DETECTING EFFICIENCY OF THE RESISTANCE- 
 
 CAPACITY COUPLED AMPLIFIER 
 
 TO 6000 METERS 
 
 DISSERTATION 
 
 SUBMITTED TO THE BOARD OF UNIVERSITY STUDIES 
 OF THE JOHNS HOPKINS UNIVERSITY. 
 
 IN CONFORMITY WITH THE REQUIREMENTS FOR THE 
 DEGREE OF DOCTOR OF PHILOSOPHY. 
 
 BY 
 W. G. BROMBACHER 
 
 BALTIMORE 
 1922 
 
DETECTING EFFICIENCY OF THE RESISTANCE- 
 
 CAPACITY COUPLED AMPLIFIER 
 
 TO 6000 METERS 
 
 DISSERTATION 
 
 SUBMITTED TO THE BOARD OF UNIVERSITY STUDIES 
 OF THE JOHNS HOPKINS UNIVERSITY. 
 
 IN CONFORMITY WITH THE REQUIREMENTS FOR THE 
 DEGREE OF DOCTOR OF PHILOSOPHY. 
 
 BY 
 W. G. BROMBACHER 
 
 BALTIMORE 
 1922 
 
<"* 
 
[Reprinted from THE PHYSICAL REVIEW, S.S., Vol. XX., No. 5. November, 
 
 DETECTING EFFICIENCY OF THE RESISTANCE-CAPACITY 
 COUPLED AMPLIFIER TO 6,000 METERS. 
 
 BY W. G. BROMBACHER. 
 
 SYNOPSIS. 
 
 Detecting Efficiency and Current Amplification of the Resistance-capacity Coupled, 
 Two-tube Amplifier. Test of Hulburt's formula, giving a relation between detecting 
 efficiency and the constants of the tubes and circuits, has been extended to 6,000 
 meters. The detecting efficiency is defined as bo/A 2 , where A and bo are the ampli- 
 tudes, respectively, of the input grid potential and of the rectified component of 
 the output plate current. It was found that (i) for any wave-length the relation 
 between 60 and A 2 is linear; (2) for constant wave-length, bo/A 2 varied with the 
 coupling capacity in accordance with the formula within about 10 per cent., being 
 practically constant for capacities greater than 200 /z^ F; (3) for constant capacities, 
 bojA 2 varied with wave-length for ranges 1,100 to 2,500 and 2,500 to 6,000 meters in 
 fair agreement with the theoretical curve. The current amplification, n = bo/Eg*, 
 where Eg is the amplitude of the potential impressed on the grid of the second 
 tube, was found to be independent of the wave-length to 6,000 meters. 
 
 Plate current of vacuum tube (Radiatron UV 201) was found to be sensitive to the 
 external temperature. 
 
 i . INTRODUCTORY. 
 
 The detecting efficiency of the, resistance-capacity coupled electron 
 tube amplifier has been discussed by E. O. Hulburt. 1 He derived a 
 formula which indicated the connection between it and the constants of 
 the electron tubes and the coupling circuits. His experiments showed 
 that the theoretical relation held in the region from 400 to 1,600 meters. 
 
 The detecting efficiency was defined by the relation lim - a , in which 
 
 A-+oA Z 
 
 A and 60 are the amplitudes, respectively, of the input grid potential 
 and of the rectified component of the output plate current. 
 
 Consider the high frequency amplifier of two tubes as shown in Fig. i . 
 
 1 PHYS. REV., 18, 165, 1921. 
 
 Fig. 1. 
 
 543906 
 
1 [SECOND 
 
 434 W. G. BROMBACHER. [SERIES. 
 
 For this type of amplifier Hulburt derived the following formula, subject 
 to the conditions that there be no rectification in the first tube and no 
 grid filament current in the second tube 
 
 gs) 
 
 in which ^4 is the amplitude of the radio frequency potential impressed 
 on the grid of the first tube, b is the rectified component of the resulting 
 radio frequency current in the plate circuit of the second tube; k is the 
 amplification constant of the first tube. r\ is the internal resistance of 
 the first tube from filament to plate. C 5 is the filament-grid capacity of 
 the second tube. Resistances r% and r$ and capacity 4 are as shown 
 in Fig. i. 
 
