nonlinear vector network analyzer applications - … · nonlinear vector network analyzer...

Nonlinear Vector Network Analyzer Applications- The PNA-X as NVNA for extracting X-Parameters -

presented by:Dr Marc LECOUVE

from original Slideset created by:Dr. David E. Root, Principal Research Scientist & Loren Betts, Research Scientist

Agilent Technologies

…Evolution of the Tools & Measurements

TOOLS:

S-Parameters

TOOLS:

S-Parameters +Figures of Merit

TOOLS:

Patchwork

NVNA +X-Parameters

TOOLS:

VNA

SA/SS/NFAPower meter

TOOLS:

Vector NetworkAnalyzer

MEASUREMENTS:

TOOLS:

SS & OscilloscopeGrease pens and

Polaroid cameras Power meter

Oscilloscope

DC Parametric Analyzer

MEASUREMENTS:

Gain

Input match

Output match

Polaroid cameras

Slotted line

Power meter

Scalar network analyzers

MEASUREMENTS:

Gain compression, IP3, IMD

PAE, ACPR, AM-PM, BER

Output match

Isolation

Transconductance

Input capacitance

MEASUREMENTS:

Bode plots

GainConstellation Diagram, EVM

GD, NF, Spectral Regrowth

ACLR, Hot “S22”

Input capacitanceGain

SWR

Y & Z parameters

Completing the puzzle

Nonlinear Caracterization

Nonlinear Simulation & Design

Nonlinear Modeling

Customer ApplicationsNonlinear

ModelingApplications

*( ) ( ) ( )F S m n T m nB X A X A P A X A P A− += + + *11 , 11 , 11( ) ( ) ( )F S m n T m n

pm pm pm qn qn pm qn qnB X A X A P A X A P A− += + +

Nonlinear Vector Network Analyzer (NVNA)

Vector (amplitude/phase) corrected nonlinear measurements from 10 MHz to 26.5 GHz

Calibrated absolute amplitude and relative phase 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 DUTwaveforms of voltages and currents of DUT

Multi-Envelope domain measurements for measurement and analysis of memory effects

X-parameters: Extension of Scattering parameters into 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 designnonlinear simulation and design

Standard PNA-X with New Nonlinear features and capability

New phase calibration standard

NVNA System Configuration

Amplitude CalibrationX-Parameter extraction/multi-tone source

Vector CalibrationVector Calibration

Phase Calibration

New!! Agilent NVNA

Phase ReferenceStandard PNA-X Network Analyzer

New!! Agilent Calibrated Phase Reference

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 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 correc tion frequencies to/from device with vector error correc tion applied View absolute amplitude and phase relationship

between frequencies to/from a device with vector correction applied (measurement plane vector correction applied (measurement plane at DUT terminals)

Useful to analyze/design high efficiency amplifiers such as class E/Famplifiers such as class E/F

Can also measure frequency multipliers1 GHz

Fundamental Frequency

Source harmonics (< 60 dBc)

Stimulus to device

2 GHz

Output from device

Input output frequencies at device terminals1 GHz

2 GHz

122.1 degree phase delta

Output harmonics

Phase relationship between frequencies at output of device

NVNA Applications (What does it do?)Measurement of narrow (fast) DC pulses with vector 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 pulses with vector correction applied (measurement plane at DUT terminals)

Less than 50 ps

Note: DC signal with 250 MHz PRF

NVNA Applications (What does it do?)Measurement of narrow (fast) View time domain (and frequency 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 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. frequency. Limited by external source not NVNA. Can measure down into the picosecond pulse widths

Note: 2 GHz RF signal 10 nsec pulsed


Measurements of multi -tone stimulus/response with Measurements of multi -tone stimulus/response with vector error correction applied

View time and frequency domain View time and frequency domain representations of a multi-tone stimulus to/from a device with vector correction applied (measurement plane at DUT terminals)plane at DUT terminals)

