advanced nonlinear device characterization utilizing · pdf fileadvanced nonlinear device...
TRANSCRIPT
Advanced Nonlinear Device Characterization Utilizing New
Nonlinear Vector Network Analyzer and X-parameters
Advanced Nonlinear Device Characterization Utilizing New
Nonlinear Vector Network Analyzer and X-parameters
presented by:
Loren BettsResearch 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 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
Standard PNA-X with New Nonlinear features and capability
New phase calibration standard
NVNA System Configuration
Amplitude Calibration
Vector Calibration
Phase Calibration
Phase Reference
X-Parameter extraction/multi-tone source
Standard PNA-X Network Analyzer
New!! Agilent Calibrated Phase Reference
New!! Agilent NVNA
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
Phase Reference
New!! Agilent Calibrated
Phase Reference
0 10 20 30 40 50 60 70 80 90 1000
0.2
0.4
0.6
0.8
1
F requency in GHz
Nor
mal
ized
Am
plitu
de
Agilent’s new IC based phase reference is superior in all aspects to existing phase reference technologies.
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
Can also measure frequency multipliers
Phase relationship between frequencies at output of device
Input output frequencies at device terminals 1 GHz
2 GHz
122.1 degree phase delta
1 GHz
Fundamental Frequency
Source harmonics (< 60 dBc)
Stimulus to device
Output from device
Output harmonics
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
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 ~ 40 ps)
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
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)
Stimulus is 5 frequencies spaced 10 MHz apart centered at 1 GHz measuring all spectrum to 20 GHz
Measure amplitude AND PHASE of intermodulation products
Generated using external source (PSG/ESG/MXG) using NVNA and vector calibrated receiver
Input Waveform
Output Waveform
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 ~80 kHz apart centered at 2 GHz. The NVNA is measuring harmonics to 16 GHz (8th harmonic)
Multi-tone often used to mimic more complex modulation (i.e. CDMA) by matching complementary cumulative distribution function (CCDF). Multi-tone 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 ~80 kHz apart centered at 2 GHz. The NVNA is measuring harmonics to 16 GHz (8th harmonic)
NVNA Applications (What does it do?)
Measure memory effects in nonlinear devices with vector error correction applied
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
Output (b2) multi-envelope waveforms
Each harmonic has a unique time varying envelope signature
NVNA Applications (What does it do?)
Measure modeling coefficients and other nonlinear device parameters
Measure, view and simulate actual nonlinear data from your device
Dynamic Load Line
Waveforms (‘a’ and ‘b’ waves)
X-parameters… More
Linear and Nonlinear Device CharacteristicsNonlinear Hierarchy from Device to System
Devices
Systems
Circuits
Transistors, diodes, …
Amplifiers, Mixers, Multipliers, Modulators, ….
Chips
Characterization
and modeling
Modules
Instrument Front-endsCell Phones Military systemsEtc.
Nonlinearities
0
0
0
0 0
20
30
( ) ( )
( )
( )
b
c
d
j
j
j
y t a b e x t
c e x t
d e x t
θ
θ
θ
= +
+
+
0 0( )( ) j w tx t Ae φ+=0 0 0
0 0 0
0 0 0
( )0 0
2( )20
3( )30
( ) b
c
d
j j t
j j t
j j t
y t a b e Ae
c e A e
d e A e
θ ω φ
θ ω φ
θ ω φ
+
+
+
⎡ ⎤= + ⎣ ⎦
⎡ ⎤+ ⎣ ⎦
⎡ ⎤+ ⎣ ⎦
( )x t ( )y t
1ω 12ω1ω 13ω
The Need for PhaseCross-Frequency Phase
Notice that each frequency component has an associated static phase shift. Each frequency component has a phase relationship to each other.
