1957 Mostafa and Shaltout: A Novel Apparatus for the Measurement of Phase Angle 63

Auxiliary Symbols

Z21Z12 Y21Y12 1 1

ZlIZ22 Y11Y22 111/1 22 1 [zj + (1 - F)ZS] [Yout + (1 -_) YR]B2

1s h21h12 (Y0.t + YR)2(Z1. + Zs)2e4'2le7*12

YR = -

ZS + ZR The value of each symbol may be substitutedZR in the parameters above

F = 1 + __t(YU + YiR)(Zn + ZS)e412'e-'l~~~~~~~~~~ B2l

Fig. 25 (conclusion).

A Novel Apparatus for the Measurementof Phase Ang e*

ABD EL-SAMIE MOSTAFA,t AND M. H. SHALTOUTt

INTRODUCTION as the main piece in the measuring equipment.'-3I N ORDER to have successful transmission of Others made use of the heterodyne principle and meas-

speech, program, television, or pulse signals over urement of phase angle is therefore effected at a singleany communication circuit, the output of this cir- frequency, generally in the audio-frequency range.4'

cuit should exactly duplicate the input in all respects Another type of phase detector which can be appliedexcept the magnitude, i.e., the amplitude and phase at low frequencies is that due to Farren.7 Its principlerelationships of all the essential frequencies constituting is that if two sinusoidal voltages of equal amplitudesthe input signal must be substantially preserved. There- but having a phase difference are added and subtracted,fore, it is important to have some means of measuring then the difference between the magnitudes of the re-the phase shift characteristics of any communication sulting addition and subtraction, obtained by usingcircuit such as concentric cables, filters, equalizers, diode rectifier circuits, is a measure of the phase angle.phase shifting networks, and amplifiers (audio and In the phase measuring apparatus of Opitz,8 the twovideo) especially those where there is an appreciable sinusoidal voltages between which the phase angle is toamount of feedback over more than two stages of be measured are converted into very nearly rectangularamplification. Again, for the study of phase angle be- waves of equal amplitudes keeping their phase differ-tween grid and plate potentials in radio frequency power ' F. de la C. Chard, "Determination of phase angle by cathodeoscillators and amplifiers, a radio frequency phase meas- ray oscillograph," J. IEE, London, vol. 83, pp. 681-684; 1938.

uringappara.Asimple and accurate 2 A. Watton, "Modulated beam cathode-ray phase meter," PROC.uring apparatus is important. A slmple and accurate IRE, vol. 32, pp. 268-272; Mav, 1944.radio and audio frequency measuring apparatus is 3 D. H. Ring, "The measurement of delay distortion in micro-wave

thereforean essential component in a telecommunica- repeaters," Bell Sys. Tech. J., vol. 27, pp. 247-264; April, 1948.tion laboratory. Instr., vol. 4, pp. 537-539; October, 1933.

There~~~~~~ar seea prvospbiain,bt ho M. Levy, "Methods and apparatus for measuring phase dis-Therearesveralprevlus pbllca1ons,both heo-tortion," Elec.'Commun., vol. 18, pp. 206-228; January, 1940.retical and experimental, concerning the measurement 6 R. F. J. Jarvis and E. F. S. Clarke, "Apparatus for the measure-ofte phs anl bewe w inl. Som of ths ment of insertion phase shift at radio frequencies," P. 0. Elec. Eng. J.,OI tn phasangl betwen tw slgnls zoe OI nesevol. 33, pp. 162-170; January, 1941.publications made use of the cathode ray oscillograph 7L. I. Farren, "Phase detectors," Wireless Eng., VOl. 23., PP. 330-

340; December, 1946.* Manuscript received by the PGI, February 8, 1955. 8 G. von Opitz, "New type of valve phase meter," Hochfreq. techn.t Faculty of Eng., Alexandria Univ., Alexandria, Egypt. und Elektroak., vol. 49, pp. 52-56; February, 1937.

64 IRE TRANSACTIONS ON INSTRUMENTATION March

ence the same as in the original sinusoidal waves. A Substitution in (1) givesmoving coil instrument in a bridge copper oxide recti-fier circuit or a thermocouple indicator is used for the ip = g e - V cos (wt + 4)) } ± CCe t V sin (&wt + 4))measurement of phase angle. + components of frequencies other than w/2r

