'l'HE STOJl Y OF Q
`
`By ESTILL I. GREEN
`
`Bell Telephon.e
`Laboratories,
`Inc.
`
`as fair as Humpty Dumpty in paying words
` SCIENTISTS were
`extra for o,·ertiJne
`work, the 11.1biquitous
`Q would rome near the to1�
`of the payroll.
`It all started
`with K.
`S . .Tohn.·on.*
`lVIany scientists
`have
`new words
`to our vocabulary.
`To only one, however,
`has
`contributed
`into a word of
`of e!eYaLing
`a letter
`of the alphabet
`come the dist·inction
`everyday
`use in many and diverse
`fields.
`LiUk: did Johnson
`dream, when
`the ratio of rnactance
`he first used the
`symbol Q to rcprci:;Pnt
`to cfferti,·e
`in a coil or a condenser,
`that \Yithin
`a span of some 30
`yPars
`resistance
`an uttrihntc
`of
`t.his same symbol would be commonly
`used to desrribe
`as a resonant
`('irntit,
`a pectraJ
`line, a mechancial
`such dissimilar
`things
`and a bounring
`vibrator,
`ball. The story of Lhis expanding
`u ·age of the
`17th letter
`of the
`alphabet
`makes an interesting
`study for the scientific
`etymologist.
`
`IF
`
`Coils and Condensers
`
`The tale begins in the teens of this century.
`It was then the usual
`practic:e,
`in appraising
`the quality
`of the devices
`which were then known
`as coils,
`and which engineers
`have now become educated
`to call induc­
`tors, to use the ratio of effective
`resistance
`to rcactance
`as a sort of figure
`of merit. Ber.a.use
`it was related
`to dissipation,
`this ratio was often
`desig­
`to as the dissipation
`nated d, and in fact it is no,Y commonly
`referred
`Strictly
`speaking,
`cl is not a. figure of
`merit but a figure of demerit.
`factor.
`since the normally
`desirable
`('Ondition
`of minimum losses
`ocr·urs
`as the
`value of cl movrs towards
`zero.
`ut·,ility
`As early as 1914, Johnson
`came to realize
`that a ratio of greater
`tban the one in vogue was it.s reciprocal.
`Johnson
`was
`for many purposes
`aware that tbe ratio dis conYenient
`for certain mathematical computa­
`tions,
`since it, permits
`the combinjng of
`different
`sources
`of loss by dirnrt
`observed, however,
`that in
`prac-t.ic·al
`cases d wonk! usuaUy
`addition. He
`involve
`one or more zeros precedjng the significant
`figures,
`whereas
`lhc
`reciprocal
`could usually
`be taken as a whole number.
`The same sort of
`which leads to lhc common use of impedance,
`and avoidance
`of
`logic,
`admittance,
`argued for putting
`reactance
`in t,he numerator
`of the ratio.
`to efiective
`re­
`For a time Johnson
`designat,ed the ratio of reactance
`K 111. It was in 1920, while working
`on
`sistance
`of a coil
`by the symbol
`the practical
`application
`of the wave filter which G. A. Campbell
`had
`some years before,
`that he for
`the first time employed
`the sym-
`invented
`
`• Theo in Western Electric
`Company's
`Engineering Dept., which ber,ame Tiell
`Telephone
`Laborat-ories
`in 1925.
`
`Momentum Dynamics Corporation
`Exhibit 1016
`Page 001
`
`