0 0 0
0 0 0
0 0 0
( )0 0
2( )20
3( )30
b
c
d
j j t
j j t
j j t
y a b e Ae
c e A e
d e A e
θ ω φ
θ ω φ
θ ω φ
+
+
+
⎡ ⎤= + ⎣ ⎦
⎡ ⎤+ ⎣ ⎦
⎡ ⎤+ ⎣ ⎦
Why Measure This?
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…..
2- and 4-port versions
Built-in second source and internal combinerfor 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
Agilent’s N5242A premier performance microwave network analyzer offers the highest performance, plus:
NVNA HardwareTake a standard PNA-X and add nonlinear measurement capabilities
Measuring Unratioed Measurements on PNA-XUnratioed Measurements – Amplitude
Works fine.Ever tried to measure phase across frequency on an unratioed
measurement?
Sweep 1 Sweep 2
11a
11b
12b
12a
01a
01b
02a
02b
Measuring Unratioed Measurements on PNA-XUnratioed 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.
Sweep 1 Sweep 2
Phase Shifted
NVNA Hardware ConfigurationGenerate 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 ConfigurationPhase 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
) ( ))( ( ) ( 1 t shah t rect t y prf pw ∗ =
0 1/prf -1/prf t
... ... *
∑ nδ (t-n(1/ prf))
0 1/prf 2/prf-1/prf -2/prf
... ... rect pw (t)
0 1/2pw -1/2pw t
))(())(()( sprfshahprfspwsincpwsY ×××××=
))(())(()( sprfshahprfspwsincpwsY ×××××=
)()()( sprfshahspwsincDutyCyclesY ××××=
Frequency Domain Representation of Pulsed DC Signal
0 10 20 30 40 50 60 70 80 90 1000
0.2
0.4
0.6
0.8
1
Frequency in GHz
Nor
mal
ized
Am
plitu
de
0 5 10 15 20 250
0.2
0.4
0.6
0.8
1
Frequency in GHz
Nor
mal
ized
Am
plitu
de
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
NVNA Hardware ConfigurationIf 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.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-1
-0.5
0
0.5
1
Frequency - 1 GHz
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-1
-0.5
0
0.5
1
Frequency - 2 GHz
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-1
-0.5
0
0.5
1
Frequency - 3 GHz
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-1
-0.5
0
0.5
1
Frequency - 4 GHz
Phase relationship between frequencies remains the same
1 GHz
2 GHz
3 GHz
4 GHz
0 0cos( )tω φ+
0 1cos(2 )tω φ+
0 2cos(3 )tω φ+
0 3cos(4 )tω φ+
Example NVNA Configuration #1Using external source for phase reference drive
Test port 3
C
R3
Test port 1
R1
Source 1
OUT 1OUT 2
Source 2 (standard)
OUT 1 OUT 2
Test port 4
R4
Test port 2
R2
35 dB65 dB
35 dB65 dB 65 dB 35
dB65 dB
Rear panel
A
35 dB
D B
SW1 SW3 SW4 SW2
J11 J10 J9 J8 J7 J4 J3 J2 J1
To port 1 or 3Calibration
PhaseReference
Ext Source inMeasurement
PhaseReference
Example NVNA Configuration #2Multi-Tone, SCMM, DC/RF, Calibrated receiver mode
Test port 3
C
R3
Test port 1
R1
Source 1
OUT 1OUT 2
Source 2
OUT 1
OUT 2
Test port 4
R4
Test port 2
R2
35 dB65 dB
35 dB65 dB 65 dB 35
dB65 dB
Rear panel
A
35 dB
D B
To port 1 or 3Calibration
PhaseReference
Ext Source inMeasurement
PhaseReference
NVNA MeasurementsComponent 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 MeasurementsStimulus/Response Setup
The user can set up a multi-dimensional 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 MeasurementsGuided 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 MeasurementsGuided 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 MeasurementsGuided 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 MeasurementsGuided 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 MeasurementsMeasurement Display
The vector corrected responses from the device can be displayed in time domain.