 Let co/27r be the frequency of the impressed voltage. 
 Let 
 
 - = gi, o>C 4 = X t , 
 ri 
 
 - = gi, wC 5 = X 6 . 
 r<i 
 
 i 
 
 - = g3, 
 
 r 
 
 One term has not been defined, which is 
 
 n "W 
 
 where E Q is the amplitude of potential impressed on the grid of the 
 second tube, n does not depend on the frequency of the impressed 
 voltage. (See Fig. 6.) 
 Let 
 
 gigs x&f, = a, 
 
 Xi(g2 + gs) + X b g 2 = b. 
 
 Then, more accurately, the formula may be written 
 
 a(a + gig 3 ) + b(b + x^ -+ 
 
 It is to be noticed that this formula gives the detecting efficiency in terms 
 
VoL.^XX. j DETECTING EFFICIENCY OF AMPLIFIER. 435 
 
 of the constants of the electron tubes and the coupling circuits. Also 
 Formula (i) is an approximation of (2), the use of which is justified under 
 obvious conditions. 
 
 The object of this paper is to make the experimental measurements 
 necessary in order to test Formula (i) for long wave-lengths, and to this 
 end measurements were made from 1,000 to 6,200 meters. 
 
 2. APPARATUS. 
 
 The apparatus consisted of a condenser potential divider, the amplifier 
 and a D'Arsonval galvanometer. The arrangement is essentially that 
 of Fig. i. The potential divider consisted of the coil L, the Weston 
 thermo-galvanometer T, and the condensers Ci, C 2 and C 3 . This appa- 
 ratus has been previously described by Hulburt and Breit. 1 The poten- 
 tial impressed on the grid of first tube may be found from 
 
 A ___ 
 " 
 
 C 2 + CiC 8 + C 2 C 3 ) 
 
 in which I is the effective current measured by T. By coupling L to a 
 suitable electron tube generating set, unmodulated high-frequency voltage 
 of a small known amplitude and frequency was impressed on the grid of 
 the first tube. The high-resistance leak r$ was connected across C 2 to 
 insure a definite value of the grid potential during the experiment. 
 The effect of r upon the impedance of C 2 was negligible because C 2 was 
 large (either .05, .1, or .2 MF) and the frequencies used were of the 
 order of io 5 . 
 
 The amplifier was a two-tube one with resistance capacity coupling. 
 The tubes were General Electric Company tubes, Radiatron type UV 201 ; 
 they were used with the filament current of .94 ampere and had a 
 common plate voltage supply of 52.3 volts. Separate storage cells 
 supplied each filament. The plate current was found to be sensitive to 
 external temperature changes, an effect explained, perhaps, by the 
 fluctuation in the amount of the absorbed gases in the glass walls of the 
 tubes. It was therefore found necessary to enclose the electron tubes in 
 covered cardboard tubes in order to keep their temperatures constant. 
 The plate battery was shunted by a 1.75 MF condenser C&. The re- 
 sistance r 2 was 115 X io 3 ohms and r 3 was 360 X io 3 ohms. The 
 resistances r , r 2 and r s were non-inductive, being of the type described 
 by Hulburt. 2 These were found to give satisfactory service. The value 
 of the resistance for high-frequency currents was assumed the same as 
 that measured with direct current. 
 
 1 PHYS. REV., 16, 274, 1920. 
 
 2 Loc. cit. 
 
43 6 W. C. BROMBACHER. 
 
 The change in the value of the rectified high-frequency component of 
 the plate current of the second tube of the amplifier, designated by b , 
 was measured by a D'Arsonval galvanometer, G, Fig. I, connected 
 across a resistance r 4 placed in the plate circuit. r 4 was 60,000 ohms. 
 The galvanometer had a resistance of 9.0 ohms and a sensibility of 
 5.8 X io~ 8 amperes per millimeter deflection on a scale 125 cms. distant. 
 PI and P 2 , Fig. i, were potential dividers, PI serving to keep the plate 
 voltage at the desired value, and P 2 to compensate for the potential drop 
 in the resistance r 4 so that the galvanometer rested approximately at 
 zero. When the grid voltage of the first tube was changed, a deflection 
 of the galvanometer resulted which was proportional to the change in the 
 rectified high-frequency component of the output plate current. 
 
 It was important that the filament currents remain constant. Any 
 change in these currents resulted in a shift of the operating point of the 
 tubes. The electron tubes were seasoned before every series of readings 
 until a reasonably constant condition of filament current and electron 
 emission was reached. In order to eliminate the error due to the usual 
 slow drift of the galvanometer, the two zero readings were averaged. It 
 was found that the grid leak r gave a constant potential of nearly zero 
 on the grid of the first tube when its value was 246 X io 3 ohms. This 
 value was not critical. For large values of r Q , the value of the grid 
 potential shifted when it was necessary to vary the value of C 3 . A 
 Kolster decremeter, calibrated by the Bureau of Standards, was used 
 to determine the wave-lengths of the high-frequency current. 
 
