Large-Signal Network Analysis

(1)

Large-Signal Network Analysis

“Going beyond S-parameters”

Dr. Jan Verspecht

“Jan Verspecht bvba”

(2)

2 • Part I

– Introduction

– Instrumentation and Calibration

• Break

– Coffee and Cookies

• Part II

– Applications

– Conclusions

(3)

• Introduction

• Signal Representations

• Instrumentation Hardware

• Calibration Aspects

(4)

4 Large-Signal Network Analysis?

• Put a D.U.T. (“network”) in realistic large-signal

operating conditions

• Completely and accurately characterize the

D.U.T. behavior

• Analyze the D.U.T. behavior using the measured

data

(5)

• Introduction

• Signal Representations

• Instrumentation Hardware

• Calibration Aspects

(6)

6 Signal Representations

)

(

1

t

V

)

(

1

t

I

D.U.T.

)

(

1

f

B

)

(

1

f

A

TUNER

)

(

2

f

A

)

(

2

f

B

)

(

2

t

V

)

(

2

t

I

TUNER

• Representation Domain

– Frequency (f)

– Time (t)

– Envelope (f,t)

• Set of Physical Quantities

– Traveling Waves (A, B)

– Voltage/Current (V, I)

• LSNA is capable of periodic and periodically modulated signals

(7)

Traveling Waves versus Current/Voltage

Ω

=

50 c

Z

Typically

2 I

Z

V

A

=

+

c

2 I

Z

V

B

=

−

c

B

A

V

=

+

c

Z

B

A

I

=

−

A

B

V

I

DUT

(8)

8 • 2-port DUT under periodic excitation

• E.g. transistor excited by a 1 GHz tone with an arbitrary

output termination

• All current and voltage waveforms are represented by a

fundamental and harmonics

• Spectral components X

_h

= complex Fourier Series coefficients

of the waveforms

Signal Class: CW Signals

Freq. (GHz)

1

2

3

4 DC

(9)

CW: Time and Frequency Domain













=

∑

=

H

h

t

f

h

j

h

e

X

t

x

0

2 Re

)

(

π

∫

−

=

1

0

2 )

(

2 f

t

f

h

j

h

f

x

t

e

dt

X

π

frequency

l

fundamenta

period

f

=

1 /

=

(10)

10 Time Domain V/I Representation

Time (ns)

(11)

• Periodically modulated version of the previous case

• e.g. transistor excited by a modulated 1 GHz tone

(modulation period = 10 kHz)

Signal Class: Modulated Signals

Freq. (GHz)

1

2

3 DC

(12)

12 Modulation: Time and Frequency Domain













=

∑ ∑

=

+

−

=

+

H

h

M

m

t

f

m

f

h

j

hm

e

C M

X

t

x

0 )

(

2 Re

)

(

π

∫

−

+

−

∞

→

=

T

t

f

m

f

h

j

T

hm

x

t

e

dt

T

X

lim

1 (

)

2 π

(

C

M

)

frequency

modulation

frequency

carrier

=

M

C

f

(13)

Modulation: Envelope Domain













=

∑

=

H

h

t

f

h

j

h

t

e

c

X

t

x

0

2 )

(

Re

)

(

π

∑

−

=

M

m

t

f

m

j

hm

h

t

X

e

M

X

(

)

2 π

(14)

14 Modulation: Time and Envelope Domain

Time (normalized)

B

₂

(Volt)

Fundamental envelope

3rd harmonic

envelope

(15)

Modulation: Frequency Domain

Fund @ 1.9 GHz

2nd @ 3.8 GHz

3rd @ 5.7 GHz

Incident

signal (a1)

Transmitted

signal (b2)

Reflected

signal (b1)

dBm dBm dBm

(16)

16 Modulation: 2D Time Domain

t

_S

(normalized)

t

_F

(normalized)

B

₂

(Volt)

)

,

(

)

(

t

x

₂

f

t

f

t

x

=

_D

_c

_M













=

∑ ∑

=

+

−

=

+

H

h

M

m

t

m

t

h

j

hm

S

F

D

t

X

e

F S

x

0 )

(

2

2 (

,

)

Re

π

(17)

