Middleton W.M. (ed.) Reference Data for Engineers: Radio, Electronics, Computer and Communications
Подождите немного. Документ загружается.
12-12
REFERENCE
DATA
FOR ENGINEERS
63
Circuit
common
of
Low
Current Amplifier
I
PHASE TRACKING
CONTROL
I
00
40
MHr
Fig.
28.
5-Hz
to
13-MHz
bridge.
(From Narimatsu,
Y.,
et
al.
“A
Versatile
LF
Impedance Amlyzer.”
Hewiett-Packard Journal,
September
1981.
0
I981
Hewlett-Packard, used with permission.)
PHASE DETECTORS INTEGRATORS MODULATORS
r
--
..
e.
osc
.B
i
1
c_
C-G
,
I
M-
I
I
CURRENT
DETECTOR
1
’d
I
I
I
-
-
L-R
SUMMING
AMPLIFIER
1
Fig. 29.
Automatic
LCR
meter,
1
MHz.
(From
Maeda,
K.,
et
al.
“An
Automatic, Precision
I
MHz Digital
LCR
Meter.”
Hewlett-Packard Journal,
March
1974.
0
I974
Hewlett-Packard, used with permission.)
MEASUREMENTS AND ANALYSIS
12-13
ELECTRICAL LENGTH
COMPENSATION
REFERENCE
CHANNEL
OUTPUT
INPUT
DIRECTIONAL
BRIDGE
50
$1
BALUN
TRANSFORMER
TEST
CHANNEL
OUTPLJT
POWER
50
if
TEST
SOURCE
1
1OOOMHr
dc
BIAS TEST PORT
Fig.
30. RF
impedance analyzer.
(From Ichino,
T.,
et
al. "Vector Impedance Analysis at
1000
MHz."
Hewlett-Packard
Journal.
Januup
1980.
0
1980
Hewlett-Packard. used with permission.)
electrical balance up to
1000
MHz
and must be magnitude and phase of reflection coefficients, trans-
temperature controlled.
*
mission coefficients, and
S
parameters
of
networks (Fig.
33).
(See Chapter
31
for
a definition
of
S
parameters.)
At microwave frequencies, it is difficult
to
build
perfect structures that have
no
frequency-response,
Impedance
directivity,
or
port-match errors.
It
is widely accepted
practice
to
reduce these errors with a mathematical
For
a 50-ohm coaxial he, calculations are:
(R
+
jX)
=
50
x
(1
+
r)1(1
-
r)
Admittance
(G
+jm
=
0.02
x
(I
-
r)i(i
+
r)
Inductance
L
=
Xi2rf
Capacitance
C
=
BI2rf
Quality factor
Q
=
/Xi/R
error-correction procedure implemented with a com-
puter.
SOURCE
&I
RECEIVER DETECTOR
I
yz;
RECEIVER DETECTOR
1
NETWORK
UNDER TEST
ti
DISPLAY
NETWORK ANALYSIS
Fig.
31.
Block diagram
of
a network analyzer
A
network
analyzer
consists of the five basic blocks
shown
in
Fig.
31.
At low frequencies, voltage and
current can be measured by probes to determine the
Z,
Y.
or
h
parameters (Fig.
32).
Typically, a network
analyzer
is
used
to
characterize small signal parameters.
For
higher frequencies (up through microwave frequen-
cies), network analyzers primarily characterize the
"1
=
21
If1
+
212'2
"z=zPl~l+~2212
I]
=YIIL',
-
>
I2
=
Y2
I
v,
+
YLLL
2
~
*
Ichmo,
T..
et ai. "Vector Impedance Analysis at
1000
MHz."
H-P Journal.
Jan.
1980.
Fig.
32
Z
and
Y
parameters typically used at
low
frequency
12-14
REFERENCE DATA
FOR
ENGINEERS
Fig.
33.
Parameters used at higher frequencies.
Sources
The most common source used for network analysis
is
a sweep oscillator. This provides a real-time frequen-
cy response of the network characteristics. When great-
er frequency accuracy is required, synthesizers are
used. However, the switching times can be long
(10
ms
to 50 ms). These synthesizers provide the best phase
accuracy and repeatability, but at the expense of fast
real-time measurements.
Receivers
There are three common receiver techniques, the
diode detector, homodyne or self-mixing, and the
heterodyne approach (both fundamental and harmonic),
usually with multiple inputs.
Test Sets
The test-set portion provides connection of the
source and receiver
to
the network under test. At low
frequencies, voltage and current probes are sufficient,
but at microwave frequencies, couplers, directional
bridges, power splitters, and slotted lines are required.
