US2284855A - Amplifier circuits - Google Patents

Description

Jun 2, 19,42. Y J, M, WEST I 2,284,855

AMPLIFIER `,CIRCUITS I I mieu Aug'. 1e, A193s;

BV J."

ATTQNEV Patented June2; 1942 t .A s r UNrrEos'rA'n-:s y PATENT i OFFICE f ammira cmcurrs Julian` West; RidgewoodrN. J.. assigner` to Beil Telephone Laboratories, Incorporated, New York, N. Y., a corporation of New York l Application August 16, 1939, Serial No. 290,354 l 8 Claims. (Cl. 179-111) I This invention relates to amplifier circuits shift as to bring about phase coinciderwe the and more particularly to negative feedbackamfeedback voltage is equal to or greater than the plifiers so designed as tovbeeifective over a wide effective input voltage the amplier is unstable band of frequencies. VIt f object is to provide but if the feedback voltage is less than the input for al high and `uniforminternal lopor ,le voltagathere is no instability. An` exceptional gain over the `whole bando! frequencies to be u case is illustrated in Nyquist Patent 1,915,440 of transmitted whilestill maintaining a` substan- June `2'1, M1933. 4However, the type of stability tial margin of safety against singing` More spe therein disclosed is not absolute and such syscically the invention relates to so modifying tems tend to become unstable when the amplithe cut-off characteristic on the lower side of l0 iler gain islreduced. lo

a band to be transmitted with a negative feed- To insurel complete stability of the `amplifier back amplifier that the gain around the feedagainst singing it is, therefore, necessaryito so` back loop has a high value over a band to be proportion the different parts of the circuit that transmitted and u falls to less than unity before before the condition of phase coincidence is a phase shift is introduced which would pro-l5 reached, the feedback voltage shallhave been duce singing. l attenuated to a value less than the effective The benefits to be derived from the use of feedinput voltage. This requirement may `be exback are described in an article by H. S. Black. i pressed in terms of certain 4transmission on Stabilized feedback amplifiers," Bell System A parameters of the circuit as follows: If the volt- Technicai Journal, January 1934. y Principal age gain or transfer ratio from the input to the among these benefits are the stabilization of the output of the amplifier be denoted by a and v effective amplification inthe presence of variathemvoltage transfer ratio ofthe feedback path tions of the energizing potentialsl applied tothe inthe reverse `direction by then the vector amplifier vacuum tube and the diminution of the ratio of the feedback voltage to the resultant effects of non-linear distortion. Thesebeneiitaz input voltage on the amplier is equal to the l are obtained when the magnitude and phase of product m3 where a may have a large value the voltage feedback to the amplifier input are over a wide portion of the frequency spectrum. such as to produce a diminution ofthe effective For complete stability, however, it is necessary amplification, and the extent to which thebenethat the magnitude of the a become less than fits' are" realized is substantially proportional to l0 unity before its phase angle becomes Zero. the amount by which the amplification is diL The vectorquantity n the real part of which minished is hereinafter called the loop gain, deflnesthe p `The degenerative action is provided by so denetl change in amplitude and phase experienced signingLthe amplifier andthe `feedback circuit by a voltage wavein traversing .the ampliner that, when .thefrequency 'has some convenient` 85 and the feedback path in sequence. This change value near the middle ef the desired operating is made up essentially of `two parts, rst a conrange, the effective input voltage is in exact stant` amplification and aconstant phase shift phase opposition to the feedback voltage. The representing the effect of the amplification faceffective input voltage is reduced in comparison tors of the vacuurntubes and, second. a variable with the voltage from thelnput wave source and 40 ldiminution of the amplitude and a variable the amplification of the system is diminished in phase shift representingthe transmission loss in proportion; As the'y frequency departs from this the passive networks of the system. Since the `near mid-point value the phase of the feedback part contributed by the vacuum tubes is convoltage changes progressively until at some frestant, all of the `variation of a is represented by quency, usually outside the operating range, it the variation. of the transmission loss of the pascomes into phase coincidence with the effective sive networks. -These passive networks include, input voltage. At this point the amplifier mayA of course, notonly the circuit from the output become unstable andI develop oscillations. This of the last stage to the input of a previous stage is most likely 'to occur at frequencies above the but include also the passivecoupling and other operating range but if suitable precautions have networks associated with and between the tubes been taken to-avoid this then it" may occur at `of the amplier. ysome 'frequency below the operating range. By using pure resistances for thefeedbaclr Whether the circuit develops oscillations or not v and coupling networks it would be possible theodepends `upon the relative values or the reed- "retically to make up constant in both ampliback and the input voltage.` If with such phase tude and phase at all frequencies and thereby off range and by the rate provide for any desired amount of feedback and an unlimited operating frequency range. In practice, however, this is impossible because of the presence of unavoidable parasitic reactances in the system. At high frequencies these parasitic reactances consist primarily of shunt capacitance, such as those Within the tube, or of series inductances; and at low frequencies they consist primarily of` series capacitance and shunt inductances. At very high .and very low frequencies these parasitic reactances `become the sole factors determining the magnitude and the variation of the feedback and are generally productive of phase changes suciently great to cause instability. To avoid this it is necessary that the magnitude of the feedback should be reduced to less than unity before the limiting frequency ranges are reached and suitable frequency intervals must be allowed for this reduction.

