Lab 4 - Photodetection and Noise
Goal
To measure characteristics of thermal noise, shot noise and gain noise.
Prelab
Background
Saleh and Tiech Section 17.4 and 17.5 1st edition or 18.4 and 18.6 in second edition.
Problems
1. An Electrical Spectrum Analyzer measures the total power into a 50 Ω load over a bandwidth specified by the resolution bandwidth. If the ESA measures -60 dBm, what is the
corresponding rms voltage and current?
2. The data set 1 set on the class web site are measured values of the rms noise voltage from a
photodiode into 50 Ω measured using an Electrical Spectrum Analyzer (ESA) in unit of µV
as a function of the mean current hii in mA over a bandwidth of 300 kHz. Using this data,
experimentally determine the value of the charge of the electron using
σi =
q
2e hii BN ,
and σv = σi R.
3. In a second experiment, an amplifier with a voltage gain of 500 and a bandwidth of 1 MHz is
used to measure the noise voltage of an input resistor at 300K. The data set of the measured
rms voltage in mV at the output of the amplifier vs. the value of
√ the resistance is given in
data set 2. By plotting the rms voltage out of the amplifier vs. R determine the value of
the Boltzmann constant k using
p
σv = 4kT BN R
Note that the data set has voltage in units of mV.
4. A photodiode with a responsivity of 0.5 A/W is connected in series with an input resistance
of 100 kΩ to an amplifier with a voltage gain of 500 and a noise bandwidth of 500 kHz.
a) Determine the input optical power when the rms noise voltage generated by the shot
noise is equal to the thermal noise generated by the resistor.
b) Determine the output rms voltage after amplification if the input optical power generates
a mean current of 1 mA in the photodiode.
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Lab
Turn on the BCP310 APD receiver. We need to let it warm up even though we will not use it until
later in the lab.
Shot Noise
Discussion The signal to noise (S/N) of the optical detector or receiver is a crucial measurement.
Some noise (thermal) comes from the electronic amplification of the signal and does not depend on
the signal (additive white noise). Other types of noise come from the statistical nature of the light
itself (shot noise) and internal gain mechanisms (amplified shot noise) and depend on the signal.
It is essential to determine what type of noise dominates a given receiver.
Lab Equipment There are three pieces of equipment used for this lab. The first is high gain low
noise amplifier The second is a scope. Turn on the amplifier and use the following settings:
• Sensitivity: 10 µA/V. (This is a gain of 105 V/A).
• Bias and input offset off.
• Filter type: We will use the high-pass 12 dB filter for the AC measurement and the low-pass
12 dB for the DC measurement. For both filter types set the filter bandwidth to 100 Hz.
• Gain mode: Low noise. For a gain of 105 this setting corresponds to a noise bandwidth of
BN =200 kHz.
DC Measurement Procedure
1. Set the filter on the amplifier to low-pass 12 dB.
2. Connect the photodiode output to the input of the current amplifier.
3. Connect the output of the current amplifier to the scope .
4. Set the current for the LED to 130 mA.
5. Read the DC voltage from the scope into a 50 Ω load . This should be on the order of 2 V.
The mean current iDC is
VDC
iDC =
G
where G = 105 is the gain of the current amplifier.
AC Measurement Procedure
1. Set the filter on the amplifier to high-pass 12 dB.
2. Connect the output of the current amplifier to the input of the electrical spectrum analyzer
using the following settings:
a) Frequency menu: Center frequency 150 kHz; span 1 kHz.
b) Amplitude menu: Scale 1 dB/div; Units dBm; Reference level -99 dBm
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c) Bandwidth menu: Resolution bandwidth 300 Hz; Video bandwidth 10 Hz; Video averaging on and set to 100.
d) Marker on and set to 150 kHz.
e) Marker function: Noise marker on - this calculates the noise power in dBm in a bandwidth of 1 Hz.
f) If everything is configured correctly, you should measure about -125 dBm/Hz which is
in the upper right hand corner.
To determine the voltage you will need the following equations for the write-up.
Total Power
The total noise power over the bandwidth of the current amplifier is
P = SBN
where S is the power per unit bandwidth measured from the spectrum analyzer and
BN = 200 kHz is the noise bandwidth of the current amplifier for a gain of 105 . You
must convert dBm (power referenced to 1 mW) into a real power in order to use this
equation. This conversion is
P = 10(dBm−30)/10
where dBm is the power in dBm. For example if the reading is -60 dBm, then the power
is 1 nW.
