adl5304 Analog Devices, Inc., adl5304 Datasheet - Page 17

• Manufacturer Part Number: adl5304
• Description: High Speed, 200 Db Range, Logarithmic Converter
• Manufacturer: Analog Devices, Inc.

Data Sheet
THEORY OF OPERATION
BASIC CONCEPTS
The
emitter voltage, V
junction transistor (see Equation 5). This is the fundamental basis
of the extended class of translinear circuits. A log amp based on this
unique property of the bipolar transistor is called a translinear log
amp to distinguish it from log amps designed for RF applications,
which use different principles while having similar objectives.
Two scaling quantities appear in Equation 5: the thermal voltage,
V
of crucial importance in determining the logarithmic slope in a
translinear log amp. V
at T = 25°C and varies in proportion to the absolute temperature
(PTAT). Saturation current, unlike V
dependent parameter. Saturation current is typically approximately
10
by a factor of more than a billion.
The temperature dependence of saturation current is compensated
in the
an identical variation, to stabilize the intercept by using the
difference between the two V
Input currents, I
of the logarithmic argument that follows:
In log ratio applications, both I
the full specified range of 1 pA to 10 mA. However, in default
operation, I
Equation 6 shows that the ΔV
logarithmic slope must be temperature stable; therefore, this is
corrected using proprietary circuit techniques. Using this
correction the relationship between a photodiode current, I
applied to INUM, and the voltage appearing at the output at
VLOG is
where:
V
it is also the volts per decade ).
I
Z
Y
T
is the extrapolated log intercept.
−16
is the log slope voltage (and, for the case of base-10 logarithms,
= kT/q, and the saturation current, I
ADL5304
A at 25°C, but exhibits enormous variation over temperature,
V
ΔV
V
ADL5304
BE
LOG
BE
= V
= V
= V
DEN
T
Y
log (I
T
exploits the logarithmic relationship between base
takes the internally preset current of I
log
log (I
NUM
by using a second reference transistor, having
BE
10
C
and I
, and the collector current, I
(I
/I
NUM
PD
T
S
)
has a process invariant value of 25.69 mV
/I
DEN
/I
Z
)
DEN
, are the numerator and denominator
)
BE
BE
NUM
s.
is still PTAT, but the required
and I
T
, is a process and device
S
. The thermal voltage is
DEN
may each vary over
C
, of a bipolar
REF
= 100 nA.
PD
Rev. 0 | Page 17 of 32
(5)
(6)
,
(7)
The relationship between V
in the default configuration from (V
VLOG. Because a decade change in the input current ratio results
in close to a 60 mV/decade change in ΔV
3.333 results in 0.2 V/decade. During fabrication, V
to 0.2 V/decade (10 mV/dB), I
and I
of 0.5 V (see Figure 44). I
ground potential even at the lowest end of the dynamic range,
when using V
voltage can cross zero at the intercept value.
The output for the value of I
For example, with an input current of 100 nA,
The slope and intercept can be adjusted to suit the application,
to either higher or lower values, without significant loss of
calibration accuracy.
OPTICAL MEASUREMENTS
It is important to understand the transducer aspects of a photo-
diode when interpreting the photodiode current relative to the
incident optical power.
In purely electrical circuits, current applied to a resistive load
results in a power proportional to the square of the current. For
a photodiode interface, however, there is a difference in scaling
because photon-generated photodiode current (I
element biased at a fixed voltage. I
power (P
the photodiode (ρ).
A similar relationship exists between the intercept current, I
and effective intercept power, P
Therefore, the V
For the
corresponds to a P
of 0.8 A/W. An optical power of 12.5 μW therefore generates
In optical applications, the interpretation of V
equivalent optical power; therefore, the slope for calculation
purposes remains 10 mV/dB (for either current or power).
V
I
I
V
V
Z
PD
Z
LOG
LOG
LOG
to 3.162 fA. When I
= ρ × P
ADL5304
= ρ × P
OPT
= 0.2 V log
= V
= 0.2 V log
) absorbed in the detector times the responsivity of
Y
OFS
Z
log
OPT
OUT
= 1.500 V. If a negative supply is used, this
10
operating in its default mode, an I
Z
(P
of 3.95 fW for a diode having a responsivity
equation for the
10
10
OPT
(100 nA/3.162 fA) = 1.500 V
(12.5 μW/3.95 fW) = 1.900 V
/P
Z
Z
PD
is small because V
PD
)
Y
= 1 pA, the output V
can be calculated using Equation 8.
and ΔV
REF
Z
.
to 100 nA, V
PD
NUM
ADL5304
is equal to the optical
BE
− V
is a factor close to 3.333
BE
DEN
; multiplying this by
) to the output of
LOG
may be written as
LOG
OFS
is always above
PD
to 1.500 V,
is as an
LOG
Z
ADL5304
) flows in an
of 3.162 fA
Y
is trimmed
has a value
Z
(10)
(11)
(12)
,
(8)
(9)