THEORETICAL ANALYSIS = g,v + Cedv/dt + components of frequencies other

Fig. 1 represents a schematic diagram of a tuned than co/2r (2)plate oscillator with an applied signal e,(=E cos wt) in hits grid circuit. The losses in the oscillatory circuit are wrepresented by a shunt arm of conductance G in order / El \ 3 /M \to simplify the analysis and the results obtained apply gf = -Ia'1 + - cos4)- a3 y -1)3as well to the more usual case where the losses areassociated with the inductance. If the oscillator is E1 32Elocked in by the applied signal and if the oscillatoryiV2I + cos) + E 2 1+ cos ) sin2 q5

circuit is slightly damped so that there is a very highimpedance to currents of the operating frequency but 1 E i + 3 1 M 3

negligible impedance to harmonic currents, then the = V [a 4 Loutput voltage v may be assumed to be of the form, 2 2 2

2v=-V cos(wt+0)). The negative sign is simply used to t(V + El cos 4) + El sin 4)} ]take care of the 180° between v and e8 at resonance. A M

El - E, and a' = a, _--1

m 1L

As the output voltage is of the form v=-V cos(wt+O),therefore the components in ip which are responsible forthe average wattful and wattless powers are those offrequency w1/2w. Therefore, only those components will

L c_ be considered. The electron tube could therefore besubstituted by a conductance ge shunted by a capaci-tance Ce [see (2) and Fig. 2 ]. Both ge and Ce depend on

es l ; the amplitude of oscillation, the amplitude of the signal,as well as the phase angle between them.

CS '

Fig. 1.

Neglecting grid current, the ac component i, of the q CXL c;G C0

- t+O)plate current is a function of the composite voltagee'{ =v+,ue,}, where ee is the total ac component of thegrid voltage, and ,u is the amplification factor of the LI-_--tube. For qualitative analysis, the amount of non-linearity may be assumed small so that power serieswith a few number of terms may be adopted. Fig. 2.

Let= aie' + a2e 2 + a3e3. ) In order to have steady synchronized oscillation, the

wattful power as well as the wattless power in Fig. 2

It is clear from Fig. 1 that must be separately in balance. Therefore,

M 2V2ge + 2V2G = 0 (3)e,= - -v+ e8,

L and

giving: wv2 = 1/L(C + Ce). (4)

e' =O(--1)Vcos(cwt+4))+,uE coscxt. Substituting g6 and Ce by their expressions and rear-L ~~~~~~~~~~rangingwe get respectively,

1957 Mostafa and Shaltout: A Novel Apparatus for the Measurement of Phase Angle 65

V = (V + IA cos ~) [i-(V + IA ~ and E= 100 mv), the frequency being constant at 800V =(V + E, cos (P) I -ml(V + IEl cos 0)2 iocls

V02 ~~~~~~kilocycles.If a portion of the output voltage is applied to another

E12 i -] oscillator, then the output of the latter is, to a highV+ 2 degree of approximation, independent of the original

signal, Fig. 8. It is again clear, aided with (6a), that thez - 2Q1V ±El cos 4) (6) relative amount of detune Z/w of the second oscillator

co 2Q V + Ei cosO +is proportional to sin 4 and is practically independent

where of the original signal, but it is inversely proportional tothe quality Q of the plate coil. If the coil is constructed

a'- G so that its quality Q is constant over a certain frequencym = ,Gband, then the relative amount of detune is also inde-

af- Gpendent of frequency in this band, Fig. 9.

_____(x-G If the detune is effected by a trimmer condenser, then/__ -(A\3 Zlw -2 (AC/C) and AC/C of the second oscillator is a-p/'(3/4)a3( -2i/|/-L3/4)a39--1y measure of the phase angle. The direction in which AC

is varied depends on whether the phase angle is leading= amplitude of oscillation were the signal absent, or lagging.

Z ( 2 w swo, WO2 = 1LC, DESCRIPTION OF THE PHASE MEASURING APPARATUS2w2

A fundamental requirement in phase measurement isand Q is the quality of the plate coil L and is equal to that the indication of the phase measuring instrumentcoC/G. Eqs. (5) and (6) are the two fundamental rela- must be independent of the amplitudes of the signalstions of a synchronized triode oscillator under steady between which the phase angle is required. Another re-state condition. Elimination of V between (5) and (6) quirement is that the measuring system must differenti-gives, ate between whether the phase angle is leading or

lagging. Both requirements are satisfied in a system(z 3 2Q (Z 2( E12_ composed of two synchronized oscillators connected in(A)3cos4) -(Z)I -- sin2 4) sinco m co Vo2 J tandem. A synchronized oscillator can give a substan-

1 E 2 tially constant output voltage in the whole synchroniz-± (- -sinE 4) =0 (7) ing range independent of the amplitude of the syn-

\2Q V01 chronizing signal so long as the latter is small, as statedbefore in the theory. Again, if a small portion of theEq. (7) gives the frequency-phase relation of the system. . '

It is clear from (6) that the maximum amount of de- output voltage is used to synchronize another oscillator,tuning =Z ccush0.P g 9 then the amplitude and phase of the output voltage of

tuning(7 go the latter is, to a high degree of approximation, inde-in(7) gives, pendent of the magnitude of the original input signal.

