UNIVERSITY OF MICHIGAN ENGINEERING RESEARCH INSTITUTE ELECTRONIC DEFENSE GROUP TECHNICAL MEMORANDUM NO. 12 SUBJECT: Report on Induced Grid Noise Measurements BY: T. E. Talpey DATE: July 16, 1953 Introduction This report contains a description of the method used to measure induced grid noise, a table showing typical magnitudes of noise likely to be found in modemrn miniature receiving tubes and a discussion of the application of this data to the design of low-noise amplifiers. In- addition, a description is included (with photographs) of equipment constructed for the measurement of fnoise at 30 mc. W,4ith the exception of a few minor changes and the addition of some data to Table I, this report is identical with Chapter IV and Appendices II and III of a thesis written by the author.*- The bibliography of the complete thesis is included for convenience, although only a few of the references are cited in this report. 1. Method of Measurement The most convenient method of measuring fluctuation noise at the frequencies employed in this study (30 mc.) is the use of a comparator diode: the noise to be measured is compared with the shot noise o: a temperature-limited diode. Fig. 1.1 presents a block diagram of the * "A Study of Induced Grid Noise" by T.E, Talpey. This thesis was submitted by the author to the University of Michigan in partial fulfillment of the requirements for the Ph.D. degree in electrical engineering and is available on microfilm.

-2apparatus employed and Section h contains a detailed description of the actual equipment. 7b l l r= | iEc e 73'ts rridb Io rE/4P. - Figure 1.1. Block diagram of the apparatus used for noise measurements. The tube to be tested (in this case the grid of the tube to be tested) is connected to the input of a high-gain, low-noise amplifier, with a very narrow bandwidth. The plate of the noise diode is also connected to the amplifier input terminals. The fluctuation currents produced by these two tubes flow through the input circuit of the amplifier and produce noise voltages which are then amplified and detected, the response of the detector giving an indication of the amount of noise present at the amplifier input. The actual process of comparing the diode shot noise with the noise to be measured is complicated somewhat by the fact that the amplifier contains several additional sources of noise which must be taken into account. Before developing the equations employed in computing the unknown noise of the tube under test, a few remarks are necessary concerning the overall characteristics of the measuring system. It is knoswn9 that the mean square noise current generated by a

-3temperature-limited diode is given accurately by the following equation: i2 = 2eIAf (1.1) up to frequencies at which the transit angle of the diode approaches one radian. The measurements reported here were made at a frequency of 30 mc., for which the diode transit angle is only about one-tenth of a radian. In Eq (1.1), e is the change on an electron, I is the d.c. current of the diode, and Af is the bandwidth. The detector used for these measurements was a crystal operating at a very low level (below one micro-ampere))and it was expected that its characteristic would be very nearly square-law; Eq (1.1) tells us that if the amplifier is linear we can expect a plot of crystal current vs. diode plate current to be a straight line. This provides us with an accurate check on the operation of the complete system, including the microammeter used to measure crystal current. Fig. 4.9 of Section 4 shows that we are completely justified in assuming that the reading of our output meter is linearly related to the mean square fluctuation current flowing through the input circuit of the amplifier. The basic principle by which measurements are made of the unknown noise of a tube under test is as follows: The increase in the reading of the output meter is noted when the source of noise to be measured is turned on. The unknown noise is then turned off and the diode turned on and adjusted so that it produces the same increase in output The diode plate current, through Eq (1), then gives us-a measure of the noise current introduced into the circuit by the tube under test. Unfortunately, this process has to be modified slightly because of the

fact that changes in the admittance of the input circuit occur as the tube under test is turned on and off. In order to develope a quantitative relationship for the unknown noise of the tube under test it is necessary to consider in detail the input circuit of the amplifier and the noise sources connected to it. Fig. 1.2 shows the equivalent r.f. circuit at the input terminals of the amplifier, the various noise sources being represented by current and voltage generators. The following notation has been used: it2 mean square noise current introduced into the circuit by the tube being tested, Gt conductance added to the circuit when the tube under test is allowed to draw plate current, id = mean square noise current produced by the temperature-limited diode = 2eIA f i~t - mean square noise current produced by the input circuit conductance, G = conductance produced by transit-time loading at g the grid of the input tube of the amplifier, eeq = mean square noise voltage representing the effect of shot noise at the plate of the input tube of the amplifier 2eI 2 f =.kTReA f =. gm

