 (max) g b 1 2 (min) g Keysight Restricted Page 7

8 Problems with Ripple Techniques Actual Source Match at each frequency point is not known (fixed delay case) Magnitude information only! Can t use to correct mismatch error. Transmission loss and reflection of delay line can be significant. Large reflected signal can cause ALC of signal generator to react and change operating point and source match. Time consuming, requires multiple delay line or sliding load settings Imprecise Vmax and Vmin determination Keysight Restricted Page 8

9 Advance Passive Automate System Needs VNA characterization Least squares fit G Keysight Restricted Page 9

10 Disadvantage of Automated Passive System Requires periodic external calibration of coupler and delay line assembly. Bandwidth limited by number of line lengths. Speed Drift error of delay lines can be significant Keysight Restricted Page 10

11 Active Techniques Signal Injection Hot S22 X-Parameters

12 Signal Injection Method Active (injection) method 1 (tested at METAS per Jürg Furrer) 2100Hz measurement plane DUT Generator Spectrum Analyzer (Zero Span) Z o Interference of - V 1, DUT Forward Wave - V 2, AUX Forward Wave * G AUX Generator V 1 Phasor Diagram V 2 V min V VSWR V V max max min 1 1 G G directional coupler 10dB f G G Maintain specified DUT test level and adjust it on spectrum analyzer (P AUX = Off) Disconnect DUT at measurement plane and adjust P AUX to the same indication on spectrum analyzer Connect DUT at measurement plane Spectrum analyzer (zero span) displays interference (f = 100 Hz) of - DUT Forward Wave (100%) - AUX Forward Wave * G (100% * G ) f G Hz Keysight Restricted Page 12 Slide provided by Jürg Furrer of METAS, «Traceable Source Match Calibration of RF & Microwave Generators» Agilent Metrology Forum May

13 Measuring Source Match G of RF & MW Generators Active (injection) method 1 : Drawbacks Spectrum without AUX modulating DUT f=100hz measurement plane DUT Generator Z o Spectrum Analyzer AUX Generator f G f AUX f Spectrum AUX is modulating DUT directional coupler (bridge) 10dB f=100hz f G G f G Hz AUX test level (at measurement plane) relatively high (identical to DUT level) DUT generator output circuit is biased by AUX test level AUX test signal is modulating the amplitude of the DUT in case of critical output stage by f mod = f (100 Hz) measured G_DUT useless (depending on DUT generator type and condition) f G f AUX f Keysight Restricted Page 13 Slide provided by Jürg Furrer of METAS, «Traceable Source Match Calibration of RF & Microwave Generators» Agilent Metrology Forum May

14 Active (injection) method 1 : Drawbacks Spectrum of measured interference voltage at directional coupler output S X ATTEN 10dB RL 0dBm MKR 102 Hz db f DUT 10dB/ MKR 102Hz dB f AUX Case 1: active (injection) methode 1 works correctly DUT level is low (Step Atten) CENTER GHz SPAN 1.000kHz RBW 10Hz VBW 10Hz SWP 477ms ATTEN RL 0dBm 10dB 10dB/ MKR 102Hz dB Case 2: active (injection) methode 1 does not work correctly DUT generator is amplitude modulated by AUX test signal DUT Step Atten = 0 db S X MKR 102 Hz db Symetrical sidebands f DUT ± 100 Hz CENTER GHz SPAN 1.000kHz RBW 10Hz VBW 10Hz SWP 477ms Keysight Restricted Page 14 Slide provided by Jürg Furrer of METAS, «Traceable Source Match Calibration of RF & Microwave Generators» Agilent Metrology Forum May

15 30dB Active Method Hot S22 measurement plane DUT Generator f G G R directional coupler (bridge) A A G R corrected VNA Generator f G - 1M Hz Po = Ps-15 db f G f G 1M Hz VNA generator lock to DUT generator and operates in frequency offset mode VNA output level must be much lower than DUT output level to minimize ALC interaction and above minimum operating level of VNA VNA calibrated at the measurement plane and measures reflection of DUT at offset frequency Keysight Restricted Page 15

16 Measure Hot S22 of a Signal Generator Keysight Restricted Page 16

17 Issues with Hot S22 Method Γ G NOT measured at the same frequency as the Signal Generator and therefore is a source of error for mismatch correction. Optimization of IFBW, offset frequency and with respect to signal generator harmonic content and IF filter shape are important factors for the measurement. Measures linear behavior only. Signal Generators contains active devices such as power amplifiers that may not operate linearly. Keysight Restricted Page 17

18 Desirable Measurement Capabilities Make accurate signal generator output power measurements with mismatch correction The ability to characterize signal generator output power flatness, over a wide range of power levels and over the entire specified frequency range. The ability to characterize signal generator source match over the entire specified power levels and frequency range. To do all the above in a single setting and do it very fast. Keysight Restricted Page 18

