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Патент USA US2137867

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Nov. 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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