Figure 1o2. Equivalent r.f. circuit of the amplifier input. The noise voltage appearing at terminals 1- 1 is amplified by the system and the output of the crystal detector is proportional to e112, that is: K Iout el (1o2) This equality is based on the assumption, discussed above, that the overall system has a square-law characteristic. Noise coming from other sources in the amplifier has been neglected as it is very small and also would be found to cancel out in the derivation which follows. With the amplifier operating alone (diode turned off, tube under test biased beyond cut-off) the reading of the output meter, Il, is given by the following expression: K = = (i7 + i)(Gc + Gg)2 + eq2 2(13) The voltages are added by their squares since the noise sources are inde

-6pendent of each other, with the exception of one component of ig2 which is in quadrature with eeq2 and hence adds as a square also. It is assumed in writing Eq (103) as well as the equations to follow that the input circuit is tuned so that there is no susceptive component in the input admittanco., This is accomplished by peaking the output by means of a small variable capacitor connected in parallel with the input circuit. Actually this adjustment is not too critical because the bandwidth of the input circuit is much greater than the remainder of the amplifier. With the amplifier and the diode operating, but with the tube under test still biased beyond cut-off, the reading of the output meter, I2, is given by: K 12 3 ell2 = (ic2 i 2 + 2eI Af) (Gc *Gg)2. eeq2. (1.4) When the diode is in operation:a small additional conductance is introduced in parallel with Gc and Gg, but this added conductance is so small compared with the sum (Gc * Gg) that it can be neglected. When the diode is turned off and the tube under test is turned on, the output becomes: K *3 (i2 + i2 it2) (G G G Gt)2 e2(15) 3 c g t c g t eq' The operation of the tube under test introduces a conductance Gt which usually cannot be neglected, A change in the input tuning capacitance is also necessary because of the change in input capacitance of the tube under test when its grid bias is changed, The bandwidth of the input circuit is also changed somewhat by the addition of Gt, but

since the bandwidth of the remainder of the amplifier is so much narrower this change does not appreciably alter the overall bandwidth of the system. Finally, with the complete circuit in operation, tube under test, diode and amplifier turned on, the output becomes: 2 2 g+ 2.(1.6) K. 14 (ic g2 it2 2eI'Af) (Gcg + 2eI f) ( G Gg + Gt)2 + eeq It is convenient to carry out the measurement procedure in such a way as to make 14 = 2I3 and I2 = 2I1. This makes the diode current I' in Eq (1.6) greater than the current I in Eq (1.4). The difference (I' - I) is denoted by&I. The simultaneous solution of Eqs (1.3) to (1.6), plus the substitution of the equation for eeq2 enables us to obtain the unknown noise current it2, and the unknown conductance Gt, in terms of HI and several other easily measured quantities. We thus obtain the formulas necessary for the experimental testing of tubes. i t2 2e(I) (f) + 4kTReq(Gc + G )2(l -o) (1.7) Gt = (Go + Gg) 1 (1.8) where I I( P 1 x -x (1.9) I3 I" The second term on the right in Eq (1.7) is considerably smaller than the first and can be considered essentially a correction term. When the unknown fluctuation current is realtively large, as for example when measurements are made of shot noise, this correction term can be neglected entirely. For the measurement of grid noise, however, it is usually necessary to include it. In computing its magnitude the quantity / is obtained from experimental data, the factor (G + Gg) is easily