It is desirable that the cut-o ranges in which the magnitude of the feedback is systematically reduced should be as small as. possible in order that the greatest operating frequency range may I be conserved. It can be shown that the phase shift component of a is greatly influenced by the course that its magnitude follows in the cutat which the magnitude diminishes. In the amplifier of this invention the Ydiminution of a is made to follow certain preferred courses which represent optimum characteristics in the sense that they permit Vthe use of maximum amounts Voi? feedback and vinvolve the minimum loss of useful frequency range while at the same time insuring complete stability against singing.

The invention will be better understood by reference to the following specification and the accompanying drawing in which:

Fig. 1 is a simplified diagram of a circuit incorporating my invention;

Fig. 2 is a detail of part of the network of Fig. 1;

Figs. 3 and '4 show curves which will explain the manner in which the inventionv is carried out; and

Fig. 5 shows a modified circuit my invention.

'I'he general theory underlying the behavior of such circuits as are shown in Fig. 1 is set forth in some detail Ain the patent to Bode 2,123,178 of July 12, 1938, and need not be included here. The invention therein disclosed is of a broad nature and in one of its specic forms illustrates the design of a feedback circuit which will appreciably improve the 'cut-off characteristic on i the upper side of the transmitted band while still maintaining a safe margin against singing. In this invention the purpose is, specifically, to im; prove the cut-off characteristics on the lower side of the transmitted band without deleteriously affecting the upper limit and while still maintaining the margin of safety against singing.

One of the advantages which I find accruing from the redesign of the a network in accordance with my invention is a large reduction in the size of some of the elements associated with this circuit This is particularly true of the so-called blocking condensers between adjacent tubes, these in some instances being reduced by a factor of as much as 100. This reduction not only contributes to economy of cest and economy of space, but also contributes to a reduction of the parasitic capacities effective for the high fre- A including the output transformer T2.

quencies which are inherent to a greater or less extent in such circuits.

As pointed out in the patent to Bode and elsewhere above it is essential that the phase shift through the a circuit shall not-exceed 360 degrecs. Since for an odd number of amplifier stages, such as in Fig. 1, there will be a net phase change of 180 degrees due to the amplifier tubes themselves, it is evident ,that the phase shift over the passive networks of the a loop inust not be allowed to exceed 180 degrees as long as a is greater than unity. The extent to which it falls below this at any frequency is a measure yof the margin againstI singing at that frequency. A full understanding /f'of the behavior of a given circuit requires then, among other things, a knowledge of the a gain around the lo'op and a knowledge of the phase shift both as functions of frequency.

