364 PROCEEDINGS OF THE IEEE. MARCH 1%8

general different from the negative sum of the real powers of the higher harmonics (area B + C in Fig. 2(b)).

In conclusion, it is interesting to observe that for the case of resistive nonlinearity where the voltage is nearly sinusoidal, there exists a relation- ship for Re AIl in terms of the real powers of the higher harmonics. A dual expression to (11) can be found for the case of a nearly sinusoidal current when Z(jno) satisfies the filter hypothesis of Aiserman.

M. VEHOVEC~ Dept. of Elec. Engrg.

Imperial College of Science and Technology London S.W.7., England

REFERENCIS

Systems (in Rusian). GIMFL, 1 9 6 0 . [ ‘I E. P. Popov and I. P. Pal‘tov, Met& of Approximntionr in the Nonlinear Control

harmonic linearization,” U. S. offia of Naval Research, Washington, D. C., Rept., March [‘IN. Minorsky, “Investigation of nonlinear oontrol syst-part 4: Method of

1963. 13’ V. Belevitch, Thewiedes Circuits Non-Liniwes en R & i m Altemtif Paris: Gauthicr-

V ia - 1959. 1. Mcdif, “Nonlinear theory of oscillators,” Magister thesis (in Slovene), University

of Ljubljana, Yugoslavia, 1966. M. Vchovec, “Nonlinear theory of oscillators,” Magister thesis (in Slovene), Uni-

versity of Ljubljana, Yugoslavia, 1 9 6 6 . I. Grosd;owski, “The interdependene of frequency variation and harmonic mn-

tent, and the probkm of constant-frequcacy oscillators,” Roc. IRE, vol. 21, pp. 95a981, July 1933.

slavia. ’ On kave from the Faculty of Electrical Engineering, University of Ljubljana, Yugo-

Differential Qnantizatioa of Televisioa Signals- open-Loop operation

Absrract-”be opcdoo~ resy.tbesis of tdevisiao sig..Lp dwqueat t o r e a l - ~ d q a a n t b t i o n k r e p o t t d

In a previous paper, Limb’ described a differential quantizer capable of producing good quality pictures having a 6rst-order entropy of less than two bits per picture element. pictures synthesized by using the encoder feedback loop as the decoder were virtually indistinguishable from the originals at a distance of eight times the picture height under standard viewing conditions.’ This letter reports on the picture quality obtained from a separate decoder which has recently been constructed and tested.

To incorporate the quantizer into a digital communications system, signal decoding at the receiver must be identical to that in the encoder feedback loop. Fig. 1 shows block diagrams of both the encoder and the decoder.

Ideally, the classified signal should contain no analog information as this would be lost during transmission. Furthermore, any analog break- through in the classifier stage would cause a reduction in the hold time of the closed-loop integrator. The inclusion of synchronous gating circuitry in the system implemented reduced the analog gain of the classifier to - 80 dB. At this level there was no noticeable reduction in the hold time.

Another possible defect in the real system is the finite mismatch in the corresponding weighter levels. This, however, has caused no noticeable degradation in the quality of the transmitted picture. In fact, a deliberate mismatch of some 13 percent in an outer level was tolerated by 50 percent of the viewers in a quality grading test.’

Altogether the pictures resynthesized by the decoder were comparable in quality to those at the encoder feedback loop. The viewer tolerance to transmission errors is yet to be determined and a program for this is al- ready under way. The results will, in part, determine the channel capacity required for transmission. This will also depend on the type of coding

NYQUlST

SIGNAL OUT

SOURCE - RECEIVER ENCODER (DIFFERENTWL OUANTlZERl

DISCRETE

SOURCE - RECEIVER DECOMR

Fig. 1 .

used. To achieve a bit rate close to the stated two bits per element would naturally require a large coding effort.3 However, as the total number of quantizing levels is only seven, straight coding would still represent a useful saving on ordinary PCM.

J. L. HULLETT Dept. of Elec. Engrg.

University of Western Australia Nedlands, Western Australia

J. 0. L m 4 Postmaster General’s Research Labs.

Melbourne, Australia

Yo&: Wilcy, 1965, pp. 285-355. ’ J. M. WoZeWatt and 1. M. Jacobs, Principles of Cornrnunicutwm Engineering. New

‘ ResRltly at &U Telephone Laboratories, Inc., Holmdel, N. J .

