Advanced Nonlinear Device Characterization Utilizing New Nonlinear Vector Network Analyzer and X-parameters presented by: Loren Betts Research Scientist
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
Nonlinear Vector Network Analyzer (NVNA) Vector (amplitude/phase) corrected nonlinear measurements from 1 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
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
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 6 MHz) Lower frequency (< 1 MHz vs 6 MHz) Much wider dynamic range due to available energy vs noise 1 Normalized Amplitude.8.6.4.2 1 2 3 4 5 6 7 8 9 1 Frequency in GHz
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
NVNA Applications (What does it do?) Measure amplitude and cross-frequency phase of frequencies to/from device with vector error correction applied View absolute amplitude and phase relationship between frequencies to/from a device with vector correction applied (measurement plane at DUT terminals) Useful to analyze/design high efficiency amplifiers such as class E/F 1 GHz Stimulus to device Fundamental Frequency Can also measure frequency multipliers Source harmonics (< 6 dbc) Output from device 2 GHz Output harmonics Input output frequencies at device terminals 1 GHz 122.1 degree phase delta Phase relationship between frequencies at output of device
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 5 ps
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) Using wideband mode (resolution ~ 1/BW ~ 1/26 GHz ~ 4 ps) Example: 1 ns pulse width at a 2 GHz carrier frequency. Limited by external source not NVNA. Can measure down into the picosecond pulse widths
NVNA Applications (What does it do?) Measurements of multi-tone stimulus/response with vector error correction applied View time and frequency domain representations of a multi-tone stimulus to/from a device with vector correction applied (measurement plane at DUT terminals) Input Waveform Stimulus is 5 frequencies spaced 1 MHz apart centered at 1 GHz measuring all spectrum to 2 GHz Output Waveform Measure amplitude AND PHASE of intermodulation products Generated using external source (PSG/ESG/MXG) using NVNA and vector calibrated receiver
NVNA Applications (What does it do?) Calibrated measurements of multi-tone stimulus/response with narrow tone spacing 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 64 frequencies spaced ~8 khz apart centered at 2 GHz. The NVNA is measuring harmonics to 16 GHz (8 th harmonic) Multi-tone often used to mimic more complex modulation (i.e. CDMA) by matching complementary cumulative distribution function (CCDF). Multitone can be measured very accurately.
NVNA Applications (What does it do?) Calibrated measurements of multi-tone stimulus/response with narrow tone spacing 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 64 frequencies spaced ~8 khz apart centered at 2 GHz. The NVNA is measuring harmonics to 16 GHz (8 th harmonic)
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
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 your device
Linear and Nonlinear Device Characteristics Nonlinear Hierarchy from Device to System Modules Systems Devices Characterization and modeling Chips Circuits Instrument Frontends Cell Phones Military systems Etc. Transistors, diodes, Amplifiers, Mixers, Multipliers, Modulators,.
Nonlinearities x() t yt () ω1 ω1 2ω1 1 3ω xt () = Ae j( w t+φ ) b () = + () jθ c jθ d jθ y t a b e x t + ce + de xt () 2 xt () 3 yt () a be Ae b ( + ) = + + ce + de jθ j ω t φ jθ 2 j2( ω t+ φ ) Ae c jθ 3 j3( ω t+ φ ) Ae d
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? b ( + ) = + c 2 2( + ) + ce Ae jθ j ω t φ y a b e Ae + de jθ j ω t φ jθ 3 j3( ω t+ φ ) Ae d 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. Measure frequency multipliers. Etc..
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 (-6 dbc) Internal modulators and pulse generators for fast, simplified pulse measurements Flexibility and configurability Large touch screen display with intuitive user interface
Measuring Unratioed Measurements on PNA-X Unratioed Measurements Amplitude Works fine. a 1 a 2 Ever tried to measure phase across frequency on an unratioed measurement? b 1 1 a 1 1 b 2 b 2 1 b 1 1 a 2 Sweep 1 Sweep 2
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
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. 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.
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.