• Introduction

• Signal Representations

• Instrumentation Hardware

• Calibration Aspects

(18)

18 Hardware: Historical Overview

• 1988 Markku Sipila & al.: 2 channel scope with one coupler at the input

(14 GHz)

• 1989 Kompa & Van Raay: 2 channel scope with VNA test-set + receiver

Lott: VNA test set + receiver (26.5 GHz)

• 1992 Kompa & Van Raay: test-set with MTA (40 GHz)

Verspecht & al.: 4 couplers with a 4 channel oscilloscope (20 GHz)

• 1994 Demmler, Tasker, Leckey, Wei, Tkachenko:

test-set with MTA (40 GHz)

Verspecht & al.: 4 couplers with 2 synchronized MTA’s

• 1996 Verspecht & al.: NNMS, 4 couplers, 4 channel converter, 4 ADC’s

• 1998 Nebus & al.: VNA test set + receiver with loadpull and pulsed capability

• 2003 Maury Microwave, Inc.: commercial introduction (LSNA)

(19)

Architecture of the LSNA prototype

TUNER

Attenuators

...

10MHz A-to-D

Computer

RF-IF converter

RF bandwidth: 600MHz - 50GHz

max RF power: 10 Watt

IF bandwidth: 8 MHz

Needs periodic modulation

(4 kHz typical)

(20)

20 RF-IF converter: Simplified Schematic

LP

1

2

3

4

1

2

3

4 RF (50 GHz)

IF (4 MHz)

f

_LO

(20 MHz)

(21)

Harmonic Sampling - Signal Class: CW

Freq. (GHz)

1

2

3 50 f

_LO

_{100 f}

_LO

_{150 f}

_LO

Freq. (MHz)

1

2

3 RF

IF

f

_LO

=19.98 MHz = (1GHz-1MHz)/50

(22)

22 • Introduction

• Signal Representations

• Instrumentation Hardware

• Calibration Aspects

(23)

Calibration: Historical Overview

• 1988 VNA-like characterization of the test-set

power calibration with a power meter

assumption of an ideal-phase receiver

• 1989 phase calibration by the “golden diode” approach (Urs Lott)

• 1994 harmonic phase calibration with a characterized SRD, traceable to

a

nose-to-nose calibrated sampling oscilloscope (Verspecht)

• 2000 IF calibration (Verspecht)

• 2000 NIST investigates “phase reference generator” approach (DeGroot)

• 2001 calibrated electro-optical sampling (D.F. Williams, P. Hale @ NIST)

(24)

24 Raw Quantities versus DUT Quantities

TUNER

Attenuators

...

10MHz A-to-D

RF-IF converter

1 D hm

a

1 D hm

b

2 D hm

a

2 D hm

b

DUT quantities

Raw quantities

1 R hm

a

R1 hm

b

Computer

2 R hm

a

R2 hm

b

(25)

The Error Model

























=













2

4

2

3

1

2

1

2

1

0

1 R

hm

R

hm

R

hm

R

hm

h

j

h

D

hm

D

hm

D

hm

D

hm

b

C

a

C

b

C

a

C

e

K

b

a

b

a

h

η

γ

φ

ε

δ

χ

β

ϕ

RF amplitude error

RF phase error

RF relative error

IF error

Raw quantities

DUT quantities

(26)

26 RF Calibration

1. Coaxial SOLT calibration

On wafer LRRM calibration

2. HF amplitude calibration with power meter

3. HF harmonic phase calibration with a SRD diode

(characterized by a nose-to-nose calibrated sampling

oscilloscope)

OR

Combined with

(27)

Coaxial Amplitude and Phase Calibration

Amplitude

(28)

28 On Wafer Amplitude & Phase Calibration

Coaxial LOS

LRRM

(29)

Calibration Traceability

Relative Cal

_{Power Cal}

National Standards (NIST)

Precision Airline

Calorimetry

Harmonic Phase

Nose-to-Nose Standard

(30)

30 Characterization of the

Harmonic Phase Reference Generator

Sampling oscilloscope

Harmonic Phase

Reference generator

(31)

Sampling Oscilloscope Characterization:

Nose-to-Nose Calibration Procedure

(32)

32 Nose-to-Nose Measurement

(33)

3 Oscilloscopes are Needed

1

2

1

3

2

(34)

34 Electro-Optic Sampling*

(D. Williams et al., NIST)

* The schematic that is shown is “U.S. Government work not subject to copyright.”

