forms with a view
to
reducing the computation time, then the Burg and geometriclattice methods should be chosen. The results obtained here are consistent with the ones reported earlier
[6,
71
and referred to in the section on
AR
modeling.
REFERENCES
1. J. Chen, C. Wu, K. Wu, and
J.
Litva, “Combining an Autoregres sive Model with the FDTD Algorithm for Improved Computa tional Efficiency,”
IEEE
MTTS
Digest,
1993, pp. 749752.
2.
J.
Litva,
C.
Wu,
K. Wu, and
J.
Chen, “Some Considerations for Using the Finite Difference Time Domain Technique to Analyze Microwave Integrated Circuits,”
IEEE Microwave Guided Waue Lett.,
Vol
MGW3,
Dec. 1993, pp. 438440. 3. V. Jandhyala,
E.
Michielssen, and
R.
Mittra, “FDTD Signal Extrapolation Using the ForwardBackward Autoregressive
(AR)
Model,”
IEEE
Microwave Guided Wave Lett.,
to
be published. 4.
Y.
Hua and
T.
K.
Sarkar, “Generalized PencilofFunction Method for Extracting Poles
of
an EM System
from
its Transient Response,”
IEEE Trans. Antennas Propagat.,
Vol. AP37, Feb.
5
W.
L.
KO
and
R.
Mittra, “A Combination of
FDTD
and Prony’s Method for Analyzing Microwave Integrated Circuits,”
IEEE Trans. Microwaue Theory Tech.,
Vol.
M7T39,
Dec. 1991, pp. 6.
S.
M. Kay and
S.
L.
Marple, “Spectrum AnalysisA Modern Perspective,”
Proc. IEEE,
Vol. 69, Nov. 1981, pp. 13801419. 7.
S
L.
Marple,
Digital Specfral Analysis,
PrenticeHall, Englewood Cliffs,
NJ,
1987. 1989, pp. 229234. 21762181.
Received
51894
Microwave and Optical Technology Letters, 7/15, 690692 1994 John Wiley
Sons,
Inc. CCC 08952477/94
A
NEW DESIGN APPROACH FOR MONOLITHIC TRANSIMPEDANCE TECHNIQUES RECEIVERS BASED ON ROOTLOCUS
Valter Cocco Piero Marietti and Alessandro Trifiletti
Diparhmento
di
lngegneria Elettronica Unrversith degli Studi di Roma ”La Sapienza” via Eudossiana
18,
00184
Roma,
Italy
KEY
TERMS
Optical receiuers, transimpedance amplifiers,
MMIC,
rootlocus tech
nique
ABSTRACT
In
this article we present a new design method for monolithic trans impedance receiuers that
is
based
on
a simple model
of
uoltage ampl er and on rootlocus eualuation
of
closedloop transimpedance transfer function.
I994 John
Wley
Sons,
Inc.
1.
INTRODUCTION
Direct detection receivers in optical links quite often use transimpedance amplifiers TZA) to achieve good gainband width product, dc coupling, and high dynamic range
[11[5].
Using this configuration and monolithic integration it
is
pos sible to obtain optical receivers with bandwidth above
2
GHz,
transimpedance gain between
60
and
70
dB
fl
and input noise current in the range
of
48
PA/
m.
requency range and small dimensions due
to
integration allow us to consider the circuit as operating with lumped elements and to use rf design techniques. Among them we think that rootlocus RL) representation is suitable to give a complete description
of
gainbandwidth constraints as a function
of
circuit parame ters. This technique has been already used to investigate the frequency behavior
of
feedback amplifiers
[6][8],
but it has to be adapted to be useful for MMIC optical receivers. The aim
of
our work is to demonstrate that gain and bandwidth performances of TZA can be deduced from a limited set of parameters of the forward amplifier, depending on topology and technological processes; it is possible to steer technological and design choices by considering the effect of the variations
of
these parameters on root locus. In Section
2
we explain how to use the
RL
technique TZA optical receivers. In Section
3
we describe a new design approach using this technique, and in Section
4
n example is presented. Concluding remarks are presented in Section
5.
2. ROOTLOCUS TECHNIQUE
FOR
OPTICAL RECEIVERS
In Figure
1
a block diagram
of
a TZA for optical receivers is shown, with a photodiode, a voltage amplifier with shuntshunt feedback made by resistor
R,,
nd a buffer stage
to
match a
504
load.
To
analyze the receiver
by
means
of
feedback theory, it is necessary
to
deduce load
effect
of
source, buffer stage and feedback network
on
forward amplifier. The
pin
photodiode is usually modeled by a parallel resistor capacitor, and the buffer stage, in this article is modeled by a capacitor.
As
a matter
of
fact, using as a buffer a MESFET in commondrain configuration, its input admittance
is
given by where
Cgs
and
g
are the input capacitance and transcon ductance of the MESFET and
rp
is the parallel
of
its output resistances and load. The second member
of
Eq.
(1)
is the input admittance
of
a series RC where
R
=
rp
and
C
=
Cgs/(l
+
gmrp).
With typical values
of
MMIC MESFET model parameters we get
R
40
R
and
C
=
Cg,/2,
and then it
is
possible to approximate
1)
ith
I
scg,/2.
2)
Moving to the input and to the output of the amplifier the load effects
of
source, buffer and feedback network, and neglecting inverse transmission parameter, we obtain the scheme
of
Figure
2
where
I
is the photogenerated current. Using the set
of
qj
parameters to describe the amplifier
it
is
straightforward
to
obtain for the amplifier and the feedback network, respectively, where
(5)
692
MICROWAVE AND OPTICAL TECHNOLOGY
LETERS
/
Vol.
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No.
15,
October
20
1994
where
Rr
Figure
1
Block diagram of a
TZA
optical receiver
Ic
r.
+
Figure
2
Model of the voltage gain stage
of
the
TZA
including loading effects
are
the
Y
parameters
of
the forward amplifier with loading effects. Let The transimpedance transfer function of the overall amplifier becomes
W s)
=
R,F s)/ l
+
F(s)).
Choosing the follow ing model for the forward amplifier:
(7)
Y,, s>
=
0,
We can rewrite Eq.
(5)
as
T(s)
=
G,
+
sC,,
Yo s)
=
Go
+
sC
y
=
0. By substitution
of
Eqs.
(8)
in Eq.
(6)
we obtain
Gl
Go
CO
p.
=

