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1、Resistor Current Noise MeasurementsFrank Seifert (Frank.Seifertaei.mpg.de)April 14, 2009IntroductionExcess low-frequency fluctuations are observed in many devices and materials 8, 22,23 that carry a current. Because most materials and devices usually show a verylow noise-level, the noise is hard to
2、measure. Several different methods of measuringthe excess noise in conducting materials have been discussed in literature 5. Sometechniques have in common that they focus on the phase sensitive readout of astandard, center-tapped Wheatstone bridge excited by one or more alternatingcurrents. These in
3、clude, amongst others the double frequency ac method 20, the0/90 subtraction method 18 and the 45 cross correlation technique 15, 16, 24, 25.The advantage of these techniques is the separation or elimination of backgroundnoise (e.g. Johnson noise) from the excess noise to be measured. On the other h
4、and,with low-noise amplifiers available today, the simple DC-measurement technique isalso very powerful 1, 10.There are several commonly used types of resistors: carbon, thin film, thick film,metal foil or wirewound. Each type has specific characteristics suitable for differentapplications with vary
5、ing requirements. Thick-film resistors are made of a mixtureof conductive particles (metallic grains) with a glassy binder and an organic fluid.This “ink” is printed on a ceramic substrate and heated in an oven. During thisfiring process the conductive particles within the glassy matrix are fused to
6、 thesubstrate and form the resistor. Thin film resistors are fabricated by sputtering ametal or alloy on an isolating substrate. Wirewound or foil-resistors are made fromfoils and wires of different metal alloys attached to an isolating substrate. All of themhave in common that the total noise can b
7、e divided into thermal noise and excessnoise. Excess current noise is the bunching and releasing of electrons associated withcurrent flow, e.g. due to fluctuating conductivity based on imperfect contacts withinthe resistive material. The amount of current-noise depends largely on the resistortechnol
8、ogy employed.Current noise in materials is directly proportional to the current flowing throughthe device. The noise power density varies with the reciprocal of the frequency (1/f),rounding off at the point where it equals thermal noise. Current-noise of resistorsis measurable and is expressed as a
9、function of the voltage drop across a resistor.The amount of noise is expressed as a resistor-noise quality index. This index, the“microvolts-per-volt” index, is an expression for the rms noise voltage, in microvolts,1LIGO-T0900200-v1per volt of applied DC voltage, in volts, transmitted in a single
10、frequency decade 3.The noise index NI is expressed in decibels, and the equation converting V/V todB isNI = 20 log10parenleftbiggvrmsVDCparenrightbiggdB in a decade (1)with vrms the root mean square noise voltage (in microvolts) and VDC the voltagedrop across the resistor. Therefore a noise index of
11、 0dB equates to 1V/V. It shouldbe noted that the same amount of noise power is transmitted in a frequency decaderegardless of the absolute frequency, if the noise has a true 1/f spectrum. In general,the mean-square noise voltage is given byv2 =f2integraldisplayf1S(f)df =f2integraldisplayf1e2(f)f df
12、(2)where S(f) is the PSD of the measured resistor current-noise in the frequency bandf1 to f2 and e2(f)f is the mean-square noise voltage spectral density at frequency f.The power spectral density of current noise is commonly assumed to be proportionalto 1/f. Then the product of the PSD and frequenc
13、y is constant and Equation 2 canbe rewritten asv2 = e2(f)f ff2integraldisplayf1dff (3)= e2(f)f f lnf2f1 (4)= e2(f)f f ln 10 for one decade(f2 = 10f1) (5)The root mean square noise voltage can now be expressed using the noise index asvrms =radicalBigv2 = VDC10NI/20radicalBigglog10 f2f1Vrms in frequen
14、cy band f1 to f2(6)= VDC10NI/20 Vrms in one decade (7)Based on the IEC recommendation 9 and MIL-STD-202, Method 308 21 formeasuring the current noise generated in fixed resistors, a low-noise measurementsetup for excess noise measurements of several commercial available resistors wasbuilt and a larg
15、e quantity of resistors was characterized.Experimental SetupAlthough the DC-measurement technique has several limitations, it has been usedto measure the excess noise of commercial available resistors used in our institute.2LIGO-T0900200-v1The disadvantage of this technique is, that the overall perf
16、ormance is limited bythe background noise (Johnson noise of the resistors and amplifier input noise).Nevertheless this technique is sufficient, because the main interest for this thesis wasto find the excess noise which limits the overall performance of the power stabilizationsetup. The measurement setup is illustrated in Figure 1.R1R2R3R4Vref = constVIDCDUTthermal isolationFFT analyzerlow-noiseamplifierlow-noise power supply PCFigure 1: Resistor
