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646 IEEE JOURNAL ON SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 7, NO. 4, JULY/AUGUST 2001
is prudent to precede the analyzer with a good lownoise amplifier
(LNA). This will lower the system noise figure to several
decibels above and ensure shotnoise limited sensitivity. Our
system has a 40dB gain amplifier with a noise figure of better
than 6 dB from 10 kHz to 40 MHz.
A typical RF spectrum analyzer has a useful frequency range
of 100 Hz–1 GHz, and it is usually desirable to augment this
with a lower frequency FFT analyzer with a range down to
0.01 Hz. The frequency boundary between the two instruments
will be determined by the noise performance of each analyzer,
its resolution bandwidth, and data acquisition speed. Modern
spectrum analyzers frequently come equipped with a “noise
measurement” function that calculates the noise power spectral
density, taking into account the shape factors of the RF and IF
filters in the analyzer. This feature should be exploited when
measuring broadband noise, as it is not accurate to simply
divide by the receiver’s 3 dB bandwidth. When encountering
coherent signals (spurs), however, they must be left in terms of
absolute power and not normalized to the receiver bandwidth
(this issue is frequently overlooked).
Fig. 4. Equivalent circuit of a transimpedance amplifier driven by a photodiode
including noise sources.
fore the output meansquared noise voltage spectral density becomes

V. PHOTORECEIVER DESIGN
A. Transimpedance Amplifiers
The measurement of shot noise on signals of large average
photocurrent presents a somewhat different set of requirements
from the usual optical signal detection. When we try to measure
very low power signals with high modulation index, we usually
use a transimpedance amplifier with very high feedback resistance
to overcome the noise in following stages. For detecting
highspeed optical data, we generally amplify the photodetector
with broadband 50 amplifiers. Neither of these approaches
is necessarily optimum for our problem (high average current),
and therefore it is useful to rethink the receiver design. The most
obvious solution is to use a transimpedance configuration with a
relatively low feedback resistance, which is required to keep the
dc output voltage within the powersupply constraints. Owing to
the prevalence of highquality lownoise operational amplifiers,
we use them in our baseband receiver circuits. Since the input
resistance of the transimpedance configuration is extremely low,
the circuit speed will be determined by photodiode and slewrate
limitations.
To optimize the photoreceiver design, we start by analyzing
the noise contributions in a standard transimpedance amplifier
and see how they vary as we adjust parameters such as feedback
resistance, average photocurrent, and circuit component noise.
The standard transimpedance amplifier shown as PR2 in Fig. 1
can be analyzed by taking account of all noise sources due to the
photodiode, the feedback resistance, and the equivalent opamp
input voltage and current noise spectral densities [32], [33].
The equivalent circuit is shown in Fig. 4. The photodiode is
modeled as having two current sources: one due to shot noise
from the dark current and the other due to Johnson noise from
the series combination of dynamic and series resistance. At the
input of the opamp are the input equivalent current and voltage
noise sources, and around the feedback resistor is the current
source due to Johnson noise. Since these noise sources are uncorrelated,
we must add them on a meansquared basis. There

/Hz (28)
where
dark current;
opamp input noise current spectral density;
opamp input noise voltage spectral density;
photodiode dynamic resistance;
photodiode series resistance.
Opamp (or any electronic amplifier) noise performance is
critical to achieving a lownoise photoreceiver. We used our
RF and FFT spectrum analyzers to verify the equivalent input
noise spectra of several opamps [33] and chose the Burr–Brown
OPA643 based on a combination of factors including noise performance,
speed, and availability.
Fig. 5 displays the variation in the meansquared noise spectral
density terms in (28) as a function of feedback resistance
for the OPA643. The sum of all noise sources is indicated by
the dashed line. The dark current noise and photodiode Johnson
noise are insignificant within the boundaries of this plot. The
noise current (2.5 pA/ ) and voltage spectral densities
(2.3 nV/ Hz) used were taken from the manufacturer’s data
sheet. Notice that this receiver will be shotnoise limited for
with mA. Also, for k , we reach a
point of diminishing returns since the shotnoise power/totalreceivernoise
power becomes constant at about 15 dB.
Another important issue in transimpedance amplifiers running
high average current is the maximum dc output voltage. To
keep this within the powersupply limits, one must balance the
needs of high average current and high feedback resistance. To
see this interaction, Fig. 5 includes constant dc output voltage
contours. For example, in order to maintain a 1V dc output,
operation on this contour would allow a feedback resistance of
1k at 1mA average photocurrent. As a reasonable compro