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Volume 37, Number 4, 2003
Editor’s Notes
2
Closed-Loop Control of Variable Optical
Attenuators with Logarithmic Analog Processing
3
Fast-Locking, High Sensitivity Tuned-IF
Radio Receiver Achieved with a 7-GHz Synthesizer
7
Electrocardiograph Front-End Design
is Simplified with MicroConverter
®
10
Product Introductions
15
Authors
15
Editor’s Notes
When analog computers with adequate bandwidth were scaled so as
to enable complete repetitive solutions, plotted on an oscilloscope
or a raster display, the effects of adjusting system parameters were
immediately visible—very helpful in seeing interrelationships among
the variables, curing stability problems, optimizing parameters, and
developing a description of system behavior in the time domain.
When scaled to actual “real time,” they could be used to simulate
portions of systems whose parameters were inconvenient to adjust.
For systems with stable continuous behavior, conveniently scaled
frequency-response studies (and now FFTs) could be performed as
if the model were the actual system. Nowadays digital computers,
teamed up with analog, data-conversion, and DSP circuitry, can run
rings around those paragons of yesteryear—but one must remember
that, when vacuum-tube analog assemblages (like the dinosaurs) ruled
the computer world, terms like “transistor” and “software” (like the
humans) had not yet been created.
The basic
linear
unit operations of an electronic analog computer
are
addition
,
coeficients
(gains/attenuations), and
integration
with
respect to time.
Nonlinear
relationships are handled by associating or
replacing linear coeficients with a block embodying (with vacuum-
tube-diode circuitry, at that time) the appropriate nonlinear output/
input relationship—such as hard nonlinearities (limits and dead
zones), linear hysteresis, squaring, and square-rooting. The most
stable way of implementing smooth functions (and multiplication)
was by the piecewise-linear use of arrays of biased (vacuum-tube)
diodes, with individually adjustable gains.
Little did we know that, within a couple of decades, a few silicon
junctions, replacing and far surpassing multiple vacuum-tube diodes in
versatility and stability, would enable the designer to create predictable
and stable nonlinearities, even (especially!) the analog-era designer’s
bête noire
, the
multiplier
. But that’s a story for another time and place.
THEN AND NOW REVISITED
As 2003 transits into 2004, the article on
page 3 brings to mind an article by one
W. Paterson,
1
appearing in the December
1963
Review of Scientiic Instruments
—just
40 years ago—describing (for the irst time,
in our recollection) ways of generating logs
and antilogs, and performing multiplication,
by combining the natural characteristics of
transistor junctions with the ability of op
amps to sink current while maintaining
a virtual ground. His perceptiveness was
conirmed very soon thereafter in a paper by J. Gibbons and H. Horn,
2
published in the September 1964
IEEE Transactions on Circuit Theory
,
pointing out that the logarithmic relationship was usable over a range
of at least nine decades.
These papers, and the subsequent manifestations of brisk creative
activity in the ield, culminated in Barrie Gilbert’s 1975 landmark
summation on
translinear circuits
,
3
published in
Electronics Letters
. The
ideas it brought together became the foundation for whole generations of
IC multipliers/dividers, log-ratio and rms devices, modulators, variable-
gain ampliiers, automatic gain controls, gain- and phase meters, and
more. This fallout is all documented in silicon-era patents, books,
journals, and advertisements—as well as hardware embedded just
about anywhere analog electronics has penetrated.
This wealth of functional capabilities was made possible by continued
improvements in solid-state theory (now a long way from the “cats’
whiskers” of the early 20
th
century) and the processing of silicon ingots
and wafers. But for anyone growing up in the present era, it’s hard
to believe that, before the ‘60s, the “solid” foundation for the era of
electronics
—in which radio communications, radar, cinema, television,
and automatic-control electronics were developed—was the low of
electrons through a
vacuum
(or of ions in a gaseous medium).
It was an era of low eficiencies, room-warming equipment, plentiful
low-cost energy, vast military spending, with a generation of engineers
and technicians inured to the routine use of 300-volt power supplies. It
was hard to believe, other than in dreams, that the future would involve
miserly husbanding of energy, imploding price and size of electronic
devices (and exploding functional density), and a mindset in which
circuits using
15-volt supplies
are considered to be energy-guzzling
dinosaurs. The vocabulary of size reduction has devolved from tube-era
“miniaturization” to “microcircuits” towards
nanocircuits
.