1 El/Vo In other words, two synchronized oscillators connectedZmax/W = 2Q -/l-(IA/V0)2 in tandem can act as a radio-frequency voltage limiter

as well as a radio-frequency constant output phaseFor small amplitudes of synchronizing voltages, shifter. The system also possesses the great advantage(E1/V)2 can be neglected compared with the unity and of high selectivity, in which case, if one of the signalsZmax will be proportional to the signal. However, for contains harmonics, the component at which thelarge signals, the relation slightly deviates from linear- oscillator is tuned will only be selected.ity, see the experimental characteristic, Fig. 7. The fundamental components of the present appara-

If the applied signal is small so that El cos 4 can be tus are two oscillators and a detector system as shownneglected compared with V, (5) and (6) reduce to, in the simplified diagram, Fig. 3. In order to eliminate

any feedback between the two oscillators and betweenV = V0 (5a) the oscillators and the detector system, it was found

1 E1 necessary to use buffer stages of the cathode follower=/ -2 -- sin 4). (6a) type (CF 1 and CF 2), as shown in the diagram. The

2Q0 ~~~~~cathode follower stage CF 2 can be connected to eitherEq. (5a) indicates that the output voltage V is constant oscillator output by a change-over switch S2. The de-independent of both the signal amplitude E and the tector system is composed of a germanium crystal X, aamount of detuning Z, provided that the amplitude of direct current amplifier, and a microammeter. Thethe applied signal is very small, see Fig. 6 (characteristic microammeter indicates maximum or minimum whenwith E=25 my). For large signals, the output voltage the voltages applied to the detector system are in phaseslightly varies, Fig. 6 (characteristics with E-=50 my or 180° out of phase, respectively.

66 IRE TRANSACTIONS ON INSTRUMENTATION Marchoscillator NI oscillator N!2 no. 1 which is made to synchronize, and adjusted to be

C, C C 1800 out of phase, with the input signal. Then a part ofthe output voltage of the first oscillator is injected into

S 2 < 5 the second oscillator which is in turn synchronized and/ | 4,,; brought in phase with the test signal. Now, the output

-A ^ of the second oscillator being synchronized and in phase'SIs, with the test signal, is applied to the detector system

together with the output of the circuit under test, where.camplifier aa they are added together, and a value proportional to

2 Ltheir sum will be shown on an indicating instrument.;1 :$ IM Maximum indication is obtained by adjusting the cali-

brated trimmer condenser C5. The amount of variationof C5 is a measure of the phase shift of the networkunder test at the operating frequency.

Fig. 3.EXPERIMENTAL VERIFICATION

Operation of the instrument is as follows. With In order to test the validity of the foregoing theo-switches S1, S2, and S3 in position "1," the main tuning retical relations and conclusions regarding the presentcondenser Cl is adjusted so that the first oscillator is in new type of the phase measuring apparatus, the follow-synchronism with the voltage vi or a portion of it, ing experimental work was carried out.using headphones for detecting the zero beat condition. Let us first start with one oscillator. Fig. 6 shows theThe oscillator itself is used as a heterodyne detector output voltage against the capacitance change of theelement for the determination of the silent interval. The trimmer condenser C2 of the first oscillator alone forbeat note, i.e., the audio-frequency output is taken several signal amplitudes at a frequency of 800 kc. Theacross a low-frequency choke in the dc supply circuit, output voltages are indicated by means of a tube volt-L3 in the complete connection diagram, Fig. 4. meter. It is clear from the characteristic, E = 25 mv, ofThe trimmer condenser C2 is adjusted so that the Fig. 6 that the amplitude of the output voltage is

