Data Sheet
ADL5304
Rev. 0 | Page 19 of 32
Bandwidth vs. Current
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 ~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
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)
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.
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
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
(~0.5 μV/√Hz). The total combined noise is ~1.15 μV/√Hz.
f3dB = 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
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.
For an ideal bipolar transistor, the voltage noise spectral density,
SNSD, referred to VBE, and caused by shot-noise mechanisms,
evaluates to
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
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.
10V
1V
100nV
10nV
1nV
100pV
100p
1n
10n
100n
1
10
100
1m
10m
N
O
ISE
SPEC
T
R
A
L
D
E
N
S
IT
Y
(V
/
Hz
)
IC (A)
09
45
9-
0
56
NOISE SPECTRAL DENSITY OF VBE
Figure 46. Noise Spectral Density of VBE vs. IC