Op amps and analog computers:
In 1963, at the time when increased
awareness of silicon’s vast repertoire of expected applications coincided
with the initial availability of viable solid-state forms, the
operational
ampliier
—as a low-cost, easy-to-handle, differential-input plug-in
modular vacuum-tube device—had been on the market for a mere 10
years. The irst appearance of the “operational” circuit architecture, as
an element that made analog computer systems feasible, had been made
only a dozen years before that, during World War II. Yet the op amp, a
prime beneiciary of the solid-state era, was now ready to come into its
own as a near-universal functional circuit block. Solving problems in
the design of the op amp itself would imbue much of electronic circuit
design with a large measure of
predictability
.
Electronic analog computers
, in their heyday (the 1940s and ‘50s), were
usually deined as a set of operational building blocks so interconnected
as to model the behavior of a physical system (thermal, mechanical,
chemical, nuclear). The model was an alternative electrical system
whose performance is described by the same set of equations (with
appropriate scale factors) that governs the performance of the system
they are modeling. Analog and (later) digital I/O structures provided
for any necessary services: initial conditions, driving functions,
interconnection programming, calibration, display, etc.
Dan.Sheingold@analog.com
Please join me in celebrating Dan Sheingold’s 35
th
anniversary at
Analog Devices. As Editor, Dan has succeeded in turning
Analog
Dialogue
into the premier technical journal of the semiconductor
industry, leading it from humble beginnings to the worldwide online
and print readership that it enjoys today. I have had the pleasure of
knowing Dan for almost 25 years, and the privilege of working with
him for the last ive. Here’s to the next ive!
Scott.Wayne@analog.com
1
“Multiplication and logarithmic conversion by operational ampliier-
transistor circuits,” by W. Paterson.
Review of Scientiic Instruments
34-12,
December, 1963.
2
“A circuit with logarithmic transfer response over 9 decades,” by J. Gibbons
and H. Horn.
IEEE Transactions of the Circuit Theory Group
CT-11-3,
September, 1964.
3
“Translinear circuits: a proposed classiication,” by B. Gilbert.
Electronics
Letters
11-1, 1975, pp.14-16.
www.analog.com/analogdialogue
dialogue.editor@analog.com
Analog Dialogue
is the free technical magazine of Analog Devices, Inc., published
continuously for 37 years—starting in 1967. It discusses products, applications,
technology, and techniques for analog, digital, and mixed-signal processing. It is
currently published in two editions—
online
, monthly at the above URL, and quarterly
in print
, as periodic retrospective collections of articles that have appeared online. In
addition to technical articles, the online edition has timely announcements, linking to
data sheets of newly released and pre-release products, and “Potpourri”—a universe
of links to important and rapidly proliferating sources of relevant information and
activity on the Analog Devices website and elsewhere. The
Analog Dialogue
site is,
in effect, a “high-pass-iltered” point of entry to the
www.analog.com
site—the
virtual world of
Analog Devices
. In addition to all its current information, the
Analog Dialogue
site has archives with all recent editions, starting from Volume 29,
Number 2 (1995), plus three special anniversary issues, containing useful articles
extracted from earlier editions, going all the way back to Volume 1, Number 1.
If you wish to subscribe to—or receive copies of—the print edition, please go to
www.analog.com/analogdialogue
and click on
<subscribe>
. Your comments
are always welcome; please send messages to
dialogue.editor@analog.com
or to these individuals:
Dan Sheingold
, Editor
[dan.sheingold@analog.com]
or
Scott Wayne
, Managing Editor and Publisher
[scott.wayne@analog.com]
.
ISSN 0161-3626 ©Analog Devices, Inc. 2004
2
Analog Dialogue Volume 37 Number 4
Closed-Loop Control of Variable
Optical Attenuators with
Logarithmic Analog Processing
Adaptive Control of a Variable Optical Attenuator
Figure 1 illustrates this classic solution applied around an adaptively
controlled VOA. The ampliied signal is low-pass iltered to help
reduce measurement noise. The iltered signal is then digitized
and the absorbance of the attenuator is computed.
If linear ampliication is used to convert the measured photocurrents
to proportional voltages, it will be necessary to calculate the ratio
of the measured signals, followed by inverse exponentiation, and
multiplication to compute the VOA’s actual absorbance.
By Eric J. Newman [eric.newman@analog.com]
Matthew Pilotte [matthew.pilotte@analog.com]
Achieving tight channel spacing in
dense wavelength-division-
multiplexing
(DWDM) networks calls for precise control of spectral
emissions and power. This requires continuous monitoring and
adjustment of network elements—such as transmission laser
sources, optical add-drops, optical ampliiers, and
variable optical
attenuators
(VOAs). These last elements are typically used to adjust
power levels across the DWDM spectrum in order to minimize
crosstalk and maintain a desired signal-to-noise ratio.