 3. VARIATION OF COUPLING CAPACITY. 
 
 The reading of the coupling condenser C 4 was varied at each reading, 
 a number of input potentials were impressed on the grid of the first tube 
 and the corresponding galvanometer deflections were noted. From the 
 reading of T, the thermo-galvanometer, and a knowledge of the capacities 
 Ci, Cz and 3, the amplitude of the change of the input grid voltage A 
 was computed, using formula (3). Three sets of readings were taken, 
 at wave-lengths 1016, 3070 and 6235 meters. The resulting curves 
 with b the ordinates and A z the abscissa, are shown in Figs. 2, 3 and 4. 
 It can be seen that for each value of C 4 for all three wave-lengths the 
 b A z curves are straight lines. This fact has been established by a 
 large number of similar curves, not shown here. The curves for any one 
 wave-length are plotted from data taken with the potential divider 
 condensers C 2 and C 3 held constant. A change in the value of C* 3 caused 
 the curve for any particular value of C 4 to shift and also to change its 
 slope. This is shown in Fig. 3 by the curve marked 628'. This fact 
 
VOL. XX 
 
 No. 
 
 DETECTING EFFICIENCY OF AMPLIFIER. 
 
 437 
 
 ZOO 
 
 400 I0" ! 
 
 feOO 
 
 Fig. 2. 
 
 Fig. 3. 
 
 can be explained by a shift in the operating point of the first tube because 
 of a shift in the normal value of the grid potential. r had the value 
 
 20C 
 
 50 100 150 . 10' 
 
 A z - VOLTS 2 
 
 Fig. 4. 
 
 13 X io 5 ohms during these readings. Another point of interest in these 
 curves is that the straight lines do not pass through the origin, although 
 
438 
 
 W. G. BROMBACHER. 
 
 [SECOND 
 [SERIES. 
 
 within the limit of experimental error they pass through a common 
 point on the A 2 axis. This seems to indicate a constant error in the 
 determination of A 2 although a check up of the calibrations revealed no 
 differences large enough for compensation. It is also of interest to notice 
 that for each wave-length there is practically the same current range 
 (&o) but that there is a large range in the value of A 2 - for 1016 meters, 
 .006 to .015; for 3070 meters, .002 to .005 and for 6235 meters, .0006 to 
 .0015 volt 2 . 
 
 The main fact, however, remains that the straight lines were obtained, 
 as is predicted by formula (i). 
 
 In order to further test formula (i) the slopes of the curves corre- 
 sponding to each value of 4 were determined and then plotted against 
 values of C 4 for each of the three wave-lengths as shown in Fig. 5. That 
 
 
 40 
 
 20 
 
 10' 
 
 3070 
 
 1016 
 
 .C4 . 
 
 200 400 MM F 600 
 
 Fig. 5. 
 
 is, experimental values of b /A 2 are plotted against values of C 4 . Then, 
 from formula (i) the theoretical value was computed. Values of the 
 constants not before given, r it the direct-current filament to plate re- 
 sistance of the first tube, was 60 X io 3 ohms; C 5 , the filament-grid 
 capacity of the second tube, was 18 MMF. This was measured in its 
 socket and included the capacity of its lead wires, which were short, 
 however. As neither n or k were determined experimentally, the com- 
 puted curve was made to coincide with the experimental curve at C 4 
 
VOL. XX. 
 No. 5. 
 
 DETECTING EFFICIENCY OF AMPLIFIER. 
 
 439 
 
 equal to 628 MMF. The computed curves are the broken lines. While 
 the agreement between the experimental and computed curve is not 
 exact, it is quite satisfactory, revealing no marked differences in behavior 
 for two of the wave-lengths considered, while for wave-length 3,070 m. 
 the agreement is good. 
 
 No change in the character of the computed curve was found whether 
 formula (2) or its approximation (i) was used. 
 
 4. VARIATION OF WAVE-LENGTH. 
 
 The coupling capacity C was kept at its maximum value of 628 MMF, 
 ro, r 3 and r 4 remained at their former values of 115 X io 3 , 360 X io 3 and 
 60 X io 3 ohms. A series of readings were taken so that the variation 
 of detecting efficiency with wave-length could be determined. The 
 experimental results are given in the full line curve of Fig. 6. 
 
