Berklee College of Music MP211 Guide to Electronic Measurements

MP211 Principles of Audio Technology

Guide to Electronic Measurements

Copyright © – Stanley Wolfe All rights reserved.

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GUIDE TO ELECTRONIC MEASUREMENTS AND LABORATORY PRACTICESelected Notes from the 2nd Edition, by Stanley Wolf

This document draws from material presented in the first three chapters of Stanley Wolf’s Guideto Electronic Measurements and Laboratory Practice, 2nd Edition, as appropriate for MP 211students. The reader is encouraged to consult the text for further information and background.

Electrical MeasurementsCharge, Voltage and Current

Electrical ChargeAtoms consist largely of electrically charged particles. The nucleus of an atom is a central coreconsisting of protons (which have a positive charge) and neutrons. The nucleus is surrounded bya swarm of electrons. The electron has an electric charge that is equal in magnitude but oppositein polarity to the charge of a proton. Therefore, an electrically neutral atom must contain anequal number of electrons and protons.

If electrons are removed from an atom, that atom is no longer electrically neutral but instead hasa net positive charge. If electrons are removed from many neutral atoms of a substance and arethen removed from the boundaries of the substance, the entire substance acquires a positivecharge. By the same token, if a neutral substance acquires extra electrons, it acquires a netnegative charge.

If two adjacent substances both acquire net positive or net negative charges (called polarities),they will repel each other. If two adjacent substances acquire different polarities or charges, theywill attract each other.

The forces of electricity are derived from these attractions and repulsions, and from themigration of electrons from one atom and one substance to another in response to forces ofattraction and repulsion.

VoltageVoltage may be expressed as the force inherent in any electrical charge. It is equivalent to thedifference in potential energy (see a Physics text) between any two adjacent substances. Often,the electrical charge of the earth itself is used as a reference, and is defined as 0 Volts (hence theterm “ground”).

CurrentElectrical current is defined as the number of charges (electrons) moving past a given point in acircuit in 1 second. The unit of current is the ampere (current itself is often expressed by theletter “I”). It may be simply thought of as the flow of electrons in a circuit, in response to theforces of attraction and repulsion (voltages) acting upon that circuit.Most of the currents found electric circuits involve the motion of electrons in solids (andvacuums in the case of vacuum tubes). Mostly, we concern ourselves with the flow of current insolid metal conductors (wires).

Electrical conductors contain essentially free electrons, which can move about quite easily withinthe boundaries of the conductor. When an electrical field or force is applied to the conductor,these electrons move in response to the applied electric field. The total number of electrons that

move past some cross-sectional area of the wire per unit of time yields the magnitude of thecurrent.

The apparent velocity of current flow is essentially the velocity of light.

Electrical UnitsThe following units are used in connection with electricity

Quantity Unit AbbreviationTime Second SCurrent Ampere AVoltage Volt VResistance Ohm ΩImpedance Ohm ZPower Watt WFrequency Hertz Hz

Sine Waves, Frequency and PhaseThe instantaneous values of electrical signals can be graphed as they vary with time. Such graphsare known as the waveforms of the signals. Signal waveforms are analyzed and measured inmany electrical applications.

Generally speaking, if the value of a signal waveform remains constant with time, the signal isreferred to as a direct-current (DC) signal. An example of a dc signal is the voltage supplied by abattery. If a signal is time varying and has positive and negative instantaneous values, thewaveform is known as an alternating-current (AC) waveform. If the variation is continuouslyrepeated (regardless of the shape of the repetition), the waveform is called a periodic waveform.

The most basic waveform is the sinusoid. It is a waveform that contains energy change at asingle frequency or rate only.

The amplitude of the sine wave describes the maximum value of the waveform, also called thepeak value. In electrical signals, it is usually expressed in volts. The frequency, f, of the sinewave is defined as the number of cycles of that waveform occurring in one second. The timeduration of any single cycle is called its period, T. The frequency and the period of any periodicwaveform are inversely proportional and may be related to each other by the expression:

f = 1/TIf two sine waves of identical frequency exist simultaneously, the difference in their values are afunction of phase angle (Ø), which may be thought of as their relative difference in timeexpressed in degrees of the cycle of one period.