For instance, a VOA can be cascaded with an
erbium-doped iber
ampliier
(EDFA) to help equalize the ampliier’s non-uniform
gain-versus-wavelength proile, improving linearity and enhancing
control of the overall system. Recursive measurement-and-control
algorithms can be used to provide quick and accurate dynamic
closed-loop control, which ensures repeatability and minimizes
production calibration and trimming. Logarithmic-ampliier
front ends condition the wide-range input signal, thus allowing
lower-resolution, lower-cost signal-processing components to be
used downstream.
10log
P
P
IN
OUT
α=
(1)
If the responsivities and transimpedance gain of the detector front
ends are equal, then
I
R
IN
TIA
ρ
V
V
IN
α
= ×
10
log
= ×
10
log
(2)
I
IOUT
R
OUT
TIA
ρ
where
R
TIA
is the
transresistance
in ohms
is the
responsivity
of the photodiode in A/W
In reality the front end transresistances will not be equal, so
additional calibration and correction is required. In a digital
solution, in order to provide acceptable precision in calculation,
the signal needs to be digitized using analog-to-digital converters
(ADCs) with suficient resolution to preserve a predetermined
level of accuracy. The design can operate as a closed loop only as
long as the input signal is large enough for the detected signals
to be above the noise loor. Variable transresistance may be
used to help extend the range of closed-loop operation. When
the measured signal levels fall below an acceptable signal level
for accurate detection, the VOA must indicate the lack of signal
power and operate open-loop, and is no longer able to fulill the
accuracy requirement.
Classic Mixed-Signal Solutions
Classic solutions have combined linear
transimpedance ampliiers
(TIAs) and high resolution signal processing to measure and
control the absorbance of the VOA. This, at irst, seems like an
attractive solution due to the low cost of the TIA front end. The
TIA is linear, however, so calculating the decibel (logarithmic)
attenuation across the VOA requires post-processing of the
measured signal. Performed digitally, this requires loating-
point processors to cope with the division and exponentiation
processes involved in the calculation. Alternatively, integer-
based processing can be performed—using exhaustive look-up
tables that were generated during production calibration. Both
approaches typically require analog-to-digital converters with at
least 14-bit resolution, and moderately high processor speeds,
to minimize measurement latency resulting from the inherent
processing overhead. The cost advantage sought in selecting
the linear TIA front end is often swamped by the cost of the
higher priced converters and processors needed to acquire the
measurement signal and compute the attenuation. Additional cost
(and production delay) is incurred if lengthy look-up tables need
to be generated during production testing.
To the Rescue—Translinear Log-Amp Circuits
Published in 1953, the Ebers-Moll equations predicted the
inherent logarithmic relationship between the base-emitter voltage
(
V
BE
) and the collector current (
I
C
) of a bipolar transistor.
1
When
fabricated on a high quality analog process, this relationship is
remarkably accurate over an
I
C
range of up to 9 decades.
Signiicant advances occurred, starting with the exploitation of
the logarithmic properties in the 1960s.
2
A signiicant landmark
was Barrie Gilbert’s description of the power(s) inherent in their
generalized
translinear
properties.
3
Over the years, the logarithmic
and related properties of bipolar junctions have been used to create
a variety of wide-range linear and nonlinear devices, including
precision multipliers and dividers, rms-to-dc converters,
4
and
modulators. They have made possible the compact, wide-range,
precision analog solution to be described.
Briely, over a range of about 9 decades, a BJT exhibits a naturally
logarithmic relationship between its collector current and its base-
to-emitter voltage,
VOA
INPUT
TAP
OUTPUT
TAP
P
IN
P
OUT
I
IN
I
OUT
VOA
DRIVER
TIA
OR LOG
TIA
OR LOG
LPF
LPF
kT
q
I
I
CONTROLLER
OR DSP
C
(3)
V
=
ln
BE
V
IN
V
OUT
S
where
I
S
is the transport saturation current, of the order of 10
–16
A,
k/q
is the ratio of Boltzmann’s constant to the charge on an electron
(1/11,605 V/K), and T is the absolute temperature in kelvins.
The thermal voltage,
kT/q
, is thus simply
proportional to absolute
temperature
(PTAT), about 25.85 mV at 300 K. Unfortunately,
the current
I
S
is poorly deined, differing signiicantly between
Figure 1. VOA adaptive control loop. Input and output optical
taps are used to measure the attenuation of the VOA. The
measured signal is compared to a desired setpoint level using
an error integrator, implemented in software. The difference
signal is used to control the attenuation of the VOA, yielding
a closed-loop design.
