Nonlinear Vector Network Analyzer Applications

Transcription

1 Nonlinear Vector Network Analyzer Applications presented by: Loren Betts and David Root Agilent Technologies

2 Presentation Outline Nonlinear Vector Network Analyzer Applications (What does it do?) Device Characteristics (Linear and Nonlinear) NVNA Hardware NVNA Measurements Component Characterization Multi-Envelope Domain X-Parameters Questions

3 Nonlinear Vector Network Analyzer (NVNA) Vector (amplitude/phase) corrected nonlinear measurements from 10 MHz to 26.5 GHz Calibrated absolute amplitude and relative phase (cross-frequency relative phase) of measured spectra traceable to standards lab 26 GHz of vector corrected bandwidth for time domain waveforms of voltages and currents of DUT Multi-Envelope domain measurements for measurement and analysis of memory effects X-parameters: Extension of Scattering parameters into the nonlinear region providing unique insight into nonlinear DUT behavior X-parameter extraction into ADS PHD block for nonlinear simulation and design New phase calibration standard Standard PNA-X with New Nonlinear features and capability

4 NVNA System Configuration X-Parameter extraction/multi-tone source Amplitude Calibration Vector Calibration New!! Agilent NVNA Phase Calibration Standard PNA-X Network Analyzer Phase Reference New!! Agilent Calibrated Phase Reference

5 Normalized Amplitude Phase Reference Agilent s new IC based phase reference is superior in all aspects to existing phase reference technologies. New!! Agilent Calibrated Phase Reference Advantages: Lower temperature sensitivity Lower sensitivity to input power Smaller minimum tone spacing (< 1 MHz vs 600 MHz) Lower frequency (< 1 MHz vs 600 MHz) Much wider dynamic range due to available energy vs noise Frequency in GHz

6 NVNA Applications (What does it do?) Time domain oscilloscope measurements with vector error correction applied View time domain (and frequency domain) waveforms (similar to an oscilloscope) but with vector correction applied (measurement plane at DUT terminals) Vector corrected time domain voltages (and currents) from device

7 NVNA Applications (What does it do?) Measurement of narrow (fast) DC pulses with vector error correction applied View time domain (and frequency domain) representations of narrow DC pulses with vector correction applied (measurement plane at DUT terminals) Less than 50 ps

8 NVNA Applications (What does it do?) Measurement of narrow (fast) RF pulses with vector error correction applied View time domain (and frequency domain) representations of narrow RF pulses with vector correction applied (measurement plane at DUT terminals) Example: 10 ns pulse width at a 2 GHz carrier frequency. Limited by external source not NVNA. Can measure down into the picosecond pulse widths

9 NVNA Applications (What does it do?) Measurements of multi-tone stimulus/response with vector error correction applied Input Waveform View time and frequency domain representations of a multi-tone stimulus to/from a device with vector correction applied (measurement plane at DUT terminals) Stimulus is 5 frequencies spaced 10 MHz apart centered at 1 GHz measuring all spectrum to 20 GHz Output Waveform

10 NVNA Applications (What does it do?) Measure amplitude and cross-frequency phase of frequencies to/from device with vector error correction applied 1 GHz Stimulus to device Fundamental Frequency View absolute amplitude and phase relationship between frequencies to/from a device with vector correction applied (measurement plane at DUT terminals) Source harmonics (< 60 dbc) Output from device 2 GHz Output harmonics Input output frequencies at device terminals 1 GHz degree phase delta Phase relationship between frequencies at output of device

11 NVNA Applications (What does it do?) Measure modeling coefficients and other nonlinear device parameters X-parameters More Waveforms ( a and b waves) Dynamic Load Line Measure, view and simulate actual nonlinear data from you device

12 NVNA Applications (What does it do?) Measure memory effects in nonlinear devices with vector error correction applied Output (b2) multi-envelope waveforms View and analyze dynamic memory signatures using the vector error corrected envelope amplitude and phase at the fundamental and harmonics with a pulsed (RF/DC) stimulus Each harmonic has a unique time varying envelope signature

13 Linear and Nonlinear Device Characteristics Nonlinear Hierarchy from Device to System Modules Systems Devices Chips Circuits Instrument Frontends Cell Phones Military systems Etc. Transistors, diodes, Amplifiers, Mixers, Multipliers, Modulators,.

