Instrumentation & Measurement Magazine 25-8 - 34

Fig. 5. (a) Measured DUT; (b) Thru or Line standards.
where N means ABCD matrix of transmission line which is
double the length of N . Then, we can extract the ABCD maL
2
L 1
trix of ideal Thru by basic matrix operations:
T TT M M M  
thru

thru
left right
∙ ∙∙ L

L
L
12 1
1
 
D


AB
C
thru
thru
thru
transforming the ABCD matrix of ideal Thru into Y-parameter
matrix. According to the ZY configuration and (4) and (5),
we can calculate the resistance, inductance and capacitance
parameters, as shown in Fig. 2, to obtain the Y-parameter matrix
of the left and right pads, converting left
Y and right
pad
pad
Y to their
ABCD parameter matrices.
Once the ABCD matrix of the left and right pads are determined,
we can extract the ABCD matrix of the transmission
line:
N T MT∙   

L11
left
pad
∙
L pad
11
right
(10)
Substituting the known matrices into the following formula
leads to the de-embedded DUT ABCD matrix:
N NT M T N


DUT
L
 (11)
11left
pad
  
· ·· ·
DUT pad
right
L
11
11
converting the ABCD matrix to general scattering matrix, and
the procedure is completed. The presented method is elegant
in terms of mathematics and design of standards since it does
not require perfectly symmetrical pads and also can avoid the
crosstalk caused by a Thru standard that is too short.
Simulation of Algorithm
Limitations of conventional Thru-only methods have been discussed,
and a general circuit is used as the DUT [10]. We set
34
(9)
up the typical ZY configuration to characterize the parasitic
effect. A general circuit is used as the DUT, and the parasitic
parameters are equivalent to π networks. Fig. 5 shows the
equivalent circuit and connections of reference DUT, measured
DUT, Thru and Line standards. Among them, R and L
are the parasitic effect caused by discontinuity of the pads and
interconnection line, and C is capacity effects between the signal
and GND. The middle part of Fig. 5a without the left and
right adapter is defined as the reference DUT, and the left and
right adapter include the pads and transmission line between
the pads and DUT. The difference between Thru and Line standards
is only in the length of element 'CPW4' (one double the
length of the other). The characteristic parameters obtained
from the whole structure are defined as measured DUT.
The de-embedding result of Thru-only and the proposed
method are given in Fig. 6 which includes changing the length
of the transmission line between the pads and DUT (the length
of thru and line standards are also changed to fit the algorithm)
and comparing the de-embedding results with the reference
DUT.
It can be seen that when the length of transmission line is
zero, the de-embedding results of the two methods are both
in good agreement with the reference DUT. When the length
of transmission line is increased to 400 μm or 800 μm, the result
of Thru-only deviates from the reference DUT. Because the
parasitic parameters are defined asymmetrically, on the other
hand, the Thru-only procedure considered the parasitic effects
into the ZY configuration. In this simulation, coplanar waveguides
are used to represent transmission line between the
pads and DUT rather than ideal " Tlines " in Advanced Design
System which cause the ZY configuration and cannot characterize
the non-ideal transmission line accurately. Besides,
IEEE Instrumentation & Measurement Magazine
November 2022
Instrumentation & Measurement Magazine 25-8

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