`

`141,
`
`Q was quite simple. uol Q for his parameter 121. His reason for choosing
`
`
`
`
`
`but He says that it did not stand for "quality factor" or anything else,
`
`
`
`
`for been pre-empted had already since the other letters of the alphabet
`other purposes,
`Q was all he had left.
`Q for coils,
`
`Johnson used a capital
`and a small q for the c o r ­
`Initially
`
`
`
`
`responding ratio in condensers (now renamed ,capadtors). Before long,
`
`
`
`using Q to both coils and condensers, however, he began to apply capital
`
`
`
`
`
`suh.scripts where differentiation was needed. The first printed use of Q
`
`
`
`seems to be in Johnson's U.S. patent No. 1,628,083, where it is applied
`on
`
`
`
`
`to the coils in an electrical network. In .Johnson's classic trcatii:;c
`
`
`
`
`"Transmission Circuits for Telephonic Communication" l31 the symbol
`in a number of places
`
`
`to designate the parameter which he
`Q appears
`
`
`
`
`
`shortened constant." Subsequently called the "coil dissipation to
`this was
`
`
`
`"dissipation constant," applying to both coils and condensers The
`
`
`constant" also were u;;ed to some terms "coil constant" and "cond<mser
`
`Later on, V. E. Legg coined the apt n.ame of "quality factor,"
`extent.
`
`
`
`
`factor" and "figure such terms as "storage while others tried to introduce
`appellations could prevail of merit." But none of these
`
`
`
`over the terse
`and trenchant
`Q.
`which has frequently been used for a reactive ele­
`
`
`
`Another measure
`
`
`ment is the power factor. i.e., the ratio of active power to total volt­
`
`
`
`At, any t,vo terminals the power factor is the cosine of the phase
`amperes.
`
`
`
`
`angle, neg­angle of the impedance, whereas of the phase Q is the tangent
`
`sign. Thu:; for the common case where reactance is large com­
`leeting
`
`
`
`pared with resistance. the power faelor is substantially equal to the dis­
`
`
`
`
`factor cl. Power engineers. "ho are accustomed to using power
`sipation
`
`
`
`
`factor to designate the ratio of acti,·e power to total volt-amperes, might
`
`
`occasionally, a need for a ratio greater than unity, ii they experience
`
`
`
`engineer. find it advantageous to borro"· Q from the communication
`
`
`Others before .Johnson had made use of the ratio of reactance to re­
`
`
`
`
`sistance for either an inductor or a capacitor (to use modern parlanr,e).
`
`
`
`,Johnson's role was to popularize this ratio and to assign to it the con­
`
`
`
`
`except the tagious .symbol Q. He did not intend to apply Q to anything
`
`
`
`
`rat,io of reactance to resistance, ,vhether of an inductor,
`a capacitor, or
`
`
`
`
`
`as disturbed, any t w o -terminal network, In fact, he was somewhat
`
`
`originators of terminology of ten are, when otlhers began to extend
`
`
`his
`
`usage-an extension which has gonP so far that a few modernists
`would
`
`
`even like to ban .Johnson's original meaning.
`
`Resonant Circuits
`
`,\1ha,t happened
`next? First was the discovery t,hat
`
`Q was a conven­
`
`
`ient symbol to apply to a resonant circuit. It was noted that the high­
`
`
`
`
`
`negli­capacitor were ordinarily frequency lo;:;ses in a, well-constructed
`of a,n inductor. Hence t,he high-frequency
`
`
`
`gible in comparison with those
`
`2
`
`Momentum Dynamics Corporation
`Exhibit 1016
`Page 002
`
`

`

`resistance of the usual inductor and capacitor resonant circuit could be
`assumed equal to the inductor resi�tancc, and the Q of �he resonant cir­
`cuit could therefore be assumed the same as tbe Q of the inductor. In
`those cases where the capacitor resistance could not be neglected, the Q
`of the resonant circuit was QLQc/(QL +Qc), wbere QL and Qc are the Q's
`of the inductor and capacitor, respectively. aL the resonant frequency. It.
`is noteworthy that this use of Q for a resonant network is uniquely re­
`lated to the resonant frequency, whereas Q when applied to an imped­
`an<'e is a property at any specified frequency.
`At this point it became apparent that Q as applied to a resonant cir­
`c-uit was an already recognized parameter which for want of a better
`name had previously been called "sharpness of resonance" 151. This per­
`mitted the establishment of SCYeral relationships which today are ele­
`mcnlary. Curves like those of Figure 1 could be drawn lo show current
`versus frequency as a function of Q for a series resonant circuit, and analo­
`gou-s cmTeS for the impedance of a parallel resonant circuit.
`
`I
`I
`I
`tc--O=oo
`I I
`
`Q = ,oo
`
`== so
`
`t
`ffi
`
`a:
`a:
`
`a
`
`FREOUENCV --+
`
`Flo. 1.
`Series
`resonanre.
`
`Once idenufied with sharpness of resotUUl<'l', Q was seen to bear a clos<'
`relationship to a familiar parameter of an osC'iJla.lory wave train of con­
`tinuously decreasing amplitude. This parameter was lbe logarithmic
`dcrrcment, which was defined as the natural logarithm of the ratio of
`two successive maxima in a damped wave train. Thus in Figure 2 the
`logarithmic decremeut o is equal to log, (A.B/CD).
`Soh1tion of the differential equation for a resonant c•ircuit comprising
`resistance, inductance, and capac·itanc·c in series gives for the logarith-
`
`Momentum Dynamics Corporation
`Exhibit 1016
`Page 003
`
`