Stimulus is 5 frequencies spaced 10 MHz apart centered at 1 GHz measuring all spectrum to 20 GHz

Input Waveform

measuring all spectrum to 20 GHz

Measure amplitude AND PHASE of intermodulation products

Generated using external source

Output Waveform

Generated using external source (PSG/ESG/MXG) using NVNA and vector calibrated receiver


Calibrated measurements of multi -tone Calibrated measurements of multi -tone stimulus/response with narrow tone spacing

View time and frequency domain View time and frequency domain representations of a multi-tone stimulus to/from a device with vector correction applied (measurement plane at DUT terminals)plane at DUT terminals)

Stimulus is 64 frequencies spaced ~80 kHz apart centered at 2 GHz. The NVNA is measuring harmonics to 16 NVNA is measuring harmonics to 16 GHz (8th harmonic)

Multi-tone often used to mimic more complex modulation (i.e. CDMA) by complex modulation (i.e. CDMA) by matching complementary cumulative distribution function (CCDF). Multi-tone can be measured very accurately.accurately.


Calibrated measurements of multi -tone 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 stimulus to/from a device with vector correction applied (measurement plane at DUT terminals)

Stimulus is 64 frequencies spaced Stimulus is 64 frequencies spaced ~80 kHz apart centered at 2 GHz. The NVNA is measuring harmonics to 16 GHz (8th harmonic)


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 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


Measure modeling coefficients and other nonlinear Measure modeling coefficients and other nonlinear device parameters

X-parameters

… More

Dynamic Load Line

Waveforms (‘a’ and ‘b’ waves)

Dynamic Load Line

Measure, view and simulate actual nonlinear data from your device

Nonlinearities

( )x t ( )y t

1ω 12ω1ω 13ω

0

0

0 0

20

( ) ( )

( )

b

c

j

j

y t a b e x t

c e x t

θ

θ

= +

+

0 0( )( ) j w tx t Ae φ+=0 0 0

0 0 0

( )0 0

2( )20

( ) b

c

j j t

j j t

y t a b e Ae

c e A e

θ ω φ

θ ω φ

+

+

= +

+

1 11 1

0

0

30

( )

( )dj

c e x t

d e x tθ

+

+ 0 0 0

0

3( )30

dj j t

c e A e

d e A eθ ω φ+

+

+

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.

Why Measure This?

If we can measure the absolute amplitude and cross-frequency phase we have knowledge of the

( )j j tθ ω φ+ = +

phase we have knowledge of the nonlinear behavior such that we can:

Convert to time domain waveforms (eg: scope mode).

0 0 0

0 0 0

( )0 0

2( )20

b

c

j j t

j j t

y a b e Ae

c e A e

θ ω φ

θ ω φ

+

+

= +

+

Measure phase relationships between harmonics.

Generate model coefficients.

0 0 0

0

3( )30

dj j t

c e A e

d e A eθ ω φ+

+

+

Measure frequency multipliers.

Etc…..

Measuring Unratioed Measurements on PNA-XUnratioed Measurements – Amplitude

Works fine.

Ever tried to measure phase across frequency on an unratioed measurement?

01a

0b

02a

0b11a

11b

12b

12a

01b 0

2b

Sweep 1 Sweep 2

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.

Phase Shiftedof the frequency spectra.

Sweep 1 Sweep 2

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) 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 frequency. A harmonic phase reference generates all the frequency spectrum simultaneously.

The harmonic phase reference frequency grid 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 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 A second phase reference standard is used to calibrate the cross-frequency phase at the device plane.

The phase reference generates a time 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 content related to the pulse repetition frequency (PRF) and pulse width (PW).

The cross-frequency phase relationship remains static.

Phase Reference

New!! Agilent Calibrated

Phase Reference

Agilent’s new IC based phase reference is superior in all aspects to existing phase reference technologies.

