adl5304 Analog Devices, Inc., adl5304 Datasheet - Page 19

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

Data Sheet
Bandwidth vs. Current
Both the response time and wideband noise of translinear log
amps are functions of the transistor collector current, I
only slightly amenable to improvement by circuit design. The
bandwidth falls at low values of I
capacitances in Q1 and the decrease in transconductance (g
of a bipolar transistor, which is a linear function of I
case of a photodiode application, the photocurrent, I
corresponding incremental emitter resistance is
and becomes extremely high at low currents (260 MΩ at I
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
C
showing the proportionality of bandwidth to current. Using a
value of 0.3 pF for C
bandwidth at I
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,
S
evaluates to
where I
approximately 0.5 μV/√Hz.
NSD
J
, the corresponding low-pass corner frequency is
, referred to V
r
f
S
100nV
100pV
−3dB
e
NSD
10µV
10nV
= 1/g
1µV
1nV
C
100p
is in μA. For example, at an I
= qI
= 14.6/√I
NOISE SPECTRAL DENSITY OF V
m
PD
= V
Figure 46. Noise Spectral Density of V
PD
/2πkTC
1n
= 100 pA is thus only 2 kHz. However,
T
BE
/I
C
J
, this becomes 20 MHz/μA. The small signal
, and caused by shot-noise mechanisms,
PD
nV/√Hz (T
10n
= kT/qI
J
100n
PD
A
I
C
C
= 27°C)
1µ
(A)
due to the effects of junction
BE
C
10µ
of 1 nA, S
100µ
BE
vs. I
NSD
C
1m
C
evaluates to
PD
, or in the
. The
C
, and
10m
C
=
m
(20)
(21)
(22)
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)
Assuming a 20 kHz net system bandwidth at this current, the
integrated noise voltage is 70 μV rms. The theoretical noise of
V
V
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 g
This voltage adds to the noise voltage of the bipolar transistor itself,
as shown in Figure 46. The r
to 25.85 MΩ at I
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
(~0.5 μV/√Hz). The total combined noise is ~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).
BE
BE
is ~3 mV/dB, and in the ADL5304, this is increased to a slope
vs. I
C
is shown in Figure 46. However, the log scaling of the
C
equals 1 nA. Together with the noise current of
m
of the logging transistor into a noise voltage.
e
of the transistor is 1/g
ADL5304
m
and equal