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