'
c,
Po
=
2
10)
We see that by changing the feedback resistor
R,,
which is proportional to feedback gain, the position
of
the poles
pi
and
po
changes and makes useless usual rootlocus tech niques. We developed a software tool able to find root locus defined by the equation
K
+
D(s)
=
0
to obtain information that can drive the design process.
3.
DESIGN GUIDELINES
AND
SOFlWARE
The design procedure that we propose consists of the follow ing steps Derive the smallsignal models
of
photodiode, forward gain block, and buffer. This step is quite critical be cause we have
to
use a simple model
to
fit the response
of
a multistage amplifier. We have also verified that in many situations the model represented by Eqs.
(7)
is accurate enough up to
10GHz.
Choose the range of value
of
feedback resistor to be used to evaluate the root locus. This choice is driven by the desired gain value. Compute and present the root locus. This step can be easily worked out by means of a software tool, which uses Cardano rule to find the poles. Examine the root locus with respect to the frequency response characteristics
of
the receiver. The locus is plotted
on
polar coordinates to obtain information about the modulus and phase
of
the roots. Under dominant pole conditions, as is usually verified, the bandwidth of the receiver can be obtained by the modulus
of
the roots, and the peaking from the phase of the roots, as follows: where
w,
is the frequency
of
the dominant poles;
w,,
=
ondm
s the frequency where
IW jw)l
has its maximum and
4
is
the angle between the
axis
jw
=
0
and the line starting in the srcin and passing through the pole. We consider a good compro mise between the requirements
of
increasing band width and
of
keeping a good shaping of impulse re sponse to choose values
of
peaking in the range
0.1
1
dB. These are obtained when
4
is in the range between
50
and
60 .
When the hypothesis of dominant poles fails Eq.
11)
has to be modified as follows: where
R
is ratio between second and first pole moduli.
MICROWAVE AND OPTICAL TECHNOLOGY LETTERS
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Vol.
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October 20
1994
693
5.
Trim the amplifier parameters.
If
no values of feedback resistor can match the design goals, then to find a solution it is possible to change the parameter set
of
the forward amplifier. This operation is useful in order to characterize the parameters that can improve perfor mance of the receiver and that can be changed in a simple way. The operation ends requiring a new extrac tion of parameter set Step
1 .
6.
Check finally the result with a circuit simulator. At the end
of
Step 4 when a set of parameters is found that shows a good performance, we check the result on a standard simulator.
4.
A
CASE STUDY
We have checked this design method on topologies using as active devices MESFETs from the DaimlerBenz E05 GaAs process. This process is characterized by
fT
=
25 GHz,
f,,,
=
45
GHz, and makes available 0.5pm gatelength devices with gate width in a range from 2001000 pm. The example we present is a receiver made by a voltage gain block in a cascode configuration, followed by a buffer stage. In Figure
3
the cascode stage loaded by a
5004
resistor is shown. The parameter set of the amplifymg net work has been optimized to fit the electrical behavior
of
the forward amplifier. The result of optimization is shown in Figure
4.
To show the accuracy
of
fitting we present in Figures
5
and
6
the location
of
the parameters of the full network CASC) and its model MDCASC). We chose a feedback resistor in the range between 1000
R
and
3000 R
with a
2004
step. The parameters
of
the model are used as input
of
our software, which worked out the root locus shown in Figure
7.
We obtained a couple
of
complex conjugate poles, and the third is outside the plot because its frequency is above
10
GHz. The bandwidth of the receiver can be estimated by the modulus of the lower frequency pole. As explained in Step
5
of Section
3
now we can change each parameter of the model to
find
which improves receiver performances. In Table
1
we present all changes we made,
vdd
T
Fet
231 A
OOA
_I