`

`mic decrement o the value 1rR/wL, or 1rRwC. Hence Q equals 1r/o. While
`
`
`
`in the earlier days much importance attached to logarithmic decrement
`
`
`
`
`of radio, in connection with the damped waves produced in a spark trans­
`
`
`through a spark gap, Q
`
`mitter by the sudden discharge of a condenser
`
`
`
`
`that today wave techniques to continuous was so much better adapted
`
`
`the term logarithmic decrement is an but forgotten.
`
`
`
`Many relations previously established for the logarithmic dccremc11t
`
`
`
`were restated in terms of Q. Thus the number of complete oscillations
`
`
`
`amplitude necessary to reach a given ratio p of initial to final amplitude
`a Q of 100, for example,
`is Q/ 1r times loge p. From this we learn that for
`
`the number of oscillations necessary to reach one per cent of the initial
`
`value is 146, while for a Q of 200 twice as many oscillations would be
`required.
`
`A
`
`C
`
`I a )
`
`
`
`f C = LOGe­
`AB
`CD
`
`TIME-+-
`
`
`
`FIG. 2. Logarithmic decrement for damped wave-train.
`
`simple decrement relationship, Through pursuit of the logarithmic
`
`
`
`
`
`
`
`
`
`manipulations yielded a useful physical pictlue, namely, that
`a.lgebraic
`
`
`
`in for a simple resonant circuit the ratio of the maximum energy stored
`
`
`
`
`either the coil or the condenser to the energy dissipated per cycle is equal
`
`
`
`
`
`the induc­across either to Q/21r. Also, for larger values of Q, the voltage
`
`
`
`
`
`tor or the capacitor of a series resonant eircuit is substantially equal to
`
`
`
`
`the current through either Q times the applied voltage t6J. Similarly
`
`
`
`
`
`is equal to Q circuit of a parallel resonant the inductor or the capacitor
`times the total current.
`An even more interesLing relationship was found between Q and the
`
`
`
`
`
`too detailed for shape of the resonance curve t7J. Through derivations
`
`
`hHrc, it turns out that for a curve showing magnitude of i m ­
`inclusion
`
`
`
`
`
`pedance or admittance of a resonant circuit frequency, Q is approxi­
`versus
`
`
`
`mately equal to the ratio of the resonant frequency to the width of
`the
`
`
`curve between the points,, on either side of resonance, where
`resonance
`v12 times the maximum or
`the ordinate is, respectively, 1/
`
`v12 times the
`minimum ordinate.
`
`4
`
`Momentum Dynamics Corporation
`Exhibit 1016
`Page 004
`
`