Advantages:

Phase Reference

Lower temperature sensitivity

Lower sensitivity to input power

Smaller minimum tone spacing (< 1 MHz vs 600 MHz) 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 noise1

0

0.2

0.4

0.6

0.8

Nor

ma

lized

Am

plitu

de

0 10 20 30 40 50 60 70 80 90 1000

Frequency in GHz

Frequency Domain Representation of Pulsed DC Signal

1

Frequency Response

Drive phase reference with a Fin frequency.

0.4

0.6

0.8

No

rma

lize

d A

mp

litu

de

frequency.

Get n*Fin at the output of the phase reference.

Example:

0 10 20 30 40 50 60 70 80 90 1000

0.2

Frequency in GHz

No

rma

lize

d A

mp

litu

de

Example:

Want to stimulate DUT with 1 GHz input stimulus and measure harmonic responses at 1, 2, 3, 4, 5

0.6

0.8

1

No

rma

lize

d A

mp

litu

de

responses at 1, 2, 3, 4, 5 GHz.

Fin = 1 GHz

Can practically use frequency

0

0.2

0.4

No

rma

lize

d A

mp

litu

de

Can practically use frequency spacings less than 1 MHz

0 5 10 15 20 250

Frequency in GHz

U9391C phase reference output signal on EXA when applying 1 GHz to the input

Measurement results with 500 MHz input frequencyon the U9391C harmonic phase reference.

Example NVNA Hardware Configuration

Source 1

OUT 1OUT 2

Source 2 (standard)

OUT 1 OUT 2

Rear panelJ11 J10 J9 J8 J7 J4 J3 J2 J1

R3R1 R4 R2

SW1 SW3 SW4 SW2

C

35 dB 35 dB

A

35 dB

D B

Test port 3Test port 1 Test port 4 Test port 2

65 dB 65 dB 65 dB 35 dB

65 dB

To port 1 or 3

Calibration MeasurementCalibration

Phase

Reference

Ext Source inMeasurement

Phase

Reference

ADD PNA stuff from Loren BettsNVNA Demo on PNA-X

Nonlinear VNA MeasurementsStimulus/Response Setup

The user can set up a multi-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 responseMulti-Envelope response

Example stimulus response setup

multidimensional sweep:1. The NVNA will set the frequency and power and measure the a and

b waves at the input and output for the fundamental frequency. b waves at the input and output for the fundamental frequency. 2. Move the receivers to the next harmonic frequency and measure

the a and b waves again. 3. When all harmonics are measured, move the power to the next

power point and measure the a and b waves for the fundamental power point and measure the a and b waves for the fundamental and all harmonics again.

4. Repeat until all power points have been measured. 5. Then move the fundamental input frequency to the next frequency 5. Then move the fundamental input frequency to the next frequency

point 6. repeat the above procedure until all the frequency points have been

measured.

Nonlinear VNA MeasurementsGuided Calibration Wizard – 3 Step Process (Vector, Amplitude,

Phase)Phase)

User is guided through all stages User is guided through all stages of calibration. Each of the three cal stages can be refreshed. No calibration shows as a ‘red’ acknowledgement.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 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 User is prompted to connect the phase reference calibration standard. Standard is USB controlled. This calibrates the cross-frequency phase.cross-frequency phase.

New!New!

Nonlinear VNA MeasurementsGuided Calibration Wizard – Amplitude Calibration

User is prompted to connect the power sensor calibration standard. power sensor calibration standard. Supports any power meters/sensors the PNA-X FW supports today and in the future.

Nonlinear VNA MeasurementsMeasurement Display

The user can display the resulting corrected waves in frequency, time, corrected waves in frequency, time, power and other domains. Can also display all formats including cross-frequency phase.


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. performance versus power. This example illustrates the phase of the second harmonic from the device as a function of input power.a function of input power.


User can customize the displayed waveforms such as 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 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 Eg: Move amplitude and phase plane (in-coax) into the fixture plane.