Mathematical Representation of Pulsed DC Signal y ( t ) = ( rect ( t )) shah 1 ( t ) pw prf -1/2pw rect pw (t) 1/2pw t * n δ (t-n(1/ prf))...... -2/prf -1/prf 1/prf 2/prf... -1/prf 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)
Frequency Domain Representation of Pulsed DC 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 Normalized Amplitude Normalized Amplitude 1.8.6.4.2 1 2 3 4 5 6 7 8 9 1 1.8.6.4.2 Frequency in GHz 5 1 15 2 25 Frequency in GHz
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. cos( ω t + φ ) 1.5 -.5 1 GHz -1.1.2.3.4.5.6.7.8.9 1 Frequency - 1 GHz cos(2 ω t + φ ) 1 Phase relationship between frequencies remains the same cos(3 ω t + φ ) 2 1.5 -.5-1.1.2.3.4.5.6.7.8.9 1 Frequency - 2 GHz 1.5 -.5 2 GHz 3 GHz -1.1.2.3.4.5.6.7.8.9 1 Frequency - 3 GHz 1 cos(4 ω t + φ ) 3.5 -.5 4 GHz -1.1.2.3.4.5.6.7.8.9 1 Frequency - 4 GHz
Example NVNA Configuration #1 Using external source for phase reference drive OUT 1 Source 1 OUT 2 Source 2 (standard) OUT 1 OUT 2 Rear panel J11 J1 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
Example NVNA Configuration #2 Multi-Tone, SCMM, DC/RF, Calibrated receiver mode OUT 1 Source 1 OUT 2 Source 2 OUT 2 OUT 1 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
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.
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
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
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.
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!
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.
Nonlinear VNA Measurements Measurement Display The vector corrected responses from the device can be displayed in time domain.
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.
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)
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.
Multi-Envelope Domain Memory Effects in Nonlinear Devices x() t y() t ω 1 ω 1 θ xt () = A e e 1 j jω t 1 1 Single frequency pulse with fixed phase and amplitude versus time 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. 2ω 1 3ω 1 () = n() jφn() t jωnt n= yt B te e Multiple frequencies envelopes with time varying phase and amplitude
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 using narrowband detection mode.
X-Parameters: A New Paradigm for Interoperable Measurement, Modeling, and Simulation of Nonlinear Microwave and RF Components
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 i a j ak = k j
Scattering Parameters Linear Systems Linear Describing Parameters Linear S-parameters by definition require that the S-parameters of the device do not change during measurement. x() t yt () a 1 b 1 e 1 1 e 1 1 e 1 11 e 1 1 a 1 1 b 1 S 21 S11 S22 S 12 1 b 2 1 a 2 11 e 2 1 e 2 1 e 2 e 2 b 2 a 2 b = S a + S a 1 11 1 12 2 b = S a + S a 2 21 1 22 2 b1 S11 S12 a1 b = S S a 2 21 22 2 S-Parameter Definition To solve VNA s traditionally use a forward and reverse sweep (2 port error correction).
Scattering Parameters Linear Systems Linear Describing Parameters If the S-parameters change when sweeping in the forward and reverse directions when performing 2 port error correction then by definition the resulting computation of the S-parameters becomes invalid. b = S a + S a 1 11 1 12 2 b = S a + S a 2 21 1 22 2 b1 S11 S12 a1 b = S S a 2 21 22 2 f r f r b1 b 1 S11 S12 a1 a 1 f r = f r b S 2 b2 21 S 22 a2 a2 Hot S22 x() t yt () This is often why customers are asking for Hot S22 because the match is changing versus input drive power and frequency (Nonlinear phenomena). Hot S22 traditionally measured at a frequency slightly offset from the large input drive signal.
X-parameters the nonlinear Paradigm: Have the potential to revolutionize the Characterization, Design, and Modeling of nonlinear components and systems X-parameters are the mathematically correct extension of S-parameters to large-signal conditions. Measurement based, device independent, identifiable from a simple set of automated NVNA measurements Fully nonlinear (Magnitude and phase of distortion) Cascadable (correct behavior in even highly mismatched environment) Extremely accurate for high-frequency, distributed nonlinear devices NVNA: Measure device X-parms PHD component : Simulate using X-parms ADS: Design using X-parms HARMONIC BALANCE H arm on ic B alan c e HB2 F req[1]= R F freq Order[1]=5 UseKrylov=no E quationn am e[1]= "R F freq" E quationn am e[2]= "R F pow er" E quationn am e[3]= "Z load"
X-parameters come from the Poly-Harmonic Distortion (PHD) Framework A 1 A 2 B = F ( DC, A, A,..., A, A,...) 1k 1k 11 12 21 22 B = F ( DC, A, A,..., A, A,...) 2k 2k 11 12 21 22 B B 1 2 Port Index Harmonic (or carrier) Index Unifies S-parameters Load-Pull, Time-domain load-pull Data and Model formulation in Frequency (Envelope) Domain Magnitude and phase enables complete time-domain input-output waveforms
X-parameters: Systematic Approximations to NL Mapping Trade measurement time, size, accuracy for speed, practicality Incident Scattered B ( DC, A, A, A,...) k 1 2 3 Multi-variate NL map X ( F ) k ( DC, A,,,,...) Simpler NL map 1 + Linear non-analytic map [ X ( DC, A ) A + X ( DC, A ) A ] ( S ) ( T ) * kj 1 j kj 1 j
X-parameter Experiment Design & Identification -3f -2f -f DC f 2f 3f 4f 5f 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 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 1 a 2 P = ( ) e ϕ
Scattering Parameters Nonlinear Systems X-parameters X X X ( * a a P + a ) b = ( a ) P + ( ) P a + ( ) ( F) j ( S) j l ( T) j l ij ij 11 ij, kl 11 kl ij, kl 11 kl kl, (1,1) Definitions i = output port index j = output frequency index k = input port index l = input frequency index Description The X-parameters provide a mapping of the input and output frequencies to one another.
