DE-EMBEDDING
OF MMIC TRANSMISSION-LINE
Peter Heymann,
Helmut Prinzler,
MEASUREMENTS
and Frank Schnieder
Ferdinand-Braun-Institut fitr H6chstfrequenztechnik
12489 Berlin / Germany
The complex propagation constant is given by
ABSTRACT
The determination of transmission-line characteristic impedance
and propagation constants from two-port S-parameter measurements is disturbed by half-wavelength resonances. We demonstrate this effect for on-wafer measurements of coplanar
lines. Two networks representing end effects embed the line
and strongly enhance the resonant effect. The de-embedding
consists in determining these networks and subtracting them
from the measured chain matrix. It is shown that simple shunt
admittances are sufficient for modeling of the end effects.
Three methods of de-embedding are presented.
g =-j7,1
=Pl
-j~l
(1)
with 1 being the physical length of the line and (3and et denoting the phase and attenuation constant, respectively. In this
notation, the chain matrix of the line reads
‘L)=l~::gJ::l
‘2)
This matrix cannot be obtained directly from a network measurement since it is embedded between the networks D1 and Dz
in any measurement situation (see Fig. 1). This yields:
INTRODUCTION
Calculating the characteristic impedance Z~(0) and the propagation constant rx(o) +j ~(o) from S-parameter measurements often yields curves with periodic deviations from the
expected smooth shape. This can be seen most clearly from the
real part of ZJO ). The deviations are related to half-wavelength resonances. They occur not only when using a test-fixture but also for on-wafer probing, even in the case of line standards on calibration substrates without discontinuities by probe
pads [1][2].
A typical measuring set-up is shown in Fig. 1. The coplanar
waveguide (CPW) is contacted by wafer probes. Probe pads or
tapers are used if the characteristic impedance of the CPW
differs from that of the measuring system (50Q).
The networks D1 and Dz represent the influence of these pads
together with the contacting elements and the end effects of the
line itself.
The de-embedding procedure consists in determining the networks Ill and Dz and extracting the line matrix (L) from the
measured matrix (M).
(M) = @l)(L)(D,)
(3)
line A
(Dl)
L-!
‘L)
lH-!?!u-
THE CHAIN MATRIX OF THE LINE
For determination of the line parameters we use the chain ma-
trix that can be easily obtained from the measured two-port
S-parameter matrix.
Fig. 1. CPW structures with wafer probes. Top: 300 with probe
pads. Center 5042with closed ground metal. Bottom: Networks:
(L) line, (D) end effects, (M) two port measurement.
1045
CH3389-4/94/0000- 1045$01.0001994
IEEE
1994 IEEE MTT-S Digest
Let us assume two shunt admittances Y, , Yz at both ends
which is justified in almost all practical cases. It follows
not necessary. A disadvantage is the need of very accurate
measuring points with a very small Af in the whole frequency
range.
[1
10
(D,,,)
= ~
(4)
~
M, JfJM1,(f,) - M1,(f,)M,,(f,)
(5)
and for the measured matrix (M):
cosg+j YzZ~sing
jZ~sin g
[j (1 +YIYZZ:)Z;sing +(YI+yJ)cosg
cosg +jY1ZLsing
(M) =
‘(M)
=-’&
(6)
does not give the correct value of Z~(0) but a periodic curve
with typical resonant structures as can bee seen from Figs. 2
and 3.
LINE CHARACTERIZATION METHODS
Y,(f,) =
The chain matrix (M) (5) yields only two complex equations
for three complex unknowns at one frequency f,, Additional
equations can be obtained from the measurements at a second
frequency f, > f,,
(7)
The system of equations is now for i = 1, 2:
MIJfJ =j Z,(~)sm g(<)
- cosg(f,)
M,,(f,)
The shunt admittance Y = G + j(i)C for optimum de-embedding
can also be determined by a minimum error method. The
idea is to compare measured and calculated chain matrix
elements at a frequency fz The calculated matrix elements are
extrapolated from a nearby frequency f] where the line parameters have been obtained by the method described in the
following.
Using (7) the propagation constant
(lo)
cosg(fl) = M,,(fl) - Y,(f,)MJfJ
is calculated
1. Two Frequency Method
M,Jf,)
2. Optimum Admittance Method
from
experimental
values
Ml,
and M12
at the
(G= O is a
good approximation). The values of g(f, ,C, ) from (1O) aud
ZJfl ,CJ from (11) are used to calculate the matrix elements
M,,’(f,) and M,,’(f2)
The phase constant f3(f,)l is linearly extrapolated to f2 according to (8b) and the characteristic impedance is calculated from
frequency
We describe three different methods to extract Z,(o) and y(o)
from the measured matrix (M).