IhCIDENT
POWER
SPLITTER
NETWORK
UNDER
TEST
TRANSMITTED
5OURCE
(Ai
With
power
splitter
DIRECTIONAL
UNDER TRANSMITTED
b
SOURCE
INCIDEhT
(E)
With directional coupler.
Fig.
34.
Transmission measurements.
Test configurations are shown
as
follows: for trans-
mission measurements: Fig. 34; for reflection measure-
ments, Fig. 35; for
S
parameters, Fig.
36;
and for
transmission and reflection measurements, Fig.
37.
Displays and Output
The most useful display
is
the digital storage
CRT
system (Fig.
38).
Data can be written into the digital
display at any speed from real time
to
very slow (digital
sweep for example) and then read out at a flicker-free
rate. The display can
also
store traces. and trace math
can be calculated to remove frequency-response errors,
etc. Almost all commercial network analyzers have a
digital
IiO
port to an external controller to provide for
data transfer and operational commands.
NETWORK
TEST
UNDER
zo
"-
INCIDENT REFLECTED
(A)
With
dual
directional coupler
DETECTOR
Z(1
(BJ
With directionol bridge
Fig.
35.
Reflection measurements.
q
lNCIDnT+
SOURCE
TEST
NETWORK
+
Fig.
36.
Measurement of
S
parameters, using directional
couplers with switching.
MEASUREMENTS AND ANALYSIS
12-15
66
INCIDENT REFLECTED
NETWORK
UNDER
3
45
d
c
t
z
i-
phase from the magnitude-only measurements. Step
two is the same as the error-correction procedure for the
four-port network analyzers. There has been some
excellent work done on six-port networks by Glen
Engen and Cletus Hoer of the National Bureau of
Standards.
The approach can be realized
in
all frequency bands
from audio to greater than
100
GHz. Great stability of
Fig.
37.
Transmission and reflection measurements.
the measurement system is required to achieve accurate
results. There are also limitations
in
measuring active
devices where power setting flexibility
is
needed and
when
SzI
does not equal
Sl2.
Typically, data gathering
time is slow but accuracy is very good.
Six-Port Network
A
six-port structure can be used to make magnitude
and phase measurements using magnitude-only detec-
tors such as the diode, thermistor, or bolometer. The
general solution is shown below (refer to Fig.
39).
Error Correction
There are error-correction procedures by which the
linear time invariant errors of the network analyzer can
be characterized and then, by an inverse mathematical
procedure, be removed from the measured data. See
references
1
through
9
(listed at the end
of
this chapter)
for descriptions of these error-correction procedures,
p,
=
(b,I2
=
IA,a
+
B,bI2
i
=
3
to
6
where
A,
and
B,
are functions of the
S
parameters
of
the
six-port network, which can be determined by calibra-
tion. Rearranging yields
Frequency and Time-Domain
Relationships
p,
=
IB,12
)bj21(A,/B,)r
+
112
i
=
3
to
6
The above four equations can be solved for
r,
the
reflection coefficient of the device under test:
where
Cj,
Si,
and
Pi
are functions of
Ai
and
Bj.
Note
that
r
consists of a sum of noncomplex terms.
A
dual six-port structure can be used to measure the
S
parameters of
a
two-port network provided that the
restriction
SI2
=
S21
is applied (Fig.
40).
The mathe-
matical approach of calibrating and measuring with the
six-port structure is divided into two steps. Step one is
the calibration of the six-port structure to determine
TESl
REF
I
I
I
With the advent of the modern computer, measuring
data in the frequency domain and then converting to the
time domain by means of the inverse-Fourier transform
has become practical. This ability
to
observe measure-
ments in the time domain adds additional insight to
microwave measurements. Many times
in
microwave
measurements, circuit discontinuities are separated by
lengths of transmission lines. Taking the Fourier trans-
form of such a circuit allows
us
to isolate the various
impulse responses to the circuit discontinuities (see Fig.
41C).
Also,
by mathematically generating a step stimulus, a
traditional time-domain reflectometer (TDR) display
with high resolution and stability is achieved (see Fig.
I
IO
PORT
--C
AID
MICROPROCESSOR
DISPLAY
MEMORY
swEEp4
IN
SWEEP
AID
I
Fig.
38.
Digital storage
CRT
system.
12-16
REFERENCE
DATA
FOR
ENGINEERS
UNKNOWN
I-
=
o/b
b5
b6
Fig.
39.
Measurements
with
six-port system.
@
SOURCE
LEXIBLE
CABLE
FLEXIBLE
CABLE
Fig. 40.
A
dual
six-port structure used
to
measure
a
two-port
network.
41D).