14 Nonlinearities x() t y() t x() t Ae j( w t ) 0 0 b0 ( ) ( ) j c0 j d0 j y t a b e x t c e d e x() t 2 x() t j j( t ) y() t a0 b0e Ae c e d e b0 0 0 j 2 j2( t ) A e c0 0 0 j 3 j3( t ) A e d0 0 0

15 The Need for Phase Cross-Frequency Phase Notice that each frequency component has an associated static phase shift. Each frequency component has a phase relationship to each other. Why Measure This? 0 0 j j( t ) y a0 b0e Ae c e d e b0 0 0 j 2 j2( t ) A e c0 0 0 j 3 j3( t ) A e d0 0 0 If we can measure the absolute amplitude and cross-frequency phase we have knowledge of the nonlinear behavior such that we can: Convert to time domain waveforms (eg: scope mode). Measure phase relationships between harmonics. Generate model coefficients. Etc..

16 NVNA Hardware Take a standard PNA-X and add nonlinear measurement capabilities Agilent s N5242A premier performance microwave network analyzer offers the highest performance, plus: 2- and 4-port versions Built-in second source and internal combiner for fast, convenient measurement setups Spectrally pure sources (-60 dbc) Internal modulators and pulse generators for fast, simplified pulse measurements Flexibility and configurability Large touch screen display with intuitive user interface

17 Measuring Unratioed Measurements on PNA-X Unratioed Measurements Amplitude RF Source Works fine. 0 a 1 0 a 2 Ever tried to measure phase across frequency on an unratioed measurement? LO Source 0 b 1 1 a 1 DUT 1 b 2 0 b 2 1 b 1 1 a 2 Sweep 1 Sweep 2

18 Measuring Unratioed Measurements on PNA-X Unratioed Measurements Phase Phase response changes from sweep to sweep. As the LO is swept the LO phase from each frequency step from sweep to sweep is not consistent. This prevents measurement of the cross-frequency phase of the frequency spectra. Phase Shifted Sweep 1 Sweep 2

19 NVNA Hardware Configuration Generate Static Phase Since we are using a mixer based VNA the LO phase will change as we sweep frequency. This means that we cannot directly measure the phase across frequency using unratioed (a1, b1) measurements. Domain Display IF and Digitization Frequency Instead ratio (a1/ref, b2/ref) against a device that has a constant phase relationship versus frequency. A harmonic phase reference generates all the frequency spectrum simultaneously. The harmonic phase reference frequency grid and measurement frequency grid are the same (although they do not have to be generally). For example, to measure a maximum of 5 harmonics from the device (1, 2, 3, 4, 5 GHz) you would place phase reference frequencies at 1, 2, 3, 4, 5 GHz. Harmonic Phase Reference RF Source LO Source ref a1 b1 a2 b2 Intermediate Frequency a1 b1 a2 b2 Input/Output Waves Signal Separation and Stimulus DUT Frequency

20 NVNA Hardware Configuration Phase Reference One phase reference is used to maintain a static cross-frequency phase relationship. A second phase reference standard is used to calibrate the cross-frequency phase at the device plane. The phase reference generates a time domain impulse. Fourier theory illustrates that a repetitive impulse in time generates a spectra of frequency content related to the pulse repetition frequency (PRF) and pulse width (PW). The cross-frequency phase relationship remains static.