`

`!2esonant Devices
`
`Tbe groundwork was uow complete, and anyone could take off in any
`clire<;tion. A natural extension from the inductor and capacitor resonant
`circ:uit, was to apply Q to any resonant structure or deviee . For t,his pw·­
`pose the dofinltion of Q in terms of energy storage and dissipation was
`directly applicable, while the relation for the shape of the resonance
`curve was broo.dened by stating it in terms of response. Thus Q became
`equal to the ratio of the resonant frequency to the bandwidth between
`those frequencies on opposito sides of reso1rnncc (known as "half-power
`_points") where the response of the resonant structure differs by 3 db
`from that at resonance. The use of Q wit,h such conn otations for tuning
`forks, piezoelectric rcson::i.tors, magnetostricti ve rodl:l, and the like soon
`became commonplace.
`
`Resonant Transmission Lines
`
`HPsonant Lrnnsmission lines came ucxt. The standing wave patterns
`
`
`for open- circujted or short-circuited bnos, exhibiting maxima and
`minima at "resona1we" points located at quarter-wave multiples from
`Lhe lerrni.i 1ftti ng end, were, of course, familiar from classical derivations.
`The t..rend to higher frequencies, espec:ially for rndio commW1ciation,
`made it increasingly advaot,ageous to utilize such r�ona-nt-line phe­
`nomena for oscillator frequency control, voltage step-up, impedance
`inversion, and the like. Since the curve of line impedance in the vicinity
`of resonance is essentially similar to that of a resonant circuit, it was a
`natural step to apply the factor Q to a. resonant transmission line. F. E.
`1\'rman [SJ showed that the Q of such a. line is equal to 1rf I a V, where .f
`is the resonant frequency, a is the real p�trt of the propagation constant,
`and Tr is the grnup velocity, i.e., the velocity with whieh signals are
`tra1 ism itted.
`
`Caviiy Resonators
`
`AL frequencies upward from �1bout 1000 me (commonly referred to as
`microwaves) resonant transmi5sion liues usually give way to cavity
`resonators. The cavity may be cylindrical, parallelepipedal, spherical. 01
`some other sha.pe, dep,encling on end use. Regardl<>A s of shape, a cavity
`resonator has tt11 infinity of resonant frequencies, starting at a ml11imum
`value and becomjng more closely spaced with increasjng frequency.
`Each resonance 1·orre.sponds to a particular standing wave pattern of the
`electromagnetic field, which is called a resonant mode, and for which the
`cavity may be considered a.s a single tuned circuit (with L and C not de­
`fined). The Q of a eavity resonator for any mode is therefore definable
`in terms of losses or bandwidth, and turns out to be a function of the
`ralio of internal volume to intcn1al area. A general oxpression for the Q
`
`0
`
`Momentum Dynamics Corporation
`Exhibit 1016
`Page 005
`
`

`

`in Schelkunoff by S. A. was derived of a cylindrical cavity resonator
`
`
`
`
`
`
`
`
`
`1934 in unpublished lecture course material. Values of
`Q for different
`
`
`
`1938 modes were published in shapes of cavity resonator and different
`
`
`
`between by Yv. W. Hansen l9J. The practical designer must distinguish
`
`
`
`(a) the nonloaded or basic Q resull;ing from theoretical consideration
`of
`
`
`
`the cavity without external coupling, and (b) the loaded or working Q
`
`
`
`obtained when microwaves are excited within the cavity by one or more
`
`
`orifices, loops, or probes.
`
`111 aterial Q
`\�Thile these various exctusions were under way, engineers concerned
`
`
`
`
`
`
`
`
`with magnetic or dielectric materi!ds discovered that Q was a convenient
`
`
`
`device for expressing the dissipation prope1iies of a material, as distinct
`
`
`of loss in the device in which the material is used. For
`from other sourc�s
`
`
`this purpose Q may be defined in tenns of energy storage,
`that is, Q
`
`equals 271' times the ratio of maximum stored energy to the energy dis­
`
`
`in the m,1terin,l per cyele.
`sipated
`
`Spectral Lines
`
`In the search for more precise standards of frequenc;y n,nd time, scien­
`
`
`
`
`
`molecular tists in recent years have turned to a new tool-atomic and
`
`
`
`
`
`The quantum theory, first advanced by Planck, states in sub­
`processes.
`stance that changes of energy in atoms and molecules are not continuous
`
`
`
`of an but occur in steps, each step being the emission or absorption
`
`which is equal to the product of amount of energy, called a quantum,
`
`
`
`
`
`
`
`Planck's constant and the radiation frequency. The frequencies which
`
`
`
`correspond to such transitions between characteristic energy states for
`to as spectral
`
`
`
`different atomic and molecular structures are referred
`
`in atoms and molecules involve
`lines.
`While many of the transitions
`
`
`
`energies which correspond to very high frequencies, there are a number
`
`
`
`of low energy tTansitions corresponding to frequeneies in the microwave
`reg10n.
`frequency for obtaining One method of employing these phenomena
`
`
`
`
`
`is to e>..'])ose a gas to electromagnetic fields in sharply defuied
`standards
`
`
`bands where low energy transitions are produced within the
`frequency
`a strong ab­
`
`r101 . .1\.mmonia gas (NH3) , for example, exhibits
`molecules
`
`
`sorption band at 23,870 me. Another method of using these furnhmental
`properties
`
`
`of matter is to employ microwave fields of sharply defined
`an atomic or molecular beam [lll. In either
`
`frequency to deflect
`case the
`
`
`
`to that of is very similar shape of the curve of response versus frequency
`
`
`
`
`a resonant circuit, which makes it convenient to describe the selectivity
`
`by an equivalent Q defined as
`
`the ratio of the frequency of maximum
`response
`
`to the 3-dh bandwidth.
`
`6
`
`Momentum Dynamics Corporation
`Exhibit 1016
`Page 006
`
`