Nonlinear VNA MeasurementsMeasurement 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 MeasurementsMeasurement 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 MeasurementsIn-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 DomainMemory Effects in Nonlinear Devices
( )x t ( )y t
1 11
Single frequency pulse with fixed phase and amplitude versus time
( ) j j tx t A e eθ ω−=
1ω
1ω
12ω
13ω
( )
Multiple frequencies envelopes with time varying phase and amplitude
( ) ( ) n nj t j tn
n
y t B t e eφ∞
− Ω
=−∞
= ∑
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.
Multi-Envelope DomainEnvelope 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 NonlinearMicrowave and RF Components
Easy to measure at high frequenciesmeasure 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 performanceCan 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
Incident TransmittedS 21
S 11Reflected S 22
Reflected
Transmitted Incident
b 1
a 1b 2
a 2S 12
DUT
Port 1 Port 2
S-parametersb1 = S11a1 + S12a2
b2 = S21a1 + S22a2
S-parameters: linear measurement, modeling, & simulation
Linear Simulation:Matrix Multiplication
Measure with linear VNA:Small amplitude sinusoids
Model Parameters:Simple algebra
0k
iij
ajk j
bSa =
≠
=
Scattering Parameters – Linear Systems
1 11 12 1
2 21 22 2
b S S ab S S a⎡ ⎤ ⎡ ⎤ ⎡ ⎤
=⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦ ⎣ ⎦
1 11 1 12 2
2 21 1 22 2
b S a S ab S a S a= += +
Linear Describing Parameters
• Linear S-parameters by definition require that the S-parameters of the device do not change during measurement.
S-Parameter Definition
To solve VNA’s traditionally use a forward and reverse sweep (2 port error correction).
21S
12S11S 22S
101e
011e
001e 11
1e
01a
01b
11a
11b
012e
102e
112e 00
2e
12b
12a
02b
02a
( )x t ( )y t
Scattering Parameters – Linear Systems
11 121 1 1 1
21 222 2 2 2
f r f r
f r f r
S Sb b a aS Sb b a a
⎡ ⎤ ⎡ ⎤⎡ ⎤=⎢ ⎥ ⎢ ⎥⎢ ⎥⎣ ⎦⎣ ⎦ ⎣ ⎦
1 11 12 1
2 21 22 2
b S S ab S S a⎡ ⎤ ⎡ ⎤ ⎡ ⎤
=⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦ ⎣ ⎦
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.
Hot S22
This is often why customers are asking for Hot S22 because the match is changing versus input drive powerand frequency (Nonlinear phenomena). Hot S22 traditionally measured at a frequency slightly offset from the large input drive signal.
( )x t ( )y t
1 11 1 12 2
2 21 1 22 2
b S a S ab S a S a= += +
• 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
Have the potential to revolutionize the Characterization, Design, and Modeling of nonlinear components and systems
H a r m o n ic B a la n c eH B 2
E q u a t io n N a m e [3 ]= " Z lo a d "E q u a t io n N a m e [2 ]= " R F p o w e r "E q u a t io n N a m e [1 ]= " R F f r e q "U s e K r y lo v = n oO r d e r [1 ]= 5F r e q [1 ]= R F f r e q
H A R M O N I C B A L A N C E
NVNA:Measure device X-parms
PHD component :Simulate using X-parms
ADS:Design using X-parms
X-parameters are the mathematically correct extension of S-parameters to large-signal conditions.
