52
`
`PHILIPS TECHNICAL REVIEW
`
`VOL. 12, No. 2
`
`AN EXPERIMENTAL "STROBOSCOPIC" OSCILLOSCOPE
`FOR FREQUENCIES UP TO ABOUT 50 Mc/s
`
`I. FUNDAMENTALS
`
`by J. M. L. JANSSEN.
`
`621.317. 7551621.3.02!U/ .6
`
`----- - - --
`The highest frequency for which a seruitive cathode·ray oscilloscope of conventional
`deaign can be corutnu:ted is limited by various circumstances Co about 10 Mc/s. An artifice
`makes it posaible, however, to reach much higher frequencies. This artifice coruists in the
`application of an electrical analogy of stroboscopic e;icposure, the commonly known method
`for studying periodical movements taking place so quickly that the eye cannot foll010 them.
`With the oscilloscope deacribed here the stroboscopic flashes of light are replaced by electrical
`pulsu which scan, as it were, the voltage curoe that is co be uamined and convert it into
`a phenomenon of 1010 periodicity, which can then be viewed on the screen of a cathode-ray
`tube in the normal way.
`- - - - - - - - - - - - - - - - - - - ----- - - -
`
`Highest frequency attainable with oscilloscopes
`of conventional design
`Cathode-ray oscilloscopes of the conventional
`type consist of a cathode-ray tube with electrostatic
`deflection, an amplifier for the voltage to be exam(cid:173)
`ined (vertical deflection), a device producing a
`sawtooth voltage for the time base (horizontal
`deflection) and some other parts with which we
`are not concerned here. Each of the three component
`parts mentioned sets a limit u,pon the highest fre(cid:173)
`quency that can be properly observed in the oscillo(cid:173)
`gram.
`If, as the frequency is increased, the duration of a
`cycle of the deflection voltage becomes comparable to
`the time taken by the electrons to traverse the space
`between the .deflection plates, a
`transit-time
`effect occurs in the cathode-ray tube. With an
`accelerating voltage of, say, 1000 V this effect .
`becomes noticeable at frequencies of the order of
`100 Mc/s.
`The amplifier sets a much lower limit. If the
`amplification is to be kept independent of the
`frequency also at high frequencies, the amplification
`per stage has to be reduced to a low level, so that
`in order to get good sensitivity a large number of
`amplifying stages are required 1). Moreover, there
`is a still more stringent requirement to be made
`of the amplifier for an oscilloscope, namely that the
`components of a non-sinusoidal voltage must be
`faithfully reproduced not only in amplitude but
`also in phase. Furthermore the amplifier must be
`capable of supplying a considerable reactive current.
`
`1) See e.g. H. J. Lindenhovius, G. Arbelet and J. C.
`van der Breggen, A millivoltmeter for the frequency
`range from 1 000 to 30 X 108 c/s, Philips Techn. Rev. ll,
`pp. 206-214, 1949/1950 (No. 7).
`
`In fact, at a frequency of, say, 10 Mc/s the anode
`capacitance of the output valve and the parallel
`capacitance of the deflection plates together form
`an impedance of only something like 1000 ohms,
`so that with a voltage of, say, 100 V between the
`plates the capacitive current amounts to about
`100 mA. A frequency of 10 Mc/s can therefore be
`regarded as being roughly the upper limit for which
`an oscilloscope amplifier can be built that answers
`reasonable requirements.
`Together with the frequency of the voltage to be
`examined there is, of course, also the frequency of
`the time base to be raised. The highest frequency
`at which a sufficiently large sawtooth voltage can be
`generated with reasonable linearity and with short
`flyback time is about 1 Mc/s. If the frequency of
`the voltage to be examined (the voltage across the
`pair of vertical deflection plates) is, say, 10 Mc/s
`then the oscillogram never comprises less than
`about ten cycles, a number which for various pur(cid:173)
`poses is more than is desirable.
`In the normal Philips oscilloscopes so far produced
`lower frequency limits than those mentioned have
`had to be chosen in order to avoid having to make
`these oscilloscopes for a wide range of applications
`unnecessarily heavy and expensive. Thus the maxi(cid:173)
`mum frequency for the vertical deflection of the
`type GM 3152 oscilloscope 2) is 1 Mc/s and that of
`the type GM 3159 3) 0.5 to 1 Mc/s (according to
`the sensitivity), whilst for both these types the
`highest time-base frequency is 150 kc/s. There are
`other types where, for special reasons, these limits
`are still lower.
