PROCEEDINGS of the23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Measurement of Current Noise and Distortion in Resistors
Youhei MIYAOKA1; Minoru Kuribayashi KUROSAWA2
1,2

Tokyo Institute of Technology, JapanABSTRACTIn RF telecommunication systems, passive intermodulation has become a significant problem to get stabletelecommunication. The passive elements’ distortions are actual problems in telecommunication systems dueto multi-carrier frequencies. In audio systems, much more frequency spectrum peaks are existed and thespectrum peaks change in time and time. If a resister generates some distortions, the distortions aresignificant problems in elector-acoustic systems. In the resistor, there is current noise generated by thecurrent flow. Due to the influence of the current noise, the current flow is not always constant, so thefluctuation may cause nonlinear response. Then, it is thought that the resistor has some nonlinearity, and theresistors’ nonlinearity causes the signal to be distorted. In this study, we first measured the current noise as aparameter, the resistance and the voltage and wattage. Then we designed measuring circuit of distortion andmeasured the distortion in the resistor. Finally, we try to find the relation between current noise anddistortion.
Keywords: Distortion, Noise, Resistor

1. INTRODUCTION
The sound of listening in the concert hall and the sound from speakers are quite different. The
former is “raw” sound, the latter is “electric” sound. The "good" and "bad" sound of the audio system
is based on the listening result, and there is only the subjective evaluation. If there is a difference insound, an objective evaluation based on physical measurement should be possible. In this study, weconsidered that distortion in analog circuits was one of the causes that affect sound. The distortion
expressed by the times of the input signal frequency is called harmonic distortion, and their sum or
difference frequency distortion expressed intermodulation. Especially, the intermodulation occur inpassive circuit is called PIM (passive intermodulation). PIM is caused by the nonlinearity of a circuitcomposed of passive elements (1). we focus on the resistor, and consider the method of measurementof distortion.

2. MOTIVATION2.1 PIM in RF telecommunication system
In the next generation communication, PIM has become a serious problem by receiving the signal
near the carrier frequency by improving the sensitivity of the receiver in addition to the broadband, andPIM is attracting high interest now. Given the above, it can be considered that the same phenomenon
has occurred in the audible area which dropped the frequency band.
2.2 Nonlinearity of resistors
As mentioned introduction, PIM is caused by the nonlinearity of a circuit composed of passiveelements. Therefore, if the signal is distorted by the resistor, the reason of distortion is due to thenonlinearity of the resistors. Resistors are consisted from a variety of materials, carbon solid, thickfilm, thin film, wirewound, or metal foil. Each resistor has specific characteristics suitable for avariety of applications with different requirements.

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miyaoka.y.ab@m.titech.ac.jp
mkur@ee.e.titech.ac.jp

2.3 Noise in resistors
There are two main noises in the resistor, the thermal noise and the current noise. Thermal noise iscalled Johonson-Nyquist noise; noise voltage of thermal noise ܸ௧௛௘௠௔௟ is expressed with following
equation 1. T is resistor conductor temperature in kelvin, R is the resistors’ value in ohms, and ݇஻ isBoltzmann constant.

Vtherm al

4k BTR [୰୫ୱ Ȁξ ](1)Current noise is excess noise generated when current flows through the resistors. The current
noise has features that the noise is directly proportional to the current flowing through the device.
Current noise has a frequency characteristic, which PSD (Power Spectral Density) in resistors isreciprocal of the frequency (1/f characteristic). Therefore, the sum of the noise ܸ௧௢௧௔௟ from theresistors is represented by the RMS (Root Mean Squares) value, by using current noise PSDܸ௖௨௥௥௘௡௧ ,2Vtotal

22.
Vthermal Vcurrent(2)

While the thermal noise is white noise, the current noise is pink noise. We assume that the current
noise is a nonlinear phenomenon and that the magnitude of the current noise represents themagnitude of nonlinearity.