input voltage v, and the output of the first oscillator are practically constant and is approximately equal to the1800 out of phase. This condition is indicated by a free oscillation amplitude, agreeing with (5a). For largerminimum deflection of the microammeter. Then applied signals, the output voltage slightly varies, theswitches S2 and S3, which are ganged together, are characteristics with E =50 mv and 100 mv in the samechanged to position "2" and the second oscillator is figure.synchronized by adjusting its main tuning condenser Fig. 7 shows the ranges of synchronization for differ-C3. Then the trimmer condenser C4 is adjusted so that ent signals, the signal frequency being 700 kc. Thethe input voltage vi and the output voltage of the second ordinate represents the maximum variation A2C of theoscillator are in phase, which is indicated by a maximum trimmer condenser C2 beyond which oscillations breakdeflection of the microammeter. Due to the change in out of synchronism. It should be noted here that if thethe stray capacitances when the switch S2 is changed signal frequency is equal to the free frequency, the out-over from position "1" to "2," it has been found neces- put voltage is not exactly 1800 out of phase with the sig-sary to readjust C2 and C4 to get an absolute maximum nal voltage. Due to the harmonics in the output voltage,deflection of the microammeter. The voltage vi is now the resistance of the plate coil, the stray capacitancesin phase with the output voltage of the second oscillator and the lead inductances, there is a slight phase shiftand 1800 out of phase with that of the first oscillator. from 1800. This is the reason why the 1800 out of phase

Finally, switch S is moved to position "2" and the is experimentally obtained.calibrated trimmer condenser C5 (=AC) is adjusted for To get the characteristics of the two cascade-maximum deflection of the microammeter. The required connected oscillators, a signal of 5.0 mv at a frequencyphase angle is directly read off the scale of C5. of 800 kc from the standard signal generator is applied

It should be noted that in case the source impedance in the grid circuit of oscillator no. 1, switches S2 and S3of the synchronizing voltage v, is high, a cathode fol- being in position "1." The tuning condenser C, is ad-lower buffer stage should be employed ahead of the first justed so that the oscillator is in synchronism with theoscillator. In case the phase-shift characteristic of a input signal using the headphones for detecting thecertain network is required, the arrangement will be zero-beat condition. Trimmer C, is then adjusted so thatshown in Fig. 5. A signal of a frequency equal to that the input signal is 1800 out of phase with the outputat which the phase is required is fed to the network voltage of oscillator no. 1. This condition is indicatedunder test. A part of this signal is applied to oscillator by a minimum deflection of the microammeter M. Then,

1957 Mostafa and Shaltout: A Novel Apparatus for the Nleasurement of Phase Angle 67

,-G PH.

TUUIJ VOLTIETER .SYST(M. t

120 *118 t1-60 - -6

Conlnection Diagram of the Phase Measuring Apparatus

|La1, La2 |Anode Coils C26, C19 Mica Condenser 500 y,uf R19 Variable WVireL01, L LGrid Coils C17 Mica Condenser 10,000 ouf Wound Re-L1, L4 IH F. Choke C18 Mica Condenser 50,000 ,u,uif sistance 15 0L2 L5 .. Os C21 Mica Condenser 5,000 ,,f R20 Variable WireL3, L6 L. F. Chokes C20,22,22 Tubular Condenser 50,000 ,4Ju Wound Re-

C1 Main Tuning Con- C24,25 Mica Condenser 10,000 ,u,uf sistance 3,000 0denser of 1st C26 Tubular Condenser 50,000 puf R21 Variable Wireoscillator 1,000 jyf R1, R8 1 Watt Resistance 1,000 0 Wound Re-

C3 Main Tuning Con- R2, R9 1 Watt Resistance 12,000 0 sistance 200 0denser of2nd R2, R10 1 Watt Resistance 5,600 0 R22 1 Watt Resistance 270,000 0Oscillator 1,000 ,u,Mf R4, R11 1 Watt Resistance 47,000 0 R23 1 Watt Resistance 470 0

C2, C4 Trimmer Con- R5 1 Watt Resistance 7,800 0 X Germanium Crys-denser 10 ,u,uf ]?5' 1 Watt Resistance 4,600 0 tal Type IN34

C5 Calibrated Trimmer R12 1 Watt Resistance 12,400 0 Ph Head PhonesCondenser 5 ,u,uf R6 1 Watt Resistance 470 0 M Micro Ammeter 100 RA

C6, C14 Mica Condenser 500 ,uf R7, R13 1 Watt Resistance 47,000 0 S1 Single Pole, Double-C7, C9 Mica Condenser 10,000 rn'uf R14, R15 1 Watt Resistance 12,000 0 throw SwitchC8, C10 Mica Condenser 500,u,uof R18 1 Watt Resistance 120,000Q0 S2, S3 Double Pole, Double-Cul, C13 Mica Condenser 100 ,/,pf R17 1 Watt Resistance 150 0 throw SwitchIC,2, C61 Mica Condenlser 500 /f R1 1 WHatt Resistance 47,000 s2

Fig. 4.

