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Summary of the de-embedding methods 去嵌入总结.pdf
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Summary of the de-embedding methods
Whit the CMOS technology moving forward and dimension of device
shrinking,parasitics of test structure have a significant impact on the
measurements。In order to get the only DUT data which is very
important for IC designers and engineers,we have to subtract the
parasitics of Pads and interconnect from the measured data。This is the
de-embedding process。In this summary ,I will generalize about ten
popular and often used de-embedding methods proposed during the
passed 20 years。First I classify these methods into five categories:
one-step,two-step,three-step,four-step and mixture。Below I will show
the equivalent models and specific derivation process of every methods。
1、ONE-STEP:
1)open without coupling of 2 signal pads:
There only one open test structure is needed and also only one time
measurement。Fig.1-1 shows the open test structure and equivalent
model。
Fig.1-1.The open test structure and equivalent model
Yp in the equivalent model denotes the coupling between pads and
DUT
Yp
(a)
(b)
(c)

grounded substrate, which is the only effect we consider in this
de-embedding method。
“Sm” denotes the measured S-parameter of DUT and test structure,and
“So” denotes the measured S-parameter of the Open structure only
(this denotation way is used for the following de-embedding methods)。
Firs S-parameters should convert to Y-parameters:Sm → Ym and So →
Yo,then Yp is obtained from Yo:
11, 12,p o o
Y Y Y
(1)
Derivation of
dut
Y
from Yp and Ym:
1, 1, 11, 2, 12 ,
2, 1, 21, 2, 22,
1, 1, 1,
2, 2, 2,
m m m m m
m m m m m
m dut p m
m dut p m
i u Y u Y
i u Y u Y
i i Y u
i i Y u
So we get
1, 1, 11, 2, 12,
2, 1, 21, 2, 22,
()
()
dut m m p m m
dut m m m m p
i u Y Y u Y
i u Y u Y Y
And
11, 12,
21, 22,
,
,
m p m
dut
m m p
Y Y Y
Y
Y Y Y
In other way:
,0
0,
p
dut m
p
Y
YY
Y
(2)

Then we get the parameters for DUT only and they can be used to verify
circuits or models。
2)open with coupling of 2 signal pads:
The only difference between this method and the upper one is the
coupling of 2 signal pads is considered and this effect is necessary,
verified by many papers。Fig.1-1 shows the equivalent models。
Fig.1-2.The open test structure and equivalent model
Using the same way of derivation for the Upper,
dut
Y
of this method
can be acquired:
dut m o
Y Y Y
(3)
3)through method without equivalent model:
As for this method,we assume the network between the probe tip
and DUT can be described by a 2-port network。Also we assume this
network is reciprocal and mirrored,and the following results are
obtained:
12, 21,aa
SS
(4)
11, 22,aa
SS
(5)
To extract the only DUT parameters,only a Through structure is
DUT
(a)
(b)
(c)

needed。Fig.1-3 shows the building blocks。
Fig.1-3.The through test structure and the cascade models
In this method,we neglect the effect of the interconnects used to
connect the two networks。First convert S-parameter to T-parameter and
get the following equation:
t a a
T T T
(6)
And
11, 11, 12, 21, 11,a a a a t
T T T T T
(7)
11, 12, 12, 22, 12,a a a a t
T T T T T
(8)
Convert T-parameters to corresponding S-parameter(implicit equation
11, 22,tt
SS
):
11, 11,
12, 12, 12, 12, 12,
1 1 1
aa
a a a a t
SS
S S S S S
(9)
22
11, 11, 11, 12, 11,
12, 12, 12, 12, 12,
()
1
a a a a t
a a a a t
S S S S S
S S S S S
(10)
Simplification:
22
12, 11, 12,
(1 )
a a t
S S S
(11)
2
11, 11, 12, 11, 11,
( )( 1) 0
a a t t a
S S S S S
11, 12, 11,
(1 )
a t t
S S S
(12)
Get the parameter of the network
Sa
Sdut
Sa
(a)
(b)
(c)

11,
11, 22,
12,
1
t
aa
t
S
SS
S
(13)
2
12, 21, 12, 11,
(1 )
a a t a
S S S S
(14)
And get the S-parameter of the network then convert it to T-parameter
a
T
。Measure the test structure with DUT,then
m a dut a
T T T T
(15)
And
11
dut a m a
T T T T
(16)
We get the T-parameter only for DUT.
2、TWO-STEP:
1)through with equivalent model:
This method incorporate the series interconnect impedances
between pads and DUT。This impedance is important especially for
the small DUT. Fig.2-1 shows the test structure and equivalent models。
Fig.2-1 test structure and equivalent model
From the measurement of the Through structure,we can get Yp and Zs:
11, 12,p t t
Y Y Y
(17)
12
1
2
s
Z
Y
(18)
Two step to extract the DUT parameter:
DUT
(a)
(b)
(c)
Zs Zs
Yp Yp
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