(9)
“(f’)
=‘J=
1
The line is a resonant system the half-wavelength resonances of
which prevent the determination of ZJO) at the resonant frequencies. There are zeros of L,, and L,, at ~1 = nrr and of L,l
and L2j at ~1 = (n-1/2)rc; n = 1,2,3,... This disturbing effect M
greatly enhanced by the networks D] and D2. The straight forward method to calculate the characteristic impedance from
the measured chain matrix with
M,,(f) = cos g(f) +Y,(~)M1z(~);
M,,(f)) - M,,(f,)
Cosg(f,) =
1,2
fl
and a number of estimated values Cz
z,(f,)
= Z,(f,) - j ~
ImZ,(fl)
(11)
1
The condition for the frequency difference Af = fz - f, is less
stringent than in method 1 since the most restricting condition
(8a) is not needed. Frequency
differences
Af up to 20% have
used successfully.
The matrix elements M,,’(f2) and M,~(fJ calculated in this way
are compared with the measured ones in the error function (12)
in order to get the optimum value of Cj:
been
It can be solved analytically if fz - f, = Af is sufficiently small,
i.e. if the following conditions are fulfilled
sin(~f~(fl)l)
l]
S #p(f,)l;
=1
cos (~f
p
(fl)l )= 1
(8a)
(12)
z, (f,) =zL(f2);
a(f2) 1= cl(f,)l;
h
These approximations are applicable for CPWS on GaAs-sub-
strate if Af (GHz) -1 (~m) < 103
Equations (9) provide the analytical solution of (7) for the
quantities ZJO) and g(~). The explicite calculation of Yz is
1046
A corresponding formula holds for the values from port 2.
The error fimction (12) has usually a distinct minimum at that
capacitance value C that gives the best shunt admittance for
de-embedding (e.g. insert in Fig.2).
3. O@imization
The optimization of the D1,~-networks using a commercial CAD
software , e.g. OCTOPUS [3], is a very effective method for
practical applications. We define the shunt admittances as
capacitances Cl and C2 which are frequency dependent and
may have positive or negative values ( C = CO+ afz ). The
values of COand a are determined by the optimization procedure using the measurement over the whole frequency range of
interest. The optimization goal is to reach a constant real part
of Z~ Whichis assumedto be constantin the frequency range
consideredand set by the mean value of the real part of Z~ of
the uncorrected data. In contrast to the previous methods 1 and
2 where only the on-sided matrix elements were used, Z~(re) is
derived from all four elements. Ths has an averaging effect
and reduces the influence of measurement errors.
From (2) and (5) it follows
ZL
u
=$=*
21
M,,
(13)
M,, -Yl M,, - Y2M,~ + Y, Y,M2,
dards without contact pads on a CASCADE MICROTECH
LRM calibration substrate. Similar effects can be seen in previous publications [1] [2].
The internrd structure of the networks describing the end effects depends on the measuring system (on - wafer or fixture)
and on the shape of the contact pads. Therefore D, and D2 not
only represent the physical stray capacitances of the open ends
but also other reactance and radiation loss in combination with
residual calibration uncertainties and asymmetry of the wafer
probes. An influence of the parasitic slot-line mode may be
excluded because of symmetric excitation in our experiment.
The same holds for the parasitic parallel plate mode since its
propagation constant differs from that of the CPW mode.
h example of de-embedding by the method 2 is shown in Fig.
2 where the real part of the characteristic impedance ZL of line
C is drawn. The same result can be obtained with method 1.
The optimum capacitance C2 has been determined from the
error fimction (12) which shows a sharp minimum (see insert
of Fig. 2). This confirms the assumption that the simple structure of the network D2 is sufficient to de-embed the line measurements. The capacitance value is in good agreement with
the length extension of the CPW open-circuit calculated in [3].
After de-embedding the propagation constant is calculated from
100
exp (g) = ~ (L,l +LZz+Z; LIZ+Z~L21)
(14)
1.5
,,:
,, ~
80
1::
EXPERIMENTS AND DISCUSSION
---------
We have measured several CPWS with an on-wafer probing
system. The measurement set-up consists of a VNA HP8510C
(f= 0.045-40 GHz) and wafer probes. Different calibration
methods (TRL, LRM and SOLT) were tested but they do not
show a significant influence on the effect under consideration.
This holds also for different microwave probe designs (coplanar and coaxial) and for the problem of contact repeatability
(within 5 ~m).
The design parameters of the lines can be seen in Fig. 1 and
Table 1. The values of Z~ in Table 1 are only the real parts.
ZJcalc) is calculated with the model described in [4] at f =
20 GHz. Z,are the measured values after de-embedding. The
GaAs-wafer is 0.4 mm, the sapphire substrate 0.5 mm thick.
The thickness of the gold layer is 2.5 pm and 6.6 Km, respectively. There is no backside metallization.