Average and Root Mean Square ValuesThe value of a DC signal is relatively easy to measure at any point in time. However, an ACsignal varies in both amplitude and polarity over its period, and measurement of the voltagevalue at any point in time during that period yields incomplete information about that AC signal.

Therefore, when waveforms possess time-varying shapes, it is no longer sufficient to measurethe value of the quantity they represent at only one instant of time. It is not possible from onemeasurement to the determine all that must be known about the signal. However, if the shape ofa time-varying waveform can be determined, it is possible to calculate some characteristic values

of the waveform shape (such as its average value). These values can be used to compare theeffectiveness of various waveforms with other waveforms, and they can also be used to predictthe effects that a particular signal waveform will have on the circuit to which it is applied.

The two most commonly used characteristic values of time-varying waveforms are their averageand their root-mean-square (RMS) values.

Average ValueThe average value of a time-varying current waveform over its period T is the value that a DCsignal current would have to have if it delivered an equal amount of electron charges in that sameperiod T. Therefore the average value of any periodic waveform is found by dividing the areaunder the curve in one period T by the time of the period, so that:

Aav = (area under curve) / length of period (in seconds)

Note that the average value for a sinusoidal waveform (sine wave) is zero!Root-Mean-Square ValuesThe second common characteristic value of a time-varying waveform is its root-mean-square(RMS) value. This value is used much more often that the average value to describe electricalsignal waveforms. This is because the average value of symmetrical waveforms is zero, as notedabove. Such a value does not provide much useful information about the properties of the signal.

The RMS value of a waveform refers to its power delivering capability. In connection with thisinterpretation, the RMS value is sometimes called the effective value. This name is used becausethe RMS value is equal to the value of a DC waveform which would deliver the same power if itreplaced the time-varying waveform.

To determine the RMS value of a waveform, we first square the magnitude of the waveform ateach instant. (This makes the value of the magnitude positive for both positive and negativevalues of the original waveform). Then the average (or mean) value is taken to get the result.Finally, the square root of this average value is taken to get the result. Because of the sequence ofcalculations that is followed, the result is given the name root-mean-square.

When referring to sine waves, it is customary to describe them in terms of their RMS values. Forexample, the 115 Volt, 60 Hz voltage that is delivered by electric power companies to domesticelectricity consumers is really a sine wave whose (peak) amplitude is about 163 volts and whoseRMS value is 115 volts. For a sine wave, the ratio between the RMS value and the peak value is.707:1. For a square wave, that ratio is 1:1.

Language of Digital Measurement SystemsSignal handling systems can be divided into two broad categories: analog systems and digitalsystems. In analog systems the information is processed and displayed in analog form. Themeasured quantity is an analog quantity (i.e., a quantity whose value can vary in a continuousmanner). In digital systems, the measurement information is processed and displayed in digitalform. In digital systems the original information may also be acquired in the form of an analogelectrical signal, but the signal is then converted to a digital signal (via a process known asquantization) for further processing and display. A digital electrical signal has the form of agroup of discrete and discontinuous pulses.

Virtually all of the digital data formats are based on the fact that signal levels in digital systemsare restricted to having binary values (i.e., only one of two possible values). These two valuesare represented by the symbols 1 and 0, which are known as binary digits. In addition, a singlebinary digit is often referred to as a bit. The digits using the decimal numbering system (0, l, 2, 3,. . . 9) are known as decimal digits. A system using 16 symbols, called hexadecimal, uses the 10decimal digits plus the first 6 letters of the alphabet (0 1 2 3 4 5 6 7 8 9 A B C D E F).

To represent a value of measured data in digital form, a group of such binary digits must be used.A value such as 25 (in decimal) could be represented in binary as 11001. This number consists of5 bits.

Electronic digital systems are typically designed to function by handling data formatted ingroups containing a specific number of bits. Each decimal digit or alphabetic character may berepresented by a group made up of a unique combination of bits. Such groups are known asdigital words, and usually contain 8, 16 or 32 bits. Eight-bit words have acquired their owndesignation and have come to be known as bytes. Note that the left-most bit of a digital word isknown as the most significant bit (MSB) and the right-most bit is the least significant bit (LSB).