3. CURRENT NOISE MEASUREMENT
3.1 Measuring method
There are standards to measure the current noise such as the IEC60195 (2) or MIL-STD-202-30 (3).
The existing standards measure the RMS value in some frequency band settled by a bandpass filter.
From the RMS noise value in a certain frequency band, we cannot recognize the noise in current
noise or not; the current noise has the 1/f characteristic (4). We need frequency distribution of thenoise value.
For this study, we chose to follow the method developed by Frank Seifert (5-6). His method is using
a full Wheatstone bridge consisted of four DUT (Device Under Test) resistors and an instrumentation
amplifier.
Figure 1 is the circuit configuration to measure the current noise using the Wheatstone bridge, thatmakes it possible to obtain frequency characteristics from the FFT result, and can overcome theproblem of IEC and MIL ahead. Here, when the noise voltage generated from each resistor ଵ ̱ସ areതതതത is,Ƚଵ ̱Ƚସ, the input voltage to the amplifier ο'V

D12  D 22  D 32  D 424.

(3)

As equation 3, assuming that four resistors have same resistance value and raised comparable noise,
it can be seen that output noise is equivalent to the noise generated from one resistor.
The experiment was carried out using 10kΩ resistors with the voltage sources of NiMH AAbatteries. The circuit had two-stage amplification; a differential amplification to the first stage, andnon-inverting amplification to the second stage. The reason for the two stage is to obtain a flat
frequency characteristic in wide range. The amplifiers were chosen in consideration of the source
impedance, first stage was AD620 (Analog Devices) and second was AD797 (Analog Devices). One
battery had a stable electromotive force of 1.3V. The amplifier output, after passing anti-aliasing
filter, was fed into an oscilloscope, which was remotely controlled by a personal computer runningon MATLAB® program for automated noise measurements. The antialiasing filter using theexperiment was 7th VCVS-Butterworth low pass filter, which cut off frequency was 100kHz. All thecircuit were fabricated by considering the wiring pattern so that the noise caused by the loop noise
was not generated by using the board design software EAGLE.

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Figure 1 – Circuit configuration
3.2 Differential excitation voltages
The measurement result is shown in Figure 2. The source voltage changed from 2.6V to 20.8V wasapplied to the Wheatstone bridge composed of 10kΩ carbon film resistors. The unit voltage value was
1.3 V fixed by the electromotive force of one battery. The current noise PSD was reciprocal of thefrequency at 1Hz to 100kHz. When the applied voltage was small with 2.6V, it was confirmed that thecurrent noise was reduced at a frequency of 1kHz or more and convergence to the line of thermal noise.
From equation 3, the thermal noise output is equivalent to the noise generated from one resistor aswell as the current noise output. The value of a 10kΩ resistor thermal noise is calculated asܸ௧௛௘௥௠௔௟ ൎ ͳǤʹͻ ൈ ͳͲି଼  ୰୫ୱ Ȁξ  from equation 1. The amplifier noise like input referred voltage
noise were small compared to the thermal noise. It is effect of anti-aliasing filter that the PSD wasrapidly damped near 100kHz.
The measurement results of various resistors are shown in figure 3; the measurement conditions
were fixed at 10kΩ and 10.4V. From the results, large noise was observed in the trimmer and thecarbon-based resistor (carbon film and carbon composition), and a small noise was seen in themetal-based resistor (metal oxide and metal film).
Considering the result of carbon film resistors and metal film resistors, we assumed that thenonlinearity is high in the carbon film resistor and the nonlinearity is low in the metal film resistor.
Namely, it is hypothesis that the carbon film resistor has large distortion and the metal film resistor
has small distortion.

Figure 2 – Carbon film resistor current noise characteristics for different excitation voltages

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Figure 3 – Current noise of leaded resistors with 10kΩ, 10.4V

