INTELLIGENT OPTO SENSOR
DESIGNER’S
NOTEBOOK
Number 3
Analysis of Noise Sources in the TSL257
Revision B
Contributed by Cecil Aswell
February 23, 2001
There are 3 primary components of noise in a light to voltage converter:
•
•
•
Thermal noise of the feedback resistor.
Shot noise of the photo current.
Circuit noise.
The TSL257 uses a 50 MΩ resistor in a Tee feedback network with a gain of 6.4 to achieve an effective resistance
of 320 MΩ. The 50 MΩ resistor generates a thermal noise voltage of 911 nV/root Hz at 27ºC as given by the
equation
vn2 = 4kTR∆F
(1)
where vn is the noise voltage, k is Boltzmann’s constant (1.38x10-23 J/K), T is absolute temperature, R is the
resistance in ohms and ∆F is the bandwidth. As seen at the output of the TSL257 thermal noise is about 5.8 µV
/root Hz at room temperature.
Shot noise is due to the random arrival of photons in the photodiode. This is given by
in2 = 2qIP∆F
(2)
where in is the shot noise current, q is the charge of an electron (1.60x10-19coulombs), IP is the photo current, and
∆F is the bandwidth.
It can easily be shown that for an ideal simple transimpedance amplifier (one op amp and one resistor) that the
thermal noise is equal to the shot noise when the signal output is 2kT/q (about 52 mV at room temperature). This is
done by setting the thermal noise equal to the shot noise multiplied by the resistor value and solving the resulting
equation. (Note that this is true for any value of resistor.)
Below the 52 mV signal level the noise will be constant (thermal noise) and above that signal level the noise will
increase as the square root of the photo current (shot noise). Let's call the point where the thermal noise is equal to
the shot noise the "noise knee". If a light to voltage converter uses gain in addition to the simple transimpedance
function the noise knee will move up accordingly.
Ignoring circuit noises, we would expect the noise knee of the TSL257 to be at 332 mV since it has a gain of 6.4.
Thus below 332 mV signal output the noise will be dominated by the feedback resistor and above 332 mV it will be
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dominated by shot noise. In fact, at frequencies below 3 kHz this is what is observed. Figure 1 shows noise power
spectral density measurements of a typical TSL257 device.
This plot also shows a peaking in noise for low level signals at frequencies above about 3 kHz. This is due to the
circuit implementation.
The RC feedback network around the op amp has a pole at about 3 kHz, implying a feedback capacitor of 1 pF.
The photodiode has a capacitance of about 50 pF, which means the transimpedance amplifier has a high frequency
noise gain of 51. Even at this high gain the circuit noise is so far below the thermal and shot noise it is negligible
over most of the output range. As would be expected in this case, the thermal and shot noise roll off at 3 kHz if the
output is above 0.5 volts.
However, the feedback capacitor is highly non-linear below about 0.7 volts and goes to about 0.3 - 0.5pF at zero
bias which causes the high frequency noise gain to double or triple as well as increasing the rolloff frequency by
the same amount. In addition, parasitic capacitance associated with the 50 MΩ resistor requires the use of high
frequency boost circuitry, resulting in an amplification of both thermal noise and circuit noise above about 3 kHz.
Figure 1. TAOS TSL257 Noise Spectral Density Measurements
30
Noise Spectral Density (uV/root(Hz))
25
20
Vout=Dark
Vout=0.5V
Vout=1.0V
15
Vout=2.0V
Vout=3.0V
Vout=4.0V
10
5
0
10
100
1000
10000
Frequency (Hz)
100000
1000000