Table 1. CPW parameters
Type
Slot
(pm)
Width, Length
(~m) (mm)
Substrate
Z~
(Q)
A
B
c
Pad
12
90
37
40
100
25
80
52
GSAS
30.5
79.5
47
9.6
9.6
2.69
0.05
(h&
Sapphire
GaAs
zL(crdc)
(S2)
30.0
78
48
50.8
resonance effects appear in all cases as long as the line is
longer than hrdf a wavelength. They were observed also for
lines of other geometry, e.g. for the homogeneous line stanThe
1047
-----
2~
20
20
/’
~,’
g
1
B
0.5
:
\
0
02468
C2 (m)
;
,<.”
:
,,
I ,,
: ,’
‘.,’
. . ------------
25
Frequency
30
(GHz)
Fig.2. Characteristic impedance of line C. (1) Without deembedding. (2) De-embedded with Yz = jceCz , Cz = 5 f!?.
Insert: Error function (12) plotted over capacitance C2
The methods 1 and 2 are useful for short lines with only one or
two resonances. For lines which are several wavelengths long,
method 3 is recommended.
The uncorrected real parts of ~ for line A and B are drawn in
Fig.3, the results after de-embedding in Fig. 4. For the propagation constants, the differences between the curves before and
af?er de-embedding can be seen in Figs. 5 and 6. The 30 Q
CPW (line A) can be de-embedded with constant capacitances,
but the 80 Q CPW (line B) requires frequency-dependent capacitances for correction of the measurement as can be deduced
from the shapes of the uncorrected curves in Fig. 3.
Optimization method 3 is preferred because the calculation of
the corrected line parameters as well as the de-embedding
capacitances is done in one step over the whole frequency
range. Also, inclusion of frequency-dependent capacitances is
easier in method 3 than in the other methods. The reduced
influence of measuring errors by using equations (13) and (14)
is another advantage of method 3. On the other hand, the network representation of D, , Dz can be unphysical (see, e. g.,
the negative capacitances in Fig. 4).
I
200
and
alpha
embedded
de–embedded
/
~
100
epsilon
.—
~b>
de-embedded
....
en@edded>
epsilon
00,.
Frequency
(GHz )
Fig.6. Attenuation a and effective dielectric constant a.~~of
line B before and after de-embedding
oo~
40
Frequency
(GHz)
CONCLUSIONS
Fig.3. Re[Z,] of line A and B before de-embedding
I
When extracting transmission-line parameters from two port
S - parameter measurements up to the millimeterwave range
the end effects cause parasitic resonances. This problem can be
solved by a suitable de-embedding procedure. For that purpose,
the line terminations are represented by networks describing the
physicrd stray capacitances of the open ends and the disturbances by the contact elements. In most cases simple shunt
capacitances are sufficient to model those parasitic. The paper
presents three different methods to determine the embedding
networks.
The procedure leads to considerable improvements which is demonstrated by on-wafer measurements of coplanar lines on
GaAs and sapphire substrate.
I
20
o
Frequency
(GHz)
ACKNOWLEDGEMENT
Fig.4.
CPW
CPW
(C in
Re[Z.] of line A and B after de-embedding with
A: C, = -21 fF, C,= 58 fF
B: Cl = -(1.5 + 0.0035. ~), C,= (1.0 + 0.0004.~)
fF, f in GHz)
400
alpha
I
alpha
like to thank Dr. W. Heinrich for many helpful discussions and Dr. R. Griindler for his continuous encouragement. This work was supported by the Deutsche Forschungsgemeinschaft.
The authors would
e~edded
de–embedded
-7”1
,,.
REFERENCES
8
1 W.H. Haydl, W. Heinrich, R. Bosch, M. Schlechtweg, P.
Tasker, J. Braunstein; “Design Data for Millimeter Wave
Coplanar Circuits.” Proc. 23. EuMiC Madrid 1993, pp.
223-228
2 Y.C. Shih; “Broadband Characterization of Conductor
Backed Coplanar wave-guide Using Accurate On-Wafer
Measurement Techniques.” Microwave Journal April 1991,
oo~m
Frequency
pp. 95-105
(GHz )
3 K. Beilenhoff,
H. Klingbeil,
W. Heinrich,
H,L. Hartnagel;
“Open and Short Circuits in Coplanar MMIC ‘s. ”
IEEE-Trans. MTT-41, 1993, pp. 1534-1537
Fig.5. Attenuation a and effective dielectric constant F,.~~
of
line A before and after de-embedding
4 OCTOPUS 2.1, Argumens GmbH Duisburg, Germany
5 W. Heinrich; “Quasi-TEM Description of MMIC Coplanar
Lines Including
IEEE-Trans.
1048
Conductor-Loss
MIT-41,
1993,
Effects.”
pp.45-52