`Naturally there is also a need for an oscilloscope
`
`1) Philips Techn. Rev. 4, 198-204, 1939.
`8) Philips Techn. Rev. 9, 202-210, 1947.
`
`RPX-Farmwald Ex. 1030, p 1
`
`

`

`AUGUST 1950
`
`"STROBOSCOPIC" OSCILLOSCOPE (FUNDAMENTALS)
`
`53
`
`for frequencies higher than 1 Mc/s. Instead of
`developing such an oscilloscope along the traditional
`lines, offering but little prospect of reaching fre·
`quencies higher than 10 Mc/s, we have found it
`preferable to strike out in an entirely different and
`more promising direction. In ~ew of the resem·
`blance it shows to the principle of stroboscopic
`exposure the oscilloscope that has now been devised
`has been called the "stroboscopic" oscilloscope.
`This first article explains the fundamentals of
`the stroboscopic method, whilst a further article
`will be devoted to the electrical design of the various
`components.
`
`Principle of the stroboscopic oscilloscope
`
`and nfi. If the voltage to be examined contains
`m harmonics of frequencies 2f0 , 3f0 ,_ mf0 then the
`frequencies 2fs, 3f., mf. also occur in the 1U1ode
`current.
`
`r tl"'---t--..,----!"--~----,-
`
`J i ____ ....._ ___ __,,___._..._=_..,..t
`
`i
`~o
`II lal :,
`l '~_._--~~~~~---~~-------t
`t 11
`
`lfi
`
`~. ---------,.,--------+----------------""T'f
`
`I
`
`•
`
`When positive voltage pulses of constant ampli·
`tude are fed to the anode of, for instance, a pentode
`(fig. 1), whilst there is only a (negative) D.C.
`(this voltage not
`voltage on the control grid
`cutting the valve oft'), then the anode ·current /2.
`consists of pulses of an amplitude depending upon
`the control-grid voltage. When in addition a small
`alternating voltage v0 is applied to the control grid
`and the frequency fo of that voltage is equal to
`the repetition frequency fi. of the pulses on the
`anode (fig. 2a), then the anode-current pulses all
`have the same amplitude, this being determined
`inter alia by the phase of the pulse with respect to
`the A.C. grid voltage. The same t~g holds when
`f 0 is an exact multiple offi (fig. 2b). But if/0 deviates
`somewhat from fi, or from nfi (where n is a whole
`number), then the phase of each pulse with respect
`to the alternating voltage differs from that of the
`preceding one (fig. 2c). The .pulses then lag or lead
`with respect
`to
`the alternating voltage and
`thereby scan that voltage poin,t by p.oint. Thus
`the anode-current pulses vary in amplitude and
`form, as it were, a series of snapshots of the
`amplitude of the alternating voltage. The lowest
`frequency f. occurring in the anode current equals
`the absolute value of the difference · between fo
`
`lilll -
`
`-:i~.-----------+----------
`E,
`
`d/6U
`
`Fig. l. Circuit of a mixing valve (pentode M1) in which the
`alternating voltage 110 to be examined is mixed with voltage
`pnlsea fed to the anode. Ra anode resistor from which the
`output voltage ia taken.
`
`Fig. 2. Diagrammatic represep.tation of the mixing process,
`representing as functions of the time t: "• = voltage pulses
`applied to the anode, 110 = alternating voltage on the control
`grid of the mixing valve, i. = anode current pulses. At (a)
`the frequency lo of t10 is equal to- the repetition frequency I'
`of the pulses, at (b) lo == 3 I; and at (c) there is a small
`dift"erence between lo and 11· In ~e last case the series
`of anode-current pulses forms a point-by-point reproduction
`of fl0 and the frequency · f. =lo -I; (generally 110 -nf;I)
`takes the place of I a-
`.