et231 A
+
Qg
I
+
VO
4
Figure 3
The cascode stage that we have used to verify our design technique
I
I
4
Figure
4
Electrical model
of
the cascode stage
EEsof

Libra

Wed
Par
3
W:
30:
58
1933

w_lndJl
Figure
5
Comparison between
Y
parameters
of
the voltage gain stage and
its
model
EEsof

Libra

Wed
Mar
3
W:
3l:
O
1993

w jwJg1
0
MAGrYElI
+
WAGrY2 WDCASC CASC
0.100
0.050
0. 000
b.
100
1.
ow
FFIEOGHZ
100.
0
Figure 6
Comparison between
Y
parameters
of
the voltage gain stage and its model
\
\
\
\
\
\
\
,.
.
.
'
500
\
so.\
\
..
.
\
.
\
,
'
\
.
\
....
Q
R=3M10
\\
....
F<O>=16.1
5.0
3 0
1.0
Gh=
Figure 7
Root
locus
of
the cascode stage
one parameter at time, and in Figures
813
subsequent changes in root locus. It
is
possible
to
increase bandwidth and to reduce peaking
of
receiver changing
C,,
C,,
and
pf,
which depend on
Cg,,
Cgd
and on the coupling
RdsCps
f
the MESFET, but these
694
MICROWAVE AND OPTICAL TECHNOLOGY LETTERS
/
Vol.
7,
No.
15,
October
20
1994
TABLE
1. List
of
the Changes Made, with the Number
of
Figure, that Shows the Effects on the Root Locus
Figure Parameter Initial value
0)
Final value
(
B)
8
G1
0
mS
1
mS
9
Cl
0 28
pF
0.1
pF
10
G2
2 2
mS
3
mS
11
c2
0.045
pF
0 02
pF
12
70
41
mS
60
mS
2 2
x
1011
s 1
5
x
1011
s1
13
Pf
..r
\
.
\\
.'
\
\
\>..
,\\
.
\\
:
U
b
I
b
I
t
0
R=3000
F<0>=4,0
0
R=lOM F<0>=6.4
1 0
ReCrl
\
\
SOo
\
600\\
\
\
\
\
,.
.. ..
.
\
..
\
.'
\
.