`

`Definition,�
`
`So the irrepressible
`symbol has ranged here, there. and everywhere.
`
`
`
`
`so For years no one tried to brand the maverick. Usage was expanding
`fast that people shied away from exact definition.
`,vhcn the ASA C42
`Staudard
`
`
`
`Definitions of Electrical Te,ms ,,ere published in 194 1 . Q \\'a.s
`
`
`
`omitted because it was looked upon as a symbol mthout a name. Tt ,\·as
`
`
`
`not until a. revision of those definitions was gotten under ,,·a.y in 1'9 n
`
`
`
`
`thn.t a committee attempted to write a complete definition of Q. �ven
`
`
`
`
`
`then, while the basie concepts were clear enough, precise wording proved
`
`
`
`
`
`cliffic11lt, and will doubtless need modification as usage spreads �1nd
`C'.hanges.
`Values of Q-Reaclors aml Resonators
`
`to unity,
`While it has been implied that Q is fn:qucntly large compared
`
`
`
`look at its size. Values which are intended
`it is now time to have a closer
`
`
`
`
`order of magnitude, and not for engineering design, arc d.is­
`to indicate
`
`
`cussed below, and the general rang,e of values is illustrated in Figure 3.
`
`
`
`To start, as K. S . . Johnson <iid, with the inductor, good present-dtty
`
`
`
`for air or molybdenum permalloy powder cores n.t
`accomplishment
`
`
`
`
`range from 50 mo<lcrately high frequencies is rep1·esented by Q's in the
`
`
`Lo 250. The introduction of the ferr:ites, whose high resistance practically
`
`
`
`eliminates high frnquency eddy cuncnt losses, has opened up new ,·istas,
`
`weight, and permitted economies in volurn-e, and cost. Q's of 300 to 500
`
`
`
`
`
`50-100 kc a.re now realized commercialJy in filter
`in the frequency range
`inductors
`
`
`
`of shell-type ferrite construction having an over- all volume of
`
`
`
`
`
`slightly more than a cubic inch. A rather spectacular recent achievement
`
`
`
`
`with a Q of more was the construc:Lion of an experimental forrit,e inductor
`than 1000.
`covers a wid,e range. Electrolytics
`give 15 or 20 at
`The Q of capacitors
`
`
`
`Ceramic types have Q's 1 kc and fall off rapidly at higher frequencies.
`
`
`
`
`le.� than 100, oil impregnated paper capacitors values of several hundred,
`
`
`or tens of thousands. and mica and air capacitors values in the thousands
`For real mammoth Q's, en1,ri.noors turn to quartz crystals
`(Fig. -l).
`
`
`for eiLher commercially Units of the air-enclosed type, as produced
`
`
`
`
`
`frequency control or network applications afford Q's from 10,000 to 100,
`
`
`
`units, particularly those designed for use
`
`000. In precision-type crystal
`at 100 kc or 5 m<.:, much higher values of Q are
`
`in frequency standards
`
`
`
`
`
`obtained by selection of the raw mate1·ial, by careful preparation of the
`
`surface of the plat,e, by design of the supporting system to prevent
`
`
`
`ener1,,ry absorption, and by evacuating the enclosure in order to reduce
`By &"Uch means, Q's of one to two million
`
`radiation to the �itmosphere.
`
`
`
`
`in devc.lop­production are realized in commercial and four to ten million
`
`
`
`
`highest units are the meu t models. The Q's obtained in quartz crystal
`ampli-
`
`
`
`
`Q'syeta-ehieved in passive man-made devices. Of course, by using
`
`7
`
`Momentum Dynamics Corporation
`Exhibit 1016
`Page 007
`
`