Multi-Envelope DomainMemory Effects in Nonlinear Devices

( )x t ( )y t

1ω

1ω

1 11

Single frequency pulse with fixed phase and amplitude versus time

( ) j j tx t A e eθ ω−=

1

12ω Can measure envelope of the

fundamental and harmonics with NVNA error correction applied. Use to analyze memory effects in nonlinear devices.

13ωmemory effects in nonlinear devices.

Get vector corrected amplitude and phase of envelope.

Use to measure and analyze memory ( )

Multiple frequencies envelopes with time varying phase and amplitude

( ) ( ) n nj t j tn

n

y t B t e eφ∞

− Ω

=−∞

= ∑

Use to measure and analyze memory effects in nonlinear devices.

Multi-Envelope Domain

Envelope DomainEnvelope Domain

Measure envelope of the Measure envelope of the fundamental and harmonics with NVNA error correction applied. Use to analyze memory effects in 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.

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

modeling, & simulation

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: Measure with linear VNA: Model Parameters:

Incident TransmittedS21

S11

a1b2

S-parametersb = S a + S a

Linear Simulation:Matrix Multiplication

Measure with linear VNA:Small amplitude sinusoids Parameters:

Simple algebra

bS11

Reflected S22Reflected

Transmitted Incident

b1

b2

a 2S12

DUT

Port 1 Port 2b1 = S11a1 + S12a2

b2 = S21a1 + S22a2 0k

iij

ajk j

bS

a =≠

=Transmitted 12 k j≠

Why X-parameters are Revolutionary:

X-parameters include the magnitude and phase of the fundamental signal, all of its harmonics and inter-modulation products, and all of their dependence on source and load impedance.

This creates an automated system for predictable simulation and measurement based nonlinear design.

X-parameters, ADS, and the NVNA can be used to reconstruct time domain waveforms, estimate performance parameters such as ACPR, EVM, and power added efficiency, design multi-stage amplifiers and subsystems, and optimize nonlinear system performance.

Have the potential to revolutionize the 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

• Measurement based, device independent, identifiable from a simple set of

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 harmonics)

• Cascadable (correct behavior in mismatched environment)• Cascadable (correct behavior in mismatched environment)

• Extremely accurate for high-frequency, distributed nonlinear devicesNVNA:

Measure device X-parmsPHD component :

Simulate using X-parmsADS:

Design using X-parms

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 [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 IC B A L A N C E

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 "

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

X-Parameters:Interoperable Measurement, Modeling, and Simulation of NonlinearMicrowave and RF Components

S- X-

Accurate for small signal measurements yes yes

Accurate for Large signal measurements no yes

S-Parm X-parm

Accurate for Large signal measurements no yes

Input & output at same frequency yes yes

Input & output at different frequencies no yes

Captures cross-frequency phase & amplitude no yes

Captures DC and RF power dependency no yes

Linear cascade to predict system performance yes yes

Nonlinear cascade to predict system performance no yes

Measurements on Nonlinear Components

mA1 2mA

B

( , ,..., , ,...)B F A A A A=

kB2kB1

11 12 21 22( , ,..., , ,...)ik ikB F A A A A=

X-parameters come from thePoly -Harmonic Distortion (PHD) Framework [3,5,12]Poly -Harmonic Distortion (PHD) Framework [3,5,12]

2A1A

B B

1 1 11 12 21 22( , , , ..., , , ...)k kB F D C A A A A=1B 2B

1 1 11 12 21 22( , , , ..., , , ...)k kB F D C A A A A=2 2 11 12 21 22( , , , ..., , , ...)k kB F D C A A A A=

Port Index Harmonic (or carrier) IndexPort Index 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.