X-parameters the nonlinear Paradigm:
X-parameters come from thePoly-Harmonic Distortion (PHD) Framework
1 1 11 12 21 22( , , , ..., , , ...)k kB F DC A A A A=
2 2 11 12 21 22( , , , ..., , , ...)k kB F DC A A A A=
Port IndexHarmonic (or carrier) Index
Data and Model formulation in Frequency (Envelope) DomainMagnitude and phase enables complete time-domain input-output waveforms
2A1A
1B 2BUnifies S-parameters Load-Pull, Time-domain load-pull
X-parameters: Systematic Approximations to NL MappingTrade measurement time, size, accuracy for speed, practicality
+Linear non-analytic map
( ) ( ) *1 1[ ( , ) ( , ) ]S T
kj j kj jX D C A A X D C A A+∑
Incident Scattered
Multi-variate NL map1 2 3( , , , , . . .)kB D C A A A
Simpler NL map
( )1( , , 0, 0, 0, ...)F
kX DC A
≈
X-parameter Experiment Design & Identification
DC f0 2f0 3f0 4f0 5f0-f0-2f0-3f0
, ,
( )11
( )( ), 1 1
,,1
*1(| |) (( ) )
ef g gh ef hef
S fF fe f
T f hgh
g
hgh
g h h
B X X A AA P a X P aP − + ⋅= +⋅+∑ ∑ 11( )j AP e ϕ=
There are two contributions at each harmonic
From different orders in NL conductance of driven system
aj2aj2*
0 15 f f−2
( ) *3, 2 j
Ti jX a⋅
0 1f f+2
( )3, 2 j
Si jX a⋅
Scattering Parameters – Nonlinear SystemsX-parameters
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.
( )*
, (1,1)
( ) ( ) ( )11 , 11 , 11( ) ( ) ( )j j l j l
ij kl klk l
F S Tij ij kl ij klb P P aa Pa aaX X X− +
≠
= + ⋅ + ⋅∑
X-Parameters Collapse to S-Parameters in Linear Systems
Definitions
• i = output port index• j = output frequency index• k = input port index• l = input frequency index
1 11 1 12 2
2 21 1 22 2
b S a S ab S a S a= += +
For small |a11| (linear), XT terms go to 0.Cross-frequency terms also go to 0
( )( ) (
, (
1
1,
),
1)
1( )F Sj j lij kl
l jk
ij j kl
l
ib P P aaX X −
=≠
= + ⋅∑Consider fundamentalfrequency (j = 1). Harmonic index is no longer needed.
( ))
1
( ( )11( )F S
i iki kk
P aab X X≠
= + ⋅∑
Assume 2 port (i and k = 1 ->
( ) ( )1 11 11 2
( ) ( )2 11 2
2
2 22
( )
( )
F S
F S
b P a
b a a
a
P
X XX X
= + ⋅
= + ⋅
1 11 1 12 2
2 21 1 22 2
b S a P S a
b S a P S a
= +
= +
For small |a11| (linear), XF
terms go to Si1·|a11|,and XS terms are equal to linear S parameters
( )*
, (1,1)
( ) ( ) ( )11 , 11 , 11( ) ( ) ( )j j l j l
ij kl klk l
F S Tij ij kl ij klb P P aa Pa aaX X X− +
≠
= + ⋅ + ⋅∑By definition, 1
1
aPa
=
Example: Fundamental Component
11
( )21,11 11 21| | 0
( ) S
AX A s
→→
11
( )21,21 11 | | 0
( ) 0T
AX A
→→
-60-25 -20 -15 -10 -5 0 5 10
|A11| (dBm)
-40
4020
0
-20
dB
( )21,21
SX
( )21,21
TX
( )21,11
SX
Reduces to (linear) S-parameters in the appropriate limit
( )( )21 11
( )21,21
2 *21 11 21 2121 11,21 11()( ) ( )( ) TF SXB AA A PAP X X A A= + +
11
( )21,21 11 22| | 0
( )S
AX A s
→→
( )21,21
( )( )21,11 11 1
2 *21 1 21,21 11 111 121 21(( ( )) ) () TSSB X A X AA A PA X A A= + +