Tbeoretid Note on the Probabilities of Peaks m Electric Power System Loads

Abstracr -A theoreticll rehtioophip between the ocearreace of- in ~ ~ ~ O d 3 u d t h e ~ o f p e i l P i n t h e e o m p o s i t e l o r d k d e - v e W . The appiiatioa of this rel.tion&ip to p d k t h g t ~ e of c ~ ~ l o r d ~ ~ k i u u s t r 8 t e d .

Electric power loads have a daily peak occurring at different times from day to day. Consider a day consisting of m demand intervals, i= 1,2, . . . , m. For each interval i, there will be an associated probability Pi(E) that the demand in interval i is the peak demand for the day. It follows then that there can be defined for -any load j , a probability Pi@,), i= 1,2, . . . , m, such that the Pi(Ej) are mutually exclusive and independent probabilities. The Occurrence of a peak demand in interval i by consumer j is denoted by Ej , j = 1,2, . . . , n.

Now consider a diversified load made up of n consumers. When the Pi(Ej) are known then the probabilities Pi(Ediv), i= 1,2, . . . , m, for the in- tervals of composite p e a k s can be estimated.

There are two factors affecting the probabilities namely:

1) Pi(Ej), j = 1, 2, . . . , n, and

Manuscript reccivcd Oaok 27, 1%7; rcviscd December 18, 1967. ’ J. 0. Limb, ‘Source-rsdver encoding of tekvision sigds,“ Roc. IEEE, voL 5 5 , peak by each component load. 2) the demand most likely to be contributed to the diversified load

pp. 3W379, Marcb 1967.

signak,” Prof. IEE(Lwdon). vol. 1 1 1 , p p . 491-502, March 1964. Manuscript received N o v e m k 10, 1967. R. D. Roster, J. W. A l h t t , and N. W. “Quality m g o f i m m television

PROCEEDINGS LETTERS 365

The contribution from the first factor can be taken into consideration analytically in a reasonably straightfonvard manner. The second con- sideration is more difficult to handle in that it varies over all i and changes +

from day to day. For simplicity, it shall be assumed here that the best value 5 to use is the expected value of the component load, that is, E(6, ,,,J of the component load j .

The problem of predicting Pi(Ediv) may then be stated. Given Pi(Ej) and E(aj j = 1,2, . . . , n, find Pi(Ediv). Three assumptions are made in deriving an expression for Pi@&.). These are as follows.

which is directly related to P,(Ediv). This weighting function is defined as

Test N: 1

”

1) Pi(Ej) and E(6, ,,-) can be combined to form a weighted probability o3

w . = E(6j -1 J m c

j = 1 . .. ...

INTERVAL

and thus 13) I M

and, letting

i = 1

The probability that the demand in interval i for a diversified load made up of n component loads is therefore

T ~ s r RESULTS Tests were carried out to verify (1 3). Each test load consisted of ten

domestic consumers. For each group of consumers the probabilities of the diversified peak occurring in each half-hour interval of the day were de- termined. Then for the composite load, the frequencies of peaks occurring in each interval were counted. Fig. 1 shows the results of two tests. The data was normalized for plotting. The shaded bars are the theoretical prob- abilities determined using (13) and the unshaded bars are the measured results.

The actual probabilities determined theoretically are not exactly the same as those measured. The measured results in almost all cases are slightly lower than the theoretical predictions. This can be attributed to normalizing on the highest magnitude observation which may have been slightly higher than expected. This deviation can be accounted for in that the amount of data used in determining the measured results was small (120 days and 20 peak intervals). The probabilities used in (1 3) were also used on an equally s m a l l quantity of data. Despite these limitations, how-

366 PROCEEDINGS OF THE IEEE, MARCH 1968

ever, the grouping of high-probability intervals and in most cases the prob- abilities are similar for the theoretical and measured cases.

The group of consumers in Test 1 were all low-usage consumers with annual kwh ranging between 1382 and 9475 and mean daily peaks be- tween 0.533 kW and 3.792 kW. The same group of consumers was used for Test 2 with the exception that the largest and smallest consumers were re- placed by two larger consumers (with air conditioning units). These con- sumers had mean daily peak demands of 5.736 kW and 5.934 kW with an- nual energy consumption of 10 604 kWh and 16 161 kWh, respectively. Their effects on the composite peak probabilities are evident when the re- sults of the two tests are compared. The differences between Tests 1 and 2 should be noted in both the theoretical and measured cases. The theo- retical predictions reflect the actual change in the pattern of peak prob- abilities.