21 Mathematical Representation of Pulsed DC Signal y ( t ) ( rect ( t )) shah 1 ( t ) pw prf -1/2pw rect pw (t) 0 1/2pw t * n (t-n(1/ prf )) /prf -1/prf 0 1/prf 2/prf... -1/prf 0 1/prf... t Y ( s) ( pw sinc ( pw s)) ( prf shah ( prf s)) Y ( s) ( pw sinc ( pw s)) ( prf shah ( prf s)) Y ( s) DutyCycle sinc ( pw s) shah ( prf s)

22 Normalized Amplitude Normalized Amplitude Frequency Domain Representation of Pulsed DC Fin n*fin Signal Frequency Response Drive phase reference with a Fin frequency. Get n*fin at the output of the phase reference. Example: Want to stimulate DUT with 1 GHz input stimulus and measure harmonic responses at 1, 2, 3, 4, 5 GHz. Fin = 1 GHz Can practically use frequency spacings less than 1 MHz Harmonic Phase Reference (HPR) Frequency in GHz Frequency in GHz

23 NVNA Hardware Configuration If we were to isolate a few of the frequencies from the phase reference we would see that the phase relationship remains constant versus input drive frequency and power GHz Frequency - 1 GHz Phase relationship between frequencies remains the same Frequency - 2 GHz GHz 3 GHz Frequency - 3 GHz GHz Frequency - 4 GHz

24 Example NVNA Configuration #1 Using external source for phase reference drive Source 1 OUT 2 OUT 1 Source 2 (standard) OUT 1 OUT 2 Rear panel J11 J10 J9 J8 J7 J4 J3 J2 J1 R1 SW1 SW3 SW4 SW2 R3 R4 R2 A C D B 65 db 35 db 35 db 35 db 65 db 65 db 65 db 35 db Test port 1 Test port 3 Test port 4 Test port 2 To port 1 or 3 Ext Source in Calibration Phase Reference Measurement Phase Reference

25 Example NVNA Configuration #2 Using internal source for phase reference drive OUT 1 Source 1 OUT 2 Source 2 OUT 1 OUT 2 R1 R3 R4 R2 A C D B 65 db 35 db 35 db 35 db 65 db 65 db 65 db 35 db Test port 1 Test port 3 Test port 4 Test port 2 To port 1 or 2 Calibration Phase Reference Measurement Phase Reference

26 Example NVNA Configuration #3 Multi-Tone, SCMM, DC/RF, Calibrated receiver mode Source 1 OUT 2 OUT 1 OUT 1 Source 2 OUT 2 Rear panel R1 R3 R4 R2 A C D B 65 db 35 db 35 db 35 db 65 db 65 db 65 db 35 db Test port 1 Test port 3 Test port 4 Test port 2 To port 1 or 3 Ext Source in Calibration Phase Reference Measurement Phase Reference

27 NVNA Measurements Component Characterization The Nonlinear VNA is a new set of firmware that runs on a standard PNA-X. Can run the normal PNA-X firmware and the NVNA firmware on the PNA-X.

28 Nonlinear VNA Measurements Stimulus/Response Setup The user can set up a multidimensional segmented sweep across input frequency and power and output response. Single tone stimulus and harmonic response Multi-tone stimulus/response DC/RF pulse response X-parameters stimulus/response Multi-Envelope response

29 Nonlinear VNA Measurements Guided Calibration Wizard 3 Step Process (Vector, Amplitude, Phase) User is guided through all stages of calibration. Each of the three cal stages can be refreshed. No calibration shows as a red acknowledgement. Vector calibration Phase calibration Amplitude calibration

30 Nonlinear VNA Measurements Guided Calibration Wizard Vector Calibration The Vector calibration uses the standard PNA-X cal wizard to generate the associated vector correction error model. Users can enter their own cal kit definitions.

31 Nonlinear VNA Measurements Guided Calibration Wizard Phase Calibration User is prompted to connect the phase reference calibration standard. Standard is USB controlled. This calibrates the cross-frequency phase. New!

32 Nonlinear VNA Measurements Guided Calibration Wizard Amplitude Calibration User is prompted to connect the power sensor calibration standard. Supports any power meters/sensors the PNA-X FW supports today and in the future.

33 Nonlinear VNA Measurements Measurement Display The user can display the resulting corrected waves in frequency, time, power and other domains. Can also display all formats including crossfrequency phase.

34 Nonlinear VNA Measurements Measurement Display The vector corrected responses from the device can be displayed in time domain.

35 Nonlinear VNA Measurements Measurement Display Power Sweep and Phase Can also analyze the device performance versus power. This example illustrates the phase of the second harmonic from the device as a function of input power.

