ADL5304ACPZ-R2 datasheet(19/32 Pages) AD

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Data Sheet

ADL5304

Rev. A | Page 19 of 32

Bandwidth vs. Current

Both the response time and wideband noise of translinear log

amps are functions of the transistor collector current, IC, and

only slightly amenable to improvement by circuit design. The

bandwidth falls at low values of IC due to the effects of junction

capacitances in Q1 and the decrease in transconductance (gm)

of a bipolar transistor, which is a linear function of IC, or in the

case of a photodiode application, the photocurrent, IPD. The

corresponding incremental emitter resistance is

re = 1/gm = VT/IPD = kT/qIPD

(20)

and becomes extremely high at low currents (260 MΩ at IC =

100 pA). Therefore, even minute capacitances associated with

the transistor can generate very long time constants.

If the net effect of these capacitances is represented loosely as

CJ, the corresponding low-pass corner frequency is

f−3dB = qIPD/2πkTCJ

(21)

showing the proportionality of bandwidth to current. Using a

value of 0.3 pF for CJ, this becomes 20 MHz/µA. The small signal

bandwidth at IPD = 100 pA is thus only 2 kHz. However,

whereas this simple model can be useful in making the basic

point, it excludes many other effects that limit its accuracy. At high

currents, the subsequent signal processing limits the maximum

overall bandwidth.

Noise vs. Current

For an ideal bipolar transistor, the voltage noise spectral density,

SNSD, referred to VBE, and caused by shot-noise mechanisms,

evaluates to

SNSD = 14.6/√IC nV/√Hz (TA = 27°C)

(22)

where IC is in µA. For example, at an IC of 1 nA, SNSD evaluates to

approximately 0.5 µV/√Hz.

10µV

1µV

100nV

10nV

1nV

100pV

100p

10n

100n

1µ

10µ

100µ

10m

IC (A)

NOISE SPECTRAL DENSITY OF VBE

Figure 46. Noise Spectral Density of VBE vs. IC

Assuming a 20 kHz net system bandwidth at this current, the

integrated noise voltage is 70 µV rms. The theoretical noise of

VBE vs. IC is shown in Figure 46. However, the log scaling of the

VBE is approximately 3 mV/dB, and in the ADL5304, this is

increased to a slope of 10 mV/dB at the VLOG pin. Therefore,

the noise at VLOG, predicted by Equation 22, is multiplied by a

factor of 3.33. Secondary sources of noise, mostly in the analog

divider used for temperature stabilization of the slope and the

input FET buffer amplifiers, add to this basic noise. The measured

data are shown in Figure 22.

Note how at low frequencies the NSD flattens for input currents

less than 10 nA, this noise is limited by the resistor that makes

the dc current. A 10 MΩ resistor was used for these three currents

with a dc bias voltage across the resistor of 1 mV, 10 mV, and

100 mV, respectively.

A 10 MΩ resistor makes a noise current of 40.7 fA/√Hz, which is

converted via the gm of the logging transistor into a noise voltage.

This voltage adds to the noise voltage of the bipolar transistor itself,

as shown in Figure 46. The re of the transistor is 1/gm and equal

to 25.85 MΩ at IC equals 1 nA. Together with the noise current of

the source resistor, this makes a noise voltage at the emitter of the

logging transistor (VNUM) of 1.05 µV/√Hz; this contrasts with

the noise voltage of the transistor itself of 0.46 µV/√Hz

(approximately 0.5 µV/√Hz). The total combined noise is

approximately 1.15 µV/√Hz.

The effect of the 10 MΩ resistor at 100 pA of dc current becomes

even more pronounced because the noise at VNUM due to the

source resistor is 10.5 µV/√Hz, whereas the transistor only

contributes 1.46 µV/√Hz for a total of 10.6 µV/√Hz.

Therefore, unless the resistor that makes the dc current becomes

very large, in general, measurement at the lower currents is

limited by the noise of the source resistor. This problem does not

exist when using a photodiode because the resistance of the

photodiode increases at the same rate as the logging transistor

(see Figure 47).

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