4. DISTORTION MEASUREMENT
4.1 Novel distortion measurement method
It has been reported that SMPTE method (7) and CCIF method (8-9) are used as a measurementof the IM for an active element (10). Both methods are measured by using two tone signal into thecircuit. The SMPTE method uses a far separated frequency combination such as ݂ଵ = 60Hz, ݂ଶ =7kHz, and the CCIF method uses a close frequency pair such as ݂ଵ = 14kHz and ݂ଶ = 15kHz. BothSMPTE and CCIF use a bandpass filter to obtain the modulated frequency signal. The bandpass filter
has passive elements that we want to evaluate. The usage of the passive element s in the filter circuit
makes the discussion to be complicated.
In the same way, there is THD (Total Harmonic Distortion) or THD + N (+Noise) as a method of
evaluating harmonic distortion, these evaluating method does not contain only harmonic distortion,and is not suitable for discussion of intermodulation. Even if the terms of the intermodulation
distortion are included, as in the case of measuring the current noise in IEC and MIL, these methods
are not appropriate because the value came out is a single scalar value. Moreover, the result is notquantitative because the harmonic distortion which can be observed depends on the measurement
environment such as the resolution of the measuring instrument. We need to investigate a newmeasurement circuit to solve these problems.
Figure 4 shows a new circuit configuration to measure the distortion. The measuring circuit us es
full Wheatstone bridge consisted of two DUT and two reference resistors; the metal foil resistor(Vishay Z-foil resistors) was chosen for the reference resistors. To the Wheatstone bridge, two typesof source signals ܸଵ and ܸଶ are applied as shown in Figure 4; ܸଵ has 1kHz + 1.1kHz mixedsinusoidal signal and ܸଶ has reversed phase same frequencies signal. Due to the unbalance of thebridge circuit, only the inter modulated signals are sensed at the output X-Y, the amplified by an
instrumentation amplifier. It is considered that unbalance of the bridge is caused by the difference ofthe distortion between the reference and the DUT. The resu lts of the two reference and two DUT arecompared with the all four reference.
The circuit output is evaluated by adapting the distortion rate of the CCIF method. The CCIF
distortion rate shows the output voltage divided by the total voltage of the original signal by apercentage. In this study, we replace these voltages with FFT output voltages. The distortion rate ‫ܪ‬ఠ
is obtained by following equation,

HZ

VZ
u 100 [%]
V1kHz  V1.1kHz(4)

where ܸఠ is the voltage at the focusing frequency ߱ calculated by FFT output.

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Figure 4 – Novel distortion measurement method
4.2 Result distortion measurement
The distortion rate obtained from the measurement are shown in figures 5 and 6: figure 5 showsthat the DUT is carbon film resistors, and figure 6 is metal film resistors. The experiment wascarried out using a sinusoidal waves of 10୮୮ and 1kHz + 1.1kHz.
In figures 5 and 6, the red plots indicate the result of all metal foil resistors of the bridge. Theblue plots indicate the result of one side metal foil resistors and the other side DUT. In comparison
between figure 5 with figure 6, the blue plots of the carbon film resistor are far off from the red plot,
whereas the metal film resistor shows close value to the red plot. From those result, it is possible tothink that the metal film resistors show the properties close to the metal foil resistors. If the reference
metal foil resistor is the ideal resistor without distortion, that is, the metal film resistor can be said tobe a resistor with small distortion, and a carbon film resistor is a resistor with large distortion.
The distortion measurement results are consistent with the assumption of the current noise
measurement; the distortion is large in the carbon film resistor and the distortion is small in themetal film resistor. Therefore, it can be said that the signal is distorted by the resistor, an d thedistortion is different depending on the type of resistor. Moreover, there is a possibility that these
phenomena are related to non-linearity.

Figure 5 – Distortion rate ‫ܪ‬ఠ in carbon film resistor

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Figure 6 – Distortion rate ‫ܪ‬ఠ in metal film resistor

5. CONCLUSIONS
We investigated the difference of nonlinearity by the type of the resistor, and experimented with a
new distortion measurement method. Focusing on the current noise as the nonlinear phenomenon of
the resistor, the current noise was measured. Finally, we found the possibility that there is a correlation
between the current noise and the distortion. However, the quantitative discussion could not bereached by various factors including the measurement equipment such as the distortion of the signal
source. Therefore, it is necessary to continue to examine the circuit in order to conduct a quantitative
discussion.

ACKNOWLEDGEMENTS
This work was supported by JKA and its promotion funds from KEIRIN RACE.

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