CONCLUSIONS At a given time for any load there is a probability that a demand will

be the peak demand. For a group of consumers the probability of their combined peak occurring at a given time can be estimated as the union of the weighted probabilities of the component load demands at that time being peak demands. This concept may be applied in predicting the effects of adding new components to an existing load. Results presented here demonstrate that the demand interval in which it is most probable that the peak will occur can be predicted accurately. Reliable estimates of other intervals which may contain peaks can also be made.

G . D. MILLER Dept. of Elm. Engrg.

University of Canterbury Christchurch 1, New Zealand

A Perfectly Conpled Transformer with a Variable T m Ratio A bstract-A variable lh&emid device (like a potentiometer) is ased

t o a c h i e v e a p e r f e c t ~ o r m e r . e t i o a r r i t h n v ~ ~ m a c t i v e networLs

The transformer described below employs one negative element. These elements are easily made using present technology. The idea of using a negative element in a transformer is not new as is seen in the literature.[’l*tzl The novelty of this transformer is the variability of the coupling coe5cient. This is the same as the turn ratio in an ordinary magnetic transformer. The main features of the device are shown in Fig. 1. Here a is the fraction 0 < a < 1 which is the ratio between the capacity of the left branch of the differential capacitor and the maximum possible capacity C. It follows that

Since the determinant of the matrix on the right is zero we have a perfectly coupled tran~former’~] for all positions of the differential capacitor. Thus,

E, = -Ela/(l - a)

and a/( 1 -a) is the transformer’s turn ratio. A variation is shown in Fig. 2. T h e lower resistor is a potentiometer

with the center connector grounded. The admittance matrix of the network is given by

1 - a

1 - a

DIFFERENTIAL C A M I T O R DIFFERENTIAL C A M I T O R

- R

tl k

Fig. 2. Current transformer.

Hence I, = Ila/(l -a). An alternate connection is obtained when the input and ground are interchanged. Then the - R is connected to ground.

D. HAZONY School of Engrg.

Case Western Reserve University Cleveland, Ohio 44106

REFWENCES ~‘~P.M.LmandB.J.Leon,“Canwn~on‘Idcaltraosformcrrralizationswithncgativc

‘z’V.Cimagalli“Onthcstabilityofi~trandormcrrraliza~ns~withactiveekments,”

[’I D. H m y , Elements of Network Synthesis. New York: Reinhold 1963, ch. 6.

resistors’,” Roc. IEEE(L.etters), vol. 55, pp. 84-85, January 1967.

Proc. IEEE(Lrrrers), vol. 55, p. 1236, July 1967.

Low Aging Quartz crystal units A b s t r a e r - A w n p c e a s i s d e s a i b e d r r h e r e b y q m u t z a y s t . l ~ I r e

T h e e r p W b l r n l r s ~ m o r t e d b y m e r a p o f g o k l r i v e t s a n d p h t e d ~

ayst.lmitsisdemolrstrrtodrt62MHz~.gig~tesbebrrf5~10-’~ perweekdQvaIaesof#10000areobtakd.

S i d c a n t progress has been made recently in fabricating VHF quartz crystal units with superior aging performance. Initial results indicate that it is possible to consistently obtain AT quariz resonators operating at 62 MHz whose aging rate is less than 5 x per week. These units exhibit no observable frequency offset or transient drift after interruption of oscillation and/or operating temperature. Their quality factor at 62 MHz is in the range of 200 OOO.

Modern crystal units for frequency control purposes in the MHz range consid’) of disks of crystalline quartz that have metal electrodes deposited on their major surfaces and are supported inside an enclosure by means of wires or ribbons attached to their circumference; the enclosures are hermetically sealed in a vacuum or inert gas atmosphere. The resonance frequency of these crystal units is subject to changes in the course of time, a phenomenon called by the generic name “aging.”

Among the many conceivable causes of aging [21*131 we considered two to be the most important, aside from leaks in the enclosure, and we made fairly elaborate efforts to suppress them and their effects to insignificant

V H p e m b d t ~ p h t o d , d S e a l e d d W h g ~ d t B e s l u n e ~ ~ C y d e .

copper.Theperiorrmrncepoterti.idthereslJtmg”~”d~free”

Manuscript received November 9,1967. Manuscript received Octoba 10,1967; misd December 1 I , 1967.