`,
`
`The analogy with stroboscopic exposure
`becomes evident here: in the two cases first men·
`tioned (f0 = fi and fo = nfi) the pulses correspond
`to synchronous flashes of light, whereby the
`exposed, periodically moving object (frequency fo)
`is made to appear to be quite stationary; in the
`case corresponding to that where fo differs some·
`what from nfi on the other hand the object appears
`to be moving slowly. It is this latter case with which
`we are concerned in the designing of :the "strobos·
`copic" oscilloscope: the amplitudes of the anode·
`I
`
`RPX-Farmwald Ex. 1030, p 2
`
`

`

`54
`
`PHILIPS TECHNICAL REVIEW
`
`VOL. 12, No. 2
`
`current pulses form "reproductions" (albeit only
`of a finite number of points) of the alternating
`voltage at the control grid, and the fundamental
`frequency of the anode current, f. = I /o - nfil,
`can be made much lower than fo· It ie in this latter
`possibility that the essential advantage of the
`stroboscopic method lies for those cases where
`fo ie beyond the range of an ordinary oscilloscope.
`
`lill
`
`+
`
`R,
`
`-::-1~+~· ~~~--""'l...~~--'
`Er
`
`11616'---~
`
`Fig. 3. Block diagram of a stroboscopic oscilloscope with uni·
`form acanning. 110 the voltage to be examined, Ml mixing valve_
`with an anode reaiator R.., F 1 low·pau filter, A ow-frequency
`amplifier, c-cathode-ray tube, T generator of a aawtooth
`voltage the frequency of which ia synchronized with the fre.
`quency f. taken from the amplifier A.
`
`A stroboscopic oscilloscope could in principle
`be devised in the following way: a resistor Ro
`(fig. 1. and fig. 3) ie inserted in the anode circuit
`of the pentode (from now on we shall call this the
`.mixing valve, since in this valve the voltage 110
`ie mixed with the impulses ') ); with the aid of a
`low-pass filter only the low frequency components
`(fs and its multiples) are extracted from the voltage
`across Ro, this filter output then being amplified
`and fed to the vertical deflection plates of a cathode(cid:173)
`ray tube.
`To give the oecillogram a linear time scale the
`voltage for the horizontal deflection has to be given
`the shape of a linear sawtooth voltage, since the
`phase of the scanning pulse with respect to the
`alternating voltage
`to be examined
`increases
`linearly with time. Furthermore, in order to get
`a stationary picture the sawtooth voltage has to
`be given the frequency fs (or a frequency of which
`fs ie a multiple).
`The repetition frequency f;, of the puls.ee has to
`be eo adjustable that a multiple of this frequency,
`nfi, can be brought close enough to fo to give
`fs = lfo -
`nf;,I a value lying below the cut-off
`frequency of the filter. And
`this has to be
`the case for all values of fa between the widest
`
`') The ratio of the amplitude of the anode-current compo·
`Jlent with frequency f. to the amplitude of the fun.
`dam.ental wave of 110 will also be called here the conversion
`conductance.
`
`possible limits; thanks to the factor n, which can be
`chosen at will, fi only needs to be adjustable within
`a limited range. If 110 contains harmonics up to and
`including the mth, then mf. must also be passed
`by the filter.
`Although it ie in principle possible for an oscillo·
`scope to be arranged along these lines, great difficul·
`ties would be encountered in its execution. With / 0 ,
`say, = 30 Mc/e, and thus nfi differing but little
`from that value, the variation in time of fi would
`have to be much lees than can be realized in practice;
`even 0.1 % variation of nfi means a change of
`30 000 c/s inf.. Ae a consequence f., and still more
`so any multiples offs, would then come to lie above
`the cut-off frequency of the filter. Moreover, it
`would be impossible to keep the sawtooth generator
`of the time-base voltage synchronized with such
`a variable f..
`With the method described below this difficulty
`ie avoided and, furthermore, another possibility
`is opened.
`
`Phase modulation of the pulses
`
`With the method applied by us the pulses are
`periodically modulated in phase (or in position,
`if this term is preferred). Thie means a modulation
`of the repetition frequency fi, the average (or
`central) value of which, fie, is so chosen that
`nfic = fo•
`On the average, therefore, the pulse generator
`is synchronized with the frequency / 0 • Without
`phase modulation the pulses would continuously
`be scanning the same point of the voltage curve
`that
`(fig. 2b), but by "moving them to and fro" -
`is to say, by periodically modulating them in
`phase -
`they are made to scan different points
`of the v0 curve.
