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Several sources of noise are observed in the lab: Technical noise: - Electro‘static’ (fluorescent lights) - Magneto‘static’ (ground loops and AC transformers) - E&M radiation (room lights into PN diodes, sparks) -Acoustic, thermoelectric, triboelectric…… George Herold, David Van Baak TeachSpin, Inc. Buffalo NY, 14214 2 Voltage Noise versus Bandwidth 2 1E-11 Y = -15.79566+1.00293 X 1E-12 1k 10k 100k Fig. 3 Voltage noise versus Bandwidth l d dh Note this log-log plot shows a linear fit with slope 1.003, indicating <Vn2> ~ ∆f consistent with expectations. Such a fit motivates forming the quotient <Vn2> / ∆f, with units Volts2/ Hertz, in the graphs below. Figure 4 shows a test of the claim that Johnson noise is ‘white’, ie. that the noise density is independent of the center frequency of the band pass filter. 3.00E-016 Apparatus Noise from 10k ohm resistor measured with band pass filter 2.50E-016 + - x100 RS 100Ω 1E-16 raw data fmax = 100kHz fmax = 33kHz fmax = 10kHz fmax = 3.3kHz Theor Theory 1E-17 1E-18 O T = 25 C (298K) 100 1k 10k 100k 1M Resistance (ohms) Fig. 5 Voltage noise versus Source Resistance Note that the amplifier noise can be successfully subtracted to reveal the Johnson noise generated by a 10 Ω resistor. For a large source resistance, capacitive effects reduce the noise content for measurements with higher maximum frequencies. The points do indeed fall on a line computed from the textbook value of Boltzmann’s constant and the ambient temperature. Figure 6 shows a measurement of the shot noise current, generated in a silicon photodiode illuminated by an incandescent light bulb. The photocurrent’s average value varies over a range of 104, and again the input-stage amplifier noise can be successfully subtracted to show that <In2> is proportional to IDC. The corrected points fall on a line computed from the textbook value of e, the charge of the electron. 2 1E-22 1.50E-016 1.00E-016 raw data amp noise resistor 5.00E-017 0.00E+000 100 1k 10k 100k Fig. 4 Voltage noise versus Center Frequency Low side Filter 1E-15 2.00E-016 Frequency (Hz) __________ *Rolf Landauer would like us to understand these separate types of fundamental noise as Johnson Noise versus Source Resistance 10 10k ohm Resistor raw data amplifier 1E-13 Effective bandwidth of measurment (Hz) The signal chain starts in the preamp stage. The first amplifier is configured appropriately for the type of measurement, and is followed by a x100 gain stage. The bandwidth ∆f is defined by adjustable low-side and high-side filters. There follows a further ggain stage, g , adjustable j from x10 to x104. An analog multiplier generates the real-time square of the filtered and amplified voltage. That square is time-averaged to yield an output voltage. A model of the whole chain is Vin→ GVin→ (GVin)2→ G2<Vin2> = Vout 1E-14 1E-19 100 Fig. 1 An oscilloscope trace of noise Fig. 1 An oscilloscope trace of noise Voltage Noise Density (V /Hz.) Figure 3 shows a test of the claim that Johnson noise gives an output signal proportional to the bandwidth ∆f used in the signal chain. Time average of V (t) (V ) Any noise signal has time average <V(t)> =0, but the mean-square value <V2(t)> is non-zero, and can serve as a measure of the noise. Because noise is distributed in frequency space, the noise measured will depend on the bandwidth ∆f. White noise is characterized by having uniform noise power per unit bandwidth, with natural units Volts2 / Hertz (V2/Hz). Two fundamental mechanisms do generate (Gaussian) white noise. All resistors (R) at non-zero temperature (T) show Johnson noise, <Vn2> = 4 kB T R ∆f. Some currents show shot noise, <In2> = 2 e IDC ∆f, where IDC is the average current. Fundamental noise* - Thermal motion of electrons (Johnson noise) - Discrete size of moving electrons (Shot noise) being related. Both are due to the motion of electrons driven either thermally or by an emf. In certain devices (diodes) it is possible to go continuously from thermal noise to shot noise. 1E-13 Data Theory Shot noise from light bulb on photodiode sense resistor = 100k Ohm 1E-23 2 What is noise? Where does it come from? Can you get rid of it? (and can you learn something from the bits you can’t get rid of?) We are only talking about electronic noise: the noise caused by the motion of electrons. Noise is generally an unwanted signal that exists ‘on top’ of the signal you want to measure. Note the vertical axis in Fig 4. has a linear scale, and the corrected data display a scatter of only +/- 1% over three decades of frequency. Figure 5 tests the claim that Johnson noise gives a voltage noise power proportional to source resistance. Shot Noise Density (A / Hz) Introduction t oduct o Noise Fundamentals: where noise is the signal Johnson Nois se Density (V^2/Hz) Abstract The measurement and theoretical examination of noise is an important and underrepresented topic in the advanced laboratory. Noise is inherent in all measurements and sets the lower limit of any physical measurement Noise can also be used to determine measurement. fundamental constants. The Johnson voltage noise from a resistor (vn2 = 4 R kBT ∆f) gives a measure of the Boltzmann constant (kB) if the resistance (R) and temperature (T) are known. The charge of the electron (e) can be determined from a DC current (I) with full shot noise (in2 = 2 e I ∆f). The apparatus that will be demonstrated can be used to measure the h Johnson h noise i from f resistors i i the in h range from 10 Ω to 10 MΩ, over a calibrated frequency range of 3 Hz to 100 kHz and temperatures from 77 to 373 K. Shot noise can be measured in currents ranging from 10 nA to 1 mA. The currents can be derived from a variety of sources: a photodiode illuminated by an incandescent light bulb or an LED; a forward biased PN junction; a diode-connected bipolar junction transistor; or from a zener diode. Some of the experimental subtleties of noise measurement will be presented, especially the effect of capacitance. High g side Filter 1E-24 1E-25 Amplifier noise subtracted raw data Theory 1E-26 -8 10 Gain 10 to 104 1kΩ Preamplifier Fig. 2 Block Diagram of Apparatus Analog Squarer Output Filter VOUT -7 10 -6 10 DC current (A) Fig. 6 Current noise versus DC Current -5 10 -4 10