Elf: computer automation and error correction for a microwave network analyzer - Instrumentation and Measurement, IEEE Transactions on

IEEE

TRANSACTIONS

ON

INSTRUMENTATION

AND

MEASUREMENT,

VOL.

31,

NO.

I,

MARCH

1988

95

Elf

Computer

Automation and

Error Correction

for

a

Microwave

Network

Analyzer

A6straet-A

microwave measurement system has been developed

which

combines a

personal

computer (PC) and

a conventional vector

network

analyzer

to yield

a full

complex-error-corrected automatic

network

analyzer.

The system

consists

of

a Hewlett-Packard HP

8410C

network

analyzer,

an

HP

8350B sweep

oscillator,

and an

IBM

PC.

A

3000-line

computer program,

called Elf,

runs

on

the

PC

performing

calibration

and measurement algorithms

and

providing a

flexible,

menu-oriented

user interface.

The

system,

when

calibrated, achieves

a worst-case

measurement error

vector

of

magnitude

5

0.02

for trans-

mission and

reflection coefficient

measurements over

the

2-

to

12.4-

GHz

frequency range and has

a measurement speed

of

three

frequency

points/s.

Elf

provides

an

inexpensive

method

for

upgrading

the

HP

8410

to achieve

the

high accuracy

of

an

automatic network

analyzer.

I.

INTRODUCTION

MICROWAVE VECTOR

network analyzer mea-

A

sures

the

complex scattering parameters

of

a micro-

wave

device

or

circuit.

These

S-parameters,

which

relate

incident and reflected travelling voltage waves

at the ports

of

the

device under

test, are the set

of

network parameters

most commonly used

for

the design

of

linear

circuits at

microwave frequencies.

Fig.

1 shows

one

configuration

in

which a vector voltmeter and reflection-transmission

test set

are

combined to yield a network analyzer. Direc-

tional couplers in the test set sample the incident and

re-

flected signals at

one

port,

and the transmitted signal

is

detected at the

other

test port.

A

coaxial relay selects

which

signal is presented to the vector voltmeter

for

com-

plex ratio measurement.

To

perform a full S-parameter

measurement,

the

device under test must be

flipped

end

for

end once during the measurement, to observe

the

re-

flection

at

both its ports, and the transmission through it

in

both directions.

With this configuration, the quantities

the

vector volt-

meter measurements will be the true S-parameters only to

the extent that certain rather stringent requirements

are

met.

The

two directional couplers must be identical and

have

very

high directivity.

The

two test ports

of

the

sys-

tem

must present

the

characteristic impedance desired

for

the measurement (usually

50

Q),

and the frequency

re-

sponses of

the

signal paths

for the

incident, reflected, and

Manuscript

received

May

14,

1987; revised July

27,

1987.

This work

was

supported

in

part

by

Caltech's

Program

in

Advanced Technology,

the

National Science

Foundation, and

the

Fannie and John

Hertz Foundation.

The

authors

are

with

the

Division

of

Engineering and Applied

Science

at the California Institute

of Technology, Pasadena, CA

91

125.

IEEE

log

number 8717646.

-1

I

1

I-

RefleCtKn-

1

trammnson

I

test

unit

Reflect

ion

Transmission

test

port

lsdaiion

pad

Device

under

iesi

Fig.

1.

A

vector voltmeter

with

a reflection-transmission test set

can be

used

to

measure

the S-parameters

of an unknown network. The

system-

atic

errors

of such

a network

analyzer

can be found through

calibration,

and

measurement

errors

removed

in

closed

form

when

certain conditions

are

met.

transmitted signals must matched in amplitude and phase.

Meeting all these criteria

over

a

broad microwave fre-

quency band is difficult,

but

happily with the advent

of

inexpensive desktop computers,

it is no

longer

necessary;

the large errors which can result from imperfections in the

reflection-transmission test set

are

systematic and can

be

calibrated out

by

measuring a few

known

standards.

Use of a computer to correct

linear

systematic errors

in

a network analyzer is the basis of such advanced instru-

ments as

the

Hewlett-Packard

HP

85

10

network analyzer.