`In place of the phase difference increasing linearly
`with time, ae with the previous method, we there·
`fore have here a phase difference varying according
`to a periodical function of time. It is not of primary
`importance what periodical function is chosen for
`this, but in order to have a linear time scale the
`voltage chosen for the horizontal deflection must be
`the same periodical function of time ae that of
`the phase difference. For both functions one could
`use, for instance, one and the same sawtooth
`function, but it is simpler to use a sinusoidal func·
`tion, especially if it ie given the frequency of
`the mains; it will be shown presently why such a
`low frequency ie. advantageous. Thie ie illustrated
`in fig. 4, where in the diagram (a) a cycle of the
`voltage v0 to be examined ie represented (superposed
`upon a grid bias E 1) and in the diagram ( b) the
`
`RPX-Farmwald Ex. 1030, p 3
`
`

`

`AUGUST 1950
`
`"STROBOSCOPIC,. OSCILLOSCOPE (FUNDAMENTALS)
`
`SS
`
`scanning pulse is shown in the state of rest (without
`phase modulation). When the phase rp of the pulse
`is made to change sinusoidally with the time t,
`n to + n (fig. 4c)
`then upon swinging from -
`
`2
`
`-2ftfot
`
`+tr
`
`-~
`
`-
`-----------·
`
`-tr
`
`0
`
`------
`-----
`________ .--__
`,...
`t' o/mS
`
`""'
`Fig. 4. Scanning with phase-modulated pulses. a) Grid voltage
`11111 of the mixing valve, consisting of the bias Ei and the
`voltage 110 to be examined. At the grid voltage E 0 the valve is
`just cut off. b) State of rest of the voltage pulse on the anode.
`c) Phase <p of the pulses swinging about the state of rest,
`and the voltage "hor for the horizontal deflection, as function
`of the time & plotted vertically downwards. The frequency of
`<p and "hor is the mains frequency (SO c/s).
`
`the pulse scans a number of points of the v0 curve
`in succession. In fig. 4a the vertical arrows 1, 2, 3 .•.
`drawn from the level E0, i.e. the grid voltage
`-
`at which the mixing valve is just cut off on the
`occurrence of a pulse -
`indicate the amplitude of
`several successive anode-current pulses, which
`are the "snapshots" of the v0 curve. The low•
`frequency components of the anode current, 'with
`the frequency of the phase modulation and a
`series ·of multiples of that frequency (inherent in
`the frequency spectrum of the phase modulation),
`bring about the vertical deflection of the electron
`beam in the cathode-ray tube. The horizontal
`deflection is brought about by Vhor (fig. 4c) varying
`synchronously with the movement of the pulse.
`The screen of the cathode-ray tube then shows
`a curve which -
`provided the instantaneous
`is a
`reproductions are sufficient in number -
`faithful picture of one cycle of the v0 curve.
`
`During the return movement of the pulse ( rp vary·
`ing from + n to -
`n according to the dotted part
`of the sinusoidal line in fig. 4c) the pulse could he
`made to scan the same v0 curve again, the spot of
`light on the screen then describing the same curve
`as before but in the reverse direction, since llhor
`then changes in the opposite sense. Better use can
`he made of the return stroke by causing the pulse
`to scan another voltage curve, so that the oscillo(cid:173)
`grams of two voltages (v01 and v011) can be obtained
`simultaneously.
`(vo11 may possibly he zero,
`in which case the spot of light describes the zero
`line on the return stroke.) We shall see in a subse·
`quent article how the alternate scanning of two
`curves can he brought about with the aid of a
`simple electronic switch.
`In fig. 4 the amplitude of rp (the "phase sweep"
`of the pulse) has been made equal to half a cycle
`of ti0 , so that exactly one whole cycle of the v0
`curve is scanned. There is nothing, however, to
`prevent the sweep being made larger or smaller
`so as to be able to scan a part of the curve that is
`more or less than one cycle. Since this scanning
`takes place in the same interval of time (1/lOOth
`sec) as that in which the horizontal movement
`completes one half cycle, the part scanned always
`covers the full width of the oscillogram. By giving
`the pulse a small sweep and inaking the state of
`rest around which it sweeps adjustable, any part
`of the v0 curve can be observed as it were micro•
`scopically. This i11 of great value for studying a
`certain ·detail, a possibility which does not exist
`when applying the method previously mentioned
`(pulses proceeding at constant &peed along the
`v0 curve).