 80- 
 
 40.10" 
 
 0- 
 
 o 
 
 2000 
 
 GOOO 
 
 METERS 4000 
 Fig. 6. 
 
 As the curve connecting the square of the input grid potential and 
 the rectified component of output plate current does not pass through 
 the origin, a series of readings was taken at each wave-length, a curve 
 drawn and the slope determined. This slope is bo/A 2 . The experimental 
 curves just mentioned were straight lines within experimental error. 
 
 In order to keep the grid potential of the first tube constant for the 
 entire range of wave-lengths used, it was found necessary to fix its value 
 near zero, which was done by making TO equal 246 X io 3 ohms. This 
 was tested by obtaining the deflection of the galvanometer when the 
 condenser C 2 was short circuited, there being no high-frequency current 
 in the input circuits. This test was made when the condensers C\ and 
 Cs had values corresponding to the range of wave-lengths used. 2 was 
 0.2 MMF throughout the run. 
 
 The computed curve, shown dotted in Fig. 6, was made to agree with 
 the experimental curve in the neighborhood of 2900 meters. It was 
 
44-O W. G. BROMBACHRR. 
 
 computed from formula (2), as the approximate formula (i) differed 
 with it over the range of wave-lengths computed. 
 
 The agreement of the two curves is substantial above 2,500 meters, 
 and, it is believed, would be even better, if the apparatus had been 
 used with better control over the grid potentials. The poor agreement 
 at lower wave-lengths is due to the difficulty of keeping conditions 
 constant for the entire range of observations. An unpublished curve, 
 detecting efficiency against wave-length, for the region between 2,500- 
 1,100 meters gives a straight line of about the same slope as the theoretical 
 curve. This is in agreement with the straight-line relation obtained by 
 Hulburt between 600-1,600 meters. Thus, the simple theory under- 
 lying Hulburt's formula is in agreement with experiments thus far made. 
 
 It is seen that the detecting efficiency at higher wave-lengths (lower 
 frequencies) becomes independent of the wave-length. 
 
 5. AMPLIFICATION. 
 
 It was necessary to test the independence of n with respect to wave- 
 length. By definition 
 
 where b is the rectified component of the output plate current and E g 
 is the amplitude of the potential variation on the grid of the second tube. 
 
 In order to measure n the input voltage was impressed directly on the 
 second tube, the first tube being disconnected, and the output plate 
 current was found for a series of wave-lengths. As before, sufficient 
 observations were made for each wave-length so that a curve could be 
 drawn and the slope determined. The slope was bo/E g 2 . The curves 
 so determined were straight lines, n was found to be sensibly constant 
 for all wave-lengths as is shown in Curve 3, Fig. 6. 
 
 If the ordinate of Curve I be divided by the ordihate of Curve 3 at 
 the same wave-length, both of Fig. 6, the quotient is the amplification 
 of the current obtained by the use of the amplifying electron tube. 
 That is, the quotient gives the number of times the rectified component 
 of the plate current, b , is increased by the use of two tubes instead of 
 one. The quotients, or current amplifications, are the ordinates on the 
 right margin of Fig. 6. If telephones are used the sound intensity 
 amplification is proportional to the square of these numbers. 
 
 This problem was suggested to me by Dr. E. O. Hulburt, now at the 
 State University of Iowa, who derived the formula underlying the 
 investigation. 
 
 JOHNS HOPKINS UNIVERSITY, 
 June, 1922. 
 
BIOGRAPHICAL NOTE. 
 
 William George Brombacher, son of Henry and Elizabeth (Case) 
 Brombacher, was born in Cleveland, Ohio, February 23, 1891. He 
 received his early education in Chicago High Schools. In 1915 he re- 
 ceived the degree of Bachelor of Arts from Lake Forest College with 
 Shield Honors and in 1917 the degree of Master of Arts from the same 
 college. The year 1918 was spent in the United States Army, stationed 
 at the Bureau of Standards. Upon leaving the army joined the Bureau 
 of Standards staff. 
 
 In the fall of 1919 he was entered at the Johns Hopkins University 
 as a graduate student and as an instructor in Physics. He followed the 
 courses of Professors Ames, Wood, and Pfund in Physics, Professor 
 Murnaghan in mathematics and Professor Reid in Geophysics. 
 
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