Note : A/blue = input, B/red = outputNote : A/blue = input, B/red = output

X-parameters: Systematic Approximations to NL MappingTrade measurement time, size, accuracy for speed, p racticality

Incident ScatteredIncident Scattered

( , , , , ...)B D C A A A

Multi-variate NL map1 2 3( , , , , ...)kB D C A A A

≈

Simpler NL map

( )1( , , 0, 0, 0, ...)F

kX DC A

≈

+Simpler NL map

Linear non-analytic map( ) ( ) *

1 1[ ( , ) ( , ) ]S Tkj j kj jX D C A A X D C A A+∑

Note : harmonic superposition principle Note : harmonic superposition principle

X-Parameter Experiment Design & IdentificationIdeal Experiment DesignIdeal Experiment Design

E.g. functions for Bpm (port p, harmonic m)

( ) ( ) ( ) *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− += + +

Perform 3 independent experiments with fixed A11 using orthogonal phases of A21

input Aqn output Bpm

( ) ( ) ( )(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− += + +

input Aqn output Bpm

ImIm( )(0) ( )

11F m

pm pmB X A P=

( ) ( ) ( )11 , 11 , 11pm 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− += + +

Re

Re

Example: Fundamental Component( )( ) ( ) 2 *()( ) ( )( ) TF SXB AA A PAP X X A A= + +( )( )

21 11( )21,21

2 *21 11 21 2121 11,21 11()( ) ( )( ) TF SXB AA A PAP X X A A= + +

( )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

( )21,11 11 21

| | 0( ) S

AX A s

→→40

20dB

( )21,11

SX20

0

-20

( )21,21

SX11

( )21,21 11 22

| | 0( )S

AX A s

→→

11

( )21,21 11

| | 0( ) 0T

AX A

→→

-60

-40

-20( )21,21

TX

-60-25 -20 -15 -10 -5 0 5 10

|A11| (dBm)Xpar reduce to (linear) Spar when in the linear region (“small A11”)

Example 1 NVNA X-parameter screenshot

Example 2 NVNA X-parameter screenshot

X-parameter Application Flow

Automated DUT X-params measured on NVNAAutomated DUT X-params measured on NVNA

Application creates data-specific instance Simulator

PHD instancesCompiled PHD Component simulates using data

MDIF File

NVNA 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 File Data-specific simulatable instance

Compiled PHD component

Harmonic Bal:

DUTΦ Ref

5

10

15

20

25

.

71

72

73

74

75

76

.

Simulation and Design

Harmonic Bal:magnitude & phase of harmonics, frequency dep. and mismatch

Measure X-Parameters -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

0

.

-28 -26 -24 -22 -20 -18 -16 -14 -12 -10 -8 -6-30 -4

70

69

.

-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

.

.

Envelope:Accurately simulate NB multi-tone or complex stimulus

ACLR Validation on Mini-Circuit amplifier ZX60-2522 M-S+

Overlay of simulated and measured spectrum under 3GPP WCDMA stimulus at 13dBm output power

ACLR lowdBc

ACLR highdBc

Simulated -43.3 -43.23GPP WCDMA stimulus at 13dBm output powerAlternate channel measured results limited by dynamic range and simulations limited by source spectral purity.

Simulated fromX-params

-43.3 -43.2

Meas. SA

-44.05 -44.12SA

Measurement-based nonlinear design with X-parameter s

ZFL-AD11+11dB gain, 3dBmmax output power

SourceConnector

80 psdelay

ZX60-2522M-S+23.5dB gain, 18dBm

max output powerLoad

v2v1

ConnectorX1

MCA_ZX60_2522MCA_ZX60_2522_1fundamental_1=fundamental

MCA_ZFL_11ADMCA_ZFL_11AD_1fundamental_1=fundamental

RR1R=25 Ohm

RR11R=50 Ohm DC_Block

DC_Block1DC_BlockDC_Block2

I_Probei2

I_Probei1

fundamental_1=fundamentalfundamental_1=fundamental

V_1ToneSRC14

Freq=fundamentalV=polar(2*A11N,0) V Amplifier Component Models from individual X-parameter measurements

