Data processing: measuring – calibrating – or testing – Calibration or correction system – Sensor or transducer
Reexamination Certificate
2001-02-14
2003-07-15
Barlow, John (Department: 2863)
Data processing: measuring, calibrating, or testing
Calibration or correction system
Sensor or transducer
Reexamination Certificate
active
06594604
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates in general to systems for measuring scattering parameters (“S-parameters”) of an electronic network having wideband input and output signals, and in particular to a system for measuring S-parameters of a non-linear, wideband network.
2. Description of Related Art
S-parameter Modeling
FIG. 1
is a simple block diagram of a two-port active or passive electronic network
10
such as an amplifier or a filter supplying an output signal of current I
2
and voltage V
2
to a load of impedance Z
L
at its output port (P
2
) in response to a sine wave input signal of current I
1
and voltage V
1
supplied to its input port (P
1
) from a signal source
12
. Port P
1
can reflect a portion of that input signal back towards its source
12
depending on the amount of mismatch between the output impedance of signal source
12
and the network's input impedance. The reflected signal's amplitude increases with the impedance mismatch, and when the network's input impedance perfectly matches the signal source's output impedance there will be no reflection at all. Similarly, load impedance Z
L
will reflect some portion of the network's output signal back towards port P
2
depending on how well the network's output impedance matches the load impedance. Amplifier
10
will also feed back some of the reflected load signal to port P
1
, a process known as “reverse gain”.
A circuit designer normally doesn't want any signal reflections because they impede power transfer in the output signal. To reduce reflections, the designer usually tries to design a multi-port network so that its input impedances match the expected output impedances of the circuits that are to supply its input signals, and so that the network's output impedances match the impedances of its anticipated loads. For high frequency applications, designers typically design circuit components so that they each have a standard input/output impedance, usually called “Z
0
”. 50 Ohms is a commonly employed impedance standard for radio frequency circuits.
Thus when designing a network such as an amplifier, a circuit designer wants not only to be able to predict the network's forward gain, but also wants to predict how much of its input and output signals will be reflected when the network is operating in a standard Z
0
impedance environment. The designer will also want to know the network's reverse gain.
Circuit designers often use a scattering parameter (“S-parameter”) model to describe the behavior of a two-port or multi-port network.
FIG. 2
is a conventional S-parameter model of the two-port network
1
of FIG.
1
. The model is called a “scattering parameter” (S-parameter) model because it takes into account signal reflections (scattering) of the network's input and output signals. The S-parameter model represents the incoming and reflected signals at port P
1
by waveform parameters a
1
and b
1
, represents the outgoing signal at port P
2
by a waveform parameter b
2
and represents the signal reflected from the load back toward the port P
2
as a waveform parameter a
2
. The following four relations define the a
1
, b
1
, a
2
and b
2
parameters in terms of the network's input and output voltages and currents:
a
1
=(
V
1
+Z
0
I
1
)/2(
Z
0
)
½
[1]
b
1
=(
V
1
−Z
0
I
1
)/2(
Z
0
)
½
[2]
a
2
=(
V
2
+Z
0
I
2
)/2(
Z
0
)
½
[3]
b
2
=(
V
2
−Z
0
I
2
)/2(
Z
0
)
½
[4]
The network model includes a set of S-parameters S
11
, S
21
, S
12
and S
22
representing the behavior of the network. The input reflection coefficient S
11
, a function of the network's input impedance, models how the network reflects the input signal in an Z
0
environment. When the network's input impedance matches Z
0
, the S
11
parameter will be 0. The S
21
parameter is the insertion gain of the network when it is operating in a Z
0
environment. An “output reflection coefficient” S
22
, a measure of signal reflection at port P
2
, is a function of the network's output impedance in relation to Z
0
. S
22
has zero value when the network's output impedance matches Z
0
. The S
12
parameter is a measure of the network's reverse gain. The S-parameter model relates the a
1
, b
1
, a
2
, and b
2
waveforms to the S
11
, S
12
, S
21
, and S
22
S-parameters as follows:
b
1
=S
11
a
1
+S
12
a
2
[5]
b
2
=S
21
a
1
+S
22
a
2
[6]
S-parameter Measurement
When the expected performance of a network design is specified in terms of the S-parameter model, a designer can use readily available computer-aided design tools to compute the S-parameters of a network design to determine how well the design meets its S-parameter specifications. After the network is fabricated, a test engineer would like to be able to measure the network's actual S-parameter values to determine whether the network meets those specifications. Since the S-parameters are an abstraction the test engineer cannot measure them directly, but he or she can compute them from signal measurements made at the network's input and output terminals as it drives a Z
0
load in response to an input sine wave signal produced by a signal source having a Z
0
output impedance.
FIGS. 3 and 4
illustrate one way to measure the S-parameters of network
10
of FIG.
1
. With port P
2
terminated with the network's characteristic impedance Z
0
and source
12
driving port P
1
as illustrated in
FIG. 3
, there will be no incident wave a
2
at port P
2
because there will be no reflection at the load. With a
2
equal to 0, equations [5] and [6] reduce to:
b
1
=S
11
a
1
[7]
b
2
=S
21
a
1
[8]
By measuring the a
1
, b
1
, and b
2
waves, with the test configuration of network
10
we can solve equations [7] and [8] to compute the S
11
and S
21
parameters.
We then terminate port P
1
with characteristic impedance Z
0
so that there is no incident wave a
1
at that port and use signal generator
12
to stimulate port P
2
. With a
1
equal to 0, equations [5] and [6] reduce to:
b
1
=S
12
a
2
[9]
b
2
=S
22
a
2
[10]
Thus by measuring the a
2
, b
1
, and b
2
waves, with the test configuration of network
10
we can solve equations [9] and [10] to compute the S
12
and S
22
parameters.
Error Correction
Unfortunately the S-parameter measurement approach described above is not highly accurate because it does not account for errors resulting from the influences of the internal impedances of the test system that must be connected to network
10
when measuring a
1
, a
2
, b
1
and b
2
.
FIGS. 5A and 5B
depict a test system
14
typically used to measure the a
1
, a
2
, b
1
and b
2
values needed to determine the S-parameters of a two-port (network) network under test
16
.
FIG. 5A
shows the test system
14
configured to make the forward measurement depicted in FIG.
3
and
FIG. 5B
shows test system
14
configured to make the reverse measurement depicted in FIG.
4
. Test system
14
includes a signal generator
18
supplying a single-frequency test sine wave signal to the network's port P
1
and a load impedance Z
0
connected to port P
2
. A directional coupler
20
senses the incident and reflected signals at port P
1
and delivers voltage waveforms a
1m
and b
1m
to a data acquisition and processing (DAP) system
24
. A similar directional coupler
22
senses the output and reflected signals at port P
2
and delivers to DAP
24
voltage waveforms b
2m
and a
2m
.
The a
1m
, b
1m
a
2
and b
2
waveforms DAP system
24
senses are not directly proportional to the a
1
, b
1
, a
2
and b
2
waveforms appearing at ports P
1
and P
2
Hainds Curtis C.
Marshall David B.
Metzger Donald M.
Barlow John
Bedell Daniel J.
Credence Systems Corporation
Lau Tung S
Smith-Hill and Bedell
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