With the time data isolated, it is possible to filter
out unwanted time-domain responses and then trans-
form back
to
the frequency domain. By means of this
technique, connector discontinuities, launches, and oth-
er unwanted responses can be filtered (or deconvolved)
from the original data (Fig.
42).
This technique can
greatly enhance measurement accuracy.
I--
2cm
50
I1
TL=Tiansmission
Line
(A)
Clrcult.
r
0
d6
-40dB
0
Hr
26
GHz
(E)
Frequency response
0
01
r
0
-0
01
0
crn
15crn
(C)
Impulse time
domain
Large-Signal
Measurements
Devices and amplifiers are often characterized in
other than class-A linear operation.
A
technique called
load-pull is one way to observe the effect of changing
device parameters as a function of load impedance and
delivered power. The load-pull measurement system is
shown in Fig.
43.
The output tuner realizes most
positive real load conditions. The power delivered to the
device and load can be measured by power meters
connected to the coupler side
arms.
The impedance of
the load can be measured with a network analyzer. Fig.
44
shows contours of constant delivered power as a
function of load impedance. These plots can be generat-
ed for the fundamental or the harmonics to give good
insight into the nonlinear behavior. With these data,
Fig.
41.
Frequency
and
time
relationships
MEASUREMENTS AND ANALYSIS
BlAS
TEE
12-17
OUTPUT
TUNER
INPUT
-
TUNER
.
Ocm
15cm
(A)
Time-gated inductor.
Fig,
42.
Time-domain filtering.
AND INPUT POWER
MEASUREMENT
SYSTEM
L
Io
R
-20
-40
0
Hz
(5)
Frequency
response
after
gating
+
900
O!
-
WQ
GHz
OUTPUT IMPEDANCE
AND OUTPUT POWER
MEASUREMENT
SYSTEM
50
!I
Y
POWER
ri
SUPPLY
POWER
SUPPLY
Fig. 43. Large-signal measurement system utilizing load-pull technique.
matching networks can be designed that will optimize
the delivered power under nonlinear operating condi-
tions.
SIGNAL ANALYSIS
Analysis of signals in the frequency domain is an
important technique to determine the characteristics of
audio,
RF,
and microwave signals. While the oscillo-
scope is the basic tool for time-domain analysis, the
spectrum analyzer provides a display of signal ampli-
tude as a function of frequency and is the basic tool for
frequency-domain analysis. The relationship between
the time and frequency domains is illustrated in Fig. 45
for the case of two sine waves. Signal amplitude vs time
and frequency is shown
in
the three-dimensional repre-
sentation of Fig. 45A.
In
the time-domain representa-
tion of Fig.
45B,
the two signal components add at each
instant
of time, producing the composite as would be
viewed
on
an oscilloscope. Fig. 45C is the frequency-
domain view. Each frequency is represented by a
vertical line, with the height representing the amplitude
and the horizontal position representing the frequency.
Although the information about the signal is the same
in
either domain, the frequency domain provides a tool to
observe small but important signal characteristics such
as a small amount of harmonic distortion.
Conceptually, a spectrum analyzer could consist of
a
parallel bank of rectangular bandpass filters each fol-
lowed by an envelope detector as in Fig. 46. The filters
cover adjacent frequency bands and do not overlap. The
detector outputs are sequentially scanned to provide an
amplitude-vs-frequency display on a cathode-ray tube.
The resolution of the spectrum analyzer, that is, its
12-18
REFERENCE DATA FOR
ENGINEERS
Fig.
44.
Contours
of
constant delivered power
vs
load
impedance under large-signal conditions.
ability to resolve closely spaced spectral lines,
is
determined by the width of the filter bandpass. Obvi-
ously, a very large number of filters would be required
to obtain wide frequency spans with narrow resolution.
Practical filters would have long time constants, thereby
requiring a long time for their outputs to reach a
steady-state value.
Another type of spectrum analyzer uses digital sig-
nal-processing techniques. Called a Fourier analyzer or
dynamic signal analyzer, it is shown in Fig.
47.
The
input waveform is sampled, and each sample is digi-
tized. The fast Fourier transform (FFT) is used to
compute the spectrum from the sampled data. This type
of analyzer solves the complexity and response-time
problems of the parallel filter analyzer; however, ADC
and computation speeds limit the input frequency to
about
10
MHz.
The most common form of spectrum analyzer for RF
and microwave frequencies is the swept superhetero-
dyne receiver shown in simplified form in Fig.
48.
A
sweep ramp provides the tuning voltage for a voltage-
tuned oscillator and
is
simultaneously applied to the
horizontal-deflection system of a cathode-ray-tube dis-
play. The local-oscillator frequency is mixed with the
input signal to produce an intermediate frequency (IF).