In the circuit of Fig. 1, there are shown three stages of amplification, with the usual batteries omitted for simplicity, and associated with the three tubes are cathode networks Z141, Zxz, Zka. primarily for establishing a self-bias. There are also the load circuits Zrl, Zig, ZB, the latter also There are condenser-resistance coupling between stages I and 2, between 2 and 3 and between 3 and I, the

incorporating f last constituting essentially the or feedback circuit. 'I'he load circuits are shown asresistive with a resistance-condenser filter, all well known in the art, but it is to be understood that these may take on the form 'of any suitable impedance.

At any one frequency one may find the insertion loss due to each of these networks and find the phase shift due to each network. The total loss, preferably expressed on a decibel scale. and the total phase shift due to the passive part of the a circuit will be the sum of these. If this shift is near to but below degrees, then one may set the total gain due to the tubes equal to the total loss of the coupling and other networks at that frequency so that the net gain around the loop at this `frequency is equal to unity. If for any frequency the shift is substantially below 180 degrees then the gain may be correspondingly raised and the amount of feedback correspondingly increased, that is, the insertion loss due to the passive networks may be reduced. However, such a change usually brings in an additional change in phase so that the permissible increase in gain is limited. It is essential that at no part of the frequency spectrum where the phase shift due to these networks exceeds 180 degrees shall the magnitude of a exceed unity.

While the three coupling circuits are shown as much the same as condenser-resistance combinations they will, in general, be of different impedance. In this figure, moreover, it will be noted that one of the couplings, namely, that between stages I and 2, has the resistive portion made up of two series resistances R1 and Rz, the latter of which is shunted by a condenser C2, these being proportioned as will be described below, the combination and proportioning in this coupling being illustrative of and constituting an important part of my invention.

For a better understanding of the ideas underlying this invention reference may be made to Fig. 2 showing a four-terminal network corresponding to the coupling circuit just mentioned. If e1 is the impressed and e2 the output voltage or attenuation or the sent Rn byk KRi.

` -Timpedanc'e of cois `will beteken; for illustrative purposes, i

y virtuallyshorted by cz so that proaches curve B;

increase the Amere increase assaut network and this will be a function of frequency. Thisattenuatlon may conveniently be expressed in .decibels by using the logarithm of the `real part of e/ei in the relation.

in the higher frequencies, `but a substantial decreaseat the lower frequencies. In fact, it can be shown that the area si for the regionv of increase of phase lshift taken to infinite frequency is equal to thearea s: for the region of decrease of phase shift taken to zero frequency.

also in the analysis of the network it will be convenient `to express Ri in terms of an arbitrary unit such that R1 is taken as unity and to repre- It will also'be convenient to express he. impedance of" the `condenser c1 in terms of a referencecapacitance' `co whose impedance at areference frequency fo-is" I n "JmT-T TJRI (2) Then at any other frequencyttaking Ril, the

The capacitanceof cz representedby a c KCI For K=0` (resistance=`R1 and cae- 0l theattenuation is `given by curve A of Fig. 3. FOLK- #4,

but still keeping cz=0, the attenuationisdecreased, the curve beingshifted toward :lower frequencies as` shown by `curve"B. If, on the other hand, the grid leakis" made upof Brand KRi, the latter shunted by capacitance cz, then theattenuation curve` may `with proper proper-- tioning take the forrmof curveC. "l'hisl is evibd It is this phenomenon that I use in my invention.v The delay in building up of phase shift as one goes'` to lower frequencies permits a substantial increase in" the attenuation` before the critical phase shift of 180 degrees is reached.

