ADL5303ACPZ-R7 datasheet(10/24 Pages) AD

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ADL5303

Data Sheet

Rev. 0 | Page 10 of 24

THEORY OF OPERATION

BASIC CONCEPTS

The ADL5303 uses an advanced circuit implementation that

exploits the logarithmic relationship between the base-to-

emitter voltage, VBE, and collector current, IC, in a bipolar

transistor.

Using these principles, the relationship between the input current,

IPD, applied to the INPT pin, and the voltage appearing at the

intermediate output VLOG pin is:

VLOG = VY log10(IPD/IZ)

(1)

where:

VY is the voltage slope (in the case of base-10 logarithms, it is

also referred to as volts per decade).

IZ is the fixed current in the logarithmic equation called the

intercept.

In the following example, the scaling is chosen so that VY is

trimmed to 200 mV/decade (10 mV/dB). The intercept is

positioned at 100 pA; the output voltage, VLOG, crosses zero

when IPD is of this value. However, the actual VLOG must always

be slightly above ground. Using Equation 2, calculate the output

for any value of IPD. Thus, for an input current of 25 nA,

VLOG = 0.2 V log10(25 nA/100 pA) = 0.4796 V

(2)

In practice, both the slope and intercept can be altered, to

either higher or lower values, without any significant loss of

calibration accuracy, by using one or two external resistors,

often in conjunction with the trimmed 2 V voltage reference

at the VREF pin.

OPTICAL MEASUREMENTS

When interpreting the IPD current in terms of optical power

incident on a photodetector, it is necessary to be clear about

the conversion (optical power to current) properties of a reverse

biased photodiode. The units of this conversion are expressed

in amps per watt and referred to as photodiode responsivity, ρ.

For the typical InGaAs PIN photodiode, the responsivity is

approximately 0.9 A/W.

It is important to note that in purely electrical circuits, current

and power are not related in this proportional manner. A

current applied to a resistive load results in a power propor-

tional to the square of the current, P = I2R. The difference in

scaling for a photodiode is because IPD flow in a reverse-biased

diode is largely dependent on the fixed built-in voltage of the

PN junction and is relatively insensitive to the external bias

voltage. In the detector diode, power dissipated is proportional

to the IPD current and the relationship of IPD to the optical

power, POPT, is preserved.

IPD = ρPOPT

(3)

The same relationship exists between the intercept current, IZ,

and an equivalent intercept power, PZ, thus,

IPZ = ρPZ

(4)

Therefore, Equation 1 can be written as

VLOG = VY log10(POPT/PZ)

(5)

For the ADL5303 operating in its default configuration, an IZ

of 100 pA corresponds to a PZ of 110 pW, for a diode having

a responsivity of 0.9 A/W. Thus, an optical power of 3 mW

generates

VLOG = 0.2 V log10(3 mW/110 pW) = 1487 V

(6)

Note that when using the ADL5303 in optical applications the

VLOG output is referred to in terms of the equivalent optical

power, the logarithmic slope remains 10 mV/dB at this output.

This can be confusing because 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

millivolts per decade to help eliminate confusion.

DECIBEL SCALING

When power levels are expressed as decibels above a reference

level (in dBm, for a reference of 1 mW), the logarithmic conver-

sion has already been performed, and the log ratio in the previous

expressions becomes a simple difference. 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; how-

ever, these are numerically different quantities.

BANDWIDTH AND NOISE CONSIDERATIONS

Response time and wideband noise of translinear log amps

are a function of the signal current, IPD. Bandwidth becomes

progressively lower as IPD is reduced, largely due to the effects

of junction capacitances in the translinear device.

Figure 9 shows ac response curves for the ADL5303 at eight

representative currents of 1 nA to 10 mA, using R1 = 750 Ω

and C1 = 1000 pF. The values for R1 and C1 ensure stability

over the full 160 dB dynamic range. More optimal values may

be used for smaller subranges. A certain amount of experi-

mental trial and error may be necessary to select the optimum

input network component values for a given application.

The relationship between IPD and the voltage noise spectral

density, SNSD, associated with the VBE of Q1, calculates to the

following:

NSD

(7)

where:

SNSD is nV/Hz.

IPD is expressed in microamps.

TA = 25°C.

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