X-Parameters Collapse to S-Parameters in Linear Systems b1 = S11a1+ S12a2 b = S a + S a 2 21 1 22 2 Definitions i = output port index j = output frequency index k = input port index l = input frequency index * ( a a P + a ) X X X b = ( a ) P + ( ) P a + ( ) ( F) j ( S) j l ( T) j l ij ij 11 ij, kl 11 kl ij, kl 11 kl kl, (1,1) b = S a P+ S a 1 11 1 12 2 b = S a P+ S a 2 21 1 22 2 For small a 11 (linear), X F terms go to S i1 a 11, and X S terms are equal to linear S parameters For small a 11 (linear), X T terms go to. Cross-frequency terms also go to ( F) j ( ij 11 l= j k, l ( 1, 1) S) j l ( ij, kl kl ) b = ( a ) P + P a ij X X Consider fundamental frequency (j = 1). Harmonic index is no longer needed. S ( ik ak) b = X ( a ) P + X i ( F) ( ) i 11 k 1 X a1 By definition, P = a Assume 2 port (i and k = 1 -> X b = ( a ) P+ a ( F) ( S) 1 1 11 12 2 ( F) ( S) 2 = X2 ( 11) P + X2 2 2 b a a 1
Example: Fundamental Component B ( A ) = X ( A ) P + X ( A ) A + X ( A ) P A ( F ) ( S ) ( T ) 2 * 21 11 21 11 21,21 11 21 21, 21 11 21 B ( A ) = X ( A ) A + X ( A ) A + X ( A ) P A ( S ) ( S ) ( T ) 2 * 21 11 21,11 11 11 21,21 11 21 21,21 11 21 4 db 2 ( S ) X 21,11 X ( A ) s ( S ) 21,11 11 A 21 11-2 -4 ( S ) X 21,21 ( T ) X 21,21 X ( A ) s X ( S ) 21,21 11 A 22 ( A ) ( T ) 21,21 11 11 A 11-6 -25-2 -15-1 -5 5 1 A 11 (dbm) Reduces to (linear) S-parameters in the appropriate limit
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 Im Re Im output B pm Re ( 11 ) B = X A P () ( F) pm pm 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 pmqn qn pmqn 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
.... 25 2 15 1 5 1-1 -2-3 -4-3 -28-26 -24-22 -2-18 -16-14 -12-1 -8-6 -4 1-1 -2-3 -4-5 -6-7 -3-28 -26-24 -22-2 -18-16 -14-12 -1-8 -6-4. -3-28 -26-24 -22-2 -18-16 -14-12 -1-8 -6-4.... 76 75 74 73 72 71 7 69-3 -28-26 -24-22 -2-18 -16-14 -12-1 -8-6 -4-115 -12-125 -13-135 -14-3 -28-26 -24-22 -2-18 -16-14 -12-1 -8-6 -4 14 12 1 8 6 4 2-2 -3-28 -26-24 -22-2 -18-16 -14-12 -1-8 -6-4.. X-parameter Application Flow Automated DUT X-params measured on NVNA Application creates data-specific instance Compiled PHD Component simulates using data NVNA DUT Measure X-Parameters Φ 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 R R11 R=5 Ohm DC_Block DC_Block1 V_1Tone SRC14 V=polar(2*A11N,) V Freq=fundamental 2 1-1 -2-3 -4 Simulator v1 I_Probe i1 PHD instances MCA_ZFL_11AD Connector MCA_ZFL_11AD_1 X1 fundamental_1=fundamental -1-5 5 1 15-15 2. v2 I_Probe MCA_ZX6_2522 i2 MCA_ZX6_2522_1 fundamental_1=fundamental DC_Block DC_Block2 Compiled PHD component Simulation and Design R R1 R=25 Ohm
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
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.
