# Патент USA US2137867

код для вставкиNov. 22,‘ 1938. H. WESSELS 2,137,867 CASCADE AMPLIFIER-CIRCUIT WITHOUT UPPER HARMONIGS Filed Feb. 24, 1956 A ‘ A Iv INVENTOR HERMAN” WESSELS ATTORNEY patented Nov. 22, 193g 2,137,867 UNITED STATES PATENT OFFICE 2,137,867 CASCADE AMPLIFIER CIRCUIT WITHOUT UPPER HARMONICS Hermann Wessels, Berlin, Germany, assignor to Allgemeine Elektricitatz Gesellschaft, Berlin, Germany, a corporation of Germany Application February 24, 1936, Serial No. 65,246 In Germany March 5, 1935 1 Claim. (Cl. 179—171) As is known, nonlinear distortions in trans mission systems of any type can be compensated in that a system presenting upper harmonics is so connected with a second system having upper harmonics that the upper harmonics compensate each other. To this end, to a tube circuit a sec ond tube circuit may for instance be connected which contains a tube whose characteristic rep resents the mirror image of the characteristic of 10 the ?rst tube, or two tubes having the same char acteristic can be used whereby however the‘ cir cuit must be such that the input voltage of the second tube is displaced in phase at 180°. The invention is based upon the last men tioned suggestion. Previous attempts have been made in producing such a circuit, but it was thereby assumed that the characteristic of the tubes used would always follow the same mathe matical law, and that furthermore almost the same working point would have to be chosen, 20 and that ?nally the quotient of load resistance and internal resistance of the ?rst tube would have to be lower than that of the second tube. The invention is worked out with particular regard to the teaching that it is of ?rst im 25 portance to compensate the second harmonics and that the higher harmonics can by additional consideration in the choice of the working point, be easily reduced to such a value that they no longer disturb the transmission. 30 The single ?gure of the drawing shows a two stage ampli?er of conventional type (although it will be understood that the invention is not lim ited to a particular number of stages) which may 35 be operated in accordance with the invention if the steepness and the coupling organs are so chosen that the following equation will be ful ?lled: Tlsz 40 Ra). ions and to utilize the end tube as favorably as possible, the equation assumes the following sim pli?ed form: isiii-Rmsrn (1+Rn) R111 It is obvious that a proper tities involved will result in tion, and it will be shown satisfying of this equation choice of the quan satisfying this equa— further on that the is the condition for eliminating second harmonic distortion in the case where the last tube’s impedance is matched by its load impedance. In contrast to this con clusion, it was thought in the prior art that in order to eliminate second harmonic distortion in a circuit of the type here considered it would be necessary to sacri?ce a proper matching of the impedances of the load and of the last tube. Very small upper harmonics can thereby be maintained inasmuch as the working point of a given tube characteristic can be so selected that the expression T becomes as small as possible. The drawing shows a circuit of a cascade am pli?er in accordance with the invention, in con nection with which the above stated relation will 25 now be derived in detail. At the grid of the ?rst tube a purely sinusoidal voltage is assumed namely: ug1=Ug1 sin to t, ' (1) it being the instantaneous value of grid voltage, 30 and U being the amplitude. from which follows the resulting control voltage expressed in terms of the instantaneous grid voltage, plate resist ance and load resistance: ‘ 35 (2) _ RaisiTz — Roz 2 (bl-E5) 1+R1'2) wherein S is the steepness; T, the differentiation of the steepness with respect to the control po 45 tential; Ra is the load resistance of each tube; and R1 is the internal resistance of each tube. Index I designates the respective constants of the ?rst tube and index 2 the respective con stants of the second tube. In matching the end 50 tube with the consumer in order to avoid re?ex It is this voltage list which when multiplied by the steepness S, commonly called mutual con 40 ductance or transconductance, gives the alternat ing plate current. For thechosen working point of the ?rst tube there follows: ia1=f(ust1) :f(Ustl sin to t) (3) In developing the Equation (3) according to Tay lor’s theorem (see Barkhausen “Lehrbuch der Elektronen Roehren” 2nd volume, “Verstaerker”, 4th edition, page 57, Formula 51) there will be 2 2,137,867 obtained by neglecting the D. C. portion and the quantities of an order greater than the second order: tential "M2 by the second tube will be separately treated according to the parts ug2 (w) and ugz (2w) in the following course of the calculation. For the part ug2 (w) there follows analogous to Equation (7): 1 -———5U,2 (“92 cos 2 w t 10 mental for the plate resistance Ral. (10) 10 1 _"zT1Ustl is the amplitude of the ampli?ed second har whereby according to Equation (9) 15 monics related to the plate resistance Ra1='0. Since however, at ?nite R31 an anode reaction occurs also for the second harmonics, the actual ly appearing amplitude of the second harmonics (Barkhausen pages 58-59) is: 20 _1___ <1+ o 5g} _ . . . (11) Rn The amplitude of the plate current of the sec ond harmonics produced in the second tube by the fundamental wave ugz ((0) will be according in which case Ral designates the plate resistance Ia2(2w/w)=—§siT2-——~—Rm 2 Ruz 3oz, . ..