The IF is detected, filtered, and applied to the vertical-
deflection plates of the CRT. To achieve broad frequen-
cy coverage with a single
local
oscillator, harmonic
mixing is often used
so
that
fs
=
nfL0
+frP
where,
f,
=
signal frequency,
fm
=
local-oscillator frequency,
fiF
=
intermediate frequency,
n=l,2,3
,....
A
4
(A)
Thnedlmmslonal coordlnatw showing
time.
frequency. and
amplitude.
(E)
Vkw
seen
In
the
tlme
doman.
(C)
Mew
seen
In
the
frequmrq
domaln.
Fig.
45.
Relationship between time and frequency domains.
(From Hewlett-Packani Application Note No.
150
on Spectrum
Analysis.
0
Hewlett-Packard,
used
with permission
,)
A tracking preselector filter at the input selects the
desired response.
Amplitude Measurement Range
The range of amplitudes that may be measured on a
spectrum analyzer depends on several factors and is
diagrammed in Fig.
49.
The minimum signal
level
is
limited by the displayed noise that is a function of the
noise figure and the
IF
bandwidth:
N
=
kToB
where,
N=
To
=
k=
F=
B=
displayed noise level, in watts,
absolute temperature, in kelvins,
Boltzmann’s constant,
spectrum-analyzer noise figure,
IF bandwidth.
12-19
II
I
1
Fig.
46.
A
multiple-filter spectrum analyzer.
(From Hewlett-Puckurd Application Note No.
150
on Spectrum Analysis.
0
Hewlett-Packard,
used
with permission.)
For
example,
a
noise factor of 100
(20
dB) and an IF
bandwidth
of
10 kHz give a displayed noise level of 41
X
lo-'' watt
(-
114 dBm).
The maximum signal level is the damage level of the
input circuitry, which is typically
+
13
dBm for an input
mixer and
+30
dBm for an attenuator. Below that level,
the input mixer compresses the input signal, causing an
DISPLAY
FFT
SAMPLER
AND PROCESSOR
INPUT
VOLTAGE-
ADC
-.
Fig.
47.
Block diagram
of
a Fourier analyzer.
INPUT
PRESELECTION
FILTER
VIDEO
IF AMP DETECTOR FILTER
:h
CRT
GENERATOR
VOLTAGE TUNED
OSCILLATOR
:h
CRT
GENERATOR
VOLTAGE TUNED
OSCILLATOR
Fig.
48.
Swept superheterodyne spectrum analyzer.
amplitude inaccuracy. The maximum signal at the input
mixer
for
less than 1 dB of gain compression
is
typically
0
dBm (1 milliwatt).
Distortion products produced within the spectrum
analyzer pose yet another constraint
on
maximum signal
amplitude.
For
a specified spurious level, the signal
level to the mixer must not exceed a given level. The
dynamic range is the ratio of the largest to the smallest
signal amplitudes that can be displayed simultaneously
with
no
internally generated spurious products being
present. Dynamic range depends
on
the display range,
the distortion characteristics, and the noise level.
Signal-Analysis Characteristics
as Determined
by
the IF Filter,
Detector, and Video Amplifier
The input mixer and local oscillator translate the
input frequency to a convenient intermediate frequency.
Typically, several conversions are used to reduce spuri-
ous
responses. The final
IF
filter, detector, video
amplifier, and display-processing circuitry largely deter-
mine the signal-analysis characteristics of a spectrum
analyzer.
The IF-filter bandwidth and shape determine the
frequency resolution
of
the analyzer, assuming the local
oscillators are sufficiently stable. Displayed
CW
signals
have the shape
of
the
IF
filter, as shown in Fig. 50.
To
resolve two equal-amplitude signals, the
IF
3-dB
bandwidth should be less than the signal separation.
Resolving unequal-amplitude signals requires narrower
bandwidths or rectangularly shaped filters. Filters ap-
proximating a rectangular shape, however, have poor
pulse response and limit the scan time. Filters approxi-
mating a Gaussian shape allow the shortest scan times
without introducing amplitude errors due
to
overshoot
12-20
0
dBm
<
-
1dB GAIN COMPRESSION
MAXIMUM INPUT LEVEL
7
-40
dBm
FOR SPECIFIED DISTORTION
I
REFERENCE
DATA
FOR
ENGINEERS
74
dB SPURIOUS FREE1
+
13
dBm DAMAGE LEVEL
1
NOISE LEVEL
‘14
dBm
{lo-kHz BANDWIDTH)
NOISE LEVEL
(10
Hz
BANDWIDTH)
-
144
dBm
Fig.