36 Nonlinear VNA Measurements Measurement Display User can customize the displayed waveforms such as the voltage or current applied to and emanating from the device. a and b waves versus sweep domain V and I versus sweep domain V versus I, I versus V Etc... Dynamic Load Line (RF I/V)

37 Nonlinear VNA Measurements In-fixture/De-embedding User can move the absolute amplitude and cross-frequency phase plane by de-embedding S- parameters of the fixture/adapter. Eg: Move amplitude and phase plane (in-coax) into the fixture plane.

38 Multi-Envelope Domain Memory Effects in Nonlinear Devices x() t y() t 1 1 x() t A e e 1 j 1 j 1t Single frequency pulse w ith fixed phase and am plitude versus tim e Can measure envelope of the fundamental and harmonics with NVNA error correction applied. Use to analyze memory effects in nonlinear devices. Get vector corrected amplitude and phase of envelope. Use to measure and analyze memory effects in nonlinear devices j ( t ) j t n n y ( t ) B ( t ) e e n n M ultiple frequencies envelopes w ith tim e varying phase and am plitude

39 Mathematical Representation of Pulsed Signal y( t) ( rect ( t) x( t)) shah 1 ( t) pw prf rect pw (t) x(t) t -1/2pw 0 1/2pw * n (t-n(1/prf)) /prf -1/prf 0 1/prf 2/prf... -1/prf 0 1/prf... t Y ( s) ( pw sinc ( pw s) X ( s)) ( prf shah ( prf s)) Y ( s) ( pw sinc ( pw s)) ( prf shah ( prf s)) Y ( s) DutyCycle sinc ( pw s) shah ( prf s)

40 Pulsed Reponse (db) Pulsed Frequency Domain Spectrum Pulsed Spectrum 0 Nulls at 1/pw Frequency Offset (Hz) This is the spectrum of a pulsed signal at a pulse repetition frequency of 1.69 khz and a pulse width of 7 us.

41 Pulsed Response (db) Pulsed Frequency Domain Spectrum(Zoom) Pulsed Spectrum(zoomed) Wanted frequency component First spectral tone at 1.69kHz=prf Frequency Offset (Hz) This is the same pulsed spectrum zoomed in on the fundamental frequency that is pulsed(center). Notice that the spectrum has components that are n*prf away from the fundamental. In pulse narrowband detection mode, ideally we would want a rectangular filter to filter out everything but the fundamental pulsed frequency.

42 Utilize PNA Adaptive ( Matched ) Digital Filter Response (db) Wanted frequency component Filtered frequency components Frequency Offset (Hz) Utilizing an adaptive digital filter we align the nulls (high-attenuation) of the filter with the unwanted pulsed spectral components leaving the fundamental frequency. Also accounts for DC cross-over of the negative pulsed spectrum.

43 db PNA-X/PNA Dynamic Range Comparison PNA / PNA-X Pulse Comparison (.001% Duty Cycle) Freq (GHz) PNA pulse PNA-X pulse (SW gate off) PNA-X pulse PNA-X CW

44 Multi-Envelope Domain Envelope Domain Measure envelope of the fundamental and harmonics with NVNA error correction applied. Use to analyze memory effects in nonlinear devices. Get vector corrected amplitude and phase of envelope. Envelope resolution down to 16.7 ns.

45 X-Parameters: A New Paradigm for Interoperable Measurement, Modeling, and Simulation of Nonlinear Microwave and RF Components

46 S-parameters: linear measurement, modeling, & simulation Easy to measure at high frequencies measure voltage traveling waves with a (linear) vector network analyzer (VNA) don't need shorts/opens which can cause devices to oscillate or self-destruct Relate to familiar measurements (gain, loss, reflection coefficient...) Can cascade S-parameters of multiple devices to predict system performance Can import and use S-parameter files in electronic-simulation tools (e.g. ADS) BUT: No harmonics, No distortion, No nonlinearities, Invalid for nonlinear devices excited by large signals, despite ad hoc attempts Linear Simulation: Matrix Multiplication S-parameters b1 = S11a1 + S12a2 b2 = S21a1 + S22a2 Measure with linear VNA: Small amplitude sinusoids Incident S 21 Transmitted a 1 S b 11 2 Reflected DUT S 22 Port 1 Port 2 Reflected b 1 a 2 Transmitted S 12 Incident Model Parameters: Simple algebra S ij b a i j ak 0 k j