Results

Cascaded S

imulation vs. M

easurement

Cascaded S

imulation vs. M

easurement

Red: C

ascade Measurem

entB

lue: Cascaded X

-parameter S

imulation

Light Green: C

ascaded Sim

ulation, No X

(T)term

sLight G

reen: Cascaded S

imulation, N

o X(T

)terms

Dark G

reen: Cascaded M

odels, No X

(S)or X

(T)term

s

34 36

dB(b2ref[::,1]/a1ref[::,1])dB(b2NoT[::,1]/a1NoT[::,1])

dB(b2NoST[::,1]/a1NoST[::,1])

Fundam

ental Gain

74 76

unwrap(phase(b2[::,1]))unwrap(phase(b2ref[::,1]))

unwrap(phase(b2NoT[::,1]))unwrap(phase(b2NoST[::,1]))

Fundam

ental Phase

30 32 34

dB(b2[::,1]/a1[::,1])dB(b2ref[::,1]/a1ref[::,1])

dB(b2NoT[::,1]/a1NoT[::,1])dB(b2NoST[::,1]/a1NoST[::,1])

70 72 74

unwrap(phase(b2[::,1]))unwrap(phase(b2ref[::,1]))

unwrap(phase(b2NoT[::,1]))unwrap(phase(b2NoST[::,1]))

-28-2

6-24

-22-20

-18-16

-14

-12-10

-8-6

-30-4

2826

Pinc

dB(b2ref[::,1]/a1ref[::,1])dB(b2NoT[::,1]/a1NoT[::,1])

dB(b2NoST[::,1]/a1NoST[::,1])

-28-26

-24-22

-20-18

-16

-14-12

-10-8

-6-3

0-4

6866

Pinc

unwrap(phase(b2[::,1]))

Pincref

unwrap(phase(b2ref[::,1]))unwrap(phase(b2NoT[::,1]))

unwrap(phase(b2NoST[::,1]))

Pincref

Results

Cascaded S

imulation vs. M

easurement

Cascaded S

imulation vs. M

easurement

Red: C

ascade Measurem

entB

lue: Cascaded X

-parameter S

imulation

Light Green: C

ascaded Sim

ulation, No X

(T)term

sLight G

reen: Cascaded S

imulation, N

o Xterm

sD

ark Green: C

ascaded Models, N

o X(S

)or X(T

)terms

Fundam

ental % E

rrorS

econd Harm

onic % E

rror

(b2[::,2]-b2ref[::,2])/b2ref[::,2]*100(b2NoT[::,2]-b2ref[::,2])/b2ref[::,2]*100

(b2NoST[::,2]-b2ref[::,2])/b2ref[::,2]*100

6 8

10 12


(b2NoST[::,1]-b2ref[::,1])/b2ref[::,1]*100

60 80

100


(b2NoST[::,2]-b2ref[::,2])/b2ref[::,2]*100

-28-26

-24-22

-20-18

-16-14

-12-10

-8-6

-30-4

2 4 60


(b2NoST[::,1]-b2ref[::,1])/b2ref[::,1]*100

-28-26

-24

-22

-20

-18

-16

-14-12

-10-8

-6-30

-4

20 400(b2[::,2]-b2ref[::,2])/b2ref[::,2]*100

(b2NoT[::,2]-b2ref[::,2])/b2ref[::,2]*100(b2NoST[::,2]-b2ref[::,2])/b2ref[::,2]*100

-28-26

-24-22

-20-18

-16-14

-12-10

-8-6

-30-4

Pinc

-28-26

-24

-22

-20

-18

-16

-14-12

-10-8

-6-30

-4

Pinc

“X-param

eters enable predictive nonlinear design from N

L data”

Summary• X-parameters are a mathematically correct superset of S-• 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 • 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 • 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