Analog Dialogue Volume 37 Number 4
3
separate devices; it is also strongly dependent on temperature,
varying by a factor of roughly 10
9
between –35C and +85C. A
single BJT alone would be a highly impractical log-amp because
of these strong temperature dependencies. To make use of BJTs
for accurate logarithmic transformations, the temperature
dependencies must be nulliied.
The
difference
between the base-emitter voltages of a
pair
of BJTs,
one operating at the photodiode current,
I
PD
, and the second
operating at a reference current,
I
REF
, can be expressed as
In terms of decibels of optical power
V
V
LOG
Y
+
I
I
V
V
(10)
=
P dB
( ) log
=
10
REF
×
10
10
log
REF
10
LOG
Y
PD
ρ
ρ
Using Equation 10 we can solve for the log-voltage in terms of
optical power in dB.
V
P dB P dB
(
)
( )
−
( )
Y
V
=
(11)
LOG
PD
Z
10
−
=
kT
q
I
I
kT
q
I
I
kT
q
I
I
I
I
V V
− =
ln
PD
S
ln
REF
S
ln
PD
S
×
S
REF
2
(4)
where
BE
1
BE
2
1
2
1
I
( )
=
REF
P dB
10log
(12)
If the two transistors are closely matched such that they exhibit
nearly identical saturation currents, then Equation 4 can be
written as
Z
ρ
This provides a linear-in-dB transfer function, allowing a simple
straight-line equation to describe the relationship of absolute
optical power to the logarithmic output voltage. In practice, the
actual reference current value and responsivity of the photodiode
will be found through a simple two-point calibration process.
By measuring the output voltage for two known values of optical
power, the slope and intercept of the straight-line equation can be
determined. Then simple subtraction and multiplication can be
used to assess the optical power in decibels without the need for
the exponentiation process or the exhaustive look-up table that
would be required if a linear TIA front end were applied.
If the numerator current is derived from the photocurrent,
I
PD
, of
an input tapped detector, and the denominator current,
I
REF
, is the
resulting photocurrent after the input signal has passed through an
absorptive element, such as a VOA, Equation 7 can then be used
to derive the attenuation in terms of the log-voltage.
=
kT
q
I
I
kT
q
I
I
PD
PD
V V
− =
ln
ln( )log
10
(5)
BE
1
BE
2
REF
REF
At an ambient temperature of 300 K, the above equation
evaluates to
I
I
PD
V V
− =
2
595
. log
mV
(6)
BE
1
BE
REF
The poorly deined and temperature dependent saturation current,
I
S
, which appears in Equation 1, has now been eliminated. To
eliminate the temperature variation of
kT/q
, this difference voltage
is applied to an analog divider with a denominator that is directly
proportional to absolute temperature. The inal output voltage is
now essentially temperature independent and can be expressed as
I
I
P
P
=
V
V
PD
V V
=
log
(7)
( )
=
α
dB
10
log
PD
REF
10
LOG
Y
(13)
LOG
Y
REF
The logarithmic slope,
V
Y
, is expressed in
volts per decade
. Typical
translinear log-amps such as the ADL5306 and ADL5310 are
scaled to provide a nominal 200 mV/decade slope. The logarithmic
slope can be increased or decreased with the addition of a simple
ixed-gain ampliier or voltage-attenuator network.
When light falls on a photodiode, the resulting photocurrent is
directly proportional to the incident optical power in watts. On
a decibel scale, the decibels of optical power are proportional to
the logarithm of the photocurrent, scaled by the responsivity of
the particular photodiode. The decibel power of any photodiode
can be written as
A similar expression could be derived for an optical ampliier
design, where it is desirable to compute the gain in dB across the
ampliier. As before, a simple two-point calibration is used to
describe the straight-line equation relating the output voltage to the
EDFA gain setting. In this manner, translinear log-amps provide
the capability to measure absolute power, optical absorbance, and
gain using a simple straight-line approximation.
Recent advances in monolithic integrated-circuit design now
allow for the manufacture of translinear logarithmic ampliiers
that provide wide-dynamic-range signal compression virtually
free from the temperature dependencies inherent in a discrete
implementation. The first complete monolithic translinear
logarithmic ampliier (log-amp), the AD8304, designed by Barrie
Gilbert, was introduced by Analog Devices in January 2002. Since
the introduction of the AD8304, logarithmic devices have become
available from other semiconductor manufacturers.
I
PD
P
watt
ρ
=
P dB
( ) log
=
10
PD
10
log
(8)
PD
watt
If the reference current in the denominator of Equation 7 is
known, the absolute power incident on the photodiode can be
calculated from the
V
LOG
voltage.