19 The 1-Port X-parameter approach (patent pending) A 0 B 0 Large signal from DUT source B 1+ = X F 1 + X S 11 a 1 + X T 11 P 2 a 1 Small signal from PNA source [1] D. E. Root et al., Broad-Band Poly-Harmonic Distortion (PHD) Behavioral Models From Fast Automated Simulations and Large-Signal Vectorial Network Measurements, IEEE Trans. MTT, vol. 53,no. 11, pp , November 2005 [2] J. Verspecht and D. E. Root, Poly-Harmonic Distortion Modeling, iieee Microwave Theory and Techniques Microwave Magazine,June, 2006 Keysight Restricted Page 19

20 Basic Definitions and Relationships B0 1 e10e01 e00e11 e00b A e e A1 B and A are the measured A and B waves e are systematic errors of the network analyzer ij A A a ; B B b B 1+ = X F 1 + X S 11 a 1 + X T 11 P 2 a 1 X F 11 ( B 1 ), X S 11 ( B 1 ), and X T 11 ( B 1 ) are the X-parameter coefficient valid for a specific value of the magnitude of the source DUT output signal B 1. S X 11 : this would be the match term for a perfectly linear device T : If a device is perfectly linear, this should be 0. X 11 X 1 F : DUT behavior of a perfectly matched device. For sig gen, this is B 1 P is the phase ( e jθ(b 1) ) of B 1 Keysight Restricted Page 20

21 How Does It Work? Procedure Step 1: Perform a Smart Power Calibration PNA-X Vector Network Analyzer Power Meter Power Sensor DUT This step obtains the e ij terms and e 10 and e 01 for absolute power measurements using the NA receivers. Keysight Restricted Page 21

22 How Does It Work? Procedure Step 2: Connect Source DUT to Calibrated PNA port. Set both instruments to the same frequency and desired power levels. Turn PNA source off and measure A 0, B 0 to obtain A 1 and B 1. B 1 e 10 e 01 e 00 e 11 e 00 = e A 10 1 e B 0 A 0 Narmalize phase of B1 and B1 with respect to phase of B1 arg j arg B1 j B1 1 1 ; 1 1 B B e A A e Keysight Restricted Page 22

23 How Does It Work? Procedure Step 3: Turn PNA source ON and set power level = Ps -15dB, measure A 0+, B 0+ to obtain new A 1+ and B B e e e e e B e10 A 1 1 e A Normalize phase of B 1+ and A 1+ with respect to phase of B 1. Subtract the large component from the combine normalized signal to obtain the small signal components. arg 0 jarg 0 B1 j 0 B1 n 1 1 ; 1 1 B B e A A e b B B ; a A A Keysight Restricted Page 23

24 How Does It Work? Additional measurements required Recall the X-parameter Expression B 1+ = X F 1 + X S 11 a 1 + X T 11 P 2 a 1 The large signal removal and phase normalization removes X 1 F from the equation and P becomes 1. b X a X a * S T n n n We have two (2) unknown quantities and need at least two independent measurements. This can be accomplished by varying the phase of the PNA source signal. For more robust results, a minimum of 4 phase changes is suggested. Θ = 0, π/2, π and 3π/2 Keysight Restricted Page 24

25 X-parameter matrix equation least squares solution θ b 0 1 θ b 1 1 θ b 2 1 = θ a 0 θ 0 1 a1 θ a 1 θ 1 1 a1 θ a 2 θ 2 1 a1 S X 11 T X 11 b 1 θ 3 a 1 θ 3 a1 θ 3 b X a X a * S T n n n Use any of the phase equations to solve for Γ G * b1 S T a1 G X11 X11 a1 a1 Keysight Restricted Page 25

26 Solve for Γ G S T Now that X11 and X11 had been determined, use any of the phase equations to solve for Γ G b X a X a * S T n n n Dropping the θn superscript * b1 S T a1 G X11 X11 a1 a1 Keysight Restricted Page 26

27 Get Power of Signal Generator B 1+ = X F 1 + X S 11 a 1 + X T 11 P 2 a 1 X 1 F is the power from the signal generator deliver into a matched load. X F 1 = B 1+ X S 11 a 1 + X T 11 a 1 Keysight Restricted Page 27

28 Uncertainty Analysis A Work in Progress S-parameter uncertainty being migrated from residual error model to covariance base error propagation methodology More DUT data needed to fully quantify various uncertainty contributors METAS VNA tools (GUM tree) being developed to deal with least squares solutions Partial derivative method is too tedious to handles the combination of power, S-parameter and X-parameter uncertainties. The GUM Tree auto differentiation method is being employed to compute uncertainties. Keysight Restricted Page 28

29 Major Sources of Uncertainty VNA Calibration Standard Uncertainty Power Sensor/Meter Calibration Uncertainty VNA post calibration drift error, both power calibration and reflection calibration. Noise Cable stability Receiver Stability Keysight Restricted Page 29

30 Measured Source Match of a Signal Generator Keysight Restricted Page 30

31 Mismatch Corrected Output Power Keysight Restricted Page 31

32 Another Example Mismatch Corrected Output Power Keysight Restricted Page 32

33 Test Speed Improvement Complete source match and absolute power level accuracy test in about 2 minutes for 201 frequency points. Old test method using power meter for power and ripple technique for source match need 5.5 minutes for power and another minute for source match magnitude. No mismatch correction. Keysight Restricted Page 33

34 Thank You For Your Attention Keysight Restricted Page 34