NonlinearSimulation

CustomerApplications

Nonlinear Modeling

Configuration Details

DescriptionN5242A - 400 10 MHz to 26.5 GHz 4-port

Opt 419: 4-port attenuators & bias tees 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 domainOpt 518: Nonlinear pulse envelope domain(requires opt 510,021,025)

Accessories:U9391C Phase reference (2 units required)U9391C Phase reference (2 units required)Power meter & sensor or USB power sensor3.5mm calibration standardsExternal source for X-parameters

PNA Applications Antenna T/R Module

Mm-waveAmplifier Test Pulsed RFAntenna

TestT/R Module

TestMm-wave

Single Connection:Gain compression,

IMD, noise figure, harmonics,

true differential,

PAE, hot S

Amplifier Test Pulsed RF

and DC

325 GHz325 GHzPNA-LPNA-L500 GHz500 GHz

PAE, hot S22

Materials Measurements

50 GHz50 GHz67 GHz67 GHz110 GHz110 GHz325 GHz325 GHz

PNA-L

PNA

PNA-X

PNA-L

PNA

PNA-X

500 GHz500 GHz

Mixer Test

NVNA

13.5 GHz13.5 GHz20 GHz20 GHz40 GHz40 GHz50 GHz50 GHz67 GHz67 GHz

Load Pull

Noise Parameters Signal Integrity

Component Characterization

X-Parameter Extraction

Pulse Envelope Domain

www.agilent.com/find/pna

6 GHz6 GHz13.5 GHz13.5 GHz

Scanning MicroscopeMicroscope

X-parameters & PHD Models: Medium of exchange between levels of the hierarchy

Top-Down Design SpecsTop-Down Design Specs

Demonstrated but not commercialize

Bottom-up verification

ESL

Electronic System Level Design

System Integrators

Nokia, Sony-Ericsson…

PHD1

Desired Specs

PHD fromsimulation

Component vendors

Skyworks, Freescale, Samsung,…NVNA2

PHD

1 PHD = Poly-harmonic Distortion Model

Skyworks, Freescale, Samsung,…NVNA

2 NVNA = Non-linear Vector Network Analyzer

References[1] J. Wood, D. E. Root, N. B. Tufillaro, “A behavioral modeling

approach to nonlinear model-order reduction for [8] D. E. Root, D. Sharrit, J. Verspecht, “Nonlinear Behavioral

Models with Memory: Formulation, Identification, and approach to nonlinear model-order reduction for RF/microwave ICs and systems,” IEEE Transactions on Microwave Theory and Techniques, Vol. 52, Issue 9, Part 2, Sept. 2004 pp. 2274-2284

[2] Agilent HMMC-5200 DC-20 GHz HBT Series-Shunt Amplifier, Data Sheet, August 2002.

Models with Memory: Formulation, Identification, and Implementation,” 2006 IEEE MTT-S International Microwave Symposium Workshop (WSL) on Memory Effects in Power Amplifiers

[9] Blockley et al 2005 IEEE MTT-S International Microwave Symposium Digest, Long Beach, CA, USA, June 2005.

[3] J. Verspecht, M. Vanden Bossche, F. Verbeyst, “Characterizing Components under Large Signal Excitation: Defining Sensible `Large Signal S-Parameters'?!,” in 49th IEEE ARFTG Conference Dig., Denver, CO, USA, June 1997, pp. 109-117.

[4] J. Verspecht, D.E. Root, J. Wood, A. Cognata, “Broad-Band,

[10] Jan Verspecht Patent US 7,038,468 B2 (issued May 2, 2006 based on a provisional patent 60/477,349 filed on June 11, 2003)

[11] Soury et al 2005 IEEE International Microwave Symposium Digest pp. 975-978

[4] J. Verspecht, D.E. Root, J. Wood, A. Cognata, “Broad-Band, Multi-Harmonic Frequency Domain Behavioral Models from Automated Large-Signal Vectorial Network Measurements,” in 2005 IEEE MTT-S International Microwave Symposium Digest, Long Beach, CA, USA, June 2005.