D.F. Williams, P.D. Hale, T.S. Clement, and J.M. Morgan, "Calibrating electro-optic sampling systems,“

(35)

• Part I

– Introduction

– Instrumentation and Calibration

• Break

– Coffee and Cookies

• Part II

– Applications

– Conclusions

(36)

36 • Part I

– Introduction

– Instrumentation and Calibration

• Break

– Coffee and Cookies

• Part II

– Applications

– Conclusions

(37)

• Waveform Measurements

• Physical Models

• State-Space Models

• Scattering Functions

• Conclusions

Part II - Outline

(38)

38 Breakdown Current

Time (ns)

(transistor provided by David Root, Agilent Technologies - MWTC)

(39)

Forward Gate Current

(40)

40 Resistive Mixer Schematic

HEMT transistor

(no drain bias applied)

(transistor provided by Dominique Schreurs, IMEC & KUL-TELEMIC)

(41)

(42)

42 High-Speed Digital Signal Integrity

Calibrated Eye Measurement On Wafer (@10GB/sec)

Oscilloscope Data

Agilent Technologies, Inc. – Used with Permission

(43)

Loadpull and Waveform Engineering

MesFET Class F

Z(f

₀

)=130+j73

Ω

Z(2f

₀

)=1-j2.8

Ω

Z(3f

₀

)=20-j97

Ω

PAE=84%

PAE

≈

50%

Data courtesy of IRCOM / Limoges (France)

HARMONIC TUNER

LSNA

(44)

44 • Waveform Measurements

• Physical Models

• State-Space Models

• Scattering Functions

• Conclusions

Part II - Outline

(45)

Physical Models

• Represent transistor behavior

• Use electrical circuit schematics

• Contain linear and nonlinear elements such as

current sources, capacitors, resistors

(46)

46 Physical Model Improvement

generators apply waveforms measured by an LSNA

“Swept power measurements under mismatched conditions”

Chalmers model to optimize

GaAs pseudomorphic HEMT

gate l=0.2 um w=100 um

Parameter Boundaries

(courtesy of Dr. Dominique Schreurs, IMEC & KUL-TELEMIC)

(47)

Before OPTIMIZATION

Time domain waveforms

Frequency domain

gate

drain

voltage

current

gate

drain

Voltage - Current State Space

(48)

48 After OPTIMIZATION

Time domain waveforms

Frequency domain

gate

drain

voltage

current

gate

drain

Voltage - Current State Space

Verification of the Optimized Model

(49)

• Waveform Measurements

• Physical Models

• State-Space Models

• Scattering Functions

• Conclusions

Part II - Outline

(50)

50 State Space Function Model

Fit with e.g. artificial neural network or spline

(David Root, John Wood, Dominique Schreurs)

...)

,

(

...)

,

(

1

2

1

2

1

2

1

2

1

2

1

1 dt

dI

dt

dV

dt

dV

V

F

I

dt

dI

dt

dV

dt

dV

V

F

I

=

(51)

Experiment Design:

Crucial to Explore Component Behavior

1 V

1 I

2 V

2 I

4.2 GHz

4.8 GHz

(52)

52 State Space Coverage through

Proper Experiment Design

(53)

• Waveform Measurements

• Physical Models

• State-Space Models

• Scattering Functions

• Conclusions

Part II - Outline

(54)

54 When to use Scattering Functions?

Scattering functions are

• Black-box frequency domain models,

• Directly derived from large-signal measurements.

Scattering functions are used

• With new less understood technology

• When there is a difficult de-embedding problem

• When there are multiple transistors in the circuit

• When the component has distributed characteristics

(55)

Theoretical Concepts

Scattering

Functions

for

Nonlinear

Behavioral Modeling

in the

Frequency

Domain

Quantities are Waves

Functional

Relationship

Input and Output are

Discrete Tone Signals

(56)

56 Quantities are Traveling Voltage Waves

( )

_













−

+

=













→













2

2 ZI

V

ZI

V

B

A

I

V

Z

Default value of Z = 50 Ohm (classic S-parameters)

(57)

Scattering Functions Describe:

• Compression characteristic

• Spectral regrowth

• AM-PM

• PAE

• Harmonic Distortion

• Fundamental loadpull behavior

• Harmonic loadpull behavior

• Time domain voltage & current

(58)

58 Notation - Graphical Illustration

k

A

₁

k

B

₁

k

A

₂

k

B

₂

,...)