Our group

at Caltech possesses a less expensive

HP

8410C

network

analyzer,

and has a need to make accurate net-

work

measurements. It was found that

by

incorporating

an

IBM

PC

with

this

analyzer,

many

of the features of the

advanced analyzers could be realized at greatly reduced

cost.

Elf,

a 3000-line Pascal program, was written to per-

form

the tasks necessary

for

calibration, measurement,

and display of the

data.

11.

THEORY

It has

been previously shown

[1]-[3]

that

for

a network

analyzer

of

the

type shown in

Fig.

1,

only

three complex

constants

are

required to completely characterize the sys-

tematic errors which arise

in

making reflection measure-

ments at a given frequency.

This

result is general. That

0018-9456/88/0300-0095$01

.OO

O

1988

IEEE

96

IEEE

TRANSACTIONS

ON

INSTRUMENTATION

AND

MEASUREMENT.

VOL.

31.

NO.

I.

MARCH

1988

Vector

voltmeter

Fig.

2.

A

reflectometer

consisting

of

an arbitrary

linear

four-port network

and a

vector voltmeter.

The

systematic errors

of

such an instrument

at

a

given frequency

are

completely characterized

by

three

complex num-

bers.

is,

it holds

for

the reflectometer of

Fig.

2,

where

M

is an

arbitrary linear four-port,

and

the vector voltmeter

has an

offset and

a

frequency response term

such that its output

reading,

Sil

is given

by

Sil

=

Co

+

CI(b4/b3)

where

C,

and

CI

are

complex constants.

For

this reflectometer, the

relation between

the observed

reflection coefficient,

Si,, 

and

the actual value

SII

at

a given

frequency

is given

by

The three complex constants,

A,

B,

and

C,

of this

bilinear

transform

can

be

determined

by

measuring three

known

impedance

standards.

When measuring an

unknown,

then,

the transform can be inverted to yield

the actual value

of

SI1, 

given

Sil.

The

fact that

the

two

are

a bilinear

transform

allows

the

introduction of

a simple error

model which is

used in many

discussions

of

reflectometers. Making

a

measurement with

a reflectometer of

the type

shown in

Fig.

2

is equivalent

to

making

a measurement with

an

ideal

reflectometer with

a linear

“error

two-port’’

placed be-

tween

the

reflectometer’s test port

and the impedance

to

be

measured.

The situation

is

a bit more

complicated

when

an

un-

known two-port

device

is to be

measured. Transmission

as well

as

reflection must

be

measured.

The

two

measure-

ment configurations required

are

shown

in

Fig.

3.

These

correspond to

the

two switch

positions in

the

measure-

ment system of

Fig.

1.

The

reflection measurement

of

Fig.

3(a) is the same

as

above except

that

here

we

measure

the

input reflection coefficient of

the two-port

with its second

port terminated in

rL,

the

impedance

of

the

transmission

test

port.

When performing

the

transmission measure-

ment,

port

2

of

the device under

test is

connected

directly

to

one

port of the

vector voltmeter, as

shown

in

Fig.

3(b),

so

the

meter

measures

b5/b3.

voltmeter

I

Vector

t

s,:=

co+c,($)

17-1 

(b)

Fig.

3.

The two

measurement

systems corresponding

to

the

two

switch

positions

in

Fig.

1.

The systematic errors

of

this

S-parameter measuring

system are characterized

by

six complex

constants

when the

criteria

out-

lined

in

the text

are met.

These

two measurements

give

two nonlinear

equations

in

the four S-parameters

of

the

unknown

device. Flipping

the network end

for end

and repeating

these

two measure-

ments yields

a total of

four equations

in

the four

unknown

S-parameters. These four

nonlinear

equations cannot,

in

general,

be

solved in

closed

fomi

[2].

The closed-form

solution which

is

commonly known

as

the

12

term

error

model

for

S-parameter measurements

is only valid

if cer-

tain conditions

are

met

by

the measurement

system. These

conditions

are

that

the impedance

seen

by

the four-port

network

M

looking

out port

4,

and the

impedance

rL

seen

by

the unknown

two-port,

do

not

change

when

the

mea-

surement system is

switched

from transmission

to

reflec-

tion

measurement.

