1084 lines
49 KiB
Plaintext
1084 lines
49 KiB
Plaintext
|
|
|||
|
|
|
|||
|
|
****************************************************************************
|
|||
|
|
|
|||
|
|
The Microwave Image Transimpedance Front-End Amplifier For Optical Receivers
|
|||
|
|
|
|||
|
|
****************************************************************************
|
|||
|
|
|
|||
|
|
|
|||
|
|
|
|||
|
|
The image impedance network used in distributed amplifiers is employed
|
|||
|
|
in the design of a transimpedance optical receiver front-end at
|
|||
|
|
microwave frequencies.
|
|||
|
|
Compared with the conventional design, for the same transimpedance the
|
|||
|
|
current design has more than twice the bandwidth, or for the same bandwidth
|
|||
|
|
it has 3 dB better sensitivity. A front-end is designed for 10 Gb/s
|
|||
|
|
transmission with a sensitivity of -25 dBm for a p-i-n detector and -33 dBm
|
|||
|
|
for an APD.
|
|||
|
|
These results compare favorably with published high-impedance receiver designs.
|
|||
|
|
Transimpedance, noise and receiver sensitivity for both p-i-n and avalanche
|
|||
|
|
photodetectors, sensitivity degradation due to post amplifier noise figure,
|
|||
|
|
stability, and enhancement of bandwidth by compensation are
|
|||
|
|
discussed.
|
|||
|
|
|
|||
|
|
"INTRODUCTION"
|
|||
|
|
|
|||
|
|
We suggest here an image transimpedance (ITZ) front-end amplifier for
|
|||
|
|
use in optical receivers\*F.
|
|||
|
|
|
|||
|
|
Presently, only analysis is available. We are building the receiver
|
|||
|
|
experimentally.
|
|||
|
|
|
|||
|
|
Compared with the conventional transimpedance amplifier with the same
|
|||
|
|
transimpedance, the ITZ front-end has more than twice the
|
|||
|
|
bandwidth.
|
|||
|
|
Alternately, for the same bandwidth, it has 3 dB better sensitivity.
|
|||
|
|
Due to the difficulty in fabricating large inductors, the ITZ is best used in
|
|||
|
|
the microwave frequency range from 5 to 20 GHz.
|
|||
|
|
|
|||
|
|
In GaAs FET distributed amplifiers, the gate-to-source (drain-to-source)
|
|||
|
|
capacitances of the FETs
|
|||
|
|
become the shunt capacitors of an artificial, lumped LC transmission line
|
|||
|
|
-- the gate (drain) line.
|
|||
|
|
The formation of the LC transmission line is based on the principle of image
|
|||
|
|
impedance.
|
|||
|
|
Such line has wide bandwidth.
|
|||
|
|
The use of the transmission line overcomes the bandwidth limitation due to
|
|||
|
|
the poles located at both the gate and drain nodes of the FETs
|
|||
|
|
because all capacitances become part of the transmission
|
|||
|
|
lines (the gate and drain lines).
|
|||
|
|
In theory a distributed amplifier has an infinite gain-bandwidth
|
|||
|
|
product.
|
|||
|
|
In practice, attenuation in the gate line limits the number
|
|||
|
|
of FETs to a few.
|
|||
|
|
As regards to bandwidth,
|
|||
|
|
in contrast to an ideal distributed line, the lumped nature of
|
|||
|
|
this LC transmission line does impose
|
|||
|
|
a bandwidth limit which is less than
|
|||
|
|
|
|||
|
|
DELTA f sub I ~=~ 1 over {pi sqrt {LC sub T}}~,
|
|||
|
|
|
|||
|
|
where L and $C sub T$ are the series inductance
|
|||
|
|
and shunt capacitance.
|
|||
|
|
Our simulated results show that the ITZ has a bandwidth larger
|
|||
|
|
than $DELTA f sub I$.
|
|||
|
|
|
|||
|
|
For optical receivers, bandwidth of the transimpedance front-end amplifier
|
|||
|
|
is often limited by
|
|||
|
|
the pole at the input node to which the photodiode is connected because
|
|||
|
|
the total input capacitance at that node, comprised of the sum of the
|
|||
|
|
photodiode capacitance $C sub p$ and amplifier input capacitance $C sub a$,
|
|||
|
|
is usually larger than that at any other node.
|
|||
|
|
For a given $C sub p$, noise is minimized when $C sub a = C sub p$.
|
|||
|
|
In doing so, the input circuit can be made into a one-section image
|
|||
|
|
impedance network.
|
|||
|
|
In the following sections, first we will briefly summarize the relevant
|
|||
|
|
features of transmission lines formed by image impedance networks.
|
|||
|
|
The results are used to design
|
|||
|
|
an ITZ front-end for 10 Gb/s transmission using a commercial HEMT (High
|
|||
|
|
Electron Mobility Transistor).
|
|||
|
|
We will discuss the transimpedance, noise and sensitivity, and stability of
|
|||
|
|
this image transimpedance amplifier/receiver and compare them with that of the
|
|||
|
|
conventional transimpedance amplifier/receiver.
|
|||
|
|
The computed sensitivity of the ITZ is compared with that of published
|
|||
|
|
high-impedance designs.
|
|||
|
|
Finally, we describe how bandwidth can be further enhanced by parallel and
|
|||
|
|
series compensation of the amplifier output circuit.
|
|||
|
|
"IMAGE IMPEDANCE AND THE ITZ FRONT-END AMPLIFIER"
|
|||
|
|
|
|||
|
|
For the infinitely cascaded chain of identical but alternately reversed 2-port
|
|||
|
|
networks shown in Fig. 1, the
|
|||
|
|
image impedances $Z sub {I1}$ and $Z sub {I2}$
|
|||
|
|
are defined as the input impedances looking into ports 1 and 2, respectively.
|
|||
|
|
In Fig. 2, a voltage source $v sub s$ with source impedance $Z sub s ~=~
|
|||
|
|
Z sub {I1}$ and a load impedance $Z sub L ~=~Z sub {I2}$ are connected to
|
|||
|
|
an image impedance network of one section.
|
|||
|
|
The ratio of the terminal voltages is\*(Rf
|
|||
|
|
|
|||
|
|
G. L. Matthaei, L. Young and E. M. T. Jones,
|
|||
|
|
Microwave Filters, Impedance-Matching Networks, and Coupling Structures,
|
|||
|
|
Artech House, Inc., Dedham, MA 1980.
|
|||
|
|
|
|||
|
|
v sub 2 over v sub 1 ~=~ sqrt {Z sub {I2} over Z sub {I1}}~~e sup {-j
|
|||
|
|
beta}~.
|
|||
|
|
|
|||
|
|
For |$v sub 2$| = |$v sub 1$|, it is required that $beta$ be real and
|
|||
|
|
$Z sub {I2} ~=~ Z sub {I1}$.
|
|||
|
|
Because the input node of the transimpedance amplifier can be
|
|||
|
|
cast into this form,
|
|||
|
|
we are particularly interested in the symmetrical $pi$-network of Fig. 3,
|
|||
|
|
in which a series inductor L is shunted on its sides by
|
|||
|
|
capacitors $C sub 1$ and $C sub 2$ ($C sub 1 = C sub 2 = C$).
|
|||
|
|
For this network, $Z sub {I1} = Z sub {I2} = Z sub I$,
|
|||
|
|
where $Z sub I$ is the image impedance.
|
|||
|
|
With $C sub T = 2C$ and $ omega =2 pi f$, the image impedance is
|
|||
|
|
|
|||
|
|
Z sub I ( omega )~=~
|
|||
|
|
Z sub {Io} over sqrt {1~-~{ omega sup 2 LC sub T /4}}
|
|||
|
|
|
|||
|
|
where
|
|||
|
|
Z sub {Io} ~=~ sqrt {L/{C sub T}}
|
|||
|
|
and
|
|||
|
|
beta ~=~ 2 {sin} sup {-1} ( omega sqrt {LC sub T /4})~.
|
|||
|
|
|
|||
|
|
For $f < DELTA f sub I ~==~ 1 over {pi sqrt {LC sub T }}$, $Z sub I ( omega
|
|||
|
|
is real and increases with frequency.
|
|||
|
|
It reaches infinity at $f~=~ DELTA f sub I $ and is
|
|||
|
|
imaginary thereafter.
|
|||
|
|
From (5), for $f << DELTA f sub I$,
|
|||
|
|
$1 over sqrt {LC sub T }$ is recognized to be the phase velocity and from (3)
|
|||
|
|
and (4) $Z sub {Io}$
|
|||
|
|
the characteristic impedance of the transmission line.
|
|||
|
|
In theory, from (2), the symmetrical and matched $pi$-network has infinite
|
|||
|
|
bandwidth, even though the infinite impedance at $f = DELTA f sub I$ renders
|
|||
|
|
the network meaningless.
|
|||
|
|
In practice for distributed amplifiers, $Z sub s$
|
|||
|
|
and $Z sub L$ are fixed resistors and the bandwidth becomes finite.
|
|||
|
|
.P
|
|||
|
|
Since the photodiode is a current source, we replace
|
|||
|
|
$v sub s$ and $Z sub s$ in Fig. 2 by a current source
|
|||
|
|
$i sub p$ and the 2-port network by one that has identical image
|
|||
|
|
impedances at each end ($Z sub {I1} = Z sub {I2} = Z sub I$), with port 2 now
|
|||
|
|
terminated by $Z sub L = Z sub I$.
|
|||
|
|
A terminal voltage
|
|||
|
|
$v sub 1 = i sub p Z sub I$ is developed which propagates
|
|||
|
|
to node 2.