,

,...,

,

(

₁₁

₁₂

₂₁

₂₂

1

1 F

A

B

_k

=

_k

,...)

,

,...,

,

(

₁₁

₁₂

₂₁

₂₂

2

2 F

A

B

_k

=

_k

(59)

Phase Normalization

• “Phase normalized” quantities are used

• Defines unambiguous phase for harmonics

• Large-signal A

₁₁

is the phase reference

(60)

60 Phase Normalization: Mathematics

• We define a reference phasor:

P

=

e

j

ϕ

(

A

11 )

• We define phase normalized quantities:

k

mk

N

mk

A

P

A

=

−

_B

_mk

N

=

_B

_mk

_P

−

k

• Special case:

A

₁₁

N

=

A

₁₁

(61)

Harmonic Superposition Principle

• In general superposition cannot be used to

describe the functional relationship between the

spectral components

(

A

)

F

(

A

)

F

(

A

)

F

+

′

≠

+

′

• The superposition principle can be used for

relatively small components (e.g. harmonics)

(62)

62 Harmonic Superposition: Illustration

1 A

2 B

(63)

Basic Mathematical Equation

• A

₁₁

assumed to be the only large-signal component

• Superposition assumed to be valid for other A

_nh

• The notation A* means the complex conjugate of A

• S and S’ are called the scattering functions

• Note that S’

_mk11

= 0

*

)

(

)

(

₁₁

N

_nh

N

nh

mknh

N

nh

N

nh

mknh

N

mk

S

A

S

A

B

=

∑

+

∑

′

(64)

64 Applications:

Compression and AM-PM conversion

N

_S

_A

B

₂₁

=

₂₁₁₁

(

₁₁

)

₁₁

11

21

11 2111

(

)

A

B

A

S

=

• Only considering B

₂₁

and A

₁₁

results in

• This can be rewritten as

• S

₂₁₁₁

(|A

₁₁

|) represents the compression and

AM-PM conversion characteristic

(65)

Large-Signal Input Match

N

_S

_A

B

₁₁

=

₁₁₁₁

(

₁₁

)

₁₁

11

11 1111

(

)

A

B

A

S

=

• Only considering B

₁₁

and A

₁₁

results in

• This can be rewritten as

• S

₁₁₁₁

(|A

₁₁

|) represents the large-signal input reflection

coefficient

(66)

66 Hot S

₂₂

*

)

(

)

(

)

(

₁₁

₂₁₂₁

₁₁

₂₁

₂₁₂₁

₁₁

₂₁

2111

21 N

N

_S

_A

_S

_A

_S

_A

B

=

+

′

• Considering B

₂₁

, A

₂₁

and A

₁₁

results in

• Multiplying both sides with P results in

• The combination of S

₂₁₂₁

and S’

₂₁₂₁

are a scientifically

sound format for “Hot S

₂₂

”

*

)

(

)

(

)

(

₁₁

₂₁₂₁

₁₁

₂₁

₂₁₂₁

₁₁

2 ₂₁

2111

21 S

A

S

A

S

A

P

A

B

=

+

′

N

(67)

Measurement Example

-60 -40 -20 0 20 40 -25 -20 -15 -10 -5 0 5 10

Scattering functions

(dB)

|A

₁₁

| (dBm)

S

₂₁₁₁

S’

₂₁₂₁

S

₂₁₂₁

• Note that the amplitude of S’

₂₁₂₁

becomes arbitrary small

for |A

| going to zero

(68)

68 Harmonic Distortion Analysis

• Only considering A

₁₁

and B

_2k

one can calculate the

harmonic distortion as a function of |A

₁₁

|

2

11

11 2311

23

11

11 2211

22

11

11 2111

21 )