If these impedances

are

switch-depen-

dent,

then

the equations

for

the S-parameters must be

solved

iteratively.

To

avoid this switch

dependence, the hardware

of

com-

mercial reflection-transmission test

sets

is

engineered

to

isolate

the detector switch

from

the

RF

measurement ports

of

the

analyzer. Attenuators

are

placed between

the

four-

port network

(M)

and

the vector voltmeter,

and between

port

2

of

the

device

under test and the transmission return

port. Also, the

input port of the

vector

voltmeter

is

matched to the line as well

as

possible, and switches which

terminate unselected lines

in

50Q

are

used.

Assuming this

isolation,

the

true

S-parameters can be written in terms

of

the observed

(primed)

values

as

(2)

(3)

E,(A

-

CS;,)

(ss;,

-

1)

-

rL(m

-

c)’

(s;,

-

D)

(si

-

D)

E~(ss;, 

-

1)

(ss;,

-

1)

-

r;(AB

-

c)’

(s;,

-

D)

(sil

-

D)

SI1

=

E(AB

-

c)(s;,

-

D)[(ss;, 

-

1)

-

rL(A

-

cs;,)]

E~(ss;, 

-

~)(Bs;,

-

1)

-

rZ(m

-

c)’(s;,

-

si,

-

r)

SI2

=

21

-

WILLIAMS

et

ai.

:

ELF

91

(4)

(5)

E(AB

-

c)(s;, 

-

D)[(Bs;,

-

1)

-

rL(A

-

CS;,)] 

E~(Bs;,

-

~)(Bs;,

-

1)

-

r;(AB

-

C)~(S;,

-

D)(s;,

-

D)

E~(A

-

CS;,)(BS;,

-

1)

-

rL(m

-

C)’(S;~

-

D)(s;,

-

D)

E~(Bs;,

-

~)(Bs;,

-

1)

-

r;

(AB

-

C)’(S;,

-

D)(s;,

-

D)‘ 

SZI

=

s22

=

Thus we see

that only

six complex constants,

A,

B,

C,

D,

E,

and

rL

are

required

to

model

the linear systematic er-

IV. SOFTWARE

DESCRIPTION

rors of

the

reflection-transmission

measurement.

In addition

to

the assumption

of

switch-independence,

another assumption

must

be

made

to

arrive

at the

result

above.

It

is

assumed that

the

only

coupling between the

reflection

and transmission test

ports

is

through

the

net-

work

under

test:

there

are

no

RF

leakage

paths

(the “leak-

age path”

which

give

rise

to the

D

term

above is

in fact

just

the

offset

term

in

the

vector voltmeter’s response).

The

assumption

of

no

RF

leakage is

good in most

sys-

tems,

since coaxial relays,

which

have

very high

isola-

tion,

are

typically used

to

switch

the

signal

paths.

If

sig-

nificant

leakage

paths

do exist, the

expressions above

become considerably

more complex. More constants and

cross terms

of

the

S-parameters

are

involved,

and inver-

sion in

closed

form

is impossible.

111.

HARDWARE

DESCRIPTION

Fig. 4 shows a block diagram

of

the hardware

of

the

Elf measurement

system.

The

computer communicates

with

the

rest of

the

system

through

two

interface

cards,

a

general-purpose

A/D-and-D/A

card

[4]

and

an IEEE-488

bus

interface card

[5]. 

In the

configuration

shown, the

IEEE-488 card is

used

to

set the frequency

of

the sweep

oscillator, and

the

A/D

card reads

the

value

of

the

net-

work

analyzer measurement from

the

horizontal

and

ver-

tical

outputs

of

the

HP

8414A

polar display

which

is used

with

the analyzer.

The

reflection-transmission

test unit was a Hewlett-

Packard

HP

8743B, which features 7-mm

precision

con-

nectors and

couplers operating from 2

to

12.4

GHz.

Any

reflection-transmission

test

unit with

7-mm connectors

could be substituted

for

this unit.

When the system was

initially

constructed,

an

IEEE-

488

compatible sweeper was

not

available,

so

there is an-

other system

configuration

option which uses

any

fre-

quency-proportional-to-voltage

microwave source.