`Fig. 5 shows how a stroboscopic oscilloscope
`with sinusoidal phase-modulated pulses can he
`designed. (Although it is not customary to use
`phase modulation of the light flashes in actual
`
`0
`
`<
`
`., ...
`
`Fig. S. Elementary block diagram of a stroboscopic oscilloscope
`with sinusoidal phase modulation. 110, Mi, Fi, A and C as in
`fig. 3. li pulse generator a harmonic of which is synchronized
`via the oscillator 0 with the synchronization voltage t11yn
`(synchronous with 110 ). li is phase-modulated by the mains
`voltage.
`
`RPX-Farmwald Ex. 1030, p 4
`
`

`

`56
`
`PHILIPS TECHNICAL REVIEW
`
`VOL. 12, No. 2
`
`strohoscopy the term "stroboscopic" is nevertheless
`used here.) As was the case with the system shown
`in fig. 3, vertical deflection is brought about by
`the output voltage of the mixing valve M 1 via a
`filter and an amplifier. An oscillator 0, supplying
`a sinusoidal voltage, is synchronized with an exter(cid:173)
`nally applied voltage Vsym which has to be syn(cid:173)
`chronous with v0 (v8yn may in fact he the voltage
`v0 itself). The output voltage from this oscillator
`synchronizes in turn a pulse generator 11, to which
`in addition a sinusoidal voltage v'P of 50 c/s is applied
`for modulating the pulse in phase. The frequency
`of the oscillator is the same as the repetition fre(cid:173)
`quency of the pulses, for which we have chosen -for
`reasons which will he explained later -
`a central
`value fie of approximately 100,000 c/s; fie is so ad(cid:173)
`justed that a multiple of it is just equal to the
`frequency fo•
`These components will be described in further
`detail in a subsequent article.
`
`Limitations of the stroboscopic oscilloscope
`
`·We shall now first investigate what limitations
`have to be considered in the case of a stroboscopic
`oscilloscope and how far these set limits to the
`uses-of such an apparatus.
`In the foregoing it has been shown that the "data"
`of the oscillogram consist only of a finite number
`of points (the peak. values of the anode-current
`pulses; see, e.g., fig. 2c). The question is in how far
`these points are able to give a faithful picture of
`the original v0 curve in spite of the gaps in between
`them. ·
`The second point that we have to consider more
`closely is the duration of the pulses. So far we
`have tacitly assumed it to be infinitely small. Of
`course such pulses cannot he realized, and we must
`therefore work with pulses of a finite duration.
`Just as the finiteness of the duration of a strobo(cid:173)
`scopic flash of light causes a certain kinetic blurring
`of the object observed, so with a finite duration
`of the electrical. pulse certain details of the v0
`curve become lost; in other words; the resolving
`power of the pulses with which we have to work
`is not unlimited.
`We shall now deal with the question of the gaps
`between the pulses and then"with that of the dura(cid:173)
`tion of the pulses.
`
`Gaps 'in the oscillogram
`H the v0 curve contains m harmonics then it is
`defined by 2m + 1 points of a cycle, since this
`number of points determines the 2m + 1 coefficients
`of the Fourier series, n·amely m coefl'ic.ients of
`
`the sine terms, m coefficients of the cosine terms
`and the constant term (D.C. voltage component).
`Given that the cycle of the curve has· p points,
`then -
`notwithstanding the gaps between these
`points -
`the curve is completely determined if
`p ~ 2m + 1, or
`
`p > 2m . • • .
`
`.
`
`.
`
`.
`
`.
`
`(1)
`
`If this condition is not satisfied the best approxima(cid:173)
`tion that-can he derived from the inadequate data
`is the curve having no more than m' = t p < m
`harmonics corresponding to :.the data. In order to
`reproduce with a 'stroboscopic oscilloscope as
`many harmonics as possible this apparatus has
`to be so designed that the picture consists of the
`largest possible number of points. This means that
`the rate of scanning (the speed at which the pulses
`move along the v0 curve) has to he as low as possible.
