Instrumentation & Measurement Magazine 25-8 - 33

structure as a combination of cascade networks. Assuming the
left-to-right reverse cascade matrix is equal to right-to-left cascade
matrix, the ABCD matrix of error boxes can be extracted
using basic matrix operations.
An improved de-embedding method is presented in this
Y ZZ YY Y
YY
 11
Y
pad  
left
 
 ZZ 
paper. It differs from the Thru-only de-embedding technique
presented in in which two lines of double length relationship
are required. In this way, we can omit the assumption such as
reciprocity ([S]=[S]T
) and avoid the crosstalk between probes
and DUT which might occur in the traditional Thru-only algorithms,
and the reference planes after de-embedding are
at both ends of the DUT. In order to renormalize the de-embedded
S-matrix to a specific impedance, such as 50 ohms, an
algorithm for electromagnetic simulation is used in this paper.
To verify the proposed method, we provide the size of standards
and DUT; subsequently, the de-embedded S-parameters
of the proposed method are in good agreement with the simulations
up to 80 GHz.
Theoretical Analysis
Thru-only De-embedding
Thru-only de-embedding is a conceptually simple method
that uses only one standard. It inserts a series impedance
Z=R+jɷL for the metal traces of the leads and a shunt admittance
Y=jɷC for the parasitic capacitance between the signal
and ground, assuming the parasitic network is symmetric. As
can be seen from Fig. 2, there is no transmission line between
the Z parameter and DUT, because the part of the transmission
line extending from the pad is contained in Z. Therefore,
the Thru-only method requires that the length of the transmission
line be as short as possible; otherwise, the parasitic
effect of the transmission line cannot be represented by a single
Z. The reference plane after de-embedding is in the central
axis of Thru.
The characteristics of the measured DUT can be expressed
as:
T TT T

l ··eft
right
M pad DUT pad
(1)
where TM is the measured T-parameter matrices of DUT, TDUT
is the intrinsic T-parameter matrices of DUT, and left
T
pad
and right
pad
T
represent the parasitic effects of test pattern, respectively. The
characteristics of the DUT can be de-embedded as:
T T TT  ·· 


DUT
left
pad M pad
The Y-parameter matrix of the Thru standard is:

Y ZZ
Y

thru

  

Y
  
 ZZ
11
22
11
22



Assuming that the Thru structure is symmetrical, the
Y-parameter matrix of the left and right is as follows,
respectively:
November 2022
Fig. 4. Thru-Line network.
IEEE Instrumentation & Measurement Magazine
33
(3)
11
right
(2)
M T NT T N Tright

L 
22 1
left L
left L right∙∙ ∙() ∙
2
(8)
Y ZZ YY
Y YY
right
pad
 11 2

 

Y
ZZ
Converting the Y-parameter matrix of the left and right
pads to the T-parameter matrix can completely eliminate the
parasitic effect. It is important to note that the process is based
on the ideal symmetry Thru standard.
Thru-Line
In this paper, we propose an improved de-embedding method
called Thru-Line, in which only two transmission lines are
used as standards, making the result of de-embedding more
accurate and suitable for general DUT. The parasitic effects
of the probe, pads and interconnect lines are equivalent to
the π network. Z represents the parasitic parameters between
the pads and the transmission line, and Y represents
the parasitic parameters between the transmission line and
GND.
As shown in Fig. 4, the ABCD matrix of the DUT can be expressed
as:
M T N N NT

eft
l ·· ·· right
DUT pad 11L DUT L pad
(6)
where MDUT represents the measured ABCD matrix of DUT
which containing all parasitic effects and errors, the left
T represent the Z and Y parameters on the left and right
respectively,
right
pad
sion line between pthe ads and DUT, and NDUT
N represents the ABCD matrix of transmisrepresents
L
1
the intrinsic ABCD matrix of DUT. The standards are two
transmission lines of length L and 2L (Thru=L, Line=2L),
and the ABCD matrix of two standards can be expressed as
follows:
M T N T
L11  ∙∙left L right
(7)
T andpad
22
12
12
22  12
12
 


11
(5)
    11  21
  
 


21
2 21



 11 22 21

(4)
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