(

)

(

)

(

P

A

S

B

P

A

S

B

A

S

B

=

(69)

Harmonic Loadpull Behavior

N

h

N

h

N

h

N

h

k

N

h

N

h

k

N

k

B

A

S

A

S

B

2

11

2

11

2

2 *

)

(

)

(

Γ

=

′

+

=

∑

h

B

₂ h

A

₂

h

Γ

11

A

• Solve the set of equations

(70)

70 New Stability Circles for Multiplier Design

DC

2

2 ω

_ω

₀₀

DC

ω

₀0

ω

₀0

2

2 ω

_ω

₀₀ 0 1. 0 1. 0 -1 . 0 10 .0 10 . 0 -1 0. 0 5. 0 5.0 -5 .0 2. 0 2. 0 -2 . 0 3. 0 3.0 -3. 0 4. 0 4.0 -4 .0 0. 2 0. 2 -0.2 0. 4 0 .4 -0. 4 0. 6 0 . 6 -0 .6 0. 8 0 . 8 -0 .8 stability_circle Swp Max 2GHz Swp Min 2GHz SCIR1 du e _p o rte SCIR2 du e _p o rte S[1 ,1 ] ca ri ch i S[2 ,2 ] ca ri ch i

Stability is not ensured

Research performed by

Prof. Giorgio Leuzzi

(71)

Practical Measurement:

Experiment Design Concept

Im

Re

*

)

(

)

(

)

(

₁₁

₂₁₂₁

₁₁

₂₁

₂₁₂₁

₁₁

₂₁

2111

21 N

N

_S

_A

_S

_A

_S

_A

B

=

+

′

• Simple example: S

₂₁₁₁

, S

₂₁₂₁

and S’

₂₁₂₁

Re

Im

• Perform 3 independent experiments

(72)

72 Typical Measurement Setup

TUNER

Large-Signal Network Analyzer

11 A

A

_mk

≠

match

Z

diplexer

in

fundamental

harmonics

(73)

-0.3-0.2-0.1 0 0.1 0.2 0.3 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 -0.6 -0.4 -0.2 0 0 0.2 0.4 0.6 0.8

Measurement Example

Input A

₂₁

(V

_p

)

Output B

₂₁

(V

_p

)

Im

Re

(74)

74 Link to Harmonic Balance Simulators

(75)

Simulated

Model

versus

Measurements

Power Transistor Waveforms

Gate

Voltage

Gate

Current

Drain

Voltage

Drain

Current

(76)

76 Scattering Functions with Modulation

1.9 GHz RFIC (CDMA)

Incident signal (a1)

Transmitted signal (b2)

(

Volt

)

(

Volt

)

(77)

--- fund

--- 2nd harm

--- 3rd harm

Input power (dBm)

Output power

(dBm)

Dynamic Harmonic Distortion:

Transmitted Signal

(78)

78 Dynamic Harmonic Distortion:

Reflected Signal

Output power

(dBm)

Input power (dBm)

--- fund

--- 2nd harm

(79)

Emulate CDMA Statistics using many

Periodic Pseudo-Random Sequences

Frequency Offset from Carrier (Hz)

Amplitude

(dBm)

(80)

80 Apply Fitting Technique

• For our example we use a piece wise polynomial

(3rd order)

)

(

11

V

a

11

(

V

)

(

V

(

V

)

21 I

Q

21

(81)

Model Verification - Spectral Regrowth

---model

Frequency Offset from Carrier (MHz)

Amplitude

(dBm)

(82)

82 • Waveform Measurements

• Physical Models

• State-Space Models

• Black-Box Frequency Domain Models

• Conclusions

(83)

Conclusions

• The dream of accurate and complete large-signal

characterization of components under realistic

operating conditions is made real

• The only limit to the scope of applications is the

imagination of the R&D people who have access to

this measurement capability

(84)

84 “Jan Verspecht bvba” Coordinates

• URL: http://www.janverspecht.com

• email: [email protected]

• fax: 32-52-31.27.85

• phone: 32-479-85.59.39

• address:

Jan Verspecht bvba

Gertrudeveld 15

B-1840 Londerzeel

Belgium

(85)

(86)

86