In

this

configuration, a voltage from the computer’s

D/A

board

is

used

to

set

the sweeper

frequency, assuming that this

frequency

is

to

voltage.

The

frequencies

at

the ends

of

the

sweep

are

measured

by

an IEEE-488

compatible microwave counter

(HP

5350A)

to

determine

the constants of the linear relation between voltage and

frequency.

Fig.

5

shows a

photograph

of

the measurement

system.

At

the

top

of

the

instrument

rack

is the

HP

5250A micro-

wave counter.

Below it

is the

HP

8410C

with

the

HP

8414A

polar display.

HP

8350B sweeper

with

HP

83592A

RF

plug-in,

which has

a frequency range

of

0.01

to

20

GHz.

At

bottom

is

an

HP

8743B

reflection-

transmission

test

set.

Elf is written in

Pascal,

using

the

Turbo Pascal

[6]

com-

piler.

It

uses the 8087 numeric coprocessor

in

the

IBM

PC

to

increase calculation speed. As

noted

above,

Elf

is

a menu-oriented

program.

Fig.

6 shows

the

hierarchy of

Elf‘s menus. At

start-up, the

main menu

is displayed.

Four

options

on

the main

menu

select immediate actions

to

be performed

and

the

remaining

four select

sub-menus

from

which

additional options can

be

selected.

The

first

half

of

the

main menu

controls the interactions

of Elf with

the hardware, dealing

with

mode selection, calibration,

and

measurement.

The

second

half

is concerned

with ma-

nipulation, storage, and display

of

the

data

after

measure-

ment. Elf

does

not

have a continuous

measurement

mode.

After each

swept-frequency

measurement

is

made,

the

data

are error-corrected and stored, and

may

then

be

saved

or

displayed in

a number of formats.

A.

Mode

Selection,

Calibration,

and Measurement

The

main menu

display shows the following:

MAIN

MENU

1.

Select number of frequency points.

2.

Select operating mode.

3.

Select frequency range.

4.

Calibrate analyzer.

5.

Make Measurement.

6.

Save data

to disk.

7.

Line stretcher.

8.

Print

data.

9.

Exit.

From this starting point, the system

can

be

calibrated

by

going

through

the

first

four

menu

items in sequence.

Then,

measurements

may

be

made

using item

5,

and the

measured

data manipulated and displayed

by

the remain-

der

of

the menu

items. Once calibrated,

the

system

may

be used

for

as

many

measurements over the calibrated

range as desired.

First, the

number

of

measurement

points

is selected.

Calibration and measurement

will

be

performed

at

this

number

of frequency

points

evenly spaced

between

the

start

and

stop frequencies selected below.

Next,

the operating mode

must

be

selected.

Selecting

‘2’

will result

in a sub-menu

which

allows the user

to se-

lect

between reflection

measurement

and

full s-parameter

measurement

modes,

with

the

option of sliding

load cal-

ibration

in

either

mode.

The choice

between reflection and full

S-parameter

measurements is offered

since a

full

S-parameter calibra-

tion and

measurement is

unnecessarily

time

consuming

98

IEEE

TRANSACTIONS

ON

INSTRUMENTATION

AND

MEASUREMENT,

VOL.

37,

NO.

I.

MARCH

1988

Operating

Frequency

S

-Parameter

range

select

menu

‘rf

Line

stretcher

menu

HP

87438

Reflection -tronsmtssm

HP8350B

test unit

sweeper

HP

8410C 

Fig.

6.

Elf‘s

menu

tree.

I

BM

Personal computer

the main

menu,

‘3’

is entered

to

select the frequency range

Fig.

4.

A

block diagram

of

the

Elf

system. The computer

controls the mea-

surement

by

setting the

sweeper

frequency and instructing the

user

to

throw switches on

the

reflection-transmission test unit.

Of

the

measurement-

The

sub-menu

FREQUENCY RANGE SELECTION MENU

Sweeper

Frequency Range

1.

HP

8620C

2.

HP

694C

3.

HP

8350B

6.

Exit

4.

Measure full range

5.

Select frequency sub-range

‘-i

Rectangular

parameter

menu

Fig.