-8measured with a high-frequency bridge, and Req can be estimated (or measured) with accuracy sufficient for such a correction term* It must be remarked that the measured input conductance, Gt, of the tube under test cannot be taken to be the input damping due to transit time ef2fcts. Small residual inductances in the leads of the tube together with inter-electrode capacitances cause the total input conductance to be greater than that due to transit time alone. Fortunately, these lead inductances have negligible effect on grid noise so that Eq (1.7) still remains valid. Bakker3 discusses the justification for neglecting the effect of lead inductance on induced grid noise and it is discussed quantitatively in Section 5 of this report. The poirt to be made here is that the application of Eq (1.7) wil1 enable us to determine the noise current induced in the grid circuit by the tube under test, but that Eq (1.8) will not yield the correct value of transit-time conductance. The separation of total input conductance into components due to transit time and lead inductance effects is not a simple task. The reader is referred to a paper by Strutt and van der Ziel49 for a discussion of this problem. 2. Measured Values of Induced Grid Noise In presenting the results of the measurements outlined in Section 1.1 we are forced to choose between a direct presentation of it2, which has the advantage of clarity, and an indirect specification of, for example, an equivalent noise temperature or an equivalent noise conductance, which are more convenient from a design engineer's point of view, Many articles in the literature com3erned with grid noise specify the equivalent plate current of a temperature-limited diode which would produce a

-9fluctuation current equal to it2o This seems to the author to be a fairly good compromise between the two points of view. The theoreticians need simply multiply the equivalent diode current by 2eAf to obtain it2 and the design engineer can use the factor 2 — to obtain the equivalent noise cond'. -L-tance, The factor is approximately equal to 20 2kT for normal room temperature. It should be emphasized that the equivalent grid-noise conductance is not the same as the transit-time conductance which loads the input circuit. The ratio of equivalent grid-noise conductance to transittime conductance is equal to the ratio of equivalent grid-noise temperature to room temperature, For many engineering design problems this ratio can be taken roughly as five, (Cf. North and FerrisS) For reasons outlined above the value of each experimentally determined mean square grid noise current is presented here in terms of an equivalent temperature-limited diode current, denoted by Ido It is calculatedbyrdividing Eq (1.7) by 2eAf, giving: Id =AI (G2 c Og)2(1p) (2-1) A summary of measurements made of the induced grid noise of several miniature tubes is presented in Table I. In come cases it was possible to measure a great many tubes of a given type; for other types only a few tubes were compared, The number of tubes examined, the average grid noise, the lowest and highest noise found in each group, the plate current at which the noise was measured and the (measured) equivalent shot noise resistance are shown for each tube type. All the measurements shown were made with a plate voltage of 150 volts and at a frequency of 30 mc. All the tubes were connected as triodes,

In addition there is a column in Table I labeled "Fopt"' indicating the lowest noise factor obtainable at 30 mc. from the average tube under the conditions of plate voltage and plate current shown. As discussed in the next section it may be possible to obtain a lower noise factor by the ue of a different combination of plate voltage, grid bias and plate current. However, the last column of Table I gives us a means of judging the merits of each tube for use in a low-noise amplifier. The method used in obtaining "Fopt"t in Table I is as follows: For the low-noise cascode amplifier it has been shown2 that the optimum value of source resistance, giving the lowest noise factor, is given approximately by: Rs - 1 (2.2) opt -- / The use of a source resistance of this amount leads to an optimum noise factor 2 i 2 F = 1 +.. (2~3) opt 2kT fgm 2 2 The factor i P' might be called a figure of merit for the tube gm with respect to its noise factor. The lower this ratio the lower the noise factor can be made. This gives us a basis for comparing tubes as to their performance in a low-noise cascode amplifier. In drawing up Table I measured values of ip2 ig2 and gm of a tube fitting the "average" column were used in conjunction with Eq (2.3). A few remarks are necessary concerning the accuracy of the data in Table I. The equivalent diode currents were obtained essentially by