This in turn permits allarger amount of gain by by means of the tubesandthusalarger value of ,iover the transmission band, there still being a fall in `value Df'ap toless than unity; before a phase shift of ldegrees is brought about; `x Y i By direct transfer from the set of phase shift to the set of attenuation curves of Figii (for which s2-Kila) one an readily, for any assumed :value of "phase` shift f a single coupling network of this` type, plot acurve showing thefamount of lossdue to the network for different values of K .Such-.a curve is shown at D for m50 degrees and it'wiil. be observed that there is amaximum loss of about 17 decibels atx-:2.5 and thatthis ocours,=

at about 4Il now for a total 'maximum phase shift shift maybe pennitted in one of the coupling dent, for at highfrequencies the portion KRi is l the effective grid impedance is R1 and the attenuation is; relatively high. `As the frequency lowers, the impedance of ci increases, which would increase the attenuation but vthe impedance of. c: also increases,

thus retarding the increase of attenuation. llt"t 5 still lower frequencies the impedance` of ci be`- comes controlling and the attenuation curve apjf shown and inevery case it will be noted that the effect of ce is to decrease the slope of the' atten-` uation curve for the intermediate frequencies below that for whichcz is virtually a short circuit KRi. Other similar families of curves could be plotted for ether values of ci.

y r frequencies but at low becomes practically ineffective. At

*to only 4 decibels.

networks, then it, is seen from curve Dvthat the maximum insertion loss for such a coupling net- 'shows that the loss for =50`degrees, amounts Similar curves could be plotted for other values of o `and some of the results are tabulated below. .From this one obtains additional information for the design of the "amplifier circuits: i

Maximum Maximum K lossin lossior decibels lil-0 las n 4 60 1+ .21 e k 1 24 9 supplementing the theory presented inthe yBode patent referred 'to above, vit Vmay be here pointed out. `without derivation, that the expres- These changes in the'form of the attenuation curves are accompanied by `changes in the phase shift curves as shown in the upper portion of" Fig.` 3. Curves A', B and C' From curve B'lit is seen Y correspond to curves A. B andlC.

that themere increase of K (or, `equivalentlyy the.

of ci) -delays somewhat the build ing up of phase 'shift 'as one goes-'to` lowerifrequencies, but the form of .the curve is not altered. The addition of capacitancev c: correspondins to curves B and B brings about,

however,a substantial change in fom-characterized by a substantial inorease in phase shift ro to me circuit sionfor the a gain foi' the circuit of Fig. 1 inthe low frequency range where the high frequency parasitic capacities may be neglected is given by [1 +s..,zx, Saz" z.,+zv,+zi,]

` 1 cf` Z', 14+Sazzx, u I Ziff-Zefijzrs i of the combined passing networks ofless than degrecs it is agreed that 50 degrees of the phase t work will be `obtained for a value of X=2.5. A v comparison with the corresponding case czv--O finite and that the source of B supply is of zero impedance.

A convenient design procedure is to break this expression for ri into four factors as follows:

To a very close approximation this is the only significant term at the middle of the useful band of the amplifier. It, therefore, gives the nominal a gain. 'I'he use of condenser-resistance filters in the B supply leads causes this gain to rise a Y few decibels at very low frequencies. The effect of this factor on the p'gain of the circuit is shown by curve I of Fig. 4 plotted with reference to anominal gain of 40 decibels and against the logarithm of frequency.

This term represents the effect of the local feedback produced by the resistances used for selfbiasing the tubes. In general, this term contributes a major part of the low frequency cutoff. For example, with one type of tube known as Western Electric 7650P tube and the value of resistance to give the correct bias voltage, the gain is reduced 21 decibels at low frequencies by this factor. The effect of this factor on the a gain is shown by curve 2 of Fig. 4.

3 d I: l Z2 (6) r Z.,+Z..,+z., Z.,+Z,+Zp This term represents'the Veect of any two of Athe simple blocking condenser grid leak combinations. 'Ihe blocking condensers yare preferably made so small that this factor begins to reduce the a gain at the point where the 2nd factor becomes less effective. The effect of this factor on the a gain is shown by curve 3 of Fig. 4, reaching a slope of 12 decibelsper octave.