Digital systems are designed to transfer digital words from one part of the system to another.Such transfers can be done in either a serial or a parallel fashion. In serial transmission, one bit ata time of the digital word is sent from part of the system to the other, and only one signal path isrequired. In parallel transmission, all the bits of the word are transmitted simultaneously, andthis requires that there be an individual signal path for each bit.

Several block diagrams referring to digital signal handling are shown below.

The above shows an analog signal being amplified (in the analog realm) and then converted (i.e.,quantified) to an array of digital numbers in an analog-to-digital convertor (A/D) and then sent(as an array of bits) to any of several digital devices, such as a printer, a digital display and/or acomputer.

In the above drawing, the basis for quantification (either D/A or A/D) is shown. A measuredvoltage of less than 2 volts equals a "0" and a measured voltage of greater than 2 volts equals a"1.”

The above drawing shows the analog representation (used for signal storage and transmission) ofa digital number. In this case, the decimal number "nine," converted to an 8-bit binary word orbyte (10001001). (The 1 at the beginning of the word denotes the beginning of the word, and isnot part of the number 9, which is 1001 in binary.)

In the above, a binary number stream of bits is sent to a digital-to-analog convertor (D/A) whereit is converted to an analog signal, which is then amplified and sent to any appropriate analogdevice.

Experimental Data and ErrorsMeasurements play an essential role in substantiating the laws of science. They are also essentialfor studying, developing and observing devices, processes and systems. The process ofmeasurement itself involves many steps before it yields a useful set of information. For thepurpose of studying measurement, the process of measurement can be viewed as a sequence offive operations:

1. Design an efficient and effective measurement system/setup. This includes the properselection of equipment, correct interconnection, and verification of correct operation.

2. Correct and intelligent operation of the measurement system/setup

3. Recording the data obtained from the measurement system in a manner that is clearand complete. This documentation should provide unambiguous and accurate data for anyfuture interpretation.

4. Establishing (via estimation) the accuracy of the measurements and the magnitudes ofpossible attendant errors.

5. Preparing a report that describes the measurements and results for those who may beinterested and who may need to use them.

All five of these items must be successfully completed before a measurement is truly useful.

Measurement Recording and ReportingThe original data sheet is a most important document. Mistakes can be made in transferringinformation, and therefore copies cannot have the validity of an original. If disputes arise, theoriginal data sheet is the basis from which they are resolved (even in courts of law). It is essentialto label, record and annotate data carefully and completely as they are taken. A short statement atthe head of the data sheet should explain the purpose of the test and list the variables to bemeasured. Items such as the date, wiring diagrams used, equipment models and serial numbers,and unusual instrument behavior should all be included. The measurement data themselvesshould be neatly tabulated and properly identified. (All this should emphasize the fact thatwriting down data on scrap papers and trusting the memory to record data is not an acceptableprocedure for recording data. Such practices will certainly lead to the eventual loss of valuabledata and the use of invalid and inaccurate data.) In general, the record of the experiment on thedata sheet should be complete enough to specify exactly what was done and, if need be, toprovide an accurate and effective guide for duplicating the work at a later date.

The report presented at the end of a measurement should also be carefully prepared. Its objectiveis to explain what was done and how it was accomplished. It should give the results that wereobtained, as well as an explanation of their significance. In addition to containing all pertinentinformation and conclusions, the report must be clearly written with proper attention to spellingand grammatical structure. To aid in organizing the report and avoid omitting importantinformation, an outline and rough draft should always be used. The rough draft can be laterpolished to produce a concise and readable document.

The form of the report should consist of three sections:

1. Abstract of results and conclusions

2. Essential details of the procedure, analysis, data and error estimates

3. Supporting information, calculations and references

In industrial and scientific practice, the abstract is likely to be read by higher-level managers andother users who are scanning reports for possible information contained in the report body. Thedetails, on the other hand, will probably be read by those needing specific information containedin the report or by others wanting to duplicate the measurement in some form. The latter groupswill be interested in the details on the data sheets, the analysis of the level of accuracy, and thecalculations and results that support the conclusions and recommendations. For these readers, thereferences from which source material and information were obtained should also be provided.

The results and conclusions of the report form its most important parts. The measurement wasmade to determine certain information and to answer some specific questions. The resultsindicate how well these goals were met.

Graphical Presentation of DataGraphical presentation is an efficient and convenient way of portraying and analyzing data.Graphs are used to help visualize analytic expression, to interpolate data, and to discuss errors.

