9IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS AND CONTROL INSTRUMENTATION, VOL. IECI-17, NO. 5, AUGUST 1970

Design Criteria for DC Switch with Resonant

Circuit Connected Between ThyristorsIOAN I. PONNER

Abstract-Based on an analysis of the circuit by Gentry et al. [13,a generalized design diagram is presented for determining optimumvalues of the L-C commutating circuit components of a dc switch witha resonant circuit connected between thyristors.With this diagram, values for the inductor and commutating ca-

pacitor can be selected that minimize component size and cost forgiven values of thyristor tum-off time and peak load current.

JN a previous work [1 ] a simple resonance-commutateddc switch was presented (Fig. 1). With T1 conducting

and T2 in its off state, voltage is applied to the load, and ca-pacitor C charges to E (positive on left-hand plate) throughL and R2. When T2 is triggered, C reasonantly dischargesthrough T2, L, and either T1 or D1. When the discharge cur-rent exceeds the load current through Ri, it reverse-biasesT1 and continues its discharge by passing through D1 and T2.The resonant discharge current of C through L reverses

the charge on C but is prevented from further oscillationby Di and T7, which now block in the forward direction.Load current through R1 drops to zero, except for the induc-tive load current which can decay through D3 by free-wheeling action. T2 now delivers power to R2, a resistancethat can be selected for low power dissipation or can actas an alternate load. When T1 is again triggered, T2 isturned off by the series resonant discharge of C in the oppo-site direction to that described previously.Assuming no resistive losses in the resonant discharge of

C, the capacitor current may be expressed as

Fig. 1. Dc switch with resonant circuit connected between thyristors.

'/0

it?~~~~~~~~~t

A91_

z~~~~~~~~~~/\w~~~~~~~~~~~8

/,a4 I0

mf .m . _

(1)C ti, = E sin vL

The circuit turn-off time tc, considered as the length oftime that the capacitor discharge current exceeds IDJ themaximum load current through R1 is

IL]tc = \ C -2 arcsin (2)

Definirng a parameter k as

k = IV E C (3)

where I, is the peak discharge current through C, for thecircuit constants L and C results in the following:

kID [1r-2 aresin i7k(

Manuscript received September 22, 1969.The author is with the Department of Applied Electronics, Poly-

technic Institute of Bucharest, Bucharest, 1Romania.

Fig. 2. Diagram for calculation of L-C pair and product LC.

and

C kIDtc r

E-_E -2 arcsin 1/k- (5)

From (4) and (5) an infinity of pairs can be found thatwill result for a desired value of t, with given values of IDand E, the parameter being k.

It is of interest to optimize the L-C pair in terms of min-imum component sizes and costs for a given application.

394

ns IftO

SIETRAN&ACTION5 ON INDUSIAL ECTRONICS AND CONTROL INSTRUMENTATION, AUGUST 1970

Forthispurpose, taking into account that E/ID R1, (4) The parameter k-and (5) may be written in the form

.a L/R1 1t - k(7r - 2 arcsin l/k)

. and

R1C kI0 t, ir- 2 arcsin l/k

Multiplying (4) with (5) results in

LC _tC2

1(7r - 2 arcsin 1/k)2

In Fig. 2 (6)-(8) are plotted as a function of parameteFrom the plots R,C/t0 and (L/R1)/t, versus k for a ginload R1 and thyristors, the values of the L-C pair maycomputed.The plot of R1C/t, versus h; for k = 1 and k = tei

to infinity and, for k = 1, 35 has a minimum value. Corquently, k = 1, 35 represents an optimum value ofparameter k regarding the minimum value of the capaciC.

395

defines the relative value of the peakdischarging current of capacitor C versus the peak of loadcurrent. This discharge current adds to the current of turn-

(6) ing-on the thyristor, constituting a supplementary stress-ing of this thyristor. For this reason low values of the pa-rameter k are desired.The LC product and consequently the plot LC/t,2 versus

k can provide an image of sizes and costs of circuit param-(7) eters for a given application. In Fig. 2 it is seen that LC/t,2

falls very rapidly for increasing values of k in the range1 < k < 3. For k > 5, LC/t02 is approximately constant andtends asymptotically to 1/Xr2 - 0.1.From the foregoing remarks on the plots represented in

(8) Fig. 2 it is shown that it is probable, for most applications,that the optimum value of the L-C pair will correspond to

r k. the k parameter values comprised in the range 2 < k < 7.ven It is however necessary to resort to trial and error proce-be dures to determine the component values that will result

in minimum total size and cost for any given application.ndstse- REFERENCESthe [1] F. E. Gentry, F. W. Gutzwiller, N. Holonyak, Jr., and E. E. vontor Zastrov, Semiconductor Controlled Rectifiers: Principles and Appli-Hcations of p-n-p Devices. Englewood Cliffs, N. J.: Prentice-

Hall, 1964, pp. 282-284.

Contributors.

Gerald Cbok (S'60-M'67) was born inHazard, Ky., on Oc-tober 31, 1937. He re-ceived the B.S. degreefrom Virginia Poly-technic Institute,Blackburn, in 1961and the Sc.D. degreefrom MassachusettsInstitute of Technol-

ogy, Cambridge, in 1965, both in electricalJ ;; 02-engineering.

From 1965 to 1968 he was on active dutyin the U.S. Air Force assigned to the F. J.Seiler Research Laboratory at the U.S. AirForce Academy, Colorado Springs, Colo.His research there was in control theory andaircraft evasion tactics. He has held facultyappointments with Colorado University,Boulder, and the Air Force Academy. He ispresently an Associate Professor of Electri-cal Engineering at the Unoersity of Vir-ginia, Charlottesville, and a Consultant toMelpar and Philip Morris.

Dr. Cook is a member of Sigma Xi, EtaKappaNu, and Tau Beta Pi.

Leonard H. Lees was

born in Birmingham,England, on Septem-her 19, 1941. He re-

ceived the B.Sc.,M.Sc., and Ph.D. de-

grees in electrical en-

gineering from theUniversity of Astonin Birmingham, Bir-mingham, England,

in 1965, 1966, and 1968, respectively.During 1965-1968 he was a Research

Assistant at the University of Aston in Bir-mingham. From 1968 to 1969 he was a Sys-tems Analyst with Computing Devices ofCanada, Ottawa, Canada. He currently is anAssistant Professor of Electrical Engineer-ing, University of Windsor, Windsor, Ont.,Canada. His research area of interest is inthe application of modern control theoryto the solution of practical industrial prob-lems.

Dr. Lses is a member of the Institution ofElectrical Engineers (London) and is a

Registered Professional Engineer in theProvince of Ontario.

-~Satish C. Moh]eji(S'67-M'70) wasborn in New Delhi,India, on August 16,

___ ~~1940. He received theB.E. (Hons) degreefrom the Universityof Bombay, Mahar-ashtra, India, in 1962and the M.Eng. de-gree from Nova Sco-

tia Technical College, Halifax, N. S., Can-ada, in 1967, both in electrical engineering.He is currently working toward the Ph.D.degree at the University of Windsor, Wind-sor, Ont., Canada.From 1962 to 1964 he was an Assistant

Engineer with World Wide Engineers andDodsal Pvt. Ltd., New Delhi. He alsoworked as an Electrical Engineer withStandard Elektric Lorenz A.G., Stuttgart,Germany, in the area of computer control.Mr. Mohleji is an associate member of

the Institution of Electrical Engineers(London) and a member of the Associationof Professional Engineers of the Province ofOntario.