Data processing: measuring – calibrating – or testing – Measurement system in a specific environment – Electrical signal parameter measurement system
Reexamination Certificate
2002-05-02
2004-12-14
Barlow, John (Department: 2863)
Data processing: measuring, calibrating, or testing
Measurement system in a specific environment
Electrical signal parameter measurement system
C324S076190
Reexamination Certificate
active
06832170
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to methods for embedding and/or de-embedding networks when, for example, making measurements using a vector network analyzer (VNA). More particularly, the present invention relates to calculations for embedding and/or de-embedding networks that are not directly amenable to chain matrix calculations, such as three-port devices and semi-balanced devices with an odd number of ports.
2. Description of the Related Art
Measurements of a device under test (DUT) using a VNA may not always be performed in a desired test environment. This is because it maybe too time intensive and/or costly to measure a DUT in a desired test environment. Accordingly, a DUT is often measured in a different environment for reasons of expediency and/or practicality, thereby requiring the use of embedding or de-embedding techniques to correct the effects of the test environment. For example, a DUT may be in a test fixture or connected via wafer probes when measurements of the DUT are made, thereby requiring the removal of the effects of the fixture or probes from the measured data for a truer picture of actual DUT performance. De-embedding techniques allows this task (i.e., removal of effects) to be performed computationally. This concept is shown in FIG.
1
A. In another example, a customer may desire to see what the performance of a DUT would be with a specific matching network attached. However it may be impractical to attach the matching network during manufacturing for cost reasons. Embedding techniques allow this task (i.e., attaching the matching network) to be performed computationally. This concept is shown in FIG.
1
B.
While most commercial simulators use nodal wave analysis or similar techniques for computing composite network results, these approaches may not be needed or wanted (e.g., based on computational or memory needs) for certain specific applications. Among these applications are embedding or de-embedding networks to/from a measurement. For two port devices, a chain matrix or cascading computation using transfer-matrices has been used to perform embedding and de-embedding. The concept is to re-arrange standard scattering-parameters (S-parameters) to form a pair of new matrices (termed T for transfer matrices) that can be multiplied for embedding and form the equivalent to the networks being concatenated or cascaded (i.e., one network being embedded). Multiplying by the inverse of the T-matrix (i.e., T
−1
) is the equivalent of de-embedding. A key-point is that the outputs from one stage map directly to the inputs of the next stage thereby allowing the matrix multiplication to make sense.
Transfer-matrices (also known to as transmission matrices) are made up of T-parameters (also known as chain-scattering-parameters and scattering-transfer-parameters) that are defined in a manner analogous to S-parameters except the dependencies have been switched to enable the cascading discussed above. In both cases the wave variables are defined as a
i
for the wave incident on port i, and b
i
for the wave returning from port i. S-parameters of an n-port device characterize how the device interacts with signals presented to the various ports of the device. An exemplary S-parameter is “S
12
”. The first subscript number is the port that the signal is leaving, while the second is the port that the signal is being injected into. S
12
, therefore, is the signal leaving port
1
relative to the signal being injected into port
2
. Referring to
FIG. 2
, the incident and returning waves and the S-parameters are shown for an exemplary two-port network
202
. These S-parameters are defined by Equation 1 below.
[
b
1
b
2
]
=
[
S
11
S
12
S
21
S
22
]
[
a
1
a
2
]
(
Equation
1
)
where,
a
1
is the traveling wave incident on port
1
;
a
2
is the traveling wave incident on port
2
;
b
1
is the traveling wave reflected from port
1
;
b
2
is the traveling wave reflected from port
2
;
S
11
is referred to as the “forward reflection” coefficient, which is the signal leaving port
1
relative to the signal being injected into port
1
;
S
21
is referred to as the “forward transmission” coefficient, which is the signal leaving port
2
relative to the signal being injected into port
1
;
S
22
is referred to as the “reverse reflection” coefficient, which is the signal leaving port
2
relative to the signal being injected into port
2
; and
S
12
is referred to as the “reverse transmission” coefficient, which is the signal leaving port
1
relative to the signal being injected into port
2
.