Graphs should always contain a title, the date the data was taken, and adequately labeled andscaled axes. A sharp pencil and straightedge should be used to draw the curves, to ensure neatand legible graphs. Plotting data on a graph as they are taken allows unexpected data points to berechecked before an experimental setup is dismantled.

It is typical that that the independent variable be plotted along the horizontal axis (the X-axis)and the dependant variable along the vertical axis (Y-axis). The data points are typically shownas small circles, the diameter of which can be proportional to the estimated error of the readings.

In addition to normal linear graphs, there are graphs utilizing linear/logarithmic axes, logarithmicaxes, and polar plots. Linear/logarithmic axes (called "semilog" or "linlog”) are graphs whereone axis is expressed in a linear way and the other in a logarithmic way. Logarithmic graphsutilize logarithmic expressions for both vertical and horizontal axes (so-called "loglog"). Polarplots are single-axis graphs (similar to pie-charts) that show the dependent variable as a linearound a point where the independent variable is degrees of a circle. These special graphs all areused extensively in audio, to a point where they are more prevalent than normal linear graphs.

Precision and AccuracyIn measurement analysis the terms accuracy and precision are often misunderstood and usedincorrectly. Although they are taken to have the same meaning in everyday speech, there is adistinction between their definitions when they are used in descriptions of experimentalmeasurements.

The accuracy of a measurement specifies the difference between the measurement and the truevalue of a quantity. The deviation from the true value is the indication of how accurately areading has been made. Precision, on the other hand, specifies the repeatability of a set ofreadings, each made independently with the same instrument. An estimate of precision isdetermined by the deviation of a reading from the mean (average) value. For example, consider adefective measuring instrument. The instrument may be giving a result that is highly repeatable,yet far prom accurate. Therefore, the precision of the measurements made with that device wouldbe good, but the accuracy would be poor. It should be noted that precision does not guaranteeaccuracy, but accuracy is limited by the precision of a measuring system.

If an instrument is specified to be accurate to within 10%, that means that no measurement willbe greater than plus or minus 10% of the actual value of the measured item. If the precision ofthat instrument is specified as 1 %, then no measurement of the measured item will vary by morethan plus or minus 1%.

Errors in MeasurementErrors are present in every experiment. They are inherent in the act of measurement itself. Sinceperfect accuracy is not attainable, a description of each measurement should include an attemptto evaluate the magnitudes and sources of its errors. From this point of view, an awareness oferrors and their classification into general groups is a first step toward reducing them andminimizing their effect.

Sometimes a specific reading taken during an experiment is rather far from the mean value. Iffaulty function of the measurement instruments is suspected as the cause of such unusual data,the value can be rejected. However, even such data should be retained on the data, properlyannotated as suspect and rejected. Even when all items involved in a measurement setup appearto be operating properly, unusual data may still be observed. We can use a guide to help decidewhen it is permissible to reject suspect data, based on statistical evaluation: individualmeasurement readings taken when all the instruments of a measurement setup appear to beoperating properly may be rejected when their deviation from the average value is four timeslarger than the probable error of one observation. Such a random error will occur less than 1%of the time, and it remains highly probable that some external influence affected themeasurement. Keep in mind that when a large error does occur, it may signal the commission ofa major measurement or system error. An attempt to locate such an error should be undertaken.Also, keeping (with proper annotation) such rejected errors can be of assistance in finding theextent and cause of error.

Principles of Measurement and Errors in Outline Form:1. Quantification

The conversion of a continuum to discrete increments

2. InterpolationThe estimation of more precise discrete increments within the given quantification

3. AccuracyAccuracy is a specification of the error between the true value and the measured value.

4. Precision and reliabilityThe precision with which a measurement is made is an expression of the consistency ofthe measurement and the range of variation of repeated measurements. A measurementcould be extremely precise, but inaccurate.

Reliability is a function of the verified accuracy of a measurement and the precision ofthe set of measurements leading to that expression. It is a prediction of the likelihood oferror in a set of measurements.

