****************************************************************************
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 nH5 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=71 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 -DT.