(Note that the set of S-parameters S
11
, S
12
, S
21
, S
22
make up an S-matrix)
The T-formulation is a bit different to allow for cascading. More specifically, in the T-formulation, b
2
and a
2
are independent parameters rather than a
1
and a
2
(as in the S-formulation of Equation 1). This does not change the operation of the circuit, just the situation under which the parameters are measured. Since T-parameters are rarely measured directly, this is usually not a concern. For a two-port network, the T-parameters are defined in Equation 2 shown below.
[
a
1
b
1
]
=
[
T
11
T
12
T
21
T
22
]
[
b
2
a
2
]
(
Equation
2
)
Two cascaded two-port networks
302
and
304
are shown in FIG.
3
. Note the arrangement is such that when two networks are connected together, b
2
of network
302
at the left maps directly onto a
1
for network
304
on the right. Similarly, a
2
for network
302
on the left maps directly onto b
1
for network
304
on the right.
The equations for computing the T-parameters in terms of the S-parameters (and vice versa) can be mathematically derived. The results are shown below in Equations 3 and 4.
[
T
11
T
12
T
21
T
22
]
=
1
S
21
[
1
-
S
22
S
11
S
21
S
12
-
S
11
S
22
]
(
Equation
3
)
[
S
11
S
12
S
21
S
22
]
=
1
T
11
[
T
21
T
11
T
22
-
T
21
T
12
1
-
T
12
]
(
Equation
4
)
The above analysis and equations are useful for embedding and/or de-embedding two-port networks. A concept for embedding and/or de-embedding four-port networks is disclosed in commonly invented and assigned U.S. patent application Ser. No. 10/050,283, entitled “Methods for Embedding and De-Embedding Balanced Networks,” filed Jan. 15, 2002, which in incorporated herein by reference in its entirety.
FIG. 4
illustrates such a four-port network
402
in which ports
1
and
2
are treated as a first pair of ports (with waves a
1
, b
1
, a
2
and b
2
being referred to as first pair waves), and ports
3
and
4
will be treated as a second pair of ports (with waves a
3
, b
3
, a
4
and b
4
being referred to as second pair waves). The S-parameters associated with four-port network
402
of
FIG. 4
are defined by Equation 5A, shown below. To enable cascading, the waves associated with ports
3
and
4
(i.e., a
3
, b
3
, a
4
and b
4
) are treated as independent variables of a T-matrix equation, and those associated with ports
1
and
2
(i.e., a
1
, b
1
, a
2
, b
2
) are treated as dependent variables. This leads to the T-matrix shown in Equation 5B below.
[
b
1
b
2
b
3
b
4
]
=
[
S
11
S
12
S
13
S
14
S
21
S
31
S
41
S
22
S
23
S
24
S
32
S
33
S
34
S
42
S
43
S
44
]
[
a
1
a
2
a
3
a
4
]
(
Equation
5
A
)
[
a
1
a
2
b
1
b
2
]
=
[
T
11
T
12
T
13
T
14
T
21
T
31
T
41
T
22
T
23
T
24
T
32
T
33
T
34
T
42
T
43
T
44
]
[
b
3
b
4
a
3
a
4
]
(
Equation
5
B
)
The four-port network of
FIG. 4
may be a balanced circuit. A balanced circuit, as defined herein, is a circuit that includes a pair of ports that are driven as a pair, with neither port of the pair being connected to ground. Examples of balanced circuits are circuits that have differential or common mode inputs. A balanced circuit need not be completely symmetrical. Balanced circuits have often been used in the pursuit of lower power consumption, smaller size, better electromagnetic interference (EMI) behavior and lower cost. This is especially tru
Anritsu Company
Meyer LLP Fliesler
Sun Xiuqin
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