Data processing: measuring – calibrating – or testing – Testing system – Of circuit
Reexamination Certificate
2002-01-15
2003-12-16
Barlow, John (Department: 2857)
Data processing: measuring, calibrating, or testing
Testing system
Of circuit
C702S085000, C324S073100, C324S601000, C324S637000, C324S638000, C714S733000, C714S734000
Reexamination Certificate
active
06665628
ABSTRACT:
BACKGROUND
1. Field of the Invention
The present invention relates to methods for virtually embedding and/or de-embedding balanced networks when, for example, making measurements using a vector network analyzer (VNA).
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 may be 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.
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
)
To extend this methodology, consider an N-port DUT where the networks to be added or subtracted are still two ports. A simple extension for N-port embedding/de-embedding is shown in
FIG. 4
, which illustrates a six-port DUT
402
(i.e., N=6). Computationally, measurements for a six-port DUT
402
have conventionally been handled by treating the calibration coefficients associated with each port as a network and then multiplying the T-matrix for the “network” of the DUT with the T (or T
−1
) matrices for “networks”
1
-
6
shown in FIG.
2
. By reducing an N-port problem to a two-port concatination problem, the above discussed methodology has typically been adequate.
Recently, however, many circuits are being designed as balanced circuits. 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 true for consumer electronics. The behavior of the class of balanced devices are illustrated in
FIGS. 5A-5D
. In these FIGS., a four-port device
502
is treated as two pairs of ports (i.e., ports
1
and
2
making up one pair, and ports
3
and
4
making up another pair), where each pair may be driven either differentially or common mode. The outputs can also be measured in a differential or common-mode sense.
FIG. 5A
illustrates a common-mode (i.e., in-phase) input and a common mode output.
FIG. 5B
illustrates a common mode input and a differential (i.e., 180 degrees out of phase) output.
FIG. 5C
illustrates a differential input and a common mode output.
FIG. 5D
illustrates a differential input and a differential output.
While the methodology discussed with reference to
FIG. 4
can be used for fixture de-embedding and certain other operations, there are occasions when this methodology is not adequate.
FIG. 6
shows one example where a four-port matching network
602
that has different behaviors for differential and common-mode signals. Accordingly, such a balanced matching network
602
cannot be well represented by a two-port network. That is, the embedding of such a structure cannot be done using a simple two-port network. For example, if the matching network of
FIG. 6
were broken down into two single ended networks (each with L/2 to ground), the common mode beha
Anritsu Company
Barlow John
Fliesler Dubb Meyer & Lovejoy LLP
Walling Meagan S.
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