|
|||
|
|
From (2) the magnitudes of $v sub 1$ and $v sub 2$ are equal; they differ only
|
|||
|
|
in phase by an amount $beta$.
|
|||
|
|
Hence, the transimpedance is $Z sub T = Z sub I e sup {-j beta}$ and as
|
|||
|
|
discussed previously it can exhibit infinite peaking.
|
|||
|
|
Similar to distributed amplifiers,
|
|||
|
|
if $Z sub L = R sub L = Z sub {Io}$ (a fixed resistance), the peaking becomes
|
|||
|
|
finite since the network is not matched over all frequencies ($Z sub L !=
|
|||
|
|
Z sub I$, the latter increasing with frequency).
|
|||
|
|
The bandwidth of the current-to-voltage gain, $Z sub T (f)$ or
|
|||
|
|
transimpedance, is therefore finite.
|
|||
|
|
Given that $Z sub I$ increases with frequency for $f < DELTA f sub I$, a larger
|
|||
|
|
load resistance of $R sub L = sqrt 2 Z sub {Io}$ will provide a better match
|
|||
|
|
over that frequency range.
|
|||
|
|
In both cases,
|
|||
|
|
simulation results to be given below show that the bandwidth of $|Z sub T
|
|||
|
|
(f)|$ is slightly larger than $DELTA f sub I$.
|
|||
|
|
|
|||
|
|
A conventional transimpedance amplifier is shown in Fig. 4.
|
|||
|
|
It consists of a feedback resistor $R sub f$ across a voltage amplifier
|
|||
|
|
of gain -A (measured with $R sub f$ in place).
|
|||
|
|
The input impedance of the amplifier is the parallel combination of $R sub {in}
|
|||
|
|
= R sub f over 1+A$ and $C sub a$.
|
|||
|
|
A photodiode with shunt capacitance $C sub p$ is connected to the input node.
|
|||
|
|
Minimum noise is attained when $C sub a$=$C sub p$\*(Rf
|
|||
|
|
|
|||
|
|
R. G. Smith and S. D. Personick, "Receiver Design For Optical Fiber
|
|||
|
|
Communication Systems," in
|
|||
|
|
|
|||
|
|
Semiconductor Devices for Optical Communication, 2nd Edition
|
|||
|
|
|
|||
|
|
H. Knessel, Ed., Springer-Verlag, New York 1982.
|
|||
|
|
|
|||
|
|
which will be assumed in the following discussion.
|
|||
|
|
For the input circuit, adding an inductor L between $C sub p$ and $C sub a$
|
|||
|
|
of value
|
|||
|
|
|
|||
|
|
(6A)
|
|||
|
|
L~=~{C sub T R sub {in} sup 2}~=~C sub T ({R sub f over {1+A}}) sup 2~~~~
|
|||
|
|
~~for~R sub {in}=Z sub {Io}~,
|
|||
|
|
|
|||
|
|
or
|
|||
|
|
|
|||
|
|
(6B)
|
|||
|
|
L~=~1 over 2 C sub T R sub {in} sup 2 ~=~ {{C sub T} over 2} ({R sub f over
|
|||
|
|
{1+}}) sup 2~~~~~~for~R sub {in}= sqrt 2 Z sub {Io}~,
|
|||
|
|
|
|||
|
|
where $C sub T$=$C sub p$+$C sub a$, forms an approximation to an ideal
|
|||
|
|
image impedance network of one section to which the photocurrent source
|
|||
|
|
$i sub p$ is connected.
|
|||
|
|
We first study the frequency response of the magnitude and phase
|
|||
|
|
of the transimpedance $Z sub T (f)$ and the input impedance $Z sub {in} (f)$ of the circuit
|
|||
|
|
in Fig. 3 for $C sub 1$=$C sub 2$=0.2 pF (a value typical of GaAs FETs)
|
|||
|
|
and $R sub {in} ~=~ 50~OMEGA$ and $100~OMEGA$, as a function of L.
|
|||
|
|
The results for $R sub {in}=50~OMEGA$ are shown in Figs. 5A-6B.
|
|||
|
|
In Fig. 5A, for L=0, $|Z sub T (f)|$ has a bandwidth of 8 GHz.
|
|||
|
|
For other L's, $|Z sub T (f)|$ can have both dips at midband and peaks
|
|||
|
|
at the band edge, the amounts of which are tabulated in the insert.
|
|||
|
|
The band edge peaking is of lesser concern since the post amplifier gain
|
|||
|
|
roll-off will reduce the peaking as long as that peaking is not too
|
|||
|
|
large (<3 dB).
|
|||
|
|
Therefore, the bandwidth depends really on how much dip in $|Z sub T (f)|$
|
|||
|
|
is allowed which in turn depends on the post amplifier frequency response.
|
|||
|
|
For the bandwidth to be useful, the post amplifier should
|
|||
|
|
not increase the dip to 3 dB.
|
|||
|
|
From (6A), L is 1 nH and
|
|||
|
|
there is no dip but a slightly excessive peak of 4 dB, with bandwidth of
|
|||
|
|
17.2 GHz.
|
|||
|
|
From (6B), L=0.5 nH; the dip and peak are, respectively, 1.5 dB (at 12 GHz) and
|
|||
|
|
2 dB (at 20 GHz), and bandwidth is increased to 24 GHz which is three times
|
|||
|
|
the input pole.
|
|||
|
|
L=0.75 nH appears to be a good compromise with only 0.3 dB dip and a
|
|||
|
|
bandwidth of about 20 GHz.
|
|||
|
|
That bandwidth is 2.5 times the input pole of $1 over {2 pi R sub {in} C
|
|||
|
|
sub T}$, the latter representing the bandwidth limit of the conventional
|
|||
|
|
transimpedance amplifier.
|
|||
|
|
From (1), for L=0.75 nH, $DELTA f sub I$ = 18.4 GHz .
|
|||
|
|
In this case, the 3-dB bandwidth of 20 GHz is larger than
|
|||
|
|
$DELTA f sub I$.
|
|||
|
|
Approximating the bandwidth of the image transimpedance amplifier by
|
|||
|
|
$DELTA f sub I ~=~ 1 over {pi R sub {in} C sub T}$, it is seen that
|
|||
|
|
|
|||
|
|
the bandwidth of the image transimpedance amplifier is at least a factor
|
|||
|
|
of two greater than that of the conventional transimpedance amplifier.
|
|||
|
|
|
|||
|
|
It is interesting to observe that the magnitude and phase of $Z sub T ( DELTA f sub I )$
|
|||
|
|
are 1 and -180\(de.
|
|||
|
|
Phase linearity is desireable to minimize pulse distortion.
|
|||
|
|
From Fig. 5B, for L$<=$1 nH, $Z sub T (f)$ is linear in phase
|
|||
|
|
up to 0.75$DELTA f sub I$.
|
|||
|
|
The magnitude and phase of the input impedance $Z sub {in} (f)$ are plotted in
|
|||
|
|
Figs. 6A and 6B.
|
|||
|
|
|$Z sub {in} (f)$| has both midband dip and band edge peak which are
|
|||
|
|
correspondingly responsible for the dip and peak in $|Z sub T (f)|$.
|
|||
|
|
The peaking of |$Z sub {in} (f)$| at the band edge causes a larger voltage
|
|||
|
|
to be developed at node 1 which is consequently transmitted to node 2.
|
|||
|
|
The phase of $Z sub {in} (f)$ is initially close to 0\(de,
|
|||
|
|
i.e., $Z sub {in}$ is resistive, and is approximately flat
|
|||
|
|
with frequency up to 0.75$DELTA f sub I$ before it falls off from thereon.
|
|||
|
|
This deviation from constant phase in $Z sub {in} (f)$ causes the phase of
|
|||
|
|
$Z sub T (f)$ to depart from linearity.
|
|||
|
|
|
|||
|
|
$|Z sub T (f)|$ for $R sub {in}=100~OMEGA$ is plotted in Fig. 7.
|
|||
|
|
L=3 nH yields a bandwidth of 10 GHz and a dip of 0.3 dB and may be considered
|
|||
|
|
optimal since the dip is very small and the peak is only 3 dB.
|
|||
|
|
Compared to the $R sub {in}=50~OMEGA$ case, $L sub {opt}~ alpha ~R sub {in} sup
|
|||
|
|
2$ and bandwidth $alpha ~{1 over {R sub {in}}}$ which agree with theory.
|
|||
|
|
Note that from (6B) L is 2 nH which gives a dip and peak of 1.5 and 2 dB,
|
|||
|
|
respectively, and a bandwidth of 12 GHz which is three times larger than
|
|||
|
|
the input pole.
|
|||
|
|
These results are similar to the $R sub {in}$=50 $OMEGA$ case.
|
|||
|
|
For the image transimpedance amplifier,
|
|||
|
|
assuming the bandwidth to be $1 over {pi R sub {in} C sub T}$ and gain to be
|
|||
|
|
$R sub f$, the gain-bandwidth product (GB) is $1+A over {2 pi C sub p}$.
|
|||
|
|
For large GB, $C sub p$ should be as small as possible and A as large
|
|||
|
|
as possible.
|
|||
|
|
As we will show later, smaller $C sub p$ also results in lower circuit noise.
|
|||
|
|
|
|||
|
|
At microwave frequencies, it is difficult to make L larger than 10 nH as
|
|||
|
|
parasitics will dominate.
|
|||
|
|
Therefore an L value less than 5 nH is preferable.
|
|||
|
|
This small value of L can be replaced by a section of transmission line.