( ) ( ) ( ) *11 , 11 , 11( ) ( ) ( )F m S m n T m n
pm pm pm qn qn pm qn qnB X A P X A P A X A P A− += + +
X-parameter Experiment Design & IdentificationIdeal Experiment Design
Perform 3 independent experiments with fixed A11 using orthogonal phases of A21
E.g. functions for Bpm (port p, harmonic m)
( ) ( ) ( )(1) ( ) ( ) (1) ( ) (1)11 , 11 , 11
F m S m n T m npm pm pm qn qn pm qn qnB X A P X A P A X A P A− += + +
( ) ( ) ( )(2) ( ) ( ) (2) ( ) (2)*11 , 11 , 11
F m S m n T m npm pm pm qn qn pm qn qnB X A P X A P A X A P A− += + +
input Aqn output Bpm
Im
ReRe
Im ( )(0) ( )11
F mpm pmB X A P=
X-parameter Application Flow
MDIF File
NVNA
DUTΦ Ref
Measure X-Parameters
Automated DUT X-params measured on NVNA
Application creates data-specific instance Simulator
v2v1
ConnectorX1
MCA_ZX60_2522MCA_ZX60_2522_1fundamental_1=fundamental
MCA_ZFL_11ADMCA_ZFL_11AD_1fundamental_1=fundamental
RR1R=25 Ohm
V_1ToneSRC14
Freq=fundamentalV=polar(2*A11N,0) V
RR11R=50 Ohm DC_Block
DC_Block1DC_BlockDC_Block2
I_Probei2
I_Probei1
PHD instances
Data-specific simulatableinstance
Compiled PHD Component simulates using data
-28 -26 -24 -22 -20 -18 -16 -14 -12 -10 -8 -6-30 -4
-30
-20
-10
0
-40
10
.
.
-28 -26 -24 -22 -20 -18 -16 -14 -12 -10 -8 -6-30 -4
-60
-50
-40
-30
-20
-10
0
-70
10
.
.
-28 -26 -24 -22 -20 -18 -16 -14 -12 -10 -8 -6-30 -4
5
10
15
20
0
25
.
.
-28 -26 -24 -22 -20 -18 -16 -14 -12 -10 -8 -6-30 -4
70
71
72
73
74
75
69
76
.
.
-28 -26 -24 -22 -20 -18 -16 -14 -12 -10 -8 -6-30 -4
-135
-130
-125
-120
-140
-115
-28 -26 -24 -22 -20 -18 -16 -14 -12 -10 -8 -6-30 -4
0
2
4
6
8
10
12
-2
14
.
.
-10 -5 0 5 10 15-15 20
-30
-20
-10
0
10
-40
20
.
.
Simulation and Design
Compiled PHD componentHarmonic Bal:magnitude & phase of harmonics, frequency dep. and mismatch
Envelope:Accurately simulate NB multi-tone or complex stimulus
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
v2v1
ConnectorX1
MCA_ZX60_2522MCA_ZX60_2522_1fundamental_1=fundamental
MCA_ZFL_11ADMCA_ZFL_11AD_1fundamental_1=fundamental
RR1R=25 Ohm
V_1ToneSRC14
Freq=fundamentalV=polar(2*A11N,0) V
RR11R=50 Ohm DC_Block
DC_Block1DC_BlockDC_Block2
I_Probei2
I_Probei1
Amplifier Component Models from individual X-parameter measurements
ZFL-AD11+11dB gain, 3dBmmax output power
SourceConnector
80 psdelay
ZX60-2522M-S+23.5dB gain, 18dBm
max output powerLoad
ResultsCascaded Simulation vs. Measurement
Red: Cascade MeasurementBlue: Cascaded X-parameter SimulationLight Green: Cascaded Simulation, No X(T) termsDark Green: Cascaded Models, No X(S) or X(T) terms
-28 -26 -24 -22 -20 -18 -16 -14 -12 -10 -8 -6-30 -4
68
70
72
74
66
76
Pinc
unw
rap(
phas
e(b2
[::,1
]))
Pincref
unw
rap(
phas
e(b2
ref[:
:,1])
)un
wra
p(ph
ase(
b2N
oT[::
,1])
)un
wra
p(ph
ase(
b2N
oST
[::,1
]))
