ADL5308ACCZ-R7 datasheet(12/22 Pages) AD

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Data Sheet

ADL5308

THEORY OF OPERATION

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Rev. 0 | 12 of 22

LOGARITHMIC TRANSFER

The logarithmic transimpedance amplifiers (TIA) produce an output

voltage that is (approximately) linearly related to the logarithm of

the input current IPD:

VLOG=SLOPE×log10 IPDIZ

(1)

The logarithmic slope (SLOPE) shows the amount by which the out-

put voltage VLOG changes for each factor of 10 (decade) change

in input current IPD, while the logarithmic intercept IZ shows the

(extrapolated) input current for which the output voltage becomes

zero. The actual device output voltage never reaches zero, but

saturates to the starting voltage of 17 mV for input currents below

10 pA. Both SLOPE and IZ can be obtained by linear regression of

the measured amplifier output voltage vs. a range of input current

levels. The ADL5308 logarithmic slope and intercept of the VLOG −

1.1 V curve are accurately factory trimmed to 200 mV/dec and 3.16

µA respectively. The reason 1.1 V is subtracted from VLOG curve

(the ideal value of VLOG at 3.16 µA) is to place the x-intercept

in the geometric middle of the specified input current range. That

way, the residual slope differences have a minimum impact on the

x-intercept and its equation can be written as:

VLOG−1.1=SLOPE×log10 IPDIZ1P1

(2)

Expressed in dB of input current, Equation 2 can be written as:

VLOG−1.1=SLOPE20× IPD, dB−IZ1P1, dB (3)

Where IPD, dB is the input current in dBA and IZ1P1,dB is the intercept

current in dBA (−110 dBA in this case).

The measurement accuracy obtained with a logarithmic amplifier is

determined by the following two factors:

►

The logarithmic conformance error

►

The temperature drift error

The logarithmic conformance error describes the deviation of the

actual TIA transfer from the ideal log-linear relationship of Equation

3, and is expressed in dB of input current:

ELC=20×VLOGT

SLOPE

+IZ1P1, dB − IPD, dB (4)

Thus ELC shows the resulting measurement error when VLOG of a

logarithmic TIA is measured and Equation 3 is used to determine

the input current that the device is sensing. Since SLOPE and

IZ are usually determined at room temperature only, ELC typically

also contains a contribution due to drift of the TIA transfer over

temperature.

The temperature drift error Edrift describes the measurement error

introduced solely due to the temperature drift of the TIA transfer,

excluding discrepancies of the actual TIA transfer to the ideal

log-linear relationship (logarithmic conformance).

EdriftT = 20SLOPE× VLOGT −VLOGTo (5)

The error, the difference between the output voltage measured

at the operating temperature T and the actual output voltage

measured at the reference temperature To, usually 25°C, is input

referred and expressed in dB (of input current) using the logarithmic

SLOPE. This is accurate as long as the error is relatively small and

the TIA transfer is approximately logarithmic (linear in dB).

OPTICAL MEASUREMENTS

A high-dynamic range optical power monitor can be constructed by

connecting the anode of a reverse biased PD to the input of the

logarithmic TIA, such that the TIA senses the photon-generated di-

ode current. Therefore, it is important to understand the transducer

aspects of a PD, that is, how to interpret the PD current relative

to the incident optical power. In the electrical circuits, the power

dissipated in a resistive load is proportional to the square of the

current, or, vice versa, the current through the load is proportional

to the square root of the dissipated power:

IR= PDISS/R

(6)

In a reverse biased PD, however, the photon-generated PD current

(IPD) itself is directly proportional to the optical power (POPT) absor-

bed in the detector:

IPD=ρ×POPT

(7)

The proportionality constant ρ shows the conversion gain from

optical power to electrical current, is called the responsivity of the

PD. Using the same responsivity, the logarithmic intercept current IZ

of the TIA can be related to an optical intercept power level PZ for

which the ideal log-linear transfer produces an output voltage equal

to zero. The transfer from measured optical power to amplifier

output voltage can therefore be expressed as:

VLOG=SLOPE×log10 POPTPz

(8)

For incident optical power expressed in dB, that is,

PdB, OPT=10×log10POPT

(9)

This becomes:

VLOG=SLOPE10× PdB, OPT−PdB, Z

(10)

Thus the logarithmic slope in mV/dB optical power equals twice the

logarithmic slope in mV/dB of input current IPD (see Equation 3).

Similarly, the optical dynamic range of the TIA in dB equals half the

electrical dynamic range in dB, that is, 70 dB optical vs. 140 dB

electrical.

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