`

`GOLF __ n
`BALL U
`ORGAN PIPE ---1
`PIANO SIRING --i------0
`I
`INDUCTORS-------
`CHURCH BELL-----------0
`' I I
`Au o 1To R LMs ---_I_ ----M"-'t,
`�*}.'''''�
`I �"f-�">''',W,W�
`MAGNET�STRICTIVE RODS _L ____
`_
`MICA C+CITORSf-----+---
`WAVE GUIDE - -------- ----------0
`TUNING JoRK ___ l _____
`_l_o
`j ______
`AIR CA+ro•s+---+ -----�
`
`COMMERCIAL ouARTZ-CRYSTAL uN1Ts-mtttmwrm:
`1
`I I I I
`I
`:::�TUYLUr:ONATJRS-----l
`______ �� ,1
`,
`I I
`I I
`SPECTRAL LINES (PRACTICAL VALUES) -------... , - ., ...... ;·""'=,;t,.....,;;::;:..a.::: --,(�-=::i;:
`.-\�"'"t:I
`I
`I I I I '
`I
`QUARTZ-CRYSTAL UNITS---------------! ,,,,,., , .. ,j
`PRECISION
`PLANET tARTH -r-----7----
`--,------T-----r------,-► 1013
`I I I I I
`I I
`-------r---►101B
`SPECTRAIL LINES fNHERENI VALUESI) -----7-----7
`104
`103
`VALUE OF Q
`
`
`
`
`
`
`
`F10. 3. Q's for various phenomena and devices.
`
`PRECISION
`TYPES
`
`COMMERCIAL
`TYPES
`
`
`
`'410. 4. Quartz crystal resonators.
`
`8
`
`Momentum Dynamics Corporation
`Exhibit 1016
`Page 008
`
`

`

`fication to off set losses, Q can in effect be made infinite, but this is an
`
`
`
`
`
`area outside present consideration.
`elements, as fre­In cavity resonators employed as frequency-fixing
`
`
`
`
`
`
`
`quency standards, as adjustable frequency meters or wavemeters, or as
`
`
`
`
`
`selective elements in filters, amplifiers, etc. , a moderate value of Q, from
`
`
`
`
`a few hundred to perhaps 10,000, is usually sufficient. In order to avoid
`
`
`
`confusion with other modes, the dominant or fundamental mode, i.e.,
`
`
`
`the mode with the lowest cutoff frequency, is usually selected for such
`
`
`
`
`applications. Another important use of cavity resonator is in so-called
`
`
`
`
`"echo boxes" (Fig. 5) for determining the over-all performance of a radar
`
`
`
`Fro. 5. Cavity resonator for radar testing
`
`by coupling the radar output into the cavity and observing the time
`
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`
`
`required for the signal returned to the radar receiver to disap­
`interval
`
`
`pear into the noise [ 121, [ 1 31 . 'fhis type of application requires extremely
`
`
`
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`from for frequencies from 40,000 to 200,000 high values of Q, ranging
`
`
`
`
`1000 to 25,000 me. Cylindrical resonators are usually employed, fre­
`
`
`quently at a mode above the fundamental.
`vary over systems and devices The Q's obtained in other resonant
`
`
`
`
`
`
`
`
`
`quite a range. Magnetostrictive rods and tuning forks give fairly high
`
`
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`Q's, while musical devices such as piano and violin strings, organ pipes,
`
`
`church bells, etc. have rather low values.
`In a maj ority of situations the desired value of Q is the highest one
`
`
`
`
`
`economically attainable. In fact, the label "high Q" is often interpreted
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`
`
`to mean "high quality." Sometimes, however, a minimum Q is the de­
`
`
`
`
`sideratum. For example, circuit designers who are plagued by the high­
`
`
`
`
`
`frequency reactance of resistors find it comforting to obtain a Q of about
`
`
`
`0.001 in a deposited carbon resistor at 100 kc. Cases also arise, hmvever,
`
`
`
`
`
`is a where it is desired neither to maximize nor to minimize Q. One such
`
`Momentum Dynamics Corporation
`Exhibit 1016
`Page 009
`
`