This term represents the effect of the remainin grid blocking condenser grid leak combination with shunt capacitance, the results being shown by curve 4 of Fig. 4 and corresponding closely in form to the attenuation curves of Fig. 3. It is this configuration that I find effective in the low In view of the delay in the building'up of the l phase shift which accompanies the introduction of the capacitance c2 it becomes evident that the condenser c1 may be substantially reduced without introducing an excessive additional phase shift. This is a marked advantage in that the A,use of a smaller condenser is cheaper and more economical of space, but still further because the reduction in the physical dimensions of the conper side of the frequency band to be transmitted. In practice I nnd that this capacity may be decreased by. a factor of as much as 10 or 100.

While the description thus far has been on the basis of altering the coupling network between stages I and 2 of Fig. 1, it should be pointed out that the total alteration desired may be accomplished at one step as described or may be distributed in any desired portions among the plurality of coupling circuits. Certain advantages would accrue from such distribution, for each of the blocking condensers could then be reduced with a corresponding reduction in parasitic capacities for high frequencies. On the other hand, it will be noted that such distribution will call for a larger number of elements, represented by the plurality of capacitances c2. Depending upon the circumstances, therefore, it may be advantageous in the one case to distribute the adjusting factors and in some other cases to conne it to one of the coupling networks. Also, while in the description the coupling network has been shown between stages l and 2 of Fig. 1, there would be certain advantages at times in placing it in one of the other positions. In some cases, for example, I would prefer to place it in the circuit representing the coupling between stages 3 and l (see Fig. 5). Such a location has a certain advantage for in general the impedance Z; in the output circuit would be small compared to Zrl and Zie. In that case the resist-ance R1 of Fig. 2 may be made appreciably smaller without this portion of the circuit acting as an appreciable shunt to Z.

Thus far in the description reference has been largely to pure ohmic resistances. Itis to be understood, however, that the impedances R1 and KRi of Fig. ,2, as well as the resistances of the other coupling circuits and of the loads, may be reactive. As a matter of fact, I nd it advantageous at times to include with R1 a suitable amount of inductive reactance as shown in Fig. 5. The principles described above hold equally well and the application of the invention to any one i particular case would then involve the plotting of attenuation and phase shifting curves which involve more, but only slightly more, labor.

What is claimed is:

1. A wave amplifying system comprising a plurality of vacuum ltube amplifying devices, impedance networks coupling said devices in tandem,.a feedback path coupling the output circuit of the last of said tandem connecteddevices with the input circuit of the first of said devices and an impedance network included in said feedback path, said impedance networks each comprising a plate circuit branch and a grid circuit branch,

said networks having a combined attenuation which is substantially constant and small relative to the combined gain of said amplifying devices at frequencies in an assigned operating range, which increases with the decrease'of frequency just below said operating range, and which has a progressively changing phase as the frequency is still further lowered, means for delaying the building up of phase shift with decreasing fre- .quencies said means comprising capacitance denser c1 reduces its capacity to ground, which f latter contributes tothe parasitic capacitiesat high frequencies. favorably on the 'cut-olf characteristic at the up- Thus the combination reacts shunting a portion of the grid circuit branch of l one of said coupling impedances, the magnitude of the.'y capacitance being such as to delay the building up of phase shift with decreasing frequencies until a frequency-level is reached at which the net gain around the feedback loop is less than unity.

2. A wave amplifying system comprising a pludem. a feedback path -of the two condensers being necting said grid leak impedance said amplifier loop circuit,

. 2528455 rality of vacuum, tube amplifying devices, im-

pedance networksv coupling said devices in tancoupling the output circuit of the last of said tandem connected devices with the input circuit of the first of said devices l and an impedance network included in said feedback path, said impedance` networks having a combined attentuation which is substantially constant and small relative tothe combined gain of said amplifying devices at frequencies in an said given frequency decibels per octave of frequency until the loop gain attains negative value not greatly different from zero, and said portioned to diminish the loop gain at a rate between zero and 6 decibels per octave at still lower frequencies for a short frequency interval whereby the total loop phase shift is held substantially different from zero at the frequency of zero assigned operating range and -which increases as l,

