White-Noise Vibration Test for Electronic TubesJohn D.. Robbins

Sylvania Electric products Inc.

INTRODUCTION

The need for vacuum tubes to operate reliably despite severe vibration, as in missiles, has stimulated anever-increasing interest in vibration testing of tubes intended for such environmental conditions. New methodsmust be developed and used which are capable of evaluating a tube's performance over a wide range of vibra-tional frequencies at relatively high acceleration levels. The conventional fixed-frequency, fixed g-level vibrationtest for tubes cannot guarantee the performance at higher frequencies. Use of sweep frequencies, feasible atlow frequencies (e.g. 10-50 cps) without severe equipment resonance problems, has been extended to fre-quencies up to 10,000 cps by careful design of transducers, tube holders and associated equipment. This methodis useful as a design test but becomes too time-consuming as a test to be performed 100% on tubes.

Another way to test tubes for vibration is to magnetically record actual multifrequency vibrational con-ditions for specific known installations, but this test method lacks generality. The white-noise vibration test hasbeen developed to overcome the disadvantages characteristic of other tests used or proposed. It covers a widerange of frequencies (100 to 5,000 cps); enables simple meter-type readings; is not tied down, specification-wise,to a particular tube application; and is believed to be adaptable to large scale testing.

THEORY If the analysis is repeated many times for dif-A theoretical explanation of white noise, vibratiorn, ferent intervals of time, all of length T, different

and white-noise vibration should be presented before values of phase angle, 0, result. 41, ¢2, c3, .- - - Willand hit-noseibrtio shuldbe resnte beore each assume values which are randomly distributedproceeding to specific details of the white-noise vibra- etwe zero and 2icadiandomhs in tionstion test. ~~~~~~~~betweenzero and 27r radians.* Thus, in equationstion test.

(1) and (2)A random-noise function (e.g. voltage) may be

described as' one that has instantaneous values that n= A random phase angle distributedvary randomly with time as shown in Figure 1. uniformly over the range (O, 2ir)

Cn - [2W (fn) A f]I

(eft)+ KM| |W(fn)At = Value ofpower representedby bandwidth AJ at fre-quency fn

I T=ARBITRARY Af Bandwidth associated with the| § ITIME nth frequency component.

l _T 2T 3T INTERVAL [ e(t) Random-noise function

FIG. 1-A Random-Noise Function. Equation (2) shows that a random-noise functioncontains all frequencies over a wide spectrum and

Such a function has no periodicity but may be thereby explains why it is also called "white noise"analyzed on a statistical basis. The instantaneous as a comparison to the visible-light spectrum.voltages plotted in Figure 1 may be analyzed as aFourier series over a time interval of length T, result- of e(t)li equation (2) ising in one set of Fourier coefficients for the followingequations.

e(t) = C, cos (wlt-41) + C2 cos (W2t-02) (3)+ ... + Cn cos (Wnt-On) (1) (Cn)

N eRMS =

or e(t) = Cncn cos (Wnt-00) (2) In =ln =1 In theory, N in equation (2) is allowed to become

infinite and Af- >0o so as to fill the entireReprinted by permission from Sylvania frequency band. In practice, a finite number of com-Engineering In.formation Service, Vol. 3, *5 .Rc,"ahmtclAayi fRno os" IT o.XIINo. 3, August, 1956. Ju olye,1943.ialAalss fRno oie,BIJ o.XII

ponents may be used, each represented by its RMS (b) Then N = number of octaves in a spectrumvalue and associated with a specific band in the having upper and lower frequencies 12 and f1.spectrum. This is mathematically valid on an energy f2 and f' must be specified to define the spec-basis, each component being resolvable into sub- trum.components by equation (2). 2N f2The RMS value for entire spectrum is then

f2 f2N N = log2- = 3.32 log1

eRMS = E (En)2 (4) (c) Substituting the above value of N into equa-4n-I tion (5) results in the following equation for

---- the RMS value of a random-noise voltage.