(1z) (1+R?><1+R1-2> 25 for the second harmonics, and which in the case of alpur‘ely'ohmic eoupling,»is equal to the plate resistanceof the vfundamental wave. Thus for the actual plate current ?owing through re sistor Rn there is: ia1=S1Usl1 sin OJ t“ flT1U.2u—1'—“ cosZwt-l4 ‘(1+ 111*) Rzl U01 to Equations (10, 11): <1 + Rn) t Ua<w>:—s1—R;+— ...(6) For the grid voltage part use (201) represent~ ing the second harmonics, substantially only the linear ampli?cation need be considered since owing to the'smallness of this part, the higher 30 harmonics determined thereby are of an order that 'is smaller than the second order. There fore, for the ampli?cation of 'llg2 (2w) an anode current is obtained: According to Equation ‘(2) there is: i?(2w)=s2—-11—2—2~U,2(2w) cos 2 m t . . . (13) 1 (1+1?) ' so that according to Equation (9): and hence ‘according to Equation (1) : Ug2(2w)= 1M 2 40 *4 (1+5???) ' ' ' (1+Rn) 59-1 3 ond harmonics produced in the second tube by the second harmonics ugz (2w) , will be in accord ance with Equations (13) and (14): gt} 3 Ra! (1 + Rn) This equation represents ‘the anode current in The alternating grid potential of the second tube ‘ugz is given for R,,))Ra1 by the equation: (8) and'i'in co'nsidering’the Equation ('7) it is given 60 by the equation: R0151 IazCZw)=Ia2(2w/2w)+Ia2(2w/w)= ,, Ra 4 ' (1+R“>(1+’~‘"—2 R51 Rm ————————T‘S’ . . . (16) wane) Rn 60 Riz Due to the phase displacement of 180° between the two parts Iaz (2w/w) and Ia2(2w/2w), also in dicated by the different "signs of the amplitudes, the second harmonics of the plate current can be V65 “(Ht-1) i‘T lR111 U;1 — ————-—12S1—2-f——§+ ‘ U”; sin w H 50 From Equation (12) and (15) there follows for the resulting amplitude of' the second harmonics of the plate current 1'32: produced by the grid potential UgI made to disappear. This occurs when the quan tity -in the brackets becomes ' equal to zero in llazmw) "The alternating grid potential ugZ forms two parts, namely the fundamental wave given by 14;: (w) ‘and the second harmonics represented by 114%2 (2w). 75 'RaZ (1+Rn> (Li-R12) 50 40 The amplitude of the plate current of the sec By inserting this value in Equation (6) the equa tion reads: 70 (14) ,1 . . . The ampli?cation ‘of the alternating grid po other words the'following condition of the in vention is ful?lled, namely: (17) This condition'will in general be ful?lled for 70 3 2,137,867’ the disappearance of the second harmonics of a resistance-capacity coupled cascade, ampli?er. In matching in accordance with a further feature of the invention, the output of the cascade with the consumer the Formula (1'?) assumes the sim pli?ed expression: 10 (Hit-I) ‘4 coupling resistance Ra1 in the anode alternating current path of the ?rst tube, a second tube cou pled to the ?rst tube and fed with the entire voltage developed across said coupling resistance, (18) a load resistance Raz in the anode circuit of the second tube, the resistance Ral satisfying the equation As tests have shown, an ampli?er circuit can be produced by the use of the idea of the in vention which has a noise factor of less than 0.05%. The direct grid potential which deter 15 mines the working point and hence the steepness S may in this case even ?uctuate within the limits of :5%, a tolerance not even utilized in ordinary grid batteries. The application of the invention moreover, is 20 not limited to the circuit shown in the drawing. In like manner it may be utilized also in cas cade circuits with more than twov tubes. What I claim is: A cascade ampli?er comprising a ?rst tube, a Fur thermore, two cascades as shown in the ?gure may abo be combined to a push-pull circuit. ' T152 __ RnsfTz Ral R412 a 10 (We) (as) where S1, S2 are the rates of change of plate cur rent with respect to grid voltage of the ?rst and second tubes respectively, T1, T2 are the rates of change of S with respect to grid voltage of the ?rst and second tubes respectively and Ru, R12 are the internal plate resistances of the ?rst and second tubes respectively, whereby the 20 output of the second tube is substantially free of second harmonics of the signals applied to the input of said ampli?er. HERMANN WESSELS.

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