`To work this out quantitatively let us first assume
`that we again have to do with the case with which
`we began our considerations about the stroboscopic
`oscilloscope, namely that of a constant repetition
`frequency fi of the pulses of which the nth harmonic
`differs somewhat from the fundamental frequency
`fa of the voltage v0 • The rate of scanning is then
`constant, corresponding to the constant differential
`fz = I fa - nfi I and with equidistant
`frequency
`"measuring data" (anode-current pulses). It is
`easily verified that fi/fz is the number of points p
`with which one cycle of the v0 curve is scanned.
`. Therefore, in order to observe even the mth har(cid:173)
`monic of this curve, provision has to be made
`to satisfy the condition
`
`fi
`fz > 2m.
`
`(2)
`
`A similar condition holds for the method actually
`applied where the pulse is modulated in phase and
`consequently also in frequency. The "measuring
`data" are now no longer equidistant as in the
`case considered above, but for small instantaneo'!ls
`values of the phase sweep (<p = 0), where the pulse
`has a high scanning speed,
`these "data" lie
`farther apart than is the case with large instan(cid:173)
`taneous values ( <p = + LI <p or -
`LI <p ), where the
`scanning speed is only low. ~ other words, the
`middle part of the oscillogram produced is built
`up from fewer data than the parts to the left or
`right of it. In order to get the same "density of
`measuring data" in this middle part as is obtained
`with uniform scanning, it is therefore necessary
`that the condition (2) shall be satisfied when the
`maximum value is substituted for J..
`
`RPX-Farmwald Ex. 1030, p 5
`
`

`

`AUGUST 1950
`
`"STROBOSCOPIC" OSCILLOSCOPE (FUNDAMENTALS)
`
`57
`
`Since the frequency v = 50 c/s with which the
`phase modulation takes place is very low compared
`with fie ~ 100,000 c/s, we may regard the situation
`as being quasi-stationary and speak of them omen t·
`ary repetition frequency f;.' of the pulses sinusoidally
`swinging about the central repetition frequency
`fie= f 0/n. We then have a variable differential
`frequency f:' = lf0 -nfi'I, for which, as will be
`derived below, we find the expression Iv· LI rp • sin 2nvt I
`(where LI rp is the phase sweep of the pulses expressed
`in radians of the v0 curve).
`
`It might be thought that the formula: (4) and (4a} hold
`only for the very special case where f ic and thus also f 0 are
`exact multiples of v, since then with each sweep the same
`points of the 110 curve are scanned every time, and that in all
`other cases therefore, where dift"erent points are scalined every
`time, the said conditions need not be complied with. Such,
`however, is not the case. A closer analysis shows that it ia a
`question of the number of points scanned by one sweep of the
`pulse, regardleBS of the question whether following sweeps
`cover the same points or dift"erent ones; it ia thus independent
`of chance values of the ratio ficfv. As a matter of fact the
`relations ( 4) and ( 4a) will presently be derived once more in
`a manner which shows this independency.
`
`H 2nf ;.& + IJ1 ia the phase of the unmodulated pulse (If' being
`an arbitrary constant) then the phase of the modulated pulse
`can be written as 2n/;.& + 'I' + (LJrp/n) cos 211:111, where LJrp/n
`ia the phase sweep ~xpressed in radians of the series of pulses.
`The momentary angular frequency of the pulses
`ia defined as the derivative of the phase with respect to time & ),
`2nv · (Llrp/n} ·sin 2nva, and the momentary fre·
`i.e. 2n/;. -
`quency fl' itself ia therefore
`
`fi'=f1c-11·(Llrp/n) : ein2nve. ••••• (3)
`
`For the momentary dift"erential frequency f.' we then find
`f.' = lfo - nfi'I = Iv· Llrp • ein 2nvtl, since n/;. = fo·
`
`Substituting for f. in (2) the maximum value of
`fa' = Iv· Llrp ·sin 2:nvtl, i.e. f.' max = v·Llrp, we get
`fie
`2
`v·Llq:i> m.' · ' ' ' ' ·
`
`(4)
`
`For the case where exactly one cycle of the v0
`curve is scanned we must have LI rp = n radians
`(cf. fig. 4c), so that (4) then becomes
`
`fie
`-
`2nv
`
`>m. . . . . .