Fundamental Phase Second Harmonic % Error
-28 -26 -24 -22 -20 -18 -16 -14 -12 -10 -8 -6-30 -4
20
40
60
80
0
100
Pinc
(b2[
::,2
]-b2
ref[
::,2
])/b
2ref
[::,
2]*1
0(b
2NoT
[::,
2]-b
2ref
[::,
2])/
b2re
f[::
,2]*
(b2N
oST
[::,
2]-b
2ref
[::,
2])/
b2re
f[::
,2]
Large-mismatch capability (load-pull)Full Nonlinear Dependence on both A1 & A2 [13]
Fundamental Gain Fundamental Phase
-25 -20 -15 -10 -5 0 5-30 10
7.0
7.5
8.0
8.5
9.0
9.5
10.0
6.5
10.5
Pinc
-25 -20 -15 -10 -5 0 5-30 10
135
140
145
150
155
130
160
Pinc
Mismatched Loads: 0 ≤ |Γ| ≤ 1
Fundamental frequency: 4 GHzPHD Behavioral Model (solid blue) Circuit Model (red points)
( )11 21( , , 0, 0, ...)F
ik ikB X A A= + Terms linear in the remaining components
Large-mismatch capability (load-pull)
Magnitude Phase
Second Harmonic
Third Harmonic
-25 -20 -15 -10 -5 0 5-30 10
-60
-40
-20
0
-80
20
Pinc
-25 -20 -15 -10 -5 0 5-30 10
-240
-220
-200
-180
-160
-140
-120
-260
-100
Pinc
-25 -20 -15 -10 -5 0 5-30 10
-80
-60
-40
-20
0
20
40
-100
60
Pinc
-25 -20 -15 -10 -5 0 5-30 10
-100
-80
-60
-40
-20
0
-120
20
Pinc
Mismatched Loads: 0 ≤ |Γ| ≤ 1
Fundamental frequency: 4 GHzPHD Behavioral Model (solid blue) Circuit Model (red points)
Large-mismatch capability (load-pull)
100 200 300 4000 500
1
2
3
4
5
0
6
time, psec
100 200 300 4000 500
0.02
0.04
0.06
0.00
0.08
time, psec
1 2 3 4 50 6
0.02
0.04
0.06
0.00
0.08
Port 2 Voltage Port 2 Current
Dynamic Load-lines (green for matched case)Mismatched Loads: 0 ≤ |Γ| ≤ 1
Fundamental frequency: 4 GHzPHD Behavioral Model (solid blue) Circuit Model (red points)
PHD-Simulated vs Load-Pull Measured Contours & Waveforms from Load-dependent X-parameters (WJ transistor)
m1m2
( ) ( ) y
m9 m10
Power Delivered
Efficiency
Red: Load-pull data
Blue: PHD model simulated
0.2 0.4 0.6 0.80.0 1.0
-5
0
5
-10
10
-0.05
0.00
0.05
0.10
-0.10
0.15
time, nsec
Mea
sure
dVol
tage
MeasuredC
urrentS
imulatedC
urrent, ASim
ulat
edV
olta
ge,
V
Measured & Simulated Waveforms
Fundamental Gamma = 0.383+j*0.31
WJ Transistor
Load-Dependent Measured X-parameters [16]
SummaryX-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
CustomerApplications
Nonlinear Modeling
NonlinearSimulation
SummaryNew 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
Configuration Details
DescriptionN5242A - 400 10 MHz to 26.5 GHz 4-port
Opt 419: 4-port attenuators & bias tees
Opt 423: Source switching & combining network
Opt 080: Frequency Offset Mode
Opt 510: Nonlinear component characterization measurements(requires 400,419,080)
Opt 514: Nonlinear X-parameters (requires 423, opt 510 & ext. source)
Opt 518: Nonlinear pulse envelope domain(requires opt 510,021,025)
Accessories:U9391C Phase reference (2 units required)Power meter & sensor or USB power sensor3.5mm calibration standardsExternal source for X-parameters