|
|||
|
|
It can be shown that when
|
|||
|
|
$Z sub o sup 2 >> omega L R sub {in}$, then L$approx Z sub o {l over v }$,
|
|||
|
|
where $Z sub o$, l and v are, respectively, the characteristic impedance,
|
|||
|
|
length and phase velocity of the transmission line.
|
|||
|
|
Using $Z sub o = 200~OMEGA$, we obtained similar results to that of using
|
|||
|
|
an actual inductor.
|
|||
|
|
|
|||
|
|
Finally, we wish to determine the sensitivity in frequency response to
|
|||
|
|
variation in element values of the circuit in Fig. 3 terminated by $R sub
|
|||
|
|
L$=100 $OMEGA$.
|
|||
|
|
For $C sub 2$=0.2 pF,
|
|||
|
|
we examine ${|Z sub T (f)|}$ with $C sub 1$ as a parameter for different
|
|||
|
|
values of L.
|
|||
|
|
In Fig. 8, we show the results of varying $C sub 1$ for L=4 nH.
|
|||
|
|
Overall, we conclude that 0.2 pF<$C sub 1$<0.3 pF and 3 nH<L<4 nH will
|
|||
|
|
give a bandwidth between 7 and 10 GHz while restricting the dip and peak
|
|||
|
|
to be less than 1 and 4 dBs, respectively.
|
|||
|
|
Therefore, the ITZ is not extremely sensitive to parameter variations.
|
|||
|
|
Up to $+-$20% variation in $C sub 1$ and $+-$15% variation in L is
|
|||
|
|
permitted.
|
|||
|
|
It is possible in practice to hold element values within this tolerance.
|
|||
|
|
|
|||
|
|
The image impedance method is used in a transimpedance front-end amplifier
|
|||
|
|
design for 10 Gb/s transmission using a
|
|||
|
|
0.5 $mu$m $times$ 300 $mu$m HEMT\*F
|
|||
|
|
|
|||
|
|
Fujitsu FHR01X.
|
|||
|
|
|
|||
|
|
with $C sub p$=0.2 pF, $R sub f = 500~
|
|||
|
|
OMEGA$, and a load
|
|||
|
|
impedance of $R sub L = 200~OMEGA$ in parallel with $C sub L$=0.2 pF.
|
|||
|
|
$C sub L$ is the input capacitance of the next circuit stage.
|
|||
|
|
First we examine the input admittance of the feedback amplifier which is
|
|||
|
|
plotted in .
|
|||
|
|
Up to 8 GHz it corresponds approximately to a
|
|||
|
|
92 $OMEGA$ resistor in parallel with a 0.2 pF capacitor, and therefore can
|
|||
|
|
be made into a one-section image impedance network.
|
|||
|
|
$C sub a$=0.2 pF, and for L=0, the original input pole is 3.4 GHz as shown in
|
|||
|
|
Fig. 10.
|
|||
|
|
To form the ITZ front-end, L=4 nH is added and the bandwidth
|
|||
|
|
increases to 7.6 GHz, more than doubling the original value.
|
|||
|
|
Due to parasitics in the FET and small mismatch between $C sub p$ and $C sub
|
|||
|
|
a$, this response is slight different from Fig. 7.
|
|||
|
|
The responses for other values of L are also shown in Fig. 10.
|
|||
|
|
"NOISE AND RECEIVER SENSITIVITY"
|
|||
|
|
|
|||
|
|
We consider a digital system with binary transmission at 10 Gb/s supported by
|
|||
|
|
our front-end amplifier of 7.6 GHz bandwidth.
|
|||
|
|
(Because a raised cosine output pulse shape is most desirable, in practice
|
|||
|
|
a receiver bandwidth of about 70-80% of the bit rate is often sufficient.
|
|||
|
|
See the discussion on raised cosine pulse shape in the following section).
|
|||
|
|
We will use $DELTA f$ to represent bandwidth and B to
|
|||
|
|
represent bit rate.
|
|||
|
|
Simulation using SPICE show that the one-stage HEMT ITZ front-end amplifier
|
|||
|
|
produces less output noise than the conventional
|
|||
|
|
transimpedance (TZ) amplifier.
|
|||
|
|
Noise comparison is made between the ITZ amplifier of Fig. 10 with L=4 nH and $R
|
|||
|
|
sub f$ = 500 $OMEGA$ (giving $DELTA f$=7.6 GHz and $|Z sub T (0)|$=409 $OMEGA$)
|
|||
|
|
and the TZ amplifier of Fig. 10 with L=0 and $R sub f$ reduced to 195 $OMEGA$
|
|||
|
|
(giving $DELTA f$=7.6 GHz and $|Z sub T (0)|$=149 $OMEGA$).
|
|||
|
|
Sensitivities of the ITZ and TZ receivers will be calculated following the
|
|||
|
|
method in [2] for the two cases of a full raised-cosine output pulse obtained by
|
|||
|
|
equalization and a non-raised-cosine output pulse shape.
|
|||
|
|
For the latter output pulse, there is intersymbol
|
|||
|
|
interference (ISI) during the decision process, causing sensitivity
|
|||
|
|
degradation.
|
|||
|
|
We treat this effect by finite extinction ratio of the optical signal.
|
|||
|
|
|
|||
|
|
The shot noise due to the gate
|
|||
|
|
current, $I sub {gate}$, of the FET is assumed to be negligible.
|
|||
|
|
This assumption is not always valid in current GaAs HEMT technology
|
|||
|
|
as $I sub {gate}$ can be as high as 100 $mu$A, thus contributing
|
|||
|
|
significant shot noise.
|
|||
|
|
As the technology of HEMT improves, it is expected
|
|||
|
|
that this current can be made negligibly small.
|
|||
|
|
In the case of the Fujitsu HEMT used in our design, the sensitivity
|
|||
|
|
degradation due to $I sub {gate}$ is well under 0.1 dB, and can be neglected.
|
|||
|
|
We also assume that the detector dark current, even when it's multiplied as in
|
|||
|
|
the case of the APD detector, contributes such low shot noise that
|
|||
|
|
the corresponding degradation in receiver sensitivity is negligible.
|
|||
|
|
This approximation is valid even for
|
|||
|
|
relatively large values of multiplied dark current (up to 100 nA).
|
|||
|
|
"Equivalent Input Noise"
|
|||
|
|
|
|||
|
|
The total rms output noise voltage computed by using SPICE for the TZ and ITZ
|
|||
|
|
front-end amplifiers are, respectively, 0.194 mV and 0.224 mV.
|
|||
|
|
Because the two amplifiers have different transimpedance, it is
|
|||
|
|
appropriate instead to express noise in terms of equivalent
|
|||
|
|
input noise.
|
|||
|
|
For the two front-ends under discussion, the ITZ is lower in equivalent input
|
|||
|
|
noise by more than a
|
|||
|
|
factor of two in rms value.
|
|||
|
|
|
|||
|
|
The mean square output noise voltage, ${v sub o sup 2} bar$, and
|
|||
|
|
equivalent circuit noise current at the input, ${i sub c sup 2} bar$, of either
|
|||
|
|
the front-end amplifier or the complete receiver are given by [2]
|
|||
|
|
|
|||
|
|
(7)
|
|||
|
|
{v sub o sup 2} bar ~=~ int from 0 to inf S ( omega ) {|
|
|||
|
|
Z sub T ( omega )|} sup 2 df~
|
|||
|
|
and
|
|||
|
|
|
|||
|
|
(8)
|
|||
|
|
{i sub c sup 2} bar ~=~ {{v sub o sup 2} bar } over {| Z sub T (0)|} sup 2
|
|||
|
|
~=~ {1 over {|Z sub T (0)|} sup 2} int from 0 to inf {S ( omega )} {|Z sub
|
|||
|
|
T ( omega )|} sup 2 df~,
|
|||
|
|
|
|||
|
|
where $S( omega )$ is the total equivalent input noise-current spectral density
|
|||
|
|
and $Z sub T ( omega )$ the transfer function of the amplifier or
|
|||
|
|
the receiver, through which the output noise voltage is evaluated.
|
|||
|
|
From (8), ${i sub c sup 2} bar$ depends only on the shape of $|Z sub T
|
|||
|
|
( omega )|$ but not its magnitude.
|
|||
|
|
(9A)
|
|||
|
|
{i sub c sup 2} bar ~=~ C sub 2 I sub 2 B~~~~~~for~S( omega )=C sub 2 ~~~~~
|
|||
|
|
(white~noise),
|
|||
|
|
|
|||
|
|
and
|
|||
|
|
|
|||
|
|
(9B)
|
|||
|
|
{i sub c sup 2} bar ~=~ C sub 3 I sub 3 B sup 3~~~~~~for~S ( omega )=C sub 3
|
|||
|
|
omega sup 2 ,
|
|||
|
|
|
|||
|
|
where
|
|||
|
|
|
|||
|
|
(10A)
|
|||
|
|
I sub 2 ~=~ {1 over {{|Z sub T (0)|} sup 2 B}} int from 0 to inf {|Z sub
|
|||
|
|
T ( omega )|} sup 2 df
|
|||
|
|
|
|||
|
|
and
|
|||
|
|
(10B)
|
|||
|
|
I sub 3 ~=~ {1 over {{|Z sub T (0)|} sup 2 B sup 3}} int from 0 to inf
|
|||
|
|
{|Z sub T ( omega )|} sup 2 f sup 2 df~.
|
|||
|
|
|
|||
|
|
$I sub 2$ and $I sub 3$ for $Z sub T ( omega )$ that convert several different
|
|||
|
|
input waveforms to raised-cosine output waveforms are given in [2].