the frequency decreases below said `operating range, the rate of increase of attenuation being at first increasingly high near the operating range,v then low at lower frequencies, and then high at still lower frequencies. j i

i 3. A negative feedback ampliner comprising a plurality of amplification stages andl a feedback path around said stages for feeding back waves in gain reducing phase within a transmission frequency band. condenser grid between two `leak resistance coupling network across the resistthe transmission said amplifier including a stopping Y stages, the stopping condenser being i of such magnitude as to produce substantiallyl i no reduction of its capacity such band but toreduce this ratio rapidly below the i transmission band, a condenser shunting a por-` tion of the resistance and of such magnitude as to substantially short-circuit the portion of resistance for frequencies inthe transmission band butto permit substantial increase of the transfer ratio at lower frequencies, the combinedeffect the transfer ratio for the rst two octaves of frequency below the transmission band but to reduce it at a much lower rate for the nextfew octaves and then to lower frequencies.

. 4. Arioop circuit discharge devices, one cathode, and the other having a grid and a cath# ode, connections for feeding waves put of the device, and means for coupling the anode and cathode of said one device to the grid and cathode of said other device, said means comprising an impedance connected between the plate and the cathode of said one device, a stopping condenser and a grid leak impedance connected in series across said first impedancefmeans conbetween the grid and the cathode of said second device, and a condenser shunting `a impedance and having as to increase the phase said` loop against singing its capacity value such below an operating to `rapidly reduce reduce itrapidly for still other deviceto the input of said one decibel loop gain, at least one of said networks comprising a stopping condenser and a grid leak impedance including in` series a resistance and a parallel combination of a resistor and a condenser.

6. An amplifier comprising `three cascaded stages of vacuum tubes forming a closed feedback loop with each 4interstage circuit including a coupling network comprising a stopping condenser and a grid leak impedance, in the case of each coupling network said grid leak impedance comprising in series a resistance and a parallel combination of 'a resistance and a shunting condenser, said shunting condenser having the value as to increase at least several fold in comparison with conditions in the absence of the shunting condenser the decibel value reached by the insertion loss of the coupling networkbefore its phase shift exceeds 60 degrees with` diminishing frequency below the operating frequency range of the amplifier. Y.

7. In a negative feedback amplifier including a plurality of stages with a feedback path for feeding waves from the output to the input in gain reducing phase throughout an operating frequency range, and including interstage networks of said leak resistance, said shunting capacity,

Y said grid leak resistance, the portion of said reportion of said grid leak margin of stability of frequency range for which` transmission around the loop has` a terially reducing said range.

5. A wave amplifying system comprising an electric space discharge amplifier,` a feedback path extending betweenthe output and forming therewith a closed frequency selective impedance networks included in said loop circuit, saidnetworks being `proportioned to provide in` combination with the gain of the amplifier a relative large loop gain at frequencies `above a given frequency van to diminish the loop gain at frequencies below substantial gainV without mathe gain around the loop and input of i the series coupling sistance that is shunted by said capacity, and i capacity connected to said last-mentioned impedance branch being proportioned with respect to one another to cause said interstagenetwork to have increasing attenua- -tion with decreasing frequencies near the lower edge of the operating frequency range to a much higher value of attenuation than would be attained without said shunting capacity, before the phase shift produced by said interstage network has reached 60 degrees and to delay increase of said phase shift above 6,0 degrees with further decrease of frequency until the attenuation has attaineda still larger value.

8. Thecombination of claim in which said shunting capacity, said grid leak resistance, the portion of said resistance that is shunted by said capacityl and said series coupling capacity are proportioned with respect to one another to cause said phase shift produced by saidv interstage network to have approximately the constant value of 45 degrees over a range of low frequencies and to cause the attenuation to increase with decreasing frequency within said range of low frequencies by a factor of more than 2 to 1 on a logarithmic scale.

JULIAN M. WEST.

, 5 at a rate between 6 and 12` networks being further -pro

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