where En = Cn = RMS value of nth component andi2 eRMS = E 3.32 log10- (6)

where the sum of the N component bands = widthof entire spectrum. Equation (6) can be adapted for any part ofThe following items control the character of a the spectrum by the values Off2andt f which

random-noise voltage. define the band area of interest.1. Bandwidth and location of the frequency spec- The final item to be specified is the amount of

trum. clipping present. In practical applications the randompeaks of a random-noise voltage are limited to some2. Total energy content. maximum value. These peaks are neither symmet-3. Distribution pattern of energy within the spec- rical nor uniformly spaced, but a peak-to-peak value

trum. may be observed on an oscilloscope.4. The degree of clipping of random peaks. The amount of clipping can be specified by theratio: peak-peak value RMS value, or else by speci-The bandwidth is defined by lower and upper fre- fying the total peak-peak value. The latter method

quencies. Actual values naturally depend upon the is used in the white-noise vibration test because itapplication involved. In practical usage the degree represents peak g values.of attenuation in the cut-off region should be defined.Energy content and energy distribution may be The theory on white-noise functions, being ery

defined in several ways. One method is to state that general, is directly applicable to white-noise vibra-the total energy equals that of some specified sin- tion with acceleration being the function under con-usoidal voltage and by also saying that the energy is sideration. However, a review of the nature of me-distributed equally among all frequencies, equally chanical vibration may remove some points of pos-per octave, or in some other manner. Another ap- sible confusion.proach is to merely specify the energy distribution g units are often used for quantitative descrip-in quantitative terms. This method is developed be- tions of acceleration or acceleration force. One glow for the equal-energy-per-octave type of spectrum which is the standard value of acceleration due toused in the Sylvania white-noise vibration test. the earth's gravity is approximately 385.9 inchesAssume the random-noise spectrum under study per §ec. per sec. For steady sinusoidal vibration the

to be divided into N parts each having the same maximum value of acceleration, measured in g's isamount of energy as represented by an RMS volt- called the g level. This maximum occurs twice inage, E. (Fractional parts would have a proportionate each cycle of a sine-wave motion.amount of energy.) Two different cases of vibration will be cited, withEquation (4) then becomes Tw difrn cae ofvbainwllbiie,wtvibration in a single direction being assumed in each

instance.eRMS | N(E)2

or eRMs = E,2 N (5) Case 1-Periodic motion of a single frequency.The following equation applies if the g level is

constant for all frequencies.The bandwidths associated with each componentnow determine the energy distribution pattern. For c(t) = C cos (wt + r, 2) (7)energy distributed equally per octave:

energy ditiutdeullc(t) and C are respectively the instantaneous and(a) E, in volts RMS, may be specified for a fre- maximum values of acceleration in g units. A deriva-quency range of one octave (for example, the tion can be obtained from most good textbooks onrange of 100 cps to 200 cps) the subject.

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Case Il-Motion about a fixed reference line with vibration test the acceleration values between peaksacceleration varying randomly. constitute a random path as discussed in the Theory

Instantaneous values of acceleration when plotted section.against time will form a curve similar to Figure 1. In the 40 cps fixed-frequency vibration test theThe analysis of this function is the same for random- average energy, as measured by the RMS value ofnoise voltage. The statistical equation for accelera- acceleration is automatically set by the peak value.tion is But in the white-noise test further specifications are

N needed to control the effective energy. The approachv 7 used is to consider the white-noise acceleration to be

c(t) = Cn COs (Wnt-0() (8) a complex function composed (with respect to energyn~1 content) of frequency components covering the

nwhole bandwidth under consideration (100-5,000which is identical in form to equation (2) for a ran- cps). The effective energy per octave is then specifieddom-noise voltage. The RMS value for acceleration is in g's RMS. (An octave is a band of frequencies which

has a ratio 2:1 between upper and lower frequencies.)The present specification uses a value of 2.3 g's RMS

CRMS = N per-octave.

/ Gn2 (9)YIPGn 2 (9) APPLICATION OF WHITE-NOISEVIBRATION TEST METHOD

where Gn = Cn= RMS value of nth com- Equipment Employed in White-Noise Testing

ponentA white-noise voltage generator, shaping circuits,

Equations (8) and (9) for random acceleration are and power amplifier are used to obtain a complexidentical in nature to equations (2) and (4) for ran- voltage-input which has its spectrum shaped so thatdom noise. It is readily apparent that a random ac- it will cause a vibrator armature to move accordingceleration can be studied through use of its voltage to the frequency spectrum required for acceleration.analog. In actual applications, an accelerometer A barium titanate accelerometer mounted on theproperly calibrated may be used to generate this armature is used in setting up equipment to meetvoltage. these test conditions. The voltmeter used in meteringThe specification of a random acceleration or the acceleration should have a true RMS response.