|
|||
|
|
|
|||
|
|
For both the 1-stage TZ and ITZ amplifiers, the two dominant sources of noise
|
|||
|
|
are the thermal noise associated with the feedback resistor $R sub f$ and
|
|||
|
|
the FET transconductance $g sub m$.
|
|||
|
|
For both amplifiers, the sum of the $R sub f ~(500 OMEGA )$ and $g sub m
|
|||
|
|
~(50 mS)$
|
|||
|
|
contributions relative to total noise is over 96% in rms values.
|
|||
|
|
The noise from the load resistor $R sub L (200 OMEGA )$ is very small relative
|
|||
|
|
to the above sources.
|
|||
|
|
|
|||
|
|
We first discuss the TZ amplifier. The mean square output noise voltage due to $R sub f$,
|
|||
|
|
calculated by SPICE, is $1.65 times {10} sup {-8} ~v sup 2$.
|
|||
|
|
To see the amount of contribution from the various noise sources, their
|
|||
|
|
equivalent input noise-current density expressions are derived
|
|||
|
|
using the simplified circuit model for the FET as shown in Fig. 11 in which all
|
|||
|
|
extrinsic (parasitic) elements are neglected.
|
|||
|
|
The equivalent input noise-current density due to $R sub f$ is
|
|||
|
|
|
|||
|
|
(11A)
|
|||
|
|
S sub {R sub f,TZ} ( omega ) ~=~ {4kT} over {R sub f} {left [
|
|||
|
|
{{(G sub f + g sub m )} sup 2 ~+~ {( omega
|
|||
|
|
C sub T - {G sub f g sub m} over { omega C sub T})} sup 2} over {{(G sub f
|
|||
|
|
- g sub m )} sup 2 ~+~ {({G sub f sup 2 - G sub f g sub m} over {omega C sub
|
|||
|
|
T})} sup 2} right ] }~,
|
|||
|
|
.EN
|
|||
|
|
.DE
|
|||
|
|
.P
|
|||
|
|
where ${G sub f}={1 over {R sub f}}$ and $C sub T = C sub p + C sub a$.
|
|||
|
|
$C sub a$ is the sum of the
|
|||
|
|
gate-source and gate-drain capacitances of the FET, $C sub {gs}$ and
|
|||
|
|
$C sub {gd}$, plus any stray capacitance $C sub s$.
|
|||
|
|
For our circuit, the term within [ ] in (11A) increases monotonically from
|
|||
|
|
1.24 to 1.74 from 0 to 10 GHz with a mean value of 1.42.
|
|||
|
|
In SPICE calculation, all parasitics are included and
|
|||
|
|
from SPICE, the above term is almost a constant, falling slightly with
|
|||
|
|
increasing frequency across the 10 GHz band with a mean of 1.22.
|
|||
|
|
The equivalent circuit derivation is seen to give good approximation
|
|||
|
|
to the exact result.
|
|||
|
|
Using the SPICE result for greater accuracy,
|
|||
|
|
|
|||
|
|
(11B)
|
|||
|
|
S sub {R sub f,TZ} ( omega )~approx~{4.88kT} over R sub f
|
|||
|
|
|
|||
|
|
and the output noise voltage or equivalent input noise current is
|
|||
|
|
proportional to B.
|
|||
|
|
|
|||
|
|
${v sub o sup 2} bar$ due to $g sub m$ calculated by SPICE is $1.7 times {10} sup {-8} ~v sup 2$, about the same as the $R sub f$ noise.
|
|||
|
|
Defining $S sub {g sub m,TZ} ( omega )$ to be the equivalent
|
|||
|
|
input noise-current density, using Fig. 11,
|
|||
|
|
we find the channel noise to be
|
|||
|
|
|
|||
|
|
(12A)
|
|||
|
|
S sub {g sub m,TZ} ( omega ) ~=~ {4kT} over {g sub m}
|
|||
|
|
{left [ 1 over {R sub f sup 2} ~+~ {( omega C sub T )} sup 2 right ] }
|
|||
|
|
{left ( {g sub m R sub f} over {{g sub m R sub f}~-~1} right )} sup 2~.
|
|||
|
|
|
|||
|
|
The last term in (12A) is a constant with a value of approximately 1.24.
|
|||
|
|
However, from SPICE, that term is frequency dependent,
|
|||
|
|
monotonically decreasing from 1.24 to 0.97 with a mean of 1.14 over
|
|||
|
|
the 10 GHz band.
|
|||
|
|
Therefore, from SPICE,
|
|||
|
|
|
|||
|
|
(12B)
|
|||
|
|
S sub {g sub m,TZ} ( omega ) ~approx~ {4.56kT} over {g sub m}
|
|||
|
|
{left [ 1 over {R sub f sup 2} ~+~ {( omega C sub T )} sup 2 right ] }~.
|
|||
|
|
|
|||
|
|
In the limit of large $R sub f$, the $R sub f$ term in (12B) can be neglected.
|
|||
|
|
In that case, from (9B), the $omega sup 2$ term in (12B) produces a circuit
|
|||
|
|
noise component proportional to $B sup 3$.
|
|||
|
|
This is the minimum circuit or FET noise since the $R sub f$ noise in (11B)
|
|||
|
|
would also be negligible.
|
|||
|
|
In practice, however, the $R sub f$ noise is not always negligible since
|
|||
|
|
the largest $R sub f$ value is limited by the required bandwidth.
|
|||
|
|
For the front-ends considered here, the $R sub f$ noise is almost equal to
|
|||
|
|
the $g sub m$ noise.
|
|||
|
|
We have used a noise bandwidth of 10 GHz in the calculation of
|
|||
|
|
equivalent input circuit noise because we assume that such bandwidth
|
|||
|
|
limitation exists, either in the post amplifier, equalizer, or the
|
|||
|
|
decision circuit, or through the cascade of these
|
|||
|
|
elements.
|
|||
|
|
|
|||
|
|
Letting $S sub {R sub L,TZ} ( omega )$ to represent the equivalent input
|
|||
|
|
noise density due to $R sub L$ for the TZ amplifier, we find from Fig. 11 and
|
|||
|
|
(12B) that
|
|||
|
|
|
|||
|
|
|
|||
|
|
(13)
|
|||
|
|
S sub {R sub L,TZ} ( omega ) ~=~ {S sub {g sub m,TZ} ( omega )} over {g sub m
|
|||
|
|
R sub L} ~approx~ {4.56kT} over {g sub m sup 2 R sub L}
|
|||
|
|
{left [ 1 over {R sub f sup 2} ~+~ {( omega C sub T )} sup 2 right ] }~.
|
|||
|
|
|
|||
|
|
This noise density is a factor of $g sub m R sub L approx 10$
|
|||
|
|
smaller than that due to $g sub m$.
|
|||
|
|
|
|||
|
|
From (11B), (12B), (13), (9A) and (9B) and neglecting the $R sub f$ term
|
|||
|
|
in (12B) and (13) since it is much smaller than the $C sub T$ term for
|
|||
|
|
f>5 GHz, the equivalent input noise current is
|
|||
|
|
|
|||
|
|
(14)
|
|||
|
|
{i sub c sup 2} bar ~=~ 4kT left [ {{1.22 I sub 2 B} over {R sub f}} ~+~
|
|||
|
|
{1.14 {{(2 pi C sub T )} sup 2} over {g sub m} I sub 3 B sup 3 {(1+{1 over
|
|||
|
|
{g sub m R sub L}})}} right ]~.
|
|||
|
|
|
|||
|
|
(14) gives the relative contribution from $g sub m$, $R sub f$ and $R sub L$.
|
|||
|
|
The noise ratio between $g sub m$ and $R sub f$ is
|
|||
|
|
|
|||
|
|
(15)
|
|||
|
|
{{i sub {c,g sub m} sup 2} bar} over {{i sub {c,R sub f} sup 2} bar} ~approx~
|
|||
|
|
{{{(2 pi C sub T )} sup 2} I sub 3 R sub f B sup 2 } over {g sub m I sub 2}~.
|
|||
|
|
|
|||
|
|
From (15), to maintain the same ratio, $R sub f$ should be varied as
|
|||
|
|
$B sup {-2}$.
|
|||
|
|
Thus, at high bit rates, $R sub f$ can be
|
|||
|
|
substantially reduced making the design of the transimpedance amplifier easier.
|
|||
|
|
As we shall show in a later section, the transimpedance amplifier compares
|
|||
|
|
favorably with the high-impedance design.
|
|||
|
|
|
|||
|
|
We now discuss the ITZ amplifier.
|
|||
|
|
The mean square output noise voltages due to $g sub m$
|
|||
|
|
and $R sub f$ are $2.1 times {10} sup {-8}~v sup 2$ and $2.8
|
|||
|
|
times {10} sup {-8}~v sup 2$, respectively.
|
|||
|
|
The $R sub f$ noise is 33% larger than the $g sub m$ noise.
|
|||
|
|
From (8), the equivalent input noise current of the ITZ amplifier is actually
|
|||
|
|
less than that of the TZ amplifier because the ITZ amplifier has a much
|
|||
|
|
larger transimpedance.
|
|||
|
|
$S ( omega )$ for the ITZ amplifier varies with frequency in a complex
|
|||
|
|
manner and will be given below.
|
|||
|
|
For the ITZ amplifier, from Fig. 11,
|
|||
|
|
the expression for the equivalent input noise-current density due to $g
|
|||
|
|
sub m$ is
|
|||
|
|
|
|||
|
|
(16)
|
|||
|
|
S sub {g sub m,ITZ} ( omega )~=~4kT {g sub m}
|
|||
|
|
{left {{{{[G sub f (1- {omega sup
|
|||
|
|
2 C sub p L})]} sup 2}~+~{[ omega {(C sub T - omega sup 2 C sub a C sub p L)}]}
|
|||
|
|
sup 2} over {{(G sub f - g sub m)} sup 2} right } }~.