`

`reverberant room or hall, "·hich has a Q derivable from the curve of decay
`
`
`
`
`
`
`
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`the time, i.e., the time for of sound intensity or from the reverberation
`
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`techniques, to drop 60 db. By suitable sound absorbing
`sound intensity
`the Q can be reduced to a very low value, making a "dead" room. On the
`
`
`
`other hand, high reflectivity for all interior surfaces gives too live a room.
`Q which lies somewhere
`there is an optimal
`
`in between, and
`In general
`
`
`
`
`depends on a number of factors, including the volume of the room and the
`
`
`
`250 to 350 provide good is utilized. type of sound for which it Q's of about
`
`
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`room acoustics for moderate sized halls, while larger values are prefer­
`
`able for large auditoriums and cathedrals.
`
`
`
`Bouncing Balls
`
`to a
`of Q may be extended
`As suggested by R. S. Duncan, t,he concept
`
`
`the height of suc­ball, the Q being determined by measuring
`
`bouncing
`
`on an w1yielding surface.
`
`
`cessive rebounds when the ball is dropped
`
`
`a vacuum but the results in air
`test should be made in
`Theoretically the
`
`
`of drop, golf balls give Q's of are about the same. For moderate heights
`
`about 8 or 9, tennis balls slightly less. In the persistent search for new
`
`
`
`it may be that the manufacturers of
`ways to attract consumer attention,
`
`
`
`golf or tennis balls will some day get around to advertising a high-Q prod­
`
`
`uct. Should they become overboastful, however, it could be pointed
`
`
`
`out that if a golf ball had the two million Q of a precision crystal, it
`
`
`to 50% of the original would after 440,000 bounces still be rebounding
`
`height.
`
`
`
`Rotating Bodies
`
`to Having gone so far with Q, it is perhaps not too much of a stretch
`
`
`
`
`
`
`
`apply it to a rotating body subject to frictional deceleration. The ratio
`
`energy lost per cycle suffices to determine the
`of the stored energy to the
`might be considered Q. Thus the gyroscope of a gyrocompass
`
`
`to have a
`Q in the order of a million or so.
`
`Traditionally nothing is as constant as the earth's rotation. Our stand­
`
`
`
`
`
`
`
`derives ard of time is the mean solar day and our standard of frequency
`
`
`
`
`from this. In reality, however, the.'5e standards are measurably unstable.
`
`
`
`The earth is constantly slowing down, m<IBtly becauise of t,idal friction,
`
`
`
`
`rate whose variations in rotational and in addition there are irregular
`
`
`
`a number cause is not wholly understood. Observations of the motions of
`
`of the day is increasing at
`
`
`of heavenly bodies indicate that the length
`
`
`
`
`the rate of 0.00164 second per century 1141. Neglecting irregular varia­
`
`
`therefore, we can as a matter of academic interest figure
`tions,
`out the
`
`
`a retardation Q of the earth as a rotating body subject to
`which may be
`
`assumed constant over the present span of human concern. As might be
`
`
`expected, the value of Q thus determined turns out to be very large-
`
`10
`
`Momentum Dynamics Corporation
`Exhibit 1016
`Page 010
`
`

