AD8304 Analog Devices, AD8304 Datasheet - Page 8

• Manufacturer Part Number: AD8304
• Description: 160 DB Logarithmic Amplifier With Photo-diode Interface
• Manufacturer: Analog Devices

AD8304
BASIC CONCEPTS
The AD8304 uses an advanced circuit implementation that
exploits the well known logarithmic relationship between the
base-to-emitter voltage, V
bipolar transistor, which is the basis of the important class of
translinear circuits :
There are two scaling quantities in this fundamental equation,
namely the thermal voltage V
I
cept for this class of log amp. V
25.69 mV at T = 25°C and varies in direct proportion to absolute
temperature, while I
dent parameter, and is typically 10
exhibits a huge variation over the temperature range, by a factor of
about a billion.
While these variations pose challenges to the use of a transistor as
an accurate measurement device, the remarkable matching and
isothermal properties of the components in a monolithic process
can be applied to reduce them to insignificant proportions, as will
be shown. Logarithmic amplifiers based on this unique property
of the bipolar transistor are called translinear log amps to distin-
guish them from other Analog Devices products designed for RF
applications that use quite different principles.
The very strong temperature variation of the saturation current
I
an identical variation, to stabilize the intercept. Similarly, pro-
prietary techniques are used to ensure that the logarithmic slope
is temperature-stable. Using these principles in a carefully
scaled design, the now accurate relationship between the input
current, I
the intermediate output pin VLOG is:
V
it is also the “volts per decade”). The fixed current I
the intercept. The scaling is chosen so that V
200 mV/decade (10 mV/dB). The intercept is positioned at
100 pA, the output voltage V
of this value. However, when using a single supply the actual
V
by using a negative supply, this voltage can actually cross zero at
the intercept value.
Using Equation (2), one can calculate the output for any value
of I
In practice, both the slope and intercept may be altered, to either
higher or lower values, without any significant loss of calibration
accuracy, by using one or two external resistors, often in conjunc-
tion with the trimmed 2 V voltage reference at pin VREF.
S
S
Overview,” B. Gilbert, Analog Integrated Circuits and Signal Processing, 9,
pp. 95–118, 1996.
For a basic discussion of the topic, see “Translinear Circuits: An Historical
Y
LOG
. These are of key importance in determining the slope and inter-
is readily corrected using a second reference transistor, having
is called the slope voltage (in the case of base-10 logarithms,
PD
V
V
V
. Thus, for an input current of 25 nA,
must always be slightly above ground. On the other hand,
BE
LOG
LOG
=
PD
=
=
V
, applied to pin INPT, and the voltage appearing at
V
T
0 2
Y
.
log( / )
log (
V
I I
10
log (
S
C
is very much a process- and device-depen-
I
10
S
PD
25
/ )
BE
I
Z
, and collector current, I
T
nA
LOG
= kT/q and the saturation current
T
/
100
has a process-invariant value of
–16
would cross zero when I
amps at T = 25°C but it
pA
)
=
0 4796
.
Y
is trimmed to
V
C
Z
, in a
is called
PD
is
(1)
(2)
(3)
Optical Measurements
When interpreting the current I
dent on a photodetector, it is necessary to be very clear about the
transducer properties of a biased photodiode. The units of this
transduction process are expressed as amps per watt. The param-
eter r, called the photodiode responsivity, is often used for this
purpose. For a typical InGaAs p-i-n photodiode, the responsivity
is about 0.9 A/W.
It is also important to note that amps and watts are not usually
related in this proportional manner. In purely electrical circuits,
a current I
proportional to the square of the current (that is, I
reason for the difference in scaling for a photodiode interface is
that the current I
V
diode is simply proportional to the current I
and the proportionality of I
preserved.
Accordingly, a reciprocal correspondence can be stated between the
intercept current, I
and Equation 2 may then be written as:
For the AD8304 operating in its default mode, its I
corresponds to a P
responsivity of 0.9 A/W. Thus, an optical power of 3 mW would
generate:
Note that when using the AD8304 in optical applications, the
interpretation of V
power, the logarithmic slope remains 10 mV/dB at this output.
This can be a little confusing since a decibel change on the
optical side has a different meaning than on the electrical side.
In either case, the logarithmic slope can always be expressed in
units of mV-per-decade to help eliminate any confusion.
Decibel Scaling
In cases where the power levels are already expressed as so
many decibels above a reference level (in dBm, for a reference
of 1 mW), the logarithmic conversion has already been per-
formed, and the “log ratio” in the above expressions becomes a
simple difference. One needs to be careful in assigning variable
names here, because “P” is often used to denote actual power as
well as this same power expressed in decibels, while clearly these
are numerically different quantities.
Such potential misunderstandings can be avoided by using “D”
to denote decibel powers. The quantity V
must now be converted to its decibel value, V
there are 10 dB per decade in the context of a power measurement.
Then it can be stated that:
where D
and D
This convention will be used throughout this data sheet.
PDB
V
V
V
. In this case, the power dissipated within the detector
I
I
Z
PD
Z
LOG
LOG
LOG
is the equivalent intercept power relative to the same level.
OPT
= ρ
= ρ
PD
=
=
=
P
is the optical power in decibels above a reference level,
V
P
0 2
20
Z
applied to a resistive load R
OPT
.
Y
log (
V
(
D
PD
Z
, and an equivalent “intercept power,” P
log (
OPT
10
Z
LOG
flows in a diode biased to a fixed voltage,
of 110 picowatts, for a diode having a
P
10
OPT
−
is in terms of the equivalent optical
3
D
/
mW
P
Z
PD
Z
)
)
mV dB
to the optical power, P
PD
/
110
/
in terms of optical power inci-
pW
)
L
=
Y
results in a power
1 487
(“volts per decade”)
PD
.
Y
´ = V
(that is, I
V
PD
Y
Z
/10, because
2
OPT
of 100 pA
R
Z
L
, thus:
PD
, is
). The
V
PDB
(4)
(5)
(6)
(7)
(8)
)