|
|||
|
|
|
|||
|
|
Across the 10 GHz noise bandwidth, the term within { } in (16) ranges from 0.001
|
|||
|
|
to 0.39 and closely approximates that calculated by SPICE.
|
|||
|
|
|
|||
|
|
From Fig. 11, the equivalent input noise-current
|
|||
|
|
density for $R sub f$ is
|
|||
|
|
|
|||
|
|
(17)
|
|||
|
|
S sub {R sub f,ITZ} ( omega ) ~=~ {4kT} over R sub f {left { {{G
|
|||
|
|
sub f sup 2 {(1 - omega sup 2 C sub p L)} sup 2} ~+~ {omega sup 2} {(C sub
|
|||
|
|
T - omega sup 2 C sub a C sub p L)} sup 2} over {{{(G sub f - g sub m )} sup
|
|||
|
|
2} ~~ left [ {{G sub f sup 2 {(1 - omega sup 2 C sub p L)} sup 2} ~+~ omega
|
|||
|
|
sup 2 {(C sub T - omega sup 2 C sub a C sub p L)} sup 2} over {{g sub m
|
|||
|
|
sup 2 {(1 - omega sup 2 C sub p L)} sup 2} ~+~ {omega sup 2} {(C sub T -
|
|||
|
|
omega sup 2 C sub a C sub p L)} sup 2} right ] } right } }~.
|
|||
|
|
|
|||
|
|
Across the noise bandwidth, the term within { } in (17) varies between 0.05 and
|
|||
|
|
5.7 and turns out again to provide good approximation to SPICE calculations.
|
|||
|
|
.P
|
|||
|
|
Finally, the equivalent input noise-current density of $R sub L$ for the ITZ
|
|||
|
|
amplifier is
|
|||
|
|
|
|||
|
|
(18)
|
|||
|
|
S sub {R sub L,ITZ} ( omega ) ~=~ S sub {g sub m,ITZ} over {g sub m R sub L}
|
|||
|
|
~=~ {{4kT} over R sub L}
|
|||
|
|
{left {{{{[G sub f (1- {omega sup
|
|||
|
|
2 C sub p L})]} sup 2}~+~{[ omega {(C sub T - omega sup 2 C sub a C sub p L)}]}
|
|||
|
|
sup 2} over {{(G sub f - g sub m)} sup 2} right } }
|
|||
|
|
|
|||
|
|
which is again a factor of $g sub m R sub L approx 10$ smaller than that due
|
|||
|
|
to $g sub m$.
|
|||
|
|
|
|||
|
|
The total equivalent input noise-current densities (approximately equal
|
|||
|
|
to the sum of the $R sub f$ and $g sub m$ contributions)
|
|||
|
|
for the TZ and ITZ amplifiers are plotted in Fig. 12.
|
|||
|
|
For the TZ amplifier, the $omega sup 2$ dependence is clearly seen.
|
|||
|
|
For the ITZ amplifier, the equivalent input noise-current density is
|
|||
|
|
smaller and almost independent of frequency up to 8 GHz; however, above 8 GHz,
|
|||
|
|
it increases rapidly with frequency.
|
|||
|
|
Up to 10 GHz, the ITZ amplifier is lower in equivalent input noise current
|
|||
|
|
than the TZ amplifier.
|
|||
|
|
As a result, the ITZ receiver has better sensitivity to be discuss next.
|
|||
|
|
|
|||
|
|
|
|||
|
|
"Receiver Sensitivity -- Noise-Free Post Amplifier"
|
|||
|
|
|
|||
|
|
For sensitivity calculation, we follow the approach in [2],
|
|||
|
|
which assumes that the signal-dependent noise is negligible
|
|||
|
|
relative to the circuit noise and that the
|
|||
|
|
probability density function of the signal noise amplitude distribution
|
|||
|
|
is gaussian.
|
|||
|
|
The variance of this gaussian function is equal to ${i sub c sup 2} bar$.
|
|||
|
|
Assuming that the occurrence of a mark or space is equally probable,
|
|||
|
|
the average photocurrent needed to achieve a given bit-error-rate (BER)
|
|||
|
|
is [2]
|
|||
|
|
|
|||
|
|
(19)
|
|||
|
|
{i sub p} bar ~=~ Q sqrt {{i sub c sup 2} bar }
|
|||
|
|
|
|||
|
|
where ${i sub p} bar$ is the average photocurrent and Q is the argument
|
|||
|
|
of the complementary error function, erfc (x), and related to BER by
|
|||
|
|
|
|||
|
|
(20)
|
|||
|
|
BER ~=~ erfc~(Q)~==~ 1 over sqrt {2 pi } int from Q to inf e sup {-({z sup 2}
|
|||
|
|
/2)} dz~.
|
|||
|
|
|
|||
|
|
|
|||
|
|
For BER in the range of ${10} sup {-9}$ to ${10} sup {-15}$,
|
|||
|
|
$Q ~approx~ 3~-~{1 over 3} {log} sub {10} (BER)$.
|
|||
|
|
For BER=${10} sup {-9}$, $Q approx 6$.
|
|||
|
|
In terms of optical measurement using a p-i-n detector, (19) becomes [2]
|
|||
|
|
|
|||
|
|
(21)
|
|||
|
|
eta P bar ~=~ {({h nu } over q )}Q sqrt {{i sub c sup 2} bar }~,
|
|||
|
|
.EN
|
|||
|
|
.DE
|
|||
|
|
.P
|
|||
|
|
where $P bar$ is the required average optical power, $eta$ is the quantum
|
|||
|
|
efficiency, $h nu$ the photon energy and q the electronic charge.
|
|||
|
|
For an avalanche photodetector (APD), the magnitude of the signal-dependent
|
|||
|
|
noise in a time slot (assumed only due to the signal within that time
|
|||
|
|
slot) is a function of the average avalanche gain M and is no longer
|
|||
|
|
negligible in comparison to the signal-independent circuit noise.
|
|||
|
|
(21) becomes [2]
|
|||
|
|
|
|||
|
|
(22)
|
|||
|
|
eta P bar ~=~ {({h nu } over q )}Q left [ { sqrt {{i sub c sup 2 } bar }
|
|||
|
|
over M } ~+~ qB I sub 1 Q F(M) right ] ~,
|
|||
|
|
|
|||
|
|
where $I sub 1$ is given in [2] for raised-cosine output and various input
|
|||
|
|
pulse shapes.
|
|||
|
|
F(M) is the excess noise factor given by\*(Rf
|
|||
|
|
|
|||
|
|
R. J. McIntyre, "Multiplication Noise in Uniform Avalanche Diodes,"
|
|||
|
|
|
|||
|
|
IEEE Trans. Electron Devices,
|
|||
|
|
|
|||
|
|
vol. ED-13, pp.164-168, 1966.
|
|||
|
|
|
|||
|
|
(23)
|
|||
|
|
F(M) ~=~ kM ~+~ (1-k)(2-{1 over M})
|
|||
|
|
|
|||
|
|
|
|||
|
|
in which $k$ is the electron and hole ionization coefficient ratio.
|
|||
|
|
(22) is optimized when [2]
|
|||
|
|
|
|||
|
|
(24)
|
|||
|
|
M~=~M sub {opt} ~=~ {1 over {k sup {half}}} { left [ {sqrt {{i sub c sup 2}
|
|||
|
|
bar } over {qB I sub 1 Q}} ~+~ k ~-~ 1 right ] } sup {half}~.
|
|||
|
|
|
|||
|
|
For p-i-n detectors, the sensitivity is calculated for input and output
|
|||
|
|
pulse shapes of NRZ and full raised-cosine, respectively, and BER=${10} sup
|
|||
|
|
{-9}$ at 10 Gb/s, at $lambda$=1.3 $mu$m.
|
|||
|
|
From (21), (9A), (9B), (11B), (12B), (13), $I sub 2$=0.562 and $I sub
|
|||
|
|
3$=0.087 for the assumed pulse shapes, we calculate for the TZ amplifier that
|
|||
|
|
$sqrt {{i sub c sup 2 } bar } ~=~ 1.0~mu A$, giving $eta P bar$ of -22.4 dBm.
|
|||
|
|
In comparison, for the ITZ amplifier, $sqrt {{i sub c sup 2 } bar } ~=~ 0,475
|
|||
|
|
~mu A$, giving $eta P bar$ of -25.6 dBm.
|
|||
|
|
$eta P bar$ against BER for both the TZ and ITZ receivers using
|
|||
|
|
the p-i-n detector are plotted in Fig. 13 as shown by the curves marked "NF=0
|
|||
|
|
dB".
|
|||
|
|
It is seen that for B=10 Gb/s, in addition to providing over 2.7 times
|
|||
|
|
higher gain, the ITZ receiver gives 3.2 dB better sensitivity than the
|
|||
|
|
TZ receiver at ${10} sup {-9}$ BER.
|
|||
|
|
|
|||
|
|
For APDs, one of the most advanced is the InGaAs SAGM (Separate
|
|||
|
|
Absorption and Multiplication regions) APD (k=0.35).
|
|||
|
|
Using this APD, at 10 Gb/s, from (24), $M sub {opt}$=23.3 for the TZ receiver
|
|||
|
|
and equals 16 for the ITZ receiver.
|
|||
|
|
Figure 14 is a plot of the calculated sensitivity of the TZ and ITZ
|
|||
|
|
receivers as a function of M.