5. Measurement Errors1. Human

A. Examples Faulty reading of data, faulty calculations, poor choice of instruments, incorrectsetup or adjustment, failure to account for side effectsB. Mathematical estimation not possibleC. Ways to reduce or eliminate Careful attention to detail; awareness of instrumentation limits and problems, useof multiple observers; use of multiple readings; motivation and awareness of needfor results

2. SystemA. Examples

1. EquipmentMechanical friction; calibration errors, damaged equipment, data taintedduring transmission

a. Mathematical estimation Comparison with standard; determine if error is constant or proportionalb. Elimination or reduction Calibration; inspection; correct application of correction after errors havebeen found; use of multiple methods of measurement

2. EnvironmentalChanges in temperature, humidity, electrical and magnetic fields

a. Mathematical estimation Careful monitoring of variables, and calculation of predicted changesb. Elimination or reductionSeal equipment; maintain temperature and humidity, shield equipmentfrom electro-magnetic and radio frequency radiation, use of equipmentthat is not affected by these factors

3. RandomExamples

Unknown effectsMathematical estimation

Use of many readings and application of laws of probabilityElimination or reduction

Careful design of equipmentUse of statistical methods for evaluation

Statistical Evaluation of Measurement Data and ErrorsStatistical methods can be very helpful in allowing one to determine the probable value of aquantity from a limited group of data. Further, the probable error of one observation and theextent of uncertainty in the best answer can also be determined. However, a statistical evaluationcannot improve the accuracy of a measurement. The laws of probability utilized by statisticsoperate only on random errors and not on system errors. Therefore, errors caused by themeasurement system must be comparatively small compared to the random errors if the results ofthe statistical evaluation are to be meaningful. If the "zero adjustment" on an instrument isincorrectly adjusted, the statistical treatment will not remove this error. But a statistical analysisof two different measurement methods may demonstrate the discrepancy. In this way, themeasurement of precision can lead to a detection of inaccuracy.

The following quantities are normally calculated using statistics:

1. Average or mean value of a set of measurements2. Deviation from the average value3. Average value of the deviations4. Standard Deviation (related to the concept of RMS)5. Probability of error size in one observation

1. Average or mean value. The most likely value of a measured quantity is found fromthe arithmetic average or mean (both words mean the same thing) value of the set ofreadings taken. The more readings that are taken, the more reliable the average will be.

The average value is calculated:aav = (a1 + a2 +. . . an) / n

where:aav = average valuea1, a2, a3, . . . = value of each readingn = number of readings

2. Deviation from the average value. This number indicates the departure of eachmeasurement from the average value. The value of the deviation may be either positive ornegative.

3. Average value of the deviations. This value will yield the precision of themeasurement. If there is a large average deviation, it is an indication that the data takenvaried widely and the measurement was not very precise. The average value of thedeviations is found by taking the absolute magnitudes (disregarding any minus signs) ofthe deviations and computing their mean.

4. Standard deviation and variance. The average deviation of a set of measurements isonly one of the methods of determining the dispersion of a set of readings. However, theaverage deviation is not mathematically as convenient for manipulating statisticalproperties as the standard deviation (also known as the root-mean-square or RMSdeviation). The standard deviation is found from the formula: s = √((d1

2 + d22+ d3

2 + . . . + dn2) / (n-1))

where:s = standard deviationd1 d2 d3. . . = deviations from the average valuen - 1 = one less than the number of measurements taken

The variance V is the value of the standard deviation a squared:V = s2

5. Probable size of error and Gaussian distribution. If a random set of errors about someaverage value is examined, we find that their frequency of occurrence relative to theirsize is described by a curve known as a Gaussian curve (or bell-shaped curve). Gauss wasthe first to discover the relationship expressed by this curve. It shows that the occurrenceof small deviations from the mean value are much more probable than large deviations.In fact, it shows that large deviations are extremely unlikely.

The curve also indicates that random errors are equally likely to be positive or negative.If we use the standard deviation as a measure of error, we can use the curve to determinewhat the probability of an error greater than a certain s value will be for eachobservation.

Error (+/-) Probability of error being greater thanIn units of standard deviation +s or -s in one observation

0.675 0.2501.0 0.1592.0 0.0233.0 0.0015

6. Probable error. From the above table we can calculate the probable error that willoccur if only one measurement is taken. Since a random error can be either positive ornegative, an error greater than +/- 0.675s is probable in 50% of the observations.Therefore, the probable error of one measurement is:

r = +/- 0.675 s