68 IRE TRANSACTIONS ON INSTRUMENTATION March

o,scillator oscillator- the ganged switches S2 and S3 are moved to position "2"IAt/ I VIMS-2 1 and oscillator no. 2 is synchronized by adjusting its

signal main tuning condenser C3. Then the calibrated trimmer9encrator a condenser C5 is varied over the whole synchronizing

range of the second oscillator, taking readings of thenet b.Ork detector output voltage of this oscillator by means of a tube

voltmeter for various settings of the trimmer condenser.Fig. 5. The experiment was repeated for several input signals

varying from 5 mv up to 250 mv at a frequency of 800kc. Fig. 8 shows the output voltage of the second oscil-lator in the whole synchronizing range for different inputsignals and at a frequency of 800 kc. It is clear that theoutput voltage is, to a high degree of approximation,independent of the applied signal and at the same timeis practically constant along the whole synchronizingrange, indicating that this system can be used as an

Et/Qoom 50SO25 excellent radio frequency voltage limiter as well as a

constant output phase shifter.

WIJ

A|>-E= 250 mv'*5-/00 my

2

-3 -2 -? 0 2 3 /5uf

Capacitance change of trip"mer C

Fig. 6.

P,Alf -3 -2 1 0 / 2 3 //f4

- Capacitance of calibrated trimmer C5

Zq 3 Fig. 8.e< 20 For the calibration of the present phase measuring

apparatus, a circuit composed of noninductive resist-ances and a set of fixed mica condensers is constructed.

, ^~~~~~~~~~~~The set of condensers is connected to a multipoint0 25 50 75 10 rotary switch thus providing different condensers for

Inlpvt JI9flQl. different phase angles which are calculated from the

Fig. 7. corresponding values of the condensers and the re-

1957 Mostafa and Shaltout: A Novel Apparatus for the Measurement of Phase Angle 69

sistances. In order to avoid the capacitances of the leads Mostafa.9 It is clear from Fig. 9 that AC/Co is practicallyconnecting the circuit used for calibration with the independent of frequency in the band between 600 kcapparatus, the different elements of the circuit together and 750 kc. This is the frequency range in which thewith switch S1 are enclosed in a copper casing which was quality Q of the plate coil of the second oscillator isdirectly plugged into oscillator no. 1 and the detector practically constant.system.

vi and V2 are the two voltages between which there isa predetermined phase angle 0. V2 is the signal generatorvoltage while vi is the voltage across the resistance ele-ment of the circuit used for calibration, so that vi isleading v2. A portion of v1 is applied to oscillator no. 1 asshown, Fig. 4. With switches Si, S2, and S3 in positions"1," the oscillator no. 1 is synchronized and its output

,laps behind v'j

voltage is brought 1800 out of phase with v1 as was de- _i _|/_!scribed before. Then, with switches S2 and S3 in position sii 09 00. 0.n 0.4 0.3 0.. 00n3 s.4 n0. 09 0.7 *.o 0.9"2," the second oscillator is synchronized by adjusting I v; /¢ds uits main tuning condenser C3 and brought in phase withv1 by varying the trimmer condenser C4 and which is_indicated by the maximum deflection of the micro-ammeter of the detector system. It was found necessary 3600kcto readjust C2 and C4 to get an absolute maximum de- A A065o0kcflection of the microammeter as stated before. Then *- 750Akcswitch Si is moved to position "2" and the calibrated Fig. 9.trimmer condenser C3 is adjusted till maximum de-flection of the microammeter is indicated. The variationAC in capacitance of the trimmer condenser C5 relative CONCLUSIONto the total tuning capacitance C0 is a measure of the Although the apparatus described was used in thephase angle 0. The same is repeated with v1 lagging be- frequency band from 600 kc to 750 kc, yet it can behind V2; in this case the variation AC of the trimmer constructed to cover several frequency bands, usingcondenser C5 is in the reverse direction, assuring that several coils, the quality of each coil must be constantthe apparatus differentiates between lagging and leading in the corresponding band. The apparatus can also bephase angles. Fig. 9 shows the calibration curves of the used in the audio-frequency band using high qualityapparatus for different frequencies. The relation be- iron-cored coils. A phase measuring apparatus based ontween AC/CO and the sine of the angle 0 is practically the principle mentioned in the paper and which can belinear. However, the straight line to the right (v3 leads used from as low as 400 c to as high as 30 mc is nowV2) is steeper than that to the left (vi lags behind V2); under construction in Alexandria, Egypt.This is ascribed to the asymmetry of the resonancecurve of a synchronized oscillator due to the harmonics A. E. S. Mostafa, "Effects of harmonics on the frequency of os-

cillation as well as on the asymmetry of the resonance curves," Trans.present in the output circuit; see Figs. 6 and 8 as well as AIEE, vol. 72, pp. 309-314; July, 1953.

C11A%5