white-noise vibration will follow the outline suggested The complete system for measuring accelerationfor random-noise functions in general, except that (including accelerometer and associated circuits suchthe peak value can be assigned a more prominent as a cathode follower and amplifier) must have flatposition in the specification. frequency response and linear amplitude response

within the requirements expected of the accelerationCOMPARISON OF WHITE-NOISE AND spectrum itself.FIXED-FREQUENCY VIBRATION

A circuit diagram for the white-noise generatorThe nature of the white-noise vibration test can used is shown in Fig. 2 and a block diagram of the

be made clear by comparing it to the cbnventional white-noise vibration set in Fig. 3. The noise voltage40 cps, 15 g vibration test. proceeds from the white-noise generator to a band-

In the 40 cps test, the tube is subjected to ac- pass filter for establishing the upper and lower fre-celeration of 15 g peak value. The peak values (posi- quencies, then through a preamplifier for shapingtive and negative crests of sine wave) occur at regular the active spectrum, next through a power amplifiertime intervals of 0.0125 seconds. In the white-noise for obtaining the drive needed for the desired magni-vibration test the tube is also subjected to accelera- tude of acceleration, and finally to the armature coiltion of 15 t peak value, but the peak values occur at of the electromechanical transducer. The design,tionlyofi15gegakintevalue buetothepe valdocrnatue similar to one originated by the National Bureau ofhighly irregular intervals due to the random nature Standards, has a helical-coil type armature movingof white noise. In practice, the peak values of white- in a constant magnetic field. The possibility of mag-noise acceleration are limited to 15 g by circuit ad- ic generationeticnoie The waty or injustments. The peak values can be displayed visually netic generation of noise must be watched for inby installing an accelerometer and applying its out- equipment design and construction. When long-leadput voltage to an oscilloscope. If the horizontal tubes are used, the method of holding the tube dis-sweep is sufficiently narrow, the CRO pattern will poses the tube leads into two horizontal layers of

havean evelpe wich orrspons totheposiive four leads each, with the leads clamped at their ex-have an envelope which corresponds to the positive treme ends. Attenuation, by lead stiffness, of theand negative peak values. high-frequency vibration g values is not a problem

In the fixed-frequency vibration test the instan- because the required amplitude becomes very smalltaneous acceleration will naturally follow a sine- (of the order of microinches) for the higher fre-wave path between peaks. But in the white-noise quencies and because the specification and equip-

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NOISE GEN. VOLTAGE AM P CATHODE - COUPLED CLIPPER

lOOK .05.pf o12A XK7__

6 D 4 7

.0 5'"f~~~~~~66D4 7 ~~~~~~~72OUTPUT

7~~~~~~~6AT6 8 1 iiA

49 55 5 47K 5 K 20K 5X K S 10( V- 125

3 4 6 3

23400~~~~~~~

6.3V

CLIPPERTO HEATERS ADJUST

IOOV- 125V5 4.7K 15 K 20K 500K

200 K

125 A.C.

3008 20Of0'

2 0{ { 20.)Af{2O~

FIG. 2-Circuit Diagram for White-Noise Generator.

ment calibration deal with the acceleration actually for this proposed test, noise frequencies above 10,000experienced by the moving armature and tube. The cps are excluded by filtering.lower frequencies are more of a problem than the The different types of readings considered for thishigh ones because the angular deflection of the leads test were as follows:at low frequencies becomes significant and thuslimits the g level obtainable with clamped leads. Tube 1. RMS value-A voltmeter with true RMS re-holders developed are suitable for vibration testing sponse could be used to obtain a single readingperpendicular or parallel to grid minor axis but not for the total noise over the entire spectrum upfor parallel to tube axis. to 10,000 cps.

2. Average value-A voltmeter could be usedVibrational Noise Output of Tube Under Test which gives a single reading for the average of

The vibration-noise output-voltage is the complex the positive values.A.C. voltage generated across a resistor (usually 3. Sub-band readings-Tube noise spectrum could10,000 ohms) in the plate circuit in accordance with be divided into sub-bands, each read by methodpresent specifications for vibration test circuit pa- (1) or (2) above.rameters. 4. Peak-to-peak value-The noise would have no

true peak-to-peak value but a reading could beThe noise output voltage doesn't necessarily have obtained which is partly a function of the re-

the same bandwidth as the acceleration input, and sponse characteristics of the measuring instru-

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Calibration Instructions for White-Noise VibratorsDRVING SYSTEM NOISE READING CIRCUIT

WHITE NOiSE The procedures and special precautions requiredGENERATOR to set up and operate a white-noise vibration test

PK-PK V.TV RMS VTVM. can best be described by listing the actual calibration.