TABLE I MEASURED VALIUES OF -INDJCED GRID:) NOISE5,AT?'30 mc. Induced Grid Noise Plate Equivalent TransconEquivalent diode current Current Shot Noise ductance Tube Number Id, in microamperes lb Resistance gm Fpt Type Examined Average Lowest Highest in ma. ReL in micromnhos 6AG5 21 7.1 5.6 7.8 7 480 6000oo 1.52 6AK5 30 2.3 1.8 2.9 10 460 5500 1.29 6AS6* 4 2.3 2.1 2.6 10 45o 5800 1.29 6AU6 17 10.6 9.2 12.7 12 420 6600 1.60 6BC5.6 6.5 6.o0 7.1 8 590 5800 1.56 6BH6* 3 11.2 10 6CB6* 10 8.7 7.2 9.7 12 410 7300 1.54 6J4 2 10.0 15 321 12, 000 1.51 6J6** 10 3.b 2.1 4.1 8 720 4400 1.42 2C51** 8 2.0 1.9 2.3 8 550 5400 1.30 404A 9 306 3.4 1.8 15 240 16,000 1.27 * Suppressor Connected to plate and screen, ** Values are for a single section. Caution: The values given in this table, while representative, should not be considered universal. When measurements are taken on only a few tubes of each type, it is quite possible that the average of such a small number may not represent a ture average of overall production.

measuring the difference,AI, between two diode currents, In many cases this difference was rather small, amounting to two or three microamperes out of about fifteen or twenty. The meter used to measure these currents was carefully calibrated beforehand to an accuracy as close as the scale could be read, fnl o microampere, Taking the worst possible cases, where the meter readingl- was in error by 0.1 microampere in one direction for the first reading and the same amount in the other direction for the second reading, the possible error inmAI would be 0.2 microampere. This would lead to an error of 10 percent for an equivalent diode current of 2,0 microamperes. The errors in Table I from this source are less than this amount, however, for the data presented here represent averages of a number of measurements on each tube. In addition, for most tubes the value of AI is larger than that assumed in the above calculation, making the percent error smaller. Besides the error introduced by uncertainties in the readings of the diode plate current meter there is an uncertainty of about the same order of magnitude in the setting of the output current to double its original value. In order to apply Eqs (1.7) to (1*9) it is necessary to make 12 = 2I1 and IL = 213, as discussed in Section 1 1oo Our inability to do this exactly results in an additional source of error, We are aided somewhat in thisn respect byp the construction of the microamnetenr the range of the microammeter is changed by a factor of two by the same switch that turns on the noise-diode plate voltage, We are then able to adjust the diode current until the needle of the output meter rests at exactly the same spot on its scale while the diode is turned off and on and the microamnmeter range snimultaneously switched from LO to 0,5 micron

amperes. This procedure increases considerably the accuracy with which we are able to obtain the conditions I2 2I1, etc. The amount of error introduced by the attenuator associated with the range switch mentioned above is well below the magnitudes of the errors which have just been considered. The errors coming from nonlinearity of the measurement apparatus are likewise much smnaller than those arising from the reading of meters. (See Fig. 4.9 of Section 4) Taking into account all of the above considerations it is estimated that the probable error in the data of the "average" column of Table I ranges from about 10 percent for those tubes having small values of induced grid noise to less than 5 percent for those tubes having a large aemount of grid noise. This is well within the limits of variability indicated in Table I for all tube types and hence entirely adequate for design purposes. Any given tube may easily vary from the values given here by more than twice the probable error of the data in Table I. The variability between tubes of a given type is indicated by the "lowest" and "highest" columns of Table I. This variability is caused for the most part by slight differences in electrode spacings, alignment of grids, etc. A few tubes were found to have abnormally high grid noise due to the presence of a small amount of gas (as indicated by a small ion current to the grid) but these tubes were not included in tabulating the data for Table I. 3, Application of Measured Grid Noise Values to Amplifier Design Table I gives the value of induced grid noise to be expected from each tube type under the conditions of plate voltage and plate current

-14specified in the table and at a frequency of 30 mc. The voltage and current have been chosen to give typical operating conditions but of course any given amplifier will probably not be operating at 30 mc. A method is required for extrapolating the data of Table I to other frequencies. Theory predicts and experiments3 have shown that the mean square induced grid noise current varies as the square of frequency, as long as the transit angle is small. Thus to obtain the induced grid noise at any frequency we need only multiply the data in Table I by the square of the ratio of the new frequency to 30 mc. For example, the equivalent diode current for the grid noise of a 6AK5 at 100 me. is 1002 x 2.3 = 25.5 microamperes. 30 lie may also wish to extend the data of Table I to other values of plate voltage and plate current. This cannot be done with anything like the accuracy of frequency extrapolation, but it is possible to make some general predictions. For example, if the grid bias is held constant (at the value giving the plate current in Table I at a plate voltage of 150 volts) then the induced grid noise will not change appreciably as the plate voltage is varied, unless the voltage is made abnormally low.J This is illustrated by the lower curve in Fig. 3.1.