`
`(4a)
`
`From these formulae it appears that it is favour(cid:173)
`able to choose a high central repetition frequency
`fie of the pulses and a low frequency for the phase
`modulation (v). As regards the latter it is an oh·
`vious solution to choose for v the mains frequency;
`any lower frequency would have to be specially
`generated, whilst moreover there would soon be
`a flickering of the picture to contend with, since
`the time base also has to have the frequency v.
`Withfie 1"1::1 100,000 c/s (see the following section)
`and v = 50 c/s we find from (4a), for the scanning
`of a complete cycle, that the highest harmonic
`that can be observed is given by m = 103/n ~ 300.
`If less than one cycle is scanned ("microscopic
`scanning", Llrp<:n)
`then the
`resolving power
`reaches to harmonics :n;/ LI 9' times as high.
`
`Duration of the pulse
`In the foregoing section we have seen that with
`infinitely small pulses the v0 curve to be examined
`can only be displayed with harmonics of up to a
`limited order ( m ), independently of the fundamental
`frequency fa· This limitation is due to the gaps.
`The following will show that actually the finite
`width of the pulse sets an absolute limitation
`upon the frequency for which a stroboscopic os·
`cilloscope can be used. If the v0 curve contains
`harmonics of a frequency higher than this limit
`f max then those harmonics are not reproduced
`(or at most but poorly), even though their order
`may not exceed the above-mentioned limit m.
`When the oscillation time of the voltage to be
`examined becomes of the same order as the duration
`T of the pulses, then the conversion conductance
`of ·the mixing process and thus the sensitivity
`of the instrument rapidly diminishes. The frequency
`limit f max may therefore be said to be of the order
`of l/T.
`,
`To define this more precisely it has to be home
`in mind that when the frequency is equal to l/T
`the s'ensitivity is zero, at least when the pulses
`are rectangular (fig. 6), since at that frequency the
`
`- t
`
`- t
`
`,, .. ,
`
`&) See e.g. Th. J. Weyers, Frequency modulation., Philips
`Techn. Rev. 8, 42-50, 1946, and in particular page 44.
`
`Fig. 6. Rectangular anode voliage pulse va of which the dura·
`tion -r is exactly equal to one cycle l/f0 of the voltage 110 to be
`examine~.
`
`RPX-Farmwald Ex. 1030, p 6
`
`

`

`58
`
`PHILIPS TECHNICAL REVIEW
`
`VOL. 12, No. 2
`
`width of the pulse just matches one cycle of the
`voltage v0 , so that the contribution that the average
`value of the anode current of the mixing valve
`receives from the positive half of this cycle is exactly
`cancelled by the contribution from the negative
`half, and thus the conversion conductance is nil.
`In a subsequent article we shall show that the
`pulses used have roughly the shape of a half sine.
`With this shape of pulse the rule also holds that
`the conversion conductance is nil at a frequency
`of 1/-r, if T is understood as being a kind of average
`width of the pulse corresponding to about 2/ 3
`of the width at the base.
`To allow for a sufficiently wide margin away
`from the state where the conversion conductance
`is zero one can take as the frequency limit
`
`1
`fmu. F=:::J- •
`2-r
`
`•
`
`•
`
`•
`
`•
`
`•
`
`(5)
`
`With a pulse duration of the order of 10-a sec
`in a subsequent article it will be shown what
`-
`difficulties stand in the way of generating pulses
`it follows that f max ~ 50 Mc/s.
`of shorter duration -
`Using the results obtained in the preceding section
`we can arrive at an equation connecting the central
`repetition frequency fie of the pulses, the frequency
`v of the phase modulation and the frequency limit
`fmax (or the pulse duration -r).