[5] D. E. Root, J. Verspecht, D. Sharrit, J. Wood, and A. Cognata, “Broad-Band Poly-Harmonic Distortion (PHD)

[12] J. Verspecht and D. E. Root, “Poly-Harmonic Distortion Modeling,” in IEEE Microwave Theory and Techniques Microwave Magazine, June, 2006.

[13] J. Verspecht, D. Gunyan, J. Horn, J. Xu, A. Cognata, and D.E. Root, “Multi-tone, Multi-Port, and Dynamic Memory Enhancements to Cognata, “Broad-Band Poly-Harmonic Distortion (PHD)

Behavioral Models from Fast Automated Simulations and Large-Signal Vectorial Network Measurements”, IEEE Transactions on Microwave Theory and Techniques Vol. 53. No. 11, November, 2005 pp. 3656-3664

[6] J. Wood, D. E. Root, editors, Fundamentals of NonlinearBehavioral Modeling for RF and Microwave Design , 1st

“Multi-tone, Multi-Port, and Dynamic Memory Enhancements to PHD Nonlinear Behavioral Models from Large-Signal Measurements and Simulations,” 2007 IEEE MTT-S Int. Microwave Symp. Dig.,Honolulu, HI, USA, June 2007.

[14] Horn et al 2008 Power Amplifier Symposium, Orlando, Jan. 2008

[15] Horn et al 2008 IEEE European Microwave Conference, Behavioral Modeling for RF and Microwave Design , 1sted. Norwood, MA, USA, Artech House, 2005.

[7] Root et al US Patent # 7295961 2007

[15] Horn et al 2008 IEEE European Microwave Conference, Amsterdam, October, 2008

[16] Simpson et al to be published in 2008 IEEE ARFTG Conference, Portland, OR December, 2008

Return Loss

Hierarchical NL Design using meas. X-params in ADS: Measured System vs Simulation: Fundamental

GainMagnitude

Return Loss

Magnitude

Blue: PHD Hierarchical ModelRed: Measurements

Magnitude


Phase Phase

Hierarchical NL Design using meas. X-params in ADS: Measured System vs Simulation: 2 nd Harmonic

B2 B1

Magnitude Magnitude

B2 B1


Magnitude


Phase Phase

Hierarchical NL Design using meas. X-params in ADS: Measured System vs Simulation: 3 rd Harmonic

B2 B1

Magnitude Magnitude

B2 B1


Magnitude

PhasePhase


Load-Dependent Measured X-parameters [16]

PHD Model Offers:

Straight forward setup and calibration• A setup and calibration that is only slightly more complex than a regular VNA measurement.Anticipate the behavior of the device under a large set of operating conditions by Anticipate the behavior of the device under a large set of operating conditions by sweeping bias points, frequencies, loads, power, all automatically

Fast characterization • <30 seconds for one bias point and frequency – fund + 2 harmonics).• <30 seconds for one bias point and frequency – fund + 2 harmonics).• Weeks to months using traditional methods

(In fact using the old method with Load Pull using passive tuners, one bias point takes about 30 minutes, at the fundamental only. Characterizing using harmonic load pull would take days to weeks. Old methods give no model nor phase (waveform) info.)

A PHD behavioral model is available almost directly after the measurement.A PHD behavioral model is available almost directly after the measurement.• based on X-parameters that gives nonlinear information about the PA, and its harmonicsEstimate and predict parameters previously not poss ible to simulate• Having a NL model allows for Harmonic Balance and envelope simulations with modulated • Having a NL model allows for Harmonic Balance and envelope simulations with modulated

sources. We can estimate and predict many parameters that were previously not possible to simulate. PhErr, EVM, ACLR, Mod Spectrum

nonlinear vector network analyzer applications - … · nonlinear vector network analyzer...

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