VNA Receiver Dynamic Accuracy Specifications and Uncertainties

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Ken Wong

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1

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6


June

25
, 20
10


V
NA
Receiver
Dynamic Accuracy Specifications

and Uncertainties



A
Top Level Overview

Ken Wong


Master Engineer, CTD Santa Rosa


1.0 Introduction

Dynamic accuracy of a vector network
analyzer

(VNA)

receiver may be defined as the linearity of the receiver over its specified
dynamic range
.


It is one of the
sources of uncertainty in
VNA

measurement

systems. Other key
sources of
uncertainty include
calibration uncertainty, connector repe
atability, cable stability a
nd repeatability, system drift and
noise
, as illustrated by figure 1

[1]
.
Cross talk errors are correctable.



Figure 1
: Signal flow graph representation of VNA error corrected measurement error model


The total S
-
parameter measurement
error

can be expressed as
functions of the systematic, random and drift & stability errors.












(1)









Dynamic accuracy is one of

the

systematic error terms:

















2
2
11 mag
2
2
1
11 phase TP1
11
2
2
21 mag
2
2
1
21 phase TP1 TP2
21
TPi
S Systematic Stability Noise
Systematic Stability Noise
S sin 2C
S
S Systematic Stability Noise
Systematic Stability Noise
S sin C C
S
C


   
 
  
   
 
   
 
 
 
 
 
 
 
 
cable phase stability and connector repe
atability at port i



Ken Wong

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10











(2)



Typical modern
network analyzer receiver
s

consist of

functi
onal blocks shown in figure 2.

The sources of signal processing errors
are represented by
the signal flow graph of figure 3.



Figure 2
: Modern VNA Receiver Block Diagram




Figure 3: Error Model


E
N

= Noise;
E
CO

= Compression Error; E
FL

= Filter Linearity Error; E
G

= Gain Setting Error; E
X
= Residua
l Cross Talk Error; E
ADC

=
Residual ADC L
inearity

Error; E
Q

= ADC Residual Quantization Error



These errors may be quantified individually,
in
assembly blocks or in totality.
An analysis of these error sources follows.


2
.0 Sources of Linearity Errors


2.1 Nois
e


Noise level is specified and tested. It is also included in the
uncertainty model.


2
.
2

C
ompression in the conversion chain.

All amplifiers have nonlinear behavior. One way to describe that nonlinear behavior is in terms of compression, the deviation

fr
om
a straight line relationship
between input and output levels. This usually occurs at high level signal input.

T
he
other
compression
mechanism is the mixer.
R
egardless of the source of the nonlinearity,
total

compression is
characterized during product

qualification test. It is also
tested

per specification

in
factory test

and field calibration
. The compression error is accounted for
separately as part of the dynamic accuracy model.

For certain VNA
product lines
, the compression is characterized and
corrected. Then, the characterization error is used instead of the actual compression error.

2
.
3

F
ilter
linearity




2
11 1 11 22 21 12 11 1 11
21 2 21 2 1 11 2 22 1 2 21 12 2
Systematic
Systematic
dynamic accuracy of receiv
er
      
      

a a a a a a
a
i
S S S S S A S
S x S S S S S A
A i
   
   


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Discrete component filters are linear at low power levels. As power level increases, inductors ca
n become nonlinear when its
magnetic core becomes saturated. Another possible cause of filter nonlinearity is cross talk or coupling between inductors.

Either case happens at higher power lev
els where the complete receiver
‘s linearity is measured.

2
.
4

G
ain Setting Error

Amplifier gain switching is designed to compensate for signal path loss variations over frequency. At any given frequency, th
e
gain setting is not change and therefore there is no error associated with gain setting.

2
.5

ADC linearity

an
d Residual Quantization Error
.

The ADC is guaranteed by its manufacturer to have integral linearity errors
within a small amount like a few LSB of an ADC’s
resolution. For example, LSB of a 14 bit ADC is a

part in 2
14
. With
a
14 bit resolution ADC and
pseudo
-
random
noise

dither
signal
of

5.4
%

at 5 sigma

of full scale
,

nonlinearity
is
negligible

[2
]. See Appendix A for details.

3
.0 Specification
Regions

Linearity of a receiver may be
divided into three regions, the compression region, the linear region and the noise+cross talk
region, figure 4
.
Specifications for each region may be treated separately. In the compression region, receiver compression
is
usually specified as 1dB compres
sion, 0.1 dB
compression at some power level
, such as
-
10
dBm
.
Table I shows the compression
specifications of a particular Network Analyzers.
Other network analyzers have different
specifications.

Table I: Compression @8 dBm Test Port Power

500 MHz to
16 GHz

<0.17 dB

16 GHz to 24 GHz

<0.23 dB

24 GHz to 26.5 GHz

<0.29 dB


A model of the receiver’s compression
characteristic is a curved fitted model based on actual measurements of sample instruments during instrument qualification
phase.

Noise floor is also a specified parameter. Table II shows the test port noise floor sp
ecification of the same instrument as Table I.

Figures 1 and 3 and equation 1 show how it is accounted for in measurement uncertainty computations.

T
able II: Test Port Noise Flo
or (dBm)

Description

Specification

Typical

500 MHz to 20 GHz

-
114

-
117

20

GHz to 24 GHz

-
110

-
115


Fig. 4: Regions of receiver linearity

compression

region

Linear region

Noise + xtalk



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24GHz to 26.5 GHz

-
107

-
113


The linear region is where the receiver should provide the best dynamic accuracy. Typically, this region covers the
-
20 dBm to
-
70
dBm input power range.
Figure 5 shows plots of dynamic accuracy sp
ecifications that includes the noise and compression
regions.