`Suppose that the fundamental frequency of the
`voltage v0 to be examined is of the lowest value
`that can be considered for stroboscopic scanning,
`thus fa = fie· Let us also assume that the highest
`(mth) harmonic of v0 has exactly the frequency
`f mu• Then m = fmax/fic· And at the same time it is
`desired that the mth harmonic is just the highest
`that can be reproduced in view of the gaps, so that
`the condition (4) holds. Let the phase sweep he
`such that, ineasured on the scale of the frequency
`f ic• which always has about the same value, it
`amounts to n radians. In the case considered he1e
`
`(fa= fie) the phase sweep is then likewise n radians
`on the scale belonging to fa and thus just sufficient
`for scanning one cycle of the v0 curve; in other cases
`(fo > f ic• n > 1) more than one cycle can be scanned.
`The condition (4) now has to be applied in the form
`(4a), and with m = fmaxlfie this becomes:
`
`or
`
`fie >/max
`fie
`2nv
`
`nv
`f ic2 > 2nv fmax F=:::J -
`•
`
`T
`
`From this equation it follows that, with T in
`the order of 10-a sec and 'II = 50 c/s, fie > about
`1001000 c/s. Since the repetition frequency of the
`pulses forms the lowermost limit of the frequency
`range of the oscilloscope, in order to keep this range
`as wide as possible fie has not been chosen any
`higher than is necessary, hence about 100,000 c/s,
`the value frequently mentioned in the foregoing.
`
`Cut-off frequency of the fil~er
`The required cut-off frequency of the low·paos
`filter (F1 in fig. 5) is directly related to the value of
`fie, as will be understood from what follows.
`At (a) in fig. 7 part of the frequency spectrum
`of the phase-modulated pulses has been drawn:
`it shows the fundamental frequency fie and some
`harmonics, (n - 1) fie• nfic and (n + 1) fie, which
`would already be present in the case of unmodulated
`pW.ses, and also the side bands due to the phase
`modulation; the distance between two adjacent
`lines of the side bands is the modulation frequency
`v. At (b) in this diagram we have represented the
`single-line spectrum of the voltage v0 (any harmonics
`of v0 are of no consequence here); this line_ lies at
`fa = nf ie· Mixing of the two spectra produces
`innumerable differential frequencies (the difference11
`between fa and all frequencies of the spectrum of
`
`I
`
`,.
`
`~c
`
`' ' ' I :_,
`i 0-----........ ~------'l---.. ----(.",.....i...W.Ul!IJ~Ll.l..U~~Ll.l..U~"""" ......... ~.l.l.L'Jl;!fl;~ ................. _
`
`I •
`I
`I
`
`Fig. 7. Frequency spectrum, (a) of the phase-modulated pul&ea, (b) of the ainueoidal
`voltage 110 • (At (a) neither the number of component& of the 1ide bands nor the intensity
`of the components are true to scale; it is only a schematic indication that the side bande
`of the multiples of/1e are richer in llOmp()nents than the eide bands of/1e itself, and that
`the outermost components of the side bands are much weaker than the majority of the
`components lying farther inwards.)
`
`RPX-Farmwald Ex. 1030, p 7
`
`

`

`AUGUST 1950
`
`"STROBOSCOPIC'' OSCILLOSCOPE (FUNDAMENTALS)
`
`59
`
`the modulated pulses). Of all these frequencies
`the filter should pass only those derived from lo
`and the side bands of nl;,c; frequencies which are
`the difference of lo and other side bands -
`in parti·
`1) fie and
`cular the adjacent side bands of (n -
`(n + I) fie -
`have to be suppressed. From this
`it follows that the cut-off frequency of the
`filter must not exceed J;,c/2 ;::,s 50,000 c/s.
`From these considerations it also follows that
`the side bands should not overlap, hence that their
`width should not be more than fic/2; in other words
`in fig. 7 they should not extend beyond the vertical
`dotted lines. Strictly speaking they actually do,
`because they consist of an infinite number of terms,
`but if, as is the case here, the· situation is to be
`regarded as quasi-stationary ('11 <_f;,c) the part of
`the side band falling outside the frequency sweep
`is of so small an amplitude as to be negligible.
`The condition that has to be satisfied to ensure
`that the side bands do not overlap is, therefore,
`that ;none of the multiples of the pulse frequency
`may hllve a greater frequency sweep than fic/2.
`For the nth harmonic (belonging to the fundamental
`fre