47 Actual Circuit Measurement-Based Nonlinear Design Generate Behavioral Model Amplifier or Mixer IC DC-20 GHz HBT HMMC5200 amp [7] Measurement-Based Model Ckt. model may not exist Ckt. models may be inaccurate Completely protect design IP Design of Module or Instrument Front End Detailed Circuit Model (SPICE/ADS) of IC Simulation-Based Model Simulation speed Design system before buying IC Completely protect design IP Easy if the circuit and system are linear: S-parameters

48 Is there an analogue to help with the nonlinear problem?

49 X-Parameters: The Nonlinear Paradigm X-parameters are the mathematically correct superset of S-parameters, applicable to both large-signal and small-signal conditions, for linear and nonlinear components. The math exists! We can measure, model, & simulate with X-parameters Each part of the puzzle has been created The pieces now fit together seamlessly Measure X-params model X-params Simulate X-params PHD component Interoperable Nonlinear Measurement, Modeling & Simulation with X-params X-parameters have the potential to do for characterization, modeling, and design of nonlinear components and systems what linear S-parameters do for linear components & systems

50 X-Parameters: Why They are Important: Predict performance of cascaded NL components X-parameters enable automated measurement-based nonlinear simulation from measured NVNA data in the presence of mismatch Key applications include PA characterization & RF system design Unambiguously identifiable from a simple set of measurements Extremely accurate for high-frequency, distributed nonlinear circuits Fully nonlinear vector quantities (Magnitude and phase of all harmonics) Cascadable (correct behavior in mismatched environment)

51 X-parameters come from the Poly-Harmonic Distortion (PHD) Framework A 1 A 2 Port Index B B 1 2 B1 k F1 k( DC, A11, A12,..., A21, A22,...) B F ( DC, A, A,..., A, A,...) 2k 2k Harmonic (or carrier) Index Spectral map of complex large input phasors to large complex output phasors Black-Box description holds for transistors, amplifiers, RF systems, etc.

52 Poly-Harmonic Distortion Modeling Framework V 4 GND 4 I4 Input signals: Incident waves A 1, A 2, A 3 A B 1 A 2 3 B 2 Independent bias parameter V 4 Output signals: Outgoing waves B 1, B 2, B 3 Dependent bias parameter I 4 B 3 A 3 Input and output signals represented as sum of modulated carriers (envelope domain representation using complex time series) PHD model relates output envelopes to input envelopes

53 Nonlinearities Cascade like S-parameters V 4 GND 4 I 4 KCL and KVL In A-B space A 1 B A 2 B 5 A 6 B 2 A 5 B 6 3 B 3 A 3 Simulator eliminates A 2 and A 5 by solving: B 2 = F(A 1,A 2,A 3,V 4, ) = A 5 B 5 = G(A 5,A 6 ) = A 2 This results in accurate nonlinear cascading capability with circuit schematics as well as other PHD models!

54 X-parameter Concept: Accuracy vs Measurement and Simulation Speed - Systematic Approximations to NL Mapping Incident Scattered Bk X ( DC, A, A, A,...) Multi-variate NL map ( F ) k ( DC, A,0,0,0,...) Simpler NL map + Linear non-analytic map 1 [ X ( DC, A ) A X ( DC, A ) A ] ( S) ( T) * kj 1 j kj 1 j

55 X-parameter Experiment Design & Identification -3f 0-2f 0 -f 0 DC f 0 2f 0 3f 0 4f 0 5f 0 a j2 * a j2 There are two contributions at each harmonic From different orders in NL conductance of driven system ( T ) * i3, j2 j 5 f f 0 1 ( F) f ( S) f h ( T ) f h e, f ( 11 ) (, 11 ) (, 11 ) ef ef gh gh ef gh gh, g, h j A11 B X A P X A P a X A P a X a 2 X ( S ) i3, j2 j f * gh f 0 1 a 2 P ( ) e