|
|||
|
|
Especially for the ITZ receiver, the optimal range of M is broad, extending
|
|||
|
|
from about 11 to 23 with a $DELTA {eta P} bar$ of only 0.2 dB over that
|
|||
|
|
range.
|
|||
|
|
Therefore, in an actual ITZ receiver using the above APD, the avanlanche
|
|||
|
|
gain need not be set precisely in order to obtain near optimum sensitivity.
|
|||
|
|
With $I sub 1 approx$0.548 for NRZ input and full raised-cosine output pulse
|
|||
|
|
shapes, at B=10 Gb/s and BER=${10} sup {-9}$, $eta P bar$ equals -32.8 dBm for
|
|||
|
|
the TZ receiver and -34.2 dBm for the ITZ receiver.
|
|||
|
|
The sensitivity advantage of the ITZ over the TZ receiver is now reduced
|
|||
|
|
to 1.4 dB.
|
|||
|
|
$eta P bar$ versus BER for both TZ and ITZ receivers using this APD are
|
|||
|
|
plotted in Fig. 15 as shown by the curves marked "NF=0 dB".
|
|||
|
|
From Fig. 13 and 15, the improvement in sensitivity by using the InGaAs
|
|||
|
|
SAGM APD ranges from 8.6-10.4 dB over the p-i-n detector.
|
|||
|
|
In practice, however, the actual sensitivity improvement is
|
|||
|
|
less due to finite gain-bandwidth product of the APD.
|
|||
|
|
Currently, the best GB for an InGaAs SAGM APD is 70 GHz\*(Rf.
|
|||
|
|
|
|||
|
|
B. L. Kasper and J. C. Campbell, "Multigigabit-per-Second Avalanche Photodiode
|
|||
|
|
Lightwave Receivers,"
|
|||
|
|
|
|||
|
|
Journal of Lightwave Technology,
|
|||
|
|
vol. LT-5, no. 10, Oct. 1987.
|
|||
|
|
|
|||
|
|
Using this diode as an example, if a bandwidth of 10 GHz is required,
|
|||
|
|
the permissible gain of M=7 would be less than $M sub {opt}$, and from Fig. 14
|
|||
|
|
would yield sensitivities of -30.3 dBm for the TZ receiver and
|
|||
|
|
-33 dBm for the ITZ receiver.
|
|||
|
|
In general, we find that practical receivers using the InGaAs SAGM APD should
|
|||
|
|
provide over 7 dB better sensitivity than using the p-i-n detector, for
|
|||
|
|
both types of front-ends.
|
|||
|
|
|
|||
|
|
We now consider the degradation in sensitivity when the output pulse shape
|
|||
|
|
is not raised-cosine.
|
|||
|
|
For example, that situation would occur if the decision circuit were
|
|||
|
|
connected directly to the front-end output without equalization.
|
|||
|
|
The sensitivity degradation occurs as a result of two separate effects:
|
|||
|
|
intersymbol interference (ISI) from adjacent time slots and greater
|
|||
|
|
noise in the signal at the decision circuit input.
|
|||
|
|
The latter effect occurs because the equalizer not only optimizes output pulse
|
|||
|
|
shape to minimize ISI but also band-limits the output noise voltage.
|
|||
|
|
For the single amplifier stage of Fig. 10 we obtain from SPICE $sqrt {{i sub c
|
|||
|
|
sup 2 } bar }$=1.3 $mu$A
|
|||
|
|
for the TZ amplifier and $sqrt {{i sub c sup 2 } bar }$=0.55 $mu$A
|
|||
|
|
for the ITZ amplifier.
|
|||
|
|
Using (21), sensitivity is $eta P bar$ = -21.3 dBm for the
|
|||
|
|
TZ receiver and -25 dBm for the ITZ receiver, at ${10} sup {-9}$ BER,
|
|||
|
|
B=10 Gb/s and $lambda$=1.3 $mu$m, using a p-i-n detector.
|
|||
|
|
In comparison, the sensitivities for a raised-cosine output pulse
|
|||
|
|
are better by 1.1 and 0.6 dB, respectively, for the TZ and ITZ receivers.
|
|||
|
|
The reason is that for an NRZ input pulse, the transfer function which yields
|
|||
|
|
a raised-cosine output pulse is more band-limiting than our front-end
|
|||
|
|
amplifier response which is essentially flat up to B.
|
|||
|
|
This result and the effect of ISI to be discussed below indicate the importance
|
|||
|
|
in controlling the output pulse shape.
|
|||
|
|
|
|||
|
|
Figure 16 shows the output pulse waveforms for a single 10 Gb/s NRZ input
|
|||
|
|
pulse, for both the TZ and ITZ amplifiers.
|
|||
|
|
We assume that these waveforms are input to the decision circuit and
|
|||
|
|
approximate the effect of ISI by that of finite extinction ratio, i.e.,
|
|||
|
|
nonzero transmitted optical power corresponding to a space.
|
|||
|
|
Attributing the amplitude of the first positive side-lobe of the output pulse
|
|||
|
|
waveform to be due to the nonzero power detected during a space, we can
|
|||
|
|
use [2] to calculate the resulting sensitivity penalty.
|
|||
|
|
From Fig. 16, given that the ratio of the peak amplitudes of the first positive
|
|||
|
|
ripple to the main-lobe is approximately 0.075 for the ITZ receiver, we
|
|||
|
|
calculate that for a p-i-n detector, a 0.7 dB sensitivity penalty is incurred
|
|||
|
|
for the ITZ receiver; there is practically no ISI and therefore no sensitivity
|
|||
|
|
penalty for the TZ receiver.
|
|||
|
|
ISI is greater in the ITZ receiver since its transfer function deviates more
|
|||
|
|
from the ideal transfer function (which produces no ISI) than that
|
|||
|
|
of the TZ receiver, as seen
|
|||
|
|
from the insert of Fig. 16.
|
|||
|
|
Note that our calculation only considers the ISI from a single pulse from the
|
|||
|
|
previous time slot, and therefore is not the worst case.
|
|||
|
|
|
|||
|
|
"Receiver Sensitivity - Including Post Amplifier Noise"
|
|||
|
|
|
|||
|
|
From (12A), (13) and (9B), in the limit of very large $R sub f$ and $R sub L$,
|
|||
|
|
${i sub c sup 2}
|
|||
|
|
bar ~alpha~ {C sub a sup 2} over {g sub m} ~alpha~ W sub g$, where $W sub
|
|||
|
|
g$ is the FET gate width.
|
|||
|
|
Noise is zero when $C sub a$=0.
|
|||
|
|
However, this would correspond to the absence of the front-end amplifier
|
|||
|
|
altogether.
|
|||
|
|
This apparent paradox arises because we have not considered post amplifier
|
|||
|
|
noise.
|
|||
|
|
When that noise is included, minimum noise is attained at non-zero value
|
|||
|
|
of $W sub g$.
|
|||
|
|
Therefore, for noise minimization, it is important to
|
|||
|
|
include the post amplifier noise which will be discussed next.
|
|||
|
|
|
|||
|
|
So far we have assumed the post amplifier to be noise-free.
|
|||
|
|
If the equalizer is lumped together with the post amplifier, the functions of
|
|||
|
|
this circuit are to produce gain and provide pulse shaping.
|
|||
|
|
In reality, the post amplifier also produces noise which degrades
|
|||
|
|
receiver sensitivity.
|
|||
|
|
The noise property of an amplifier is often given in terms of noise figure (NF)
|
|||
|
|
which in turn is defined only for a resistive source impedance as follows:
|
|||
|
|
|
|||
|
|
(25)
|
|||
|
|
NF ~==~ {input~(S/N)} over {output~(S/N)}
|
|||
|
|
or
|
|||
|
|
|
|||
|
|
(26)
|
|||
|
|
NF ~==~ {Total~available~output~noise~power} over {Available~output~noise
|
|||
|
|
~power~due~only~"to"~R sub s}
|
|||
|
|
|
|||
|
|
where $(S/N)$ is the signal-to-noise power ratio of the amplifier
|
|||
|
|
and $R sub s$ is the source resistance.
|
|||
|
|
Strictly speaking, the output impedance of the front-end amplifier is not
|
|||
|
|
a pure resistance but also includes a reactance.
|
|||
|
|
However, the reactance is smaller than the resistance so that we can
|
|||
|
|
treat the output impedance as a resistor of value $R sub o$.
|
|||
|
|
For $R sub s$=$R sub o$ the noise of the post amplifier can be expressed in
|
|||
|
|
terms of an equivalent noise voltage at its input, ${v sub i sup 2} bar$,
|
|||
|
|
by
|
|||
|
|
|
|||
|
|
(27)
|
|||
|
|
{v sub i sup 2} bar ~=~ 4kT {R sub o} {({NF} bar ~-~1)}B
|
|||
|
|
|
|||
|
|
where ${NF} bar$ is the average of the spot noise figure of the post amplifier.
|
|||
|
|
In terms of ${i sub c sup 2} bar$ at the input of the front-end amplifier,
|
|||
|
|
|
|||
|
|
(28)
|
|||
|
|
{i sub c sup 2} bar ~=~ {4kT {R sub o} {({NF} bar ~-~1)}B} over {{| Z sub {fe}
|
|||
|
|
(0) |} sup 2 }
|
|||
|
|
|
|||
|
|
where $Z sub {fe} (0)$ is the transfer function of the front-end at f=0.
|
|||
|
|
Adding this to the original equivalent input noise current of the front-end
|
|||
|
|
amplifier, we can use (21) and (22) to compute the degradation in sensitivity
|
|||
|
|
due to noise in the post amplifier.