L. . . and operating' instructions for a typical installation.

B.P FILTER NO. I These instructions are for establishing a vibrationI I spectrum with the following characteristics:

Bandwidth 100-5000 cpsPREAMPLFIFER Peak g's 15EQUJALIZER BP FILTER NO.2 RMS g's = 2.3 g's RMS per octave

POWER I The calibration procedure uses a barium titanateAMPLIIER TUBEIUNDER accelerometer having a sensitivity of 1 mV RMS per

UT TEST CIRITU 3E- U RIgRMS or 2 mV peak-to-peak per g peak.,-.G.Ol 1. Connect the calibration equipment as shown in

ID-c-C VIBRATOR TGOTOEXTERNAL block diagram of Fig. 4.FIELD SUPPLY POWER SUPPLY GROUND 2. Turn on all equipment and allow it to warm up

for five minutes.

3. Set band-pass filter No. 1 so that the low fre-FIG. 3- Block Diagram of White-Noise Vibration Equip. quency limit is 100 cps and the upper frequency

limit is 5000 cps.ment. The reading would also depend greatlyupon input acceleration peaks which actually 4. Set band-pass filter No. 3 of Fig. 4 to the limitscontribute relatively little to the input energy of 100 cps and 5000 cps and turn on the vibrator.and which depend upon the clipping circuits Adjust the preamplifier volume control to give aalmost exclusively. Use of this method would reading of 5.4 mV on the True RMS meter andrequire tight control on peak values of accelera- 30 mV peak-to-peak on the CRO.tion input.

5. Sonic analyzer readings-Limit values couldbe assigned for the magnitude of noise-frequency ACCELEROMETER CATHODE FOLLOWERcomponents as determlned by a sonic analyzer.Different limit values may be used for differentsections of the band. VIBRATOR

Sonic analyzer readings were used for several B.P. FILTER NO.3months in an experimental run on a production basisbut results were not satisfactory. The test was time-consuming in that each sweep of the sonic analyzerrequired a full second and many sweeps were re-quired to show a good overall picture of the noiseoutput. TRUE RMS VT.VM. CROTwo types of readings are now being taken and

are proposed for specifications. The first is a peak-to-peak value as obtained on a peak-to-peak readingV.T.V.M., the reading requiring usual averaging by FIG. 4-Block Diagram of the Calibration Setupthe operator. The second reading is taken on a V.T.-V.M. which has scales marked in volts RMS but is 5. Use"the variable band-pass filter No. 3 to readactually more of an averaging device. Figure 3 shows the fli octaves:these two voltmeters being used-

It must be remembered that relatively high values 100- 200 cpsof noise can be expected for peak-to-peak readings. 200- 400 cpsFor a pure sine wave alone the peak-to-peak value 400- 800 cpsis 2.8 times the RMS value and the occurrence of 800-1600 cpsharmonics even in fixed, single-frequency vibration 1600-3200 cpsalways tends to raise this ratio rather than lower it. 3200-5000 cpsThus a tube with 50 millivolt RMS output for 15 9 Adjust the preamplifier bass and treble con-40 cps vibration could read over 300 mV Pk-Pk. An trols to give a reading on the True RMS metereven higher ratio of Pk-Pk 10 can be expected of 2.3 mV for each of these octaves. The CR0RMS _L1 may have readings varying from 13 to 17 mVfor white-noise vibration output. peak-to-peak.

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6. Repeat steps 4 and 5 until true RMS readings WHITE-NOISE VIBRATION SPECIFICATIONfor each .octave are as near as possible to thedesired 2.3 mV. Note that the 100-200 cps and A representative,specification iS as follows:the 3200-5000 cps octaves will have low read- 1. T.U.T. circuit parameters are the same as forings. This is to be expected from the cutoff comparable 15 g, 40 cps vibration tests decharacteristics of the shaping filter and the fact scribed in Mil-E-1.that 3200-5000 cps does not represent a fulloctave. 2. The tube shall be rigidly mounted on a table

vibrating such that the instantaneous values of7. Set band pass filter No. 3 to the limits of 10 cps acceleration shall constitute approximately a

and 20,000 cps and read the True RMS meter. "White Noise" spectrum which is free fromThis reading should be less than 5.8 mV. This discontinuities from 100 cps to 5000 cps. Theis a test of the ability of the shaping filter to con- spectrum of instantaneous acceleration shall betrol the vibration spectrum. such that each octave of bandwidth delivers