\
_
....
....
IntrlA
\
\
,,
_.
.'
.
SO* \
60*\\
\
'
..
.'
\
\
..
\
.
\
.
\
....
...'
R=3000
.>\
\\
::
?,
F<O>=lC.
.
\
>,W
\=*
'
\
.'.
..\\
v
....
'
,
C..
0
R=lM)O
F<O>=l2.8
\
\
.
\ ,,...
.
..r
\
.
\\
_'
\
\
\>..
.\\
.
v.
.
\\
I
?
b
I
1
5.0
3.0
1 0
\
\
SOo
\
600\\
\
\
\
.'
\
,.
.. ..
.
\
\
..
ohz
5.0
3 0
1 0
tSl
\
..\
..r
\
I
5.0
3.0
Figure
8
Rootlocus change due to a variation
of
G,
3
\
\
500
\
60*\\
\
\
.cp
.
.'
'
\
3 0
\
..
\
,
.
.
\
0
R=3000
\
\
.....
F<O>=S6.
.,.'\
\\
....
.'
\
..'.\
.:
5
\.
.
\
\*
.
..
'
'\
0
R=1000
F<0>=12.
5.0
3.0 1.0
Gh=
Figure 9
Rootlocus change due to a variation
of
C,
0
R=3MKI
F<O>=lP.
(1
R=1000
F<O>=lO.
,..
.t
5.0
3.0
1 0
Figure 10
Rootlocus change due to a variation
of
G
5.0
3.0
1 0
Qhz
Figure
11
Rootlocus change due to a variation
of
C
0
R=3000
F<0>=23.6
0
R=lOOO
F<0>=18.7
1 0
.0
3 0
Figure
12
Rootlocus change due
to
a variation
of
pr
parameters are almost fixed in a specific MMIC process. We can easily change the output conductance of the cascode stage and set it to
G
=
2.8 mS.
In
Figure 14
is
shown the root locus of the receiver after changing the load resistor to
357
0
and for the feedback resistor in the range 12001600
a
n Table
2
we present the final performance of the
TZA
in terms of the natural fre quency of the poles, their phase, and the low frequency gain of receiver. In Table
3
a comparison between simulation of full circuit and rootlocus technique designs is shown.
MICROWAVE AND OPTICAL TECHNOLOGY LETTERS
/
Vol.
7,
No.
15,
October
20
1994
695
5.0
3 0
Figure
14
Root locus
of
the modified cascode stage
TABLE
2.
Final Performance in Terms of Natural Frequency
of
the Poles, their Phase and
Low
Frequency Gain
of
the Direct Path
of
the Stage TABLE 3. Comparison between Transimpedance Performance Deduced from our Design Techniques and the Simulation
of
the Full Network
R.L. Full Network
T O)
dBl 62.2
T
on
dBl 61.2 Peaking [dB] 0.6 62.2 61.4 0.8
The final circuit parameter optimization shows an increase of bandwidth of
1
GHz,
with the same value
of
peaking, and an excellent agreement still holds between
RL
tool results and circuit simulation. We have tested this design approach on several configura tions of forward amplifier as single commonsource stage, cascode stage with inductive peaking, and cascode with dif ferent MESFET gate widths, always finding an excellent agreement between the results of the
RL
tool and the circuit simulation except for the single commonsource stage. This was due to high reverse gain
of
this stage which makes it impossible to fit the forward amplifier stage with the unilat eral model described by Eqs.
7).
We have overcome this problem using an improved model for forward amplifier.
CONCLUSION
We presented
a
new design method for transimpedance am plifier that can be used to understand how process character istics and topology can influence performances of TZA through the use
of
a simple model. This model sums up the behavior
of