|
|||
|
|
The average $R sub o$ for both amplifiers is about 50 $OMEGA$.
|
|||
|
|
|
|||
|
|
In Fig. 17 the calculated sensitivity is plotted against ${NF} bar$
|
|||
|
|
for the ITZ and TZ receivers for BER=${10} sup {-9}$ at B=10 Gb/s and
|
|||
|
|
for both the p-i-n and APD detectors.
|
|||
|
|
As before the input and output pulse shapes are assumed to be NRZ and
|
|||
|
|
raised-cosine, respectively.
|
|||
|
|
Optimal avalanche gain at each ${NF} bar$ value is assumed for the APD.
|
|||
|
|
Relative to the APD, the sensitivity penalty variation with ${NF} bar$ in using
|
|||
|
|
a p-i-n detector is greater, for both the ITZ and TZ receivers, because the
|
|||
|
|
APD provides internal gain.
|
|||
|
|
In going from a noise-free post amplifier to one that has a 10 dB noise figure,
|
|||
|
|
for p-i-n detectors, the ITZ and TZ receivers suffer about 2.3 dB and 3.2 dB
|
|||
|
|
sensitivity penalty, respectively; for APDs, that degradation is 1 dB
|
|||
|
|
for the ITZ receiver and 1.5 dB for the TZ receiver.
|
|||
|
|
The ITZ receiver suffers less penalty than the TZ receiver because
|
|||
|
|
greater gain (transimpedance) is provided by the front-end amplifier in the
|
|||
|
|
former.
|
|||
|
|
|
|||
|
|
In Figs. 13 and 15 we plotted sensitivity versus BER for the ITZ and TZ
|
|||
|
|
receivers over the range of BER from ${10} sup {-6}$ to ${10} sup {-15}$ as a
|
|||
|
|
function of post amplifier average noise figure (${NF} bar$).
|
|||
|
|
A family of curves each representing different ${NF} bar$s
|
|||
|
|
(0, 5 and 10 dB) is shown for each type of receiver.
|
|||
|
|
A practical number for ${NF} bar$ is 5 dB.
|
|||
|
|
Using that value, from Figs. 13 and 15, the degradation in receiver sensitivity
|
|||
|
|
for a p-i-n detector in going from ${NF} bar$=0 dB to ${NF} bar$=5 dB
|
|||
|
|
(over the entire BER range shown) is about 0.9 dB for the ITZ receiver and 1.3
|
|||
|
|
dB for the TZ receiver.
|
|||
|
|
Therefore, for
|
|||
|
|
|
|||
|
|
practical receivers using the p-i-n detector, at 10 Gb/s operation the ITZ
|
|||
|
|
receiver should provide over 3.5 dB better sensitivity than the conventional
|
|||
|
|
transimpedance receiver.
|
|||
|
|
|
|||
|
|
Using the APD detector, for the same noise figure, the penalties are about 0.4
|
|||
|
|
dB and 0.6 dB, respectively, for the ITZ and TZ receivers.
|
|||
|
|
These results assume large enough GB of the APD such that $M sub {opt}$
|
|||
|
|
is always attained.
|
|||
|
|
$M sub {opt}$ increases with ${NF} bar$.
|
|||
|
|
For APD GB of 70 GHz and $M=7<M sub {opt}$, the sensitivity degradation
|
|||
|
|
going from ${NF} bar$=0 dB to ${NF} bar$=5 dB (over the ${10} sup {-6}$
|
|||
|
|
to ${10} sup {-15}$ BER range) is 0.7 dB for the ITZ receiver and 1.1 dB
|
|||
|
|
for the TZ receiver.
|
|||
|
|
Therefore, for
|
|||
|
|
|
|||
|
|
practical
|
|||
|
|
receivers using the above APD, at 10 Gb/s operation the ITZ receiver should
|
|||
|
|
be 3 dB better in sensitivity than the conventional transimpedance
|
|||
|
|
configuration.
|
|||
|
|
|
|||
|
|
It is interesting to note that the ITZ/p-i-n receiver with a post amplifier
|
|||
|
|
of ${NF} bar$=10 dB still has about a 1 dB sensitivity superiority over the
|
|||
|
|
TZ/p-i-n receiver with a noise-free post amplifier, across the entire BER
|
|||
|
|
range; in comparison, that superiority for APDs is 0.4 dB.
|
|||
|
|
|
|||
|
|
The calculated sensitivities at ${10} sup {-9}$ BER for the various receiver
|
|||
|
|
configurations, at average post amplifier noise figure values of 0, 5
|
|||
|
|
and 10 dB, are summarized in Table 1.
|
|||
|
|
|
|||
|
|
|
|||
|
|
"Comparison With Published Results"
|
|||
|
|
|
|||
|
|
Recently published results on high speed receivers include a complete
|
|||
|
|
APD/FET receiver operating at 8 Gb/s with 6.9 GHz bandwidth\*(Rf
|
|||
|
|
|
|||
|
|
B. L. Kasper et al.,
|
|||
|
|
"An APD/FET Optical Receiver Operating at 8 Gbit/s,"
|
|||
|
|
|
|||
|
|
Journal of Lightwave Technology,
|
|||
|
|
vol. LT-5, no.3, March 1987.
|
|||
|
|
|
|||
|
|
and a p-i-n/FET front-end with 8 GHz bandwidth\*(Rf.
|
|||
|
|
|
|||
|
|
J. L. Gimlett,
|
|||
|
|
"Low-Noise 8 GHz PIN/FET Optical Receiver,"
|
|||
|
|
|
|||
|
|
Electronics Letters,
|
|||
|
|
vol. 23, no.6, March 1987.
|
|||
|
|
|
|||
|
|
Both receivers are of the high-impedance type.
|
|||
|
|
In the former, an InGaAs SAGM APD with GB=60 GHz was used in conjunction with
|
|||
|
|
a two-stage GaAs MESFET preamplifier, followed by an RC differentiator and a
|
|||
|
|
post amplifier comprised
|
|||
|
|
of cascaded commercial wide-band amplifiers plus a transversal equalizer (for
|
|||
|
|
bandwidth enhancement).
|
|||
|
|
Sensitivity of -25.8 dBm was measured.
|
|||
|
|
The latter receiver consists of an InGaAs p-i-n photodiode connected to a
|
|||
|
|
three-stage GaAs MESFET preamplifier, and reports a measured equivalent
|
|||
|
|
input noise-current density of <$1.44 times {10} sup {-22}~A sup 2 over Hz$.
|
|||
|
|
|
|||
|
|
As discussed in Sec. 3.2, when using an InGaAs APD with GB=70 GHz, the
|
|||
|
|
ITZ receiver which incorporates a noise-free post amplifier and perfect
|
|||
|
|
equalization (to obtain raised-cosine output pulse shape) has an
|
|||
|
|
expected sensitivity of $eta P bar$ = -33 dBm.
|
|||
|
|
A 10 dB average post amplifier noise figure would cause the sensitivity
|
|||
|
|
to degrade by about 1 dB, and should ISI exist due to imperfect equalization,
|
|||
|
|
an additional dB of degradation may be incurred.
|
|||
|
|
In that case, the predicted sensitivity of $eta P bar$ = -31 dBm would still be
|
|||
|
|
about 5 dB better than the results of [6].
|
|||
|
|
Of course, we must note that the comparison is between predicted and
|
|||
|
|
experimental results.
|
|||
|
|
In Fig. 18 we have plotted the square root of equivalent input noise-current
|
|||
|
|
densities of the TZ and ITZ front-ends as well as the front-end of [7].
|
|||
|
|
For the front-end of [7] we show both the calculated and measured results.
|
|||
|
|
It is seen that the computed equivalent input noise current of the ITZ
|
|||
|
|
front-end and that of [7] are comparable, and we would expect that the
|
|||
|
|
two receivers have similar sensitivities.
|
|||
|
|
|
|||
|
|
The above comparison lead to a very important and interesting discovery --
|
|||
|
|
the ITZ receiver which is of the transimpedance configuration has equal
|
|||
|
|
or superior sensitivity in comparison with the best high-impedance
|
|||
|
|
receivers of comparable bandwidth.
|
|||
|
|
Up to this time, the high-impedance configuration has always boasted
|
|||
|
|
the best sensitivity [4].
|
|||
|
|
However, in systems application, the transimpedance design is usually
|
|||
|
|
favored due to greater ease in manufacture as well as providing larger
|
|||
|
|
dynamic range.
|
|||
|
|
The ITZ receiver combines the advantages of both the high-impedance
|
|||
|
|
and transimpedance types.
|
|||
|
|
|
|||
|
|
"STABILITY"
|
|||
|
|
|
|||
|
|
Since the S-parameters of the HEMT are available, it is convenient to examine
|
|||
|
|
the stability of the front-end amplifier by the stability factors K and
|
|||
|
|
$B sub 1$\*(Rf,
|
|||
|
|
|
|||
|
|
G. Gonzalez,
|
|||
|
|
Microwave Transistor Amplifiers Analysis and Design,
|
|||
|
|
Prentice-Hall, Inc., Englewood Cliffs, NJ 1984.