Typical readings for a calibrated vibrator follow: 2.3 g's RMS acceleration. With this the case,the RMS value of acceleration for any band-Band in cps mV RMS mV Pk-Pk width within the specified spectrum is equal to:100- 5000 5.4 30100- 200 1.8 15 GRMS= 2.3 g 3.32 log1o (f2. f1)200- 400 2.2 15400- 800 2.6 17 f2 and f, are the upper and lower frequencies800- 1600 2.4 15 respectively of the band under consideration.1600- 3200 2.2 15 The degrees of clipping of the peak acceleration3200- 5000 2.0 15 shall be such that the peak value of acceleration10-20000 5.7 30 is at least 15 g's. The voltage (ep) produced

across the resistor (Rp) as a result of vibrationOPERATING INSTRUCTIONS FOR WHITE-NOISE shall be coupled through a compensating am-VIBRATION EQUIPMENT (PRODUCTION SET) plifier to a low-pass filter. The compensating

amplifier shall have a high input impedance1. Connect the equipment components as shown (0.25 megohm or more) and shall be adjusted to

in block diagram of Fig. 3. compensate for any insertion losses caused bythe filter. The combined frequency response of2. Be sure the vibrator is calibrated as described in the filter and compensating amplifier shall be

the calibration instructions, flat with +0.5 db from 50 cps to 8000 cps; shall3. Select the proper adaptor plug for the tube type be down no more than 5 db at 10,000 cps and at

being tested and insert it in the multiple pin 20 cps; and down at least 40 db at 12,000 cps.socket on the tube-under-test circuit junction For reading the peak-to-peak value of outputbox. voltage, the filter output shall be fed directly

to the input of a peak-to-peak electronic volt-4. Adjust the tube-under-test power supply to meter while the RMS value shall be measured

give the proper voltage for the tube type being with an RMS V.T.V.M. The impedances of thetested. plate and screen voltage supplies shall not ex-'

ceed that of a 40 pf capacitor at 10 cps.5. Set band-pass filter No. 2 so the lower frequencylimit is 0.2 cps and the upper frequency limit One principal advantage that this type of white-is 10 000 cps. noise specification has over other approaches (thatis10,000 cps. specify transducer electrical input) is that direct

6. Set the peak-to-peak meter to the 100 volt control of the acceleration spectrum minimizes testrange. This meter is sensitive and easily slammed variations due to different clamping arrangements,by transients occurring in the loading and un- short tube leads vs long tube leads, etc.loading operation of the tube. Tiherefore, it is A discussion of the origin of actual parameters isbest to leave it on the 100 volt scale at all times in order. The data currently available on the vibra-except when the tube noise is actually being tional environments of various military vehicles isread. If there is an RMS noise limit for the tube sketchy at best. Accordingly it was necessary to settype being tested turn the RMS meter to the the specifications in an arbitrary manner, consistentscale containing this RMS limit. with the maximum capabilities of the test equipment

7. Load the tube and the special tube adaptor onto and tubes being tested. The upper frequency limitwas established on the basis of the upper limit gen-erally regarded as important. The lower limit was8. Switch on the vibrator and turn the peak-to- selected to avoid hum problems which could produce

peak meter down to the scale where a constant erroneous results and because the amplitude of vibra-reading is obtained. Check the reading on the* tion at 15 g, and lower frequencies became excessiveRMS meter if the tube type has an RMS limit, for the test equipment and tube leads.

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The value of 2.3 g's RMS per octave was also value is 2.75 for the white-noise test or approximatelychosen somewhat arbitrarily. The total RMS value twice the 1.41 ratio characteristic of a sine wave.of 5.4 g's RMS resulting from the use of this param-eter is compatible with the 15 g peak and is about as CONCLUSIONhigh an RMS value as is obtainable without clippingexcessively. Note: the total RMS value can be This study has provided an equipment and thecalculated from the expression necessary specification controls which will permit the

vibrational testing of vacuum tubes over a range of2.3 g's RMS/octave x / 5.6 the audio frequency spectrum. It also provides the

necessary speed of testing which is necessary to per-mit the delivery of tubes in volume if a national

where 5.6 the number of octaves natural log of emergency requires it. It should be a distinct ad-5000 cPs The ratio of peak value to total RMS vancement toward meeting the needs of equipment100 cps intended for military vehicular service.

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