`

`about 1013
`
`devices.
`
`, which is far beyond the range of Q's obtained in man-made
`
`Atomic and Molecular Q's
`
`1016 to transitions is very large, The Q which is inherent in .molecular
`
`
`
`
`
`
`
`
`• Considerable broadening is caused, however, by molecular colli­
`1018
`
`conditions the Q ob­
`sions and by Doppler effect, so that under working
`tained by the absorption method may be of the order of 100,000 to one
`
`million
`
`
`
`r1s1. With the beam deflection method, using cesium or thallium
`
`
`
`
`atoms, it appears possible to obtain Q's of 30 million to 50 million. These
`
`
`
`phenomena (either absorption or beam deflection)
`quantum-mechanical
`
`
`
`frequency and time stand­seem to offer the best promise for non-aging
`
`
`
`stand­the changing ards which will eventually be needed to supplement
`
`rotation. ard provided by the earth's
`
`
`In the meanwhile, Q, having al­
`on to
`
`ready ranged from the atom to the planet, will doubtless move
`and cosmic realms.
`subatomic
`REFERENCES
`
`
`material, 1914. 1. JonNSON, K. S. Unpublished
`
`
`
`material, October 11, 1920. 2. JOHNSON, K. S. Unpublished
`
`Communica tion. D. Van
`
`3. JOHNSON, K. S. Tranemi88'!on
`
`Circuits for Telephonic
`
`
`Noetrand, 1925, Weetern Electric, 1924.
`4. SHEA, T. E. Transmis8ion
`
`D. Van Nostrand, 1929.
`
`Networks and Wave Filters.
`
`
`
`
`No. Circular of the Bureau of Standards 5. Radio Instruments and Measurement.!,
`
`74, First Edition, March 23, 1918.
`
`
`6. Thia relationship was made use of in the Q meter which wa.R invented by H. A.
`Snow in 1934.
`
`
`7. TERMAN, F. E. Radio Engineering. McGraw-Hill, 1932.
`
`8. TERMAN, F. E. "Resonant Lines in Radio Circuits,"
`
`Electrical Engineering,
`July 1934, p. 1046.
`9. HANSEN, W. W. "A Type of Elect,rical Resonator,"
`
`Jrmrnal of Applied Physics,
`
`October 1938, p. 654.
`
`10. TOWNES, C. H. "The Ammonia Spectrum and Line Shapes Near l .25 Centi­
`meter Wave Length," Phys. Rev., November 1946, p. 665.
`
`11. RABI, I. I., ZACHARIAS, J. R., �1n.T,M.�N, S., and Kuscn, P. "A New Method for
`
`
`Nuclear Magnetic Moment,s," Phys. Rev., Vol. 53, p. 318, 1938.
`Measuring
`
`
`
`
`12. GREEN, E. I., FrsHER, H.J., and FERGUSON, J. G. "Techniques and Facilities
`for Microwave Radar Testing,"
`
`
`Journa�july 1946, p. 435.
`Bell System Technical
`13. WILSON, I. G., SCHRAMM, C. W., and KtNllER, J.P. "High Q1u.esonant
`Cavities
`
`
`
`Journal, July 1946, p. 408. for Microwave Testing " Bell System Technical
`
`Time," Physics Today, August 14. BROUWER, D. "The Accurate l:\-Ieasurement of
`
`1951, p. 6.
`
`
`
`Standards," 15. LYONS, HAROLD. "Spect,ral Lines a.s Frequency
`Anna/$ of the New
`
`November 1952, p. 8:31.
`York Academy of Science,
`
`I I
`
`Momentum Dynamics Corporation
`Exhibit 1016
`Page 011
`
`

`

`
`
`Published in
`
`AMERICAN SCIENTIST
`
`
`
`Vol. 43, pp. 584-594, October, 1955
`
`
`
`
`
`J
`
`
`
`Printed in the UNITED STATES OF AMERICA
`
`Momentum Dynamics Corporation
`Exhibit 1016
`Page 012
`
`

`

`M O NO G R A P H 2 4 9 1
`
`BELLTELEPBONESYSTEM
`
`T E C H N I C A L P UB L I C A T I O N S
`
`The story of Q
`
`'I;--·----
`
`gaa;-_,.._
`......__,___
`---....
`11.G., ........
`._ ..... -tllllllll
`----
`
`---
`-------
`---.-
`--
`--
`------·--
`
`E. I. Green
`
`Momentum Dynamics Corporation
`Exhibit 1016
`Page 013
`
`