5.

The

Elf

system

as

implemented at

Caltech,

using an

HP

8350B

sweeper with

HP

83592A

rfplug-in,

an

HP

8410C

network analyzer

with

HP

8414A

display

unit

and

HP

841

1A

harmonic frequency

converter,

and

an

HP

8743B

reflection-transmission test unit.

The

IBM

personal

computer is

shown with the

EGA

display.

when

one

only wishes

to

measure a

reflection coefficient.

The

sliding

load

calibration option is

offered

for better

accuracy

in

high-frequency

measurements. Imperfections

in

the

precision

50-Q

load

used

as

one

of

the calibration

standards become more

significant with increasing

fre-

quency, causing errors in the determination

of

the zero-

reflection

point. The locus

of

reflection coefficients of

a

sliding load

as it

moves

is a small circle

about

the zero-

reflection

point,

so

the

point

can

be

determined even

in

the presence

of imperfections

in

the

load. The

effect is to

calibrate

to

the characteristic impedance

of

the line the

load

is sliding

in,

and not

to

the

load

itself.

Having selected

the

measurement

mode and

returned to

The

first two

choices

were

non-IEEE-488 sweepers

which

were

modified

to

be

voltage controlled sources.

Choice three

is the

IEEE-488

controlled

sweeper. Choice

four

is used with

the voltage-controlled sweepers:

it uses

the

counter

to

measure the extremes

of

the

frequency

sweep of

the source. Selection

five can then

be

used to

choose a sub-range

of

the

frequency

sweep

of the

source.

When

the

IEEE-488

controlled sweeper is

used,

only

step

five

is needed to

select the frequency sweep range. Choice

six returns to

the

main

menu.

With the

operating mode,

frequency

range,

and number

of

points

selected, the analyzer

is ready

for calibration.

The

question of

choice

of calibration standards then

arises.

Due

to small nonlinearities which

are

not calibrated out

by

the procedure described

in Section

11,

the

network

ana-

lyzer tends

to

be most

accurate

when measuring reflection

and transmission coefficients

close

to

those

of

the calibra-

tion

standards

used.

Since the

only requirements

for

cal-

ibration

is three (or six)

known

standards, the standards

can be chosen

to

be

close

to

the

expected measurement

values

for

maximum

accuracy.

For

example,

when mea-

suring

a high

impedance device

at

the end

of

a transmis-

sion

line,

one

might

choose an open circuit

on

the

same

length of

line

as

one

of

the calibration standards.

In

Elf,

a default general-purpose set

of

standards

is programmed

in.

To

choose another

set of

standards, a

mathematical

model

of

the new

standards as a

function

of

frequency

WILLIAMS

et

a!.

:

ELF

99

must be

entered. This involves changing a

few

lines

of

Elf's

Pascal source

code,

and recompiling it.

The

default

set of

standards is a short

circuit,

an open circuit, a

matched

load, and a straight through (the

matched load

and

straight

though

are

measured in

both reflection

and

transmission

to

give

the total

of six

standards).

The

matched load

can

be

either

fixed

or

sliding,

as

noted

above.

The

short circuit and open circuit

models

assume

that

a Wiltron

model

22A50 7-mm precision

open/short

is used.

This

standard

has

a shielded open circuit

on

one

end and a delayed short circuit

on the

other.

The

short

circuit is

0.050

in from the connector reference plane,

and

is modeled

as

this

length of

transmission

line

terminated

in

a perfect

short circuit.

The

shielded open is

modeled

as

a frequency-dependent capacitance.

The

model used is

from

[3],

C

=

0.079

+

4

x

10-5f2

where

C

is the ca-

pacitance

in picofarad's,

andfis

the

frequency in gigahertz.

When

the calibration option is selected from the

main

menu, a series of messages

appear on

the screen guiding

the

operator

through the calibration procedure. At any

step

the procedure

may

be

aborted,

or

the

previous step

may

be

repeated. Similarly,

when

option five, 'Make

measure-

ment' is selected a series

of

messages guide the operator

through

the

measurement procedure.

B.