56 X-Parameter Experiment Design & Identification Ideal Experiment Design E.g. functions for B pm (port p, harmonic m) B X ( A ) P X ( A ) P A X ( A ) P A ( F ) m ( S ) m n ( T ) m n * pm pm 11 pm, qn 11 qn pm, qn 11 qn Perform 3 independent experiments with fixed A 11 using orthogonal phases of A 21 input A qn output B pm Im Im Re Re B X A P (0) ( F) pm pm 11 m 11, 11, 11 B X A P X A P A X A P A (1) ( F ) m ( S) m n (1) ( T ) m n (1)* pm pm pm qn qn pm qn qn 11, 11, 11 B X A P X A P A X A P A (2) ( F ) m ( S) m n (2) ( T ) m n (2)* pm pm pm qn qn pm qn qn

57 Example: Fundamental Component B ( A ) X ( A ) P X ( A ) A X ( A ) P A ( F ) ( S ) ( T ) 2 * , , B ( A ) X ( A ) A X ( A ) A X ( A ) P A ( S ) ( S ) ( T ) 2 * , , , db 20 ( S ) X 21,11 X ( A ) s ( S ) 21,11 11 A ( S ) X 21,21 ( T ) X 21,21 X ( A ) s X ( S ) 21,21 11 A 0 22 ( A ) 0 ( T ) 21, A A 11 (dbm) Reduces to (linear) S-parameters in the appropriate limit

58 X-parameter Application Flow Automated DUT X-params measured on NVNA Application creates data-specific instance Compiled PHD Component simulates using data NVNA Simulator PHD instances DUT Measure X-Parameters Ref MDIF File Harmonic Bal: magnitude & phase of harmonics, frequency dep. and mismatch Envelope: Accurately simulate NB multi-tone or complex stimulus Data-specific simulatable instance Compiled PHD component Simulation and Design

59 Measurement on the NVNA Switching from general measurements to X-parameter measurements is as simple as selecting Enable X-parameters Measuring X-parameters for 5 harmonics at 5 fundamental frequencies with 15 power points each (75 operating points) can take less than 5 minutes DC bias information can be measured using external instruments (controlled by the NVNA) and included in the data

60 PHD Design Kit The MDIF file containing measured X-parameters is imported into ADS by the PHD Design Kit, creating a component that can be used in Harmonic Balance or Envelope simulations.

61 PHD Design Kit The component is ready for use in simulation and design!

62 Example Results ACPR, IM3 simulations PHD components can be used in Envelope simulation to provide estimates of ACPR and IM3 with guaranteed accuracy in the narrow-band limit

63 Measurement-based nonlinear design with X-parameters Source ZFL-AD11+ 11dB gain, 3dBm max output power Connector 80 ps delay ZX M-S+ 23.5dB gain, 18dBm max output power Load Amplifier Component Models from individual X-parameter measurements

64 db(b2[::,1]/a1[::,1]) db(b2ref[::,1]/a1ref[::,1]) db(b2not[::,1]/a1not[::,1]) db(b2nost[::,1]/a1nost[::,1]) unwrap(phase(b2ref[::,1])) unwrap(phase(b2not[::,1])) unwrap(phase(b2nost[::,1])) unwrap(phase(b2[::,1])) Results Cascaded Simulation vs. Measurement Red: Cascade Measurement Blue: Cascaded X-parameter Simulation Light Green: Cascaded Simulation, No X (T) terms Dark Green: Cascaded Models, No X (S) or X (T) terms 36 Fundamental Gain 76 Fundamental Phase Pinc Pinc Pincref

65 (b2[::,1]-b2ref[::,1])/b2ref[::,1]*100 (b2not[::,1]-b2ref[::,1])/b2ref[::,1]*1 (b2nost[::,1]-b2ref[::,1])/b2ref[::,1]* (b2[::,2]-b2ref[::,2])/b2ref[::,2]*10 (b2not[::,2]-b2ref[::,2])/b2ref[::,2]* (b2nost[::,2]-b2ref[::,2])/b2ref[::,2]* Results Cascaded Simulation vs. Measurement Red: Cascade Measurement Blue: Cascaded X-parameter Simulation Light Green: Cascaded Simulation, No X (T) terms Dark Green: Cascaded Models, No X (S) or X (T) terms Fundamental % Error Second Harmonic % Error Pinc X-parameters enable predictive nonlinear design from NL data Pinc

