Slide 1 Goals of the Lab: Understand the origin and properties of thermal noise Understand the origin and properties of optical shot noise In this lab, You will qualitatively and quantitatively determine the resistance-, temperature and frequency dependence of thermal noise as well as the light intensity dependence of optical shot noise. You will learn how to measure and how to control noise in experimental systems.
Background: Noise For a general overview about the origins the nature and the description of noise, refer to the lecture notes. Slide 2 Thermal noise: For electrical measurements of thermal noise (which never exceed the GHz range due to the speed limitations of electronics), it is reasonable to assume a noise spectral density: and hence, a noise voltage Shot noise: Shot noise is due to random arrival times of either individual charge carriers in a current (electrical shot noise) or photons in a light beam (optical shot noise). For electrical shot noise, we assume a noise spectral density: and hence, a noise power Applied to optical shot noise we obtain a noise power
Slide 3 Principal sketch of the experiments 1,2: Measurement of thermal Differential voltage amplifier PAR113 Tektronix TDS1012 Oscilloscope DVM Keithley 1000 Stanford Research SR760 Spectrum Analyzer shielded resistor shielded resistor Krohn-Hite 3100A active bandpass filter resistor without shielding Note that the clamps holding the resistor allow also a quick resistor change In order to measure noise produced by a thermal resistor, the resistor is connected to the input of a voltage amplifier. The output of the amplifier is then connected an active band pass filter and channel 1 of the oscilloscope. The output of the band pass is connected to channel 2 of the oscilloscope. Thus, the oscilloscope allows to observe the noise of both, the filtered and unfiltered signal. Connect the spectrum analyzer and the digital voltage meter (DVM) to the filtered signal.
Slide 4 Carry out the following experiment: 1. Thermal rms noise and noise spectrum (100kΩ resistor) With a 100kΩ resistor attached to the input of the PAR 113 differential amplifier, measure the root mean square voltage v rms and noise spectral density at room temperature. The gain of the PAR 113 should be set to 10 4, high pass filter set to 0Hz and low pass filter set to 300 khz. The output should be sent to an oscilloscope, DVM and spectrum analyzer. Be sure to include the gain of the amplifier in your measurement of the thermal noise of the resistor and comparison with theory. For this measurement, you may assume that the amplifier noise is negligible above 1kHz. 1a. Observe the thermal noise voltage across the resistor on the spectrum analyzer. With the input sensitivity correctly adjusted on the spectrum analyzer, and display showing power spectral density (V 2 /Hz ), you will observe the noise spectrum of the 100kΩ resistor. Note that the value of the noise spectrum is shown at the top of the screen, corresponding to that part of the spectrum to which the cursor is pointing. The value seen at the top is the noise voltage spectral density (V/ Hz), which is the square root of the power spectral density (V 2 /Hz). Record the noise spectrum. Note that it is flat above a frequency of 10 Hz and that spikes at fixed frequencies are found in the spectrum. These spikes are pick-up signals which come from various sources in the lab (line, computer monitors, etc.). Neglect these spike when making the following measurements. The noise below 10Hz is called 1/f noise or flicker noise. It is typically greater than the thermal or shot noise at these frequencies. Sketch the theoretical thermal noise spectrum on the measured spectrum. Point out the differences between measured and theoretical values on the graph and explain their origin.
Slide 5 1b. Now measure the thermal noise spectrum as in part a, but reduce the low pass filter frequency of the PAR 113 amplifier to 10 khz. Record the spectrum. Explain the change in the noise spectrum seen on the spectrum analyzer, and explain the primary features. 2. Measure rms thermal noise and compare with integrated power spectral density Select a 10kHz bandwidth (1kHz high pass and 11kHz low pass) for the pass band of the KH filter. Measure the rms noise voltage with the DVM and record it and the measurement bandwidth. Record the noise spectrum seen on the spectrum analyzer. Show that the rms noise voltage and spectral values measured are consistent using the equations shown on slide 2. Sketch the predicted noise spectrum (theoretical) on the graph which contains the measured spectrum analyzer data. Note and explain any deviations. 3. Thermal noise dependence upon resistance a. Measure the thermal rms noise voltage of 4 different resistors (1k,10k,100k, 1MΩ) at room temperature using the same settings as in part 2. (10kHz bandwidth). Measure the v rms for each resistor with the DVM and plot the results on a log-log scale (noise voltage versus resistance). Additionally, plot the corresponding voltage noise spectral density S t (f), obtained from the flat portion of the spectrum on the spectrum analyzer (in V/ Hz) for each resistor. b. Compare the measured noise voltage (v rms ) and voltage spectral density for each resistor with the predictions of Johnson noise theory using the experimental parameters (bandwidth, resistance, temperature). Discuss how the noise (v rms and voltage spectral density should depend upon resistance). Explain any discrepancies between measured and theoretical values.
Slide 6 4 Thermal noise dependence upon temperature Using the set up described in silde 3, measure the v rms value of a 100k ohm resistor with the DVM at room temperature (~300K) and at liquid nitrogen temperature (~77K). Compare your results with thermal noise theory. 5 Thermal noise dependence upon bandwidth (15 min) Using the set up described in silde 3, measure the vrms value using the DVM as a function of the detection bandwidth. Adjust the KH filter to achieve a 1kHz, 10kHz and 100kHz passband bandwidth. For a 1kHz bandpass, adjust the high pass to 1kHz, and the low pass to 2kHz, for 10kHz bandpass, adjust the low pass to 11kHz, and so on. Record the measured values for each bandwidth and compare with theory.
Slide 7 white light lamp photodiode detector current source for lamp white light lamp photodiode detector voltage amplifier active band pass filter voltmeter 6 Measurement of shot noise Measure the average photo-current and shot noise current in a 10kHz detection bandwidth of a white light lamp illuminated photo-diode detector as a function of illumination power (or average photocurrent). Measure the average photocurrent using DVM. Calibrate the bandwidth to an exact value using thermal noise of a 100kΩ resistor. Vary the power of the lamp in order to vary the incident intensity on the detector. Plot the square of the noise current versus the average photo-current. Identify the shot noise limited region of the graph by comparing the measured data points with a line representing the theoretical relation between rms shot noise current and average current. Explain any deviations.