Voltage from Power
The voltage given the average measured power is
P =
2
VAC
2R
where the factor of 2 is because this is a modulated signal and the cosine-squared term
averages to 1/2. Solving for the voltage, we have
√
VAC = 100P
where we have used R = 50Ω.
Current from Voltage
The current out of the photodiode that produces this voltage is then iAC = VAC /G
where G = 105 is the gain of the current amplifier.
g) Repeat for three more settings of the current into the LED.
RIN from a Laser Diode
We now will compare the noise spectrum from the white light source with that for a laser diode.
1. Replace the LED with a laser diode and repeat the measurements done for the LED.
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2. Set the output power of the laser diode to 0.5 mW.
3. Set the amplifier sensitivity to 200 µA/V for the DC measurement.
4. Set the amplifier sensitivity to 100 µA/V for the AC measurement.
How does the measurement of iAC for the laser compare to the mean value for the LED?
APD mean current as a function of voltage and light level
The gain for an APD depends on the reverse bias voltage. In this section of the lab, we will measure
the gain for several setting of the bias voltage.
1. Turn on the BCP 310B. Without any light input to the APD, connect the Detector Out
of the APD part of the BCP 310B to an ammeter. Use the offset voltage to set the mean
current out of the APD to zero.
2. Turn the light level to its lowest value and set the gain of the APD to 0.0. Record the current
as a function of the light level using the same control knob setting.
You may not be able to use all values of the light output because the APD may overload.
3. Repeat for APD gain settings of 4, 7.0, 8.5, and 9.5 being sure to re-zero the mean current
out of the APD for each gain setting before turning on the light source. When completed,
you should have five sets of data.
Shot Noise and Gain for an APD
Discussion Our reference noise measurements will be made with the APD with the gain set to
zero. With the gain set to the lowest value, the APD will behave somewhat like a photodiode and
we can use these settings as a reference for when there is internal gain.
1. Turn off the BCP 310B, connect the Detector Out cable to the input of the electrical spectrum analyzer (ESA) using the following settings: Center: 10 MHz, Span 1 MHz, Resolution
bandwidth 300 kHz, Video bandwidth 10 Hz, Y-axis setting: Linear, Reference Level. 14 µV.
If everything is set correctly, there should be an approximately straight-line trace at about
2.5 µV rms. Set the marker to the center which is 10 MHz. Record the value at the marker.
This is the noise of the spectrum analyzer with no signal present.
2. Without turning on the light source, turn on the BCP 310B. The additional signal seen is
the dark current noise. This should be about 10 µV. This is the noise generated by thermally
excited carriers. The sum of the dark current noise and ESA noise needs to be subtracted
from each noise measurement.
3. Now turn on the light source to the lowest setting. Set the gain to 0. Record the rms noise
voltage for all light source settings that do not saturate the detector.
4. Repeat for gain settings of 4, 7.0, 8.5, and 9.5. Note that you have to change the setting on
the linear scale of the ESA to measure the complete range of values. You also will not be
able to record as many points before the APD saturates.
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Post Lab
1. Plot i2AC vs. 2iDC BN and fit a straight line to the curve. Compare this slope to the charge
of an electron e.
2. Explain the difference between the noise measured for a LED and the noise measured for a
laser. Which source generates more noise?
3. For the APD gain setting of 0, plot the rms current noise vs. the square-root of the mean
current. Determine the slope and compare this slope to the slope determined in Prelab.
Is the APD at the lowest gain setting operating like a photodiode? Justify your answer.
4. Assuming that the values for the gain setting of zero correspond to a gain of 1 with no excess
noise, determine the mean gain G for each of the gain settings.
5. Plot the current noise variance σi2 vs. the mean current for each of the five gain settings.
Assuming the the electron charge is known in each case, and using the mean gain G from the
previous question, determine the excess noise factor for each gain setting and then plot the
excess noise vs. the gain. Does this plot resemble Figure 17.5-4 in the book? Explain why
they may be different.
6. For the maximum light setting that does not overload the APD at a gain of 9.5, plot the
signal to noise vs. gain and discuss the results.
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