
Data Sheet
ADL5304
Rev. 0 | Page 17 of 32
THEORY OF OPERATION
BASIC CONCEPTS
The
ADL5304 exploits the logarithmic relationship between base
emitter voltage, VBE, and the collector current, IC, of a bipolar
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.
VBE = VT log (IC/IS)
(5)
Two scaling quantities appear in Equation 5: the thermal voltage,
VT = kT/q, and the saturation current, IS. The thermal voltage is
of crucial importance in determining the logarithmic slope in a
translinear log amp. VT has a process invariant value of 25.69 mV
at T = 25°C and varies in proportion to the absolute temperature
(PTAT). Saturation current, unlike VT, is a process and device
dependent parameter. Saturation current is typically approximately
1016A at 25°C, but exhibits enormous variation over temperature,
by a factor of more than a billion.
The temperature dependence of saturation current is compensated
in the
ADL5304 by using a second reference transistor, having
an identical variation, to stabilize the intercept by using the
difference between the two VBEs.
Input currents, INUM and IDEN, are the numerator and denominator
of the logarithmic argument that follows:
ΔVBE = VT log (INUM/IDEN)
(6)
In log ratio applications, both INUM and IDEN may each vary over
the full specified range of 1 pA to 10 mA. However, in default
operation, IDEN takes the internally preset current of IREF = 100 nA.
Equation 6 shows that the ΔVBE is still PTAT, but the required
logarithmic slope must be temperature stable; therefore, this is
corrected using proprietary circuit techniques. Using this
correction the relationship between a photodiode current, IPD,
applied to INUM, and the voltage appearing at the output at
VLOG is
VLOG = VY log10(IPD/IZ)
(7)
where:
VY is the log slope voltage (and, for the case of base-10 logarithms,
it is also the volts per decade ).
IZ is the extrapolated log intercept.
The relationship between VY and ΔVBE is a factor close to 3.333
in the default configuration from (VNUM VDEN) to the output of
VLOG. Because a decade change in the input current ratio results
in close to a 60 mV/decade change in ΔVBE; multiplying this by
3.333 results in 0.2 V/decade. During fabrication, VY is trimmed
to 0.2 V/decade (10 mV/dB), IREF to 100 nA, VOFS to 1.500 V,
and IZ to 3.162 fA. When IPD = 1 pA, the output VLOG has a value
of 0.5 V (see Figure 44). IZ is small because VLOG is always above ground potential even at the lowest end of the dynamic range,
when using VOFS = 1.500 V. If a negative supply is used, this
voltage can cross zero at the intercept value.
The output for the value of IPD can be calculated using Equation 8.
For example, with an input current of 100 nA,
VLOG = 0.2 V log10(100 nA/3.162 fA) = 1.500 V
(8)
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 (IPD) flows in an
element biased at a fixed voltage. IPD is equal to the optical
power (POPT) absorbed in the detector times the responsivity of
the photodiode (ρ).
IPD = ρ × POPT
(9)
A similar relationship exists between the intercept current, IZ,
and effective intercept power, PZ.
IZ = ρ × PZ
(10)
Therefore, the VOUT equation for the ADL5304 may be written as VLOG = VYlog10(POPT/PZ)
(11)
For the ADL5304 operating in its default mode, an IZ of 3.162 fA corresponds to a PZ of 3.95 fW for a diode having a responsivity
of 0.8 A/W. An optical power of 12.5 μW therefore generates
VLOG = 0.2 V log10(12.5 μW/3.95 fW) = 1.900 V
(12)
In optical applications, the interpretation of VLOG is as an
equivalent optical power; therefore, the slope for calculation
purposes remains 10 mV/dB (for either current or power).