49.
Typical spectrum-analyzer input signal range.
or ringing. The fastest scan rate for Gaussian-shaped
filters is approximately given by:
R
=
BW2
where,
R
=
maximum scan rate in Hds,
BW
=
3-dB
IF
filter bandwidth.
The detector following the IF amplifier is an envelope
detector that provides a video signal proportional to the
input RF
or
microwave signal. The bandwidth of the
detector should exceed the widest resolution bandwidth
to preserve the fidelity of signal modulation. However,
post-detection low-pass filtering is often useful to
provide signal integration-for example, to recover
low-level signals in the presence of random noise.
While analog spectrum analyzers apply the video
signal directly to the vertical-deflection system of the
Fig.
50.
Displayed
CW
signal
has
shape corresponding
to
IF
filter bandpass.
display, newer instrumentation using digital displays
first performs an
A/D
conversion. Having the video data
in digital form allows further opportunities for signal
processing. Trace-to-trace maximums or minimums can
be stored and displayed.
For
instance, the occupied
spectrum of the FM signal shown in Fig.
51
is easily
determined from the “max hold” trace.
Trace-to-trace signal averaging is possible without the
sweep-time limitation associated with video filtering.
Fig.
52
shows the result of digital averaging
on
a
noise-modulated signal. The signal power distribution
and average frequency are much more apparent.
Digital storage of multiple traces allows arithmetic
operations among traces. Fig. 53 shows how trace
arithmetic is used to correct for amplitude errors in a
measurement system. Trace B may contain measure-
ment-system correction factors, antenna factors, etc.
TIME
AND
FREQUENCY
MEASUREMENT
The measurements of time and frequency were
among the first to be made in a digital form. The world
standard definition of
1
second is the length
of
time it
takes for a cesium 131 atom to “vibrate”
9
192
631
770
times, itself a digital representation. Most simply,
frequency can be measured by counting the number of
phase cycles taking place within a second, again a
digital representation. Frequency may be measured over
any interval
of
time, however, and not just over
1
second.
A
class
of
instruments called counters can be used
to
measure time, frequency, phase, the number
of
events,
or several other parameters. They offer a precise mea-
surement in a relatively short measurement time, afford-
MEASUREMENTS AND ANALYSIS
12-21
(A)
Normal spectrum-analyzer disploy
(E)
Dlgltolly
processed
"max
hold" trace
Fig.
5
1.
Occupied spectrum
of
an
FM
signal.
ing good measurement throughput.
Most of these
measurements are accomplished by first converting the
signal to be measured into a pulse train. This is done by
sending the signal through a buffer amplifier and then a
comparator. Once this is done, the pulse train can be
counted with digital logic. The method of counting
depends on the desired measurement.
Also
found in all
counters is a time base. This is usually a signal, derived
from a calibrated
IO-MHz
quartz crystal, which can
also be counted.
Time
Measurement
To
measure time, the counter simply counts the
number of IO-MHz time-base cycles that take place
during the time to be measured. The quantization of
time is the inverse of
10
MHz, or
100
ns.
The start and
stop signals come from the user's input signal. The
length of a period can be measured by gating the
time-base counter open at the start
of
the period and
closing the gate at the end of the period. (This is shown
in
the shaded portion of Fig.
54.)
A
time interval measurement is the time between two
separate signals. The gate is opened upon receiving a
signal from one input channel, and it is closed upon
receiving a signal from a second input channel. The
basic measurement architecture is the same as for a
(Aj
Normal
truce
(E)
100
digitoily
averaged
truces
Fig.
52.
Noise-modulated
FM
signal.
period measurement, except that there are
now
two
inputs, each with its own comparator, feeding into the
gating logic. Slope switches for both input channels
permit use of the rising or falling edge of a signal to
open or close the gate. Pulse width, rise and fall times,
and relative phase also can be measured.
Resolution extension can be done in several ways.
One way is to use a higher frequency time base.
A
500-MHz time base gives
2-11s
resolution.
If
the signal
is repetitive, a second resolution extension method is
to
average. Time interval averaging
is
accomplished by
accumulating several measurements and taking their
average. Resolution is extended by the square root of the
number
of
measurements averaged.
A
third method
is
called interpolation. This uses interpolation circuitry to
measure the time between the edge of the signal pulse
and the next time-base pulse edge at both the opening
and closing of the gate. Extensions of
10
to
1000
times
the resolution are found. By employing combinations of
these techniques, the resolution can
be
extended
to
better than
1
ps.
Frequency Measurement
Simple counters measure frequency by counting
input pulses during a decade value of time, such as
0.
I,
1,
or
10
seconds. This makes the process of dividing