|
|||
|
|
|
|||
|
|
and also the source and load stability circles, where
|
|||
|
|
|
|||
|
|
|
|||
|
|
(29)
|
|||
|
|
K ~=~ {1~-~{{|S sub {11}|} sup 2}~-~{{|S sub {22}|} sup 2}~+~{{| DELTA |} sup
|
|||
|
|
2}} over {2 {|S sub {12} S sub {21}|}}
|
|||
|
|
and
|
|||
|
|
|
|||
|
|
(30)
|
|||
|
|
B sub 1 ~=~ 1~+~{{|S sub {11}|} sup 2}~-~{{|S sub {22}|} sup 2}~-~{| DELTA |}
|
|||
|
|
sup 2
|
|||
|
|
|
|||
|
|
where $DELTA ~=~ S sub {11} S sub {22} ~-~ S sub {12} S sub {21}$ and
|
|||
|
|
$S sub {ij}$ is the ${ij} sup {th}$ component of the scattering matrix.
|
|||
|
|
A two-port network is unconditionally stable, i.e., independent of source
|
|||
|
|
and load impedances when $K$>1 and $B sub 1$>0.
|
|||
|
|
These conditions guarantee that the real parts of the input and output
|
|||
|
|
impedances of the two-port network are positive.
|
|||
|
|
When $K$<1 and/or $B sub 1$<0, the network is potentially unstable.
|
|||
|
|
In this case the source and load stability circles will give the range
|
|||
|
|
of source and load impedance values within which $K$>1 and $B sub 1$<1
|
|||
|
|
for stable operation.
|
|||
|
|
|
|||
|
|
The Fujitsu HEMT alone is potentially unstable due to internal feedback by the
|
|||
|
|
gate-drain capacitance $C sub {gd}$.
|
|||
|
|
However, when sufficient feedback by $R sub f$ is applied, the FET becomes
|
|||
|
|
unconditionally stable.
|
|||
|
|
For $K$ and $B sub 1$ calculation, we have included $C sub p$, $C sub L$
|
|||
|
|
and $R sub L$ in the two-port network, i.e., the source and load impedances
|
|||
|
|
are infinite.
|
|||
|
|
$K$ and $B sub 1$ as a function of $R sub f$ (for $R sub f$ from 200 to
|
|||
|
|
2 k$OMEGA$) for the TZ and ITZ amplifiers are plotted in Figs. 18A and 18B,
|
|||
|
|
respectively.
|
|||
|
|
In both cases, when $R sub f$<1 k$OMEGA$, both amplifiers are unconditionally
|
|||
|
|
stable.
|
|||
|
|
Since the $R sub f$ value used in our design is 500 $OMEGA$, there is
|
|||
|
|
substantial margin to guard against potential instability.
|
|||
|
|
|
|||
|
|
|
|||
|
|
"ENHANCEMENT OF BANDWIDTH BY PARALLEL AND SERIES INDUCTIVE COMPENSATION"
|
|||
|
|
|
|||
|
|
In the above ITZ front-end using the Fujitsu HEMT, we found that the
|
|||
|
|
bandwidth can be further extended by compensating the output circuit.
|
|||
|
|
The output circuit can be parallel compensated by an inductor $L sub p$ in
|
|||
|
|
series with $R sub L$, and additionally, series compensated by an inductor
|
|||
|
|
$L sub s$ in series with $C sub L$.
|
|||
|
|
The output voltage is taken across $C sub L$ which represents the input
|
|||
|
|
capacitor of the next stage.
|
|||
|
|
$L sub p$ increases the impedance of $R sub L$ while $L sub s$ reduces the
|
|||
|
|
shunting effect of $C sub L$.
|
|||
|
|
The result for using $L sub p$ and $L sub s$ in conjunction with the image
|
|||
|
|
impedance front-end is shown in Fig. 19.
|
|||
|
|
The inductor at the input node (now referred to as $L sub {in}$) is decreased
|
|||
|
|
to 2 nH to provide a wider bandwidth
|
|||
|
|
but also greater midband dip and band edge peak.
|
|||
|
|
$L sub p$=8 nH compensates for the dip and $L sub s$=0.5 nH offsets the
|
|||
|
|
peak.
|
|||
|
|
The bandwidth increases from 7.6 GHz to over 12 GHz, and phase linearity is
|
|||
|
|
maintained up to 10 GHz.
|
|||
|
|
Therefore, using three inductors, the bandwidth is increased by almost a factor
|
|||
|
|
of four over the original TZ amplifier.
|
|||
|
|
|
|||
|
|
|
|||
|
|
Summary :
|
|||
|
|
|
|||
|
|
|
|||
|
|
We have suggested an image transimpedance front-end amplifier for an optical
|
|||
|
|
receiver at microwave frequencies.
|
|||
|
|
The photodiode capacitance and the input capacitance of the amplifier form
|
|||
|
|
the shunt capacitors of an artificial transmission line of one section.
|
|||
|
|
The bandwidth of the image transimpedance front-end is found to be two to
|
|||
|
|
three times larger than the conventional transimpedance front-end.
|
|||
|
|
.P
|
|||
|
|
Depending on the desired bandwidth, the image transimpedance may
|
|||
|
|
suffer minor midband dip and band edge peaking.
|
|||
|
|
For a 1.5 dB dip and 2 dB peak, the bandwidth is three times that of the
|
|||
|
|
conventional design.
|
|||
|
|
For 10 Gb/s transmission
|
|||
|
|
the image transimpedance amplifier is not sensitive to component variation
|
|||
|
|
up to $+-$15%.
|
|||
|
|
Using the image impedance method, the transimpedance and bandwidth of a
|
|||
|
|
$0.5~mu m~times~300~mu m$ Fujitsu HEMT amplifier
|
|||
|
|
are 409 $OMEGA$ and 7.6 GHz, respectively.
|
|||
|
|
In comparison, in the conventional transimpedance amplifier design for
|
|||
|
|
the same transimpedance, the bandwidth is only 3.2 GHz.
|
|||
|
|
|
|||
|
|
Compared to the TZ amplifier redesigned for identical
|
|||
|
|
bandwidth as the ITZ amplifier, assuming noise-free post amplification
|
|||
|
|
and NRZ input and full raised-cosine output pulse shapes, in
|
|||
|
|
addition to providing 2.7 times greater transimpedance, the ITZ
|
|||
|
|
receiver has about 3.2 dB better sensitivity for p-i-n detectors
|
|||
|
|
and 1.4 dB better sensitivity for InGaAs SAGM APDs,
|
|||
|
|
over the BER range from
|
|||
|
|
${10} sup {-6}$ to ${10} sup {-15}$.
|
|||
|
|
Using the same APD with a gain-bandwidth product of 70 GHz, the calculated
|
|||
|
|
sensitivity of either receiver is about 7 dB better than when using a p-i-n
|
|||
|
|
detector.
|
|||
|
|
|
|||
|
|
A raised-cosine output pulse shape obtained with an equalizer is superior
|
|||
|
|
to a non-equalized output pulse shape in terms of both lower noise and
|
|||
|
|
zero ISI.
|
|||
|
|
Specifically, the lower noise
|
|||
|
|
translates to about 1 dB better sensitivity, for both receivers using p-i-n
|
|||
|
|
detectors at ${10} sup {-9}$ BER and B=10 Gb/s;
|
|||
|
|
the ISI caused by the non-raised-cosine output pulse
|
|||
|
|
shape causes about 0.7 dB sensitivity penalty.
|
|||
|
|
|
|||
|
|
The noise contributed by the post amplifier can impose significant
|
|||
|
|
sensitivity penalty.
|
|||
|
|
For an average noise figure of 10 dB in the post amplifier with $R sub o$=50
|
|||
|
|
$OMEGA$, the penalties range from 2.3-3.2 dB for a p-i-n detector and
|
|||
|
|
1-1.5 dB for the InGaAs SAGM APD.
|
|||
|
|
For practical implementation of the ITZ receiver which includes post
|
|||
|
|
amplifier average noise figure of 5 dB and APD gain-bandwidth product of
|
|||
|
|
70 GHz, it should provide 3 dB better sensitivity than the conventional
|
|||
|
|
transimpedance receiver for either the p-i-n or APD detector, at 10 Gb/s
|
|||
|
|
operation over the BER range from
|
|||
|
|
${10} sup {-6}$ to ${10} sup {-15}$.
|
|||
|
|
|
|||
|
|
The sensitivity of the ITZ receiver compares favorably with that of
|
|||
|
|
published high-impedance designs with the added advantages of large dynamic
|
|||
|
|
range and ease of fabrication.
|
|||
|
|
|
|||
|
|
The bandwidth of the image transimpedance amplifier can be further enhanced
|
|||
|
|
by inductive compensation.
|
|||
|
|
For example, we have shown that when the load of our HEMT amplifier is
|
|||
|
|
both parallel and series compensated, the bandwidth is increased from
|
|||
|
|
7.6 GHz to over 12 GHz.
|
|||
|
|
|
|||
|
|
Figures 1-18
|
|||
|
|
Table 1
|
|||
|
|
|
|||
|
|
Cover Sheet Only:
|
|||
|
|
DvMs 211, 213, 214
|
|||
|
|
R. Gnanadesikan
|
|||
|
|
J. M. Rowell
|
|||
|
|
W. D. Warters
|
|||
|
|
|
|||
|
|
|
|||
|
|
Divisions 21360, 21470
|
|||
|
|
DvMs/DsMs 213, 214
|
|||
|
|
K. A. Bischoff
|
|||
|
|
M. M. Choy
|
|||
|
|
A. G. Chynoweth
|
|||
|
|
J. L. Gimlett
|
|||
|
|
Chinlon Lin
|
|||
|
|
E. Nussbaum
|
|||
|
|
|
|||
|
|
|
|||
|
|
Note: There are still some EMAC prompts in here, sorry about that..every time I try to edit them i get "Fatal Internal Error"..I wonder what that means <Smirk!> -DT.
|
|||
|
|
|
|||
|
|
|