Measurement-based nonlinear design with X-parameters Source ZFL-AD11+ 11dB gain, 3dBm max output power Connector 8 ps delay ZX6-2522M-S+ 23.5dB gain, 18dBm max output power Load R R11 R=5 Ohm DC_Block DC_Block1 V_1Tone SRC14 V=polar(2*A11N,) V Freq=fundamental v1 I_Probe i1 MCA_ZFL_11AD Connector MCA_ZFL_11AD_1 X1 fundamental_1=fundamental v2 I_Probe MCA_ZX6_2522 i2 MCA_ZX6_2522_1 fundamental_1=fundamental DC_Block DC_Block2 R R1 R=25 Ohm Amplifier Component Models from individual X-parameter measurements
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 Phase Second Harmonic % Error 76 74 72 7 68 unwrap(phase(b2nost[::,1])) unwrap(phase(b2not[::,1])) unwrap(phase(b2ref[::,1])) unwrap(phase(b2[::,1])) 66-3 -28-26 -24-22 -2-18 -16-14 -12-1 -8-6 -4 1 8 6 4 2 (b2[::,2]-b2ref[::,2])/b2ref[::,2]*1 (b2not[::,2]-b2ref[::,2])/b2ref[::,2]* (b2nost[::,2]-b2ref[::,2])/b2ref[::,2] -3-28 -26-24 -22-2 -18-16 -14-12 -1-8 -6-4 Pinc Pincref Pinc
Large-mismatch capability (load-pull) Full Nonlinear Dependence on both A1 & A2 [13] 1.5 Terms linear in the ( 11, 21,,,...) remaining components Mismatched Loads: Γ 1 B = X A A + ik ( F ) ik Fundamental Gain 16 Fundamental Phase 1. 9.5 9. 8.5 8. 7.5 7. 155 15 145 14 135 6.5-3 -25-2 -15-1 -5 5 1 Pinc Fundamental frequency: 4 GHz 13-3 -25-2 -15-1 -5 5 1 PHD Behavioral Model (solid blue) Circuit Model (red points) Pinc
Large-mismatch capability (load-pull) Mismatched Loads: Γ 1 Magnitude 2-1 Phase Second Harmonic Third Harmonic -2-4 -6-8 -3-25 -2-15 -1-5 5 1 2-2 -4-6 -8-1 Pinc -12-14 -16-18 -2-22 -24-26 6 4 2-2 -4-6 -8-3 -25-2 -15-1 -5 5 1 Pinc -12-3 -25-2 -15-1 -5 5 1 Pinc Fundamental frequency: 4 GHz -1-3 -25-2 -15-1 -5 5 1 PHD Behavioral Model (solid blue) Circuit Model (red points) Pinc
Large-mismatch capability (load-pull) Mismatched Loads: Γ 1 Dynamic Load-lines (green for matched case).8.6.4.2 Port 2 Voltage. 1 2 3 4 5 6 Port 2 Current 6 5 4.8.6 3 2 1.4.2 1 2 3 4 5 time, psec Fundamental frequency: 4 GHz. 1 2 3 4 5 time, psec PHD Behavioral Model (solid blue) Circuit Model (red points)
PHD-Simulated vs Load-Pull Measured Contours & Waveforms from Load-dependent X-parameters (WJ transistor) Red: Load-pull data Blue: PHD model simulated ( ) ( ) y Fundamental Gamma =.383+j*.31 m9 m1 1 WJ Transistor Measured & Simulated Waveforms.15 m1 m2 Power Delivered SimulatedVoltage, V MeasuredVoltage 5-5.1.5. -.5 SimulatedCurrent, A MeasuredCurrent Efficiency -1 -.1..2.4.6.8 1. time, nsec
Load-Dependent Measured X-parameters [16]
Summary X-parameters are a mathematically correct superset of S- parameters for nonlinear devices under large-signal conditions Rigorously derived from general PHD theory; flexible, practical, powerful X-parameters can be accurately measured by automated set of experiments on the new Agilent NVNA instrument Together with the PHD component, measured X-parameters can be used in ADS to design nonlinear circuits All pieces of the puzzle are available and they fit together! Nonlinear Measurements Nonlinear Modeling Nonlinear Simulation Customer Applications
Summary New Nonlinear Vector Network Analyzer based on a standard PNA-X New phase calibration standard Vector (amplitude/phase) corrected nonlinear measurements from 1 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
Configuration Details Description N5242A - 4 1 MHz to 26.5 GHz 4-port Opt 419: 4-port attenuators & bias tees Opt 423: Source switching & combining network Opt 8: Frequency Offset Mode Opt 51: Nonlinear component characterization measurements (requires 4,419,8) Opt 514: Nonlinear X-parameters (requires 423, opt 51 & ext. source) Opt 518: Nonlinear pulse envelope domain (requires opt 51,21,25) Accessories: U9391C Phase reference (2 units required) Power meter & sensor or USB power sensor 3.5mm calibration standards External source for X-parameters