Manipulation, Storage

and

Display

By

stepping through

the

first five

main

menu

items,

the

analyzer is calibrated and a measurement performed.

The

remaining menu

items allow

the

measurement data

to be

manipulated in

a limited

way,

stored

on disk,

and

dis-

played

in several formats.

Entering

menu

item seven

calls

up

the

software line

stretcher. This allows the user

to

apply a phase shift, lin-

ear

with

frequency,

to

the measured phase

data,

thus ef-

fectively

shifting

the

position of

the reference plane from

that

at

which

the

analyzer

was

calibrated. This

is

often

convenient

when

the

device under test is

unavoidably

sep-

arated

from

the

calibrated reference plane

by

a length of

504

line.

From the line stretcher menu,

the

user

can

enter

a length of

line

to

move the reference plane,

or

Elf

can

perform

a least squares linear

fit

of

the phase data

to

arrive

at

an

estimate

of

the line

stretch value.

Item

six

on

the main

menu

allows

the

user

to

store all

measured

and line-stretched

data,

as

well

as

all calibration

constants,

in

a disk

file.

The

data

are

dumped

into

an

ASCII text

file, organized in columns

with

appropriate

headings.

There

is

no

provision

for

reading

data

or

cali-

bration

constants back in from disk

files.

Finally, item eight

on

the main

menu

allows the user

to

display

the

measured

or

line-stretched

data, either

as

a

table

or

on

a Smith chart

or

rectangular

plot.

One

quantity

may

be plotted

at

a time

and

the

user

may

choose a

mag-

nitude,

phase,

or

decibel plot

for

the

rectangular

plot,

with

any

scale desired.

There are

two versions of Elf.

One

sup-

ports

the

IBM

Color

Graphics Adapter (CGA), giving a

640

X

200

pixel

single color graphics plot.

The other

sup-

ports

the

IBM

Enhanced Graphics Adapter

(EGA),

giving

a

640

x

350

pixel

two-color

plot.

In

either case, hard

OW

t

Q03

/-

/I

am

OD2

001

2

a

6D

8.0

100

120

Frequency.

Gtiz

I

21)

4.0

60

8D

100

126

Fnquency.

OHz

(b)

Fig.

7.

(a)

Measurement

of

S,,

and

(b)

S,,

of

a length

of

precision

coaxial

line.

Worst-case reflection

or

transmission coefficient

error

is estimated

at

k0.005

for frequencies

from

2

to

5

GHz,

kO.01

for

5

to

10

GHz,

and

k0.02

for

10

to

12.4

GHz.

Over

this entire range, performance

is

limited

by

electronic

noise,

not repeatability

of

microwave

connections.

copy of

the

plot

can be

generated

on

a dot

matrix

printer

by

use of a graphics screen

dump.

Elf differs from

the

system

of [3] chiefly in

the

addition

of

the transmission measurement capability. Measure-

ment

speed and accuracy

are

about

the

same. Also,

Elf

adds the software

line

stretcher, and rectangular

plotting

capability.

Elf

does not,

however, provide

for

easy

input

of

calibration models

by

the user

as

does the NRAO sys-

tem.

V.

SAMPLE

MEASUREMENT

Fig.

7

shows

magnitude plots

of

the measured

values

of

SII

and

S2,

for

a 10.35-cm length of

precision

air

coax-

ial

line

(Hewlett-Packard

model

11566A)

over

the fre-

quency

range

of

2 to

12.4

GHz. The

measurements de-

viate

from

the

ideal values

of

zero and unity, respectively,

by

approximately

f0.02

in

magnitude

for the

transmis-

sion measurement

and

f0.05 

for

the

reflection measure-

ment.

The

maximum

phase deviation

is about 2 degrees.

These deviations

result

from imperfections

in

the line

and

its

connectors, and

from

measurement

error.

Imperfec-

tions in

the line can

be

seen

in

the

reflection coefficient

data

as a series

of ripples

spaced

approximately

at

multi-

ples

of 1.45 GHz

which

is the

half-wave resonant

fre-

quency of

a 10.35-cm line. Experiments indicate

that

measurement

error

is generated mainly

by

electronic noise

and not by repeatability

problems

with

the

microwave