Figure 5: Typical Plot of Magnitude Dynamic Accuracy Specification

4
.0 Measurement System, Method and Limitations


4.1 General Method

Typically receiver linearity is measured
by comparing the

receiver’s measure power change to

a known

level of power change. This
define power level change may be established by a precision power sensor,
a precision AC voltmeter
a precision attenuator or a
precision power level
signal generator
.
Linearity, then
, may be defined as:














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?•?Ž?‹?˜?‹
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?¿
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4.2 Noise and Cross Talk Errors

It is
evident from F
igure
1

that the receiver’s
measured power

includes noise

power
.











































Measurements made at signal power levels that
a
re impacted by
noise

power and cross talk power will be highly compromised.

Table III shows the impact of noise power and cross talk power to measured power.



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Table III:

Worst Case Measurement Error Caused by Noise and Cross Talk


noise power

( dBm)

-
110




cross talk power

(dBm)

-
130




IFBW

10 Hz

1K Hz

signal (dBm)

rms

peak

rms

peak

-
50

0.000004

0.000006

0.000043

0.000061

-
60

0.000044

0.000061

0.000435

0.000609

-
70

0.000439

0.000614

0.004345

0.006082

-
80

0.004384

0.006137

0.043257

0.060440

-
90

0.043644

0.060979

0.414322

0.569582

-
100

0.417873

0.574379

3.012471

3.804645

-
110

3.031961

3.827373

10.417873

11.764964

-
120

10.453230

11.801259

20.047512

21.496501

-
130

20.086002

21.535100

30.008677

31.468719


Since cross talk level is below
noise, its contribution to measurement uncertainty is less significant. From Table III, it is evident
that at
-
6
0 dBm signal level, noise + cross talk error contributions is about 0.00
0
6 dB peak at 1KHz IFBW
setting. This level of
error is still
acceptable relative to other sour
ces of measurement errors. At
-
7
0 dBm signal level

and smaller
, measurement
variations
are

too
large

to be meaningful

when a linearity error specification of < 0.01 dB is desired
.


Linearity of the receiver at low power le
vels, <
-
70 dBm, depends solely on the linearity of the ADC. Given that a Gaussian
dithering signal is employed to remove ADC linearity errors, no additional linearity testing is required at these low signal
levels.


4.3 Reference Linearity

Linearity of t
he measurement system must be significantly better than the linearity of the receiver. Theoretically, linearity of
thermal couple power sensors should be <0.003 dB over a 10 dB power level change. If performed as expected, it
may

be

used
as

a
linearity

r
eference.
Some of the systematic linearity errors may be quantified and removed.
However, other factors that can
cause linearity

measurement

errors must be quantifi
ed and addressed as well.


4.4 System Drift

Because of the number data points that must
be measured, the test time can be lengthy. Instrument drift, both short term and
long term, is a major consideration.
Measurement system repeatability and reproducibility must be performed to obtain Type
-
A
uncertainties. These studies are test station an
d test method specific.

Appendix
A
:
ADC Linearity Improvement with Dither

The figure below shows the transfer function of an analog
-
to
-
digital converter (ADC) that is worst case in terms of meeting its
vendor specifications while still causing linearity p
roblems: It has a step change of error at the midpoint of the input voltage.

This
is known as quantizing error.

It has been demonstrated in [2], [3], and [4] that by adding a
dithering signal to the input, the ADC’s quantizing error can
be cancelled. For dithering signal of the Gaussian form, the
most natural and least sensitive to dithering level changes
and error
s, the deviation of the averaged transfer
characteristic from a straight line may be express as below for


Ken Wong

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dithering signal with an amplitude standard deviation greater than 0.3 of LSB
:



Without dithering, the quantizing error















(




)


where


= quantization step
, s = signal


With dithering,


̅
̅
̅
̅








(

̅





)

(




́
)

where


́




;





= standard deviation of the

Gaussian
dithering signal.

With a dithering signal at 1.1% of full scale,


̅
̅
̅
̅



, therefore
deviation from a straight line
, exp(
-
2

2
10
4
),

is essentially zero.

At relatively large signal region to the level of dither noise, ADC's integral non
-
linearity (INL) can not be cancelled.


If the ADC has
a manufacturer specification of +/
-
3
-
LSB INL, so in the worst case the error at a full
-
scale input of ADC would be less than




1 / 2^14 * 3 * 2 (bipolar scaling) ~= 370 [ppm] ~= 3 [mdB]


This is negligibly small compared to a typical receiver compression error at large signal region.

Also
this error element would be
tested with receiver compression test.

References:

[1] D. Rytting,
“Network Analyzer Accuracy Overview”, 58
th

ARFTG Conference Digest, Nov. 29, 2001,

[2
] P. Carbone, D. Petri, “Effect of Additive Dither on the Resolution of I
deal Quantizers”, IEEE Transactions on Instrumentation and
Measurement, Vol. 43, No. 3, June 1994 pp.389
-
396

[
3
]
B. Brannon,
“Overcoming Converter Nonlinearities with Dither”, Analog Devices AN
-
410

[4
]
M.F. Wagdy, “Effect of Various Dither Forms on
Quantization Errors of Ideal A/D Converters”, IEEE Transactions on Instrumentation
and Measurement, Vol. 38, No. 4, August 1989, pp 850
-
855

Figure A.1: ADC Quantizing Er
r
or