Application to a VOA
In a
digitally variable optical attenuator
(DVOA) application, input
and output optical taps are used to measure the absolute optical
power at the input and output ports. The power measurements
can then be processed to compute the absorbance of the DVOA
for a particular attenuation setting. Using closed-loop techniques,
V
V
LOG
Y
I I
(9)
PD
REF
P
= = ×
10
PD
ρ ρ
4
Analog Dialogue Volume 37 Number 4
the attenuation can be dynamically controlled to maintain
a desired level of attenuation based on the input and output
power measurements. This mode of operation is called
automatic
attenuation control
, or AAC. An alternate mode,
automatic power
control
(APC), is necessary when the output power of the DVOA
is required to remain at a constant level regardless of input optical
power variations (as long as the input level exceeds the desired
output level by the minimum insertion loss of the VOA).
In either mode of operation, the loop is typically implemented in the
form of a mixed-signal solution, where a digital MicroConverter
®
is
programmed to process the analog inputs and drive the appropriate
control signal to maintain the necessary level of attenuation. In
a fast control loop, an analog solution may be required in order
to eliminate the latency associated with the digital portion of the
loop. The circuit described below utilizes the ADL5310 dual
translinear logarithmic ampliier, which is capable of interfacing
two independent photodiodes for measurement of the absolute
power on two separate optical supervisory channels. This device
allows for absolute measurement of the output optical signal, while
simultaneously providing a measure of the attenuation.
in a residual error as the overall power levels change. Over a
5-decade power range, the residual error could be as much as
2.5 dB. This can be acceptable in some situations—where fast
all-analog closed-loop control is necessary, and accuracy can be
compromised in order to allow a simple hardware solution. In a
solution where mixed-signal techniques can provide fast enough
response, the residual error could be predicted and minimized
by monitoring the absolute power on one detector and using a
look-up table for error correction.
1.4
1.2
1
- CHANNEL 1
1.0
0.8
0.6
0.4
21
- CHANNEL 2
Automatic Attenuation Control and Automatic Power Control
Two buffered outputs can be obtained by utilizing the ADL5310’s
on-chip op amps. The circuit coniguration of Figure 2 makes
available a measurement of the absolute power incident on
photodiode PD1, as well as a measure of absorbance observed
between the two ports. Test results using an uncalibrated VOA
are provided in Figure 3. The outputs provide the desired
linear-in-dB transfer functions needed for closed-loop analog
control. Automatic attenuation and power control can be achieved
by applying the appropriate output to a separate error integrator;
its output drives the control voltage of the VOA.
The solution in Figure 2 assumes that the individual logarithmic-
slopes of each channel are identical. In reality the channel-to-
channel slope mismatch could be as high as 5%. This will result
0.2
0
0
10
20
30
40
50
ATTENUATION (dB)
Figure 3. Transfer functions for the two outputs. Channel 1
provides the absolute output power, while Channel 2 provides
the relative attenuation between the two channels.
The test results in Figure 3 are subject to the inaccuracies of
the VOA used in the lab. The measurement was repeated with
calibrated current sources to better assess the accuracy of the
design. Figure 4 illustrates the full dynamic range capabilities
and log-conformance of the circuit in Figure 2. The accuracy is
better than 0.1 dB over a 5-decade range.
5V
21
(dB)
=
OUT2
VPOS
I
IN2
I
IN1
= 0.20 log10
R2
1M
1k
ADL5310
R1
1M
SCL2
BIN2
4.7nF
C
OM
M
INP2
R2
1M
R1
1M
LOG
I
LOG2
VSUM
TEMPERATURE
COMPENSATION
PD2
1nF
1nF
IRF2
LOG
EPM605
InGaAs
PIN
2M
1
(dB)
= 0.20 log10
VRDZ
V
REF
=
OUT1
I
IN2
100pA
0.1
F
BIAS
GENERATOR
R4
4.99k
SCL1
BIN1
2M
PD1
IRF1
LOG
I
LOG1
EPM605
InGaAs
PIN
VSUM
TEMPERATURE
COMPENSATION
1nF
INP1
1nF
LOG
COMM
1k
VNEG
COMM
4.7nF
Figure 2. Hardware implementation of VOA control using a logarithmic front end. The ADL5310 is conigured to provide an
absolute power measurement of the optical signal power incident on PD1, while the difference voltage reveals the absorbance
across the VOA. The wide dynamic range allows the loop to remain locked over a broad range of input signals.
Analog Dialogue Volume 37 Number 4
5
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