the circuit making possible
to
concentrate on a few parameters. In this article we have checked this approach on a particular case and we have found excellent results both in terms of agreement between circuit simulator and our tool and
in
terms
of
improvement
of
circuit performances.
ACKNOWLEDGMENTS
This
paper was carried out
in
the framework
of
a cooperation between the “Dipartimento di Ingegneria Elettronica”
of
the Univer sity
of
Rome
“LA
Sapienza” and the ESAESTEC research center of Noordwijk. We thank very much
Dr.
G. Gatti for his material and intellectual support.
REFERENCES
1.
M. Makiuchi, H. Hamaguchi, T. Kumai, and
0.
Wada, “GaAs Optoelectronic Integrated Receiver Array Exhibiting Highspeed Response and Little Crosstalk,”
ZEE Electron. Lett.,
Vol.
22, No. 17, Aug. 1986, pp. 893894. 2.
Y.
Archambault, D. Pavlidis, and J. P. Guet, “GaAs Monolithic Integrated Optical Preamplifier,”
ZEEE
J
Lightwave Technol.,
Vol.
LT5,
No.
3, March 1987, pp. 355367. 3.
N.
Uchida,
Y.
Akahori, M. Ikeda,
A.
Kohzen, J. Yoshida, T. Kokubun, and
K.
Suto,
“A
622 Mb/s HighSensitivity Monolithic InGaAsInP pinFET Receiver OEIC Employing a Cascode Preamplifier,”
ZEEE Photon. Technol. Lett.,
Vol.
PTL3,
No.
6, June 1991, pp. 540542. 4. D. C. W.
Lo,
Y.
K.
Chung, and
S.
R. Forrest,
“A
Monolithically Integrated In,,,,Gao,,,As Optical Receiver with VoltageTunable Transimpedance,”
ZEEE Photon. Technol. Lett.,
Vol.
PTL3,
No.
8, 5. A. A. Ketterson, M. Tong, J.W. Seo, K. Nummila, J. J. Morikuni, S.M. Kang, and Ilesanmi Adesida, “A HighPerformance
Al
GaAs/InGaAs/GaAs Pseudomorphic MODFETBased
Mono
lithic Optoelectronic Receiver,”
ZEEE Photon. Technol. Lett.,
Vol.
PTL4,
No.
1, Jan. 1992, pp. 7376. 6. M.
S.
Ghausi and D.
0.
Pederson, “A New Design Approach for Feedback Amplifiers,”
IRE Trans. Circuit Theory,
Vol.
PGCT8, No. 3, Sept. 1961, pp. 274284. 7. M.
S.
Ghausi, “Optimum Design
of
the ShuntSeries Feedback Pair with a Maximally Flat Magnitude Response,”
IRE Trans. Circuit Theory,
Vol. PGCT8, No. 4, Dec. 1961, pp. 448453. 8. E. J. Angelo, Jr.,
Electronic Circuits
2nd
ed.), McGrawHill, New York, 1964, pp. 597624. Aug. 1991, pp. 757760.
Received
51894
Microwave and Optical Technology Letters, 7/15, 692696 1994 John Wiley
Sons,
Inc. CCC 08952477/94
NUMERICAL ANALYSIS OF RECTANGULAR WAVEGUIDE COUPLERS USING
A
2D
/
FDTD ALGORITHM MULTIPLESLOT NARROWWALL
Enrique
A.
Navarro
Communications Research Laboratory McMaster University Hamilton, Ontario, Canada, L8S
4K1*
KEY
TERMS
Finitedifferencetimedomain method, waveguide discontinuities, couplers
ABSTRACT
Slot narrowwall couplers are simple but effective directional couplers.
A
simple and ejjicient approach to analyze these devices using the
FDTD
algorithm
is
presented. The technique uses
a
synthetic excitation and
a
*
Permanent address: Department
of
Applied Physics, Universitat de ValBncia, Doctor Moliner
50,
46100 Burjassot (Valsncia), Spain.
696
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1994