66 X-parameters versus Hot S Blue lines with circles: Hot S 22 prediction Red lines with circles: X parameter prediction Elliptical shape is proof of non-analytic linear mapping Multicolored solid lines: Port 2 input & scattered B with large drive on port 1 Fundamental A-wave at Port X-parameters predict output match under large input drive. Hot S 22 does not Fundamental B-wave at port 2 B X ( A ) A B A A ( S ) ( S ) ( T ) * 21 X 21,21( 11 ) 21 X 21,21( A1 1) A2 1

67 PHD Results: Transportability 27 Ohm validation measurementbased model X-parameters from 50 Ohm measurements v v time, psec time, psec i i time, psec Measurement-Based PHD Model time, psec Independent NVNA Data

68 circ1 Eff_contours_p circ1 Pdel_contours_p m in P le im Example Results Load Pull Simulation with X-parameters m1 m6 indep(eff_contours_p) (0.000 to ) indep(circ1) (0.000 to ) indep(pdel_contours_p) (0.000 to ) indep(circ1) (0.000 to ) Power and Efficiency contours extremely accurate near 50 ohms, correct trends over a wide region

69 PAE_contours_p PAE_contours_pref Pdel_contours_p Pdel_contours_pref PHD Extensions Load Pull Multi-tone/Mixer indep(pae_contours_pref) (0.000 to ) indep(pae_contours_p) (0.000 to ) indep(pdel_contours_pref) (0.000 to ) indep(pdel_contours_p) (0.000 to ) Full nonlinear dependence on load for accuracy across the entire smith chart! Demonstrated in simulation, but not yet automated in measurement

70 mag(vout[3]) mag(vout[2]) mag(phdmodel_2_b[1]) mag(phd_2_b[1]) Vout[3] mag(vin[1]) mag(vout[1]) PHD Extensions: Dynamic Memory Fundamental Input Fundamental Input time, usec Fundamental Output Fundamental Output time, usec time, usec 2nd Harmonic Output Third Harmonic 3rd Harmonic Output Mag & Mag Phase& Phase Gain Reduces as device heats up time, usec time, usec B 21 phase(vout[3]) time, usec time, usec time, usec mag(phd_1_a[1]) mag(phdstatic_1_a[1]) A 11 time ( sec to 50.00us

71 Conclusions: X-params are supersets of S-params for nonlinear components under large-signal drive Fast, easy to use, interoperable nonlinear measurement, modeling, and simulation for measurement-based design Powerful cascading of nonlinear behavior Commercialized with release of NVNA instrument Additional design capabilities ready for future NVNA enhancements Nonlinear Measurements Nonlinear Measurements Nonlinear Modeling Applications

72 Configuration Details Description N5242A MHz to 26.5 GHz 4-port Opt 419: Opt 423: Opt 080: Opt 510: Opt 514: Opt 518: 4-port attenuators & bias tees Source switching & combining network Frequency Offset Mode Nonlinear component characterization measurements (requires 400,419,080) Nonlinear X-parameters (requires 423, opt 510 & ext. source) Nonlinear pulse envelope domain (requires opt 510,021,025) Accessories: U9391C Phase reference (2 units required) Power meter & sensor or USB power sensor 3.5mm calibration standards External source for X-parameters

73 Summary New Nonlinear Vector Network Analyzer based on a standard PNA-X New phase calibration standard Vector (amplitude/phase) corrected nonlinear measurements from 10 MHz to 26.5 GHz Calibrated absolute amplitude and relative phase (cross-frequency relative phase) of measured spectra traceable to standards lab 26 GHz of vector corrected bandwidth for time domain waveforms of voltages and currents of DUT Multi-Envelope domain measurements for measurement and analysis of memory effects X-parameters: Extension of Scattering parameters into the nonlinear region providing unique insight into nonlinear DUT behavior X-parameter extraction into ADS PHD block for nonlinear simulation and design