-1511_____.. I 1__ 30 2'x 10' r I RAISING Eb -., "I I" 1_ 0 2 4 6 _ 12 PLATE CURRENT IN MA. Figure 3.1. Mean sqquare induced grid noise current in (amperes)2 per cycle bandwidth vs. plate current for one -half of a 636 double triode at 50 mc. Upper.curve: Ab increased by reducing grid bias. Lower curve: b inc I I eas.'y increasing plte volt e. = -.9 v, an Eb - _ 100 v for both curves ~~~~~~~~- O. ____X[ 1t~Lll|L 111111111_I tI LI~ 2 4 6. 8' _I0 ___Tm 121111-n~~ 111111

-16If the grid bias and plate voltage are varied Simultaneously in such a way as to hold the plate current constant, then the induced grid noise wTill decrease witlh increasingly negative grid biases, as shown in Fig. 3.2. The accurate prediction of the magnitude of this reduction is rather difficult and not of enough practical value to warrant a detailed study. Fig. 3.2 indicates that for a given plate current (or transconductance) the tube should be operated with as high a negative grid bias and as high a positive plate voltage as possilcie without exceeding the plate dissipation rating of the tube. If the plate voltage is held constant and plate current varied by changing the grid bias a variation of grid noimsimilar to that shown in Fig. 3.3 a is observed. The same grid noise data is plotted vs. transconductance in Fig. 3.3 b. The exact calculation of induced grid noise by extrapolation from a given point on one of these curves is not possible, because the curves are widely different from one tube to the next —the bends

-17l: I' L. I _ _ _ _ _ _ _ _ __ _ _ T40x I 0'_ LFIL 1__ ____ ___T I II,,I II I I _I_ _I __4_1 30 J t., CONTROL-GRID BIAS VOLTAGE FiIgure 3.2. Upper curve: Experimental values of the mean square induced grid noise current in (amperes)2 per cycle bandwidth vs. controlp.grid bias for one-half of a 6J6 double triode at 50 mc, with constant plate current of 8 ma. The values are corrected for shot.noise in the dc grid current which occurred at low bias voltages. Lower curve: Values predicted on the basis of transit time theory, adjusted to mtch experiment at large negative biases. large negtive biases.

-18 — Ld JCr (a) (b) 16 S6 Figure 3.3. Typical plots of induced grid noise as a function of (a) plate current and (b) transconductance. The equivalent noise-diode currents (Id) for these curves were taken from measurements of the induced grid noise of a 6J6 at 30 mc. are in different places, slopes are not the same, etc. Far some tubes the curve of Id vs. gm turns out to be nearly a straight line and in these cases it might be possible to make some sort of a rough linear extrapolation which would be sufficiently accurate. In the majority of cases, however, the most that can be said is that grid noise increases with gi although not linearly. This fact has one important application in the design of lownoise amplifiers. It is sometimes stated* that the input tube of a lownoise amplifier should be operated with low grid bias and high plate current, in order to produce a high value of gm, For some tubes, and at low frequencies, this statement is correct, but in many cases it leads to a poorer noise factor than the optimum obtainable from the tube under *t See, for example, page 637 of Reference 6,

proper operatihg conditions.. The reason for this is quite simple: as plate current is increased (by reducing grid bias) the equivalent shot noise resistance, Req = g., decreases and induced grid noise increases, eq g M as shown by Fig. 3.3. If induced grid noise should increase faster than Rq decreases, -L-ihen a deterioration of the amplifier noise factor may result. For a 6AK5 operating at 30 mc. the induced grid noise is too small to cause any appreciable deterioration but for most other tubes and for the 6AK5 at higher frequencies the effect on noise factor is by no means negligible. Tests were made on the noise factor of a cascode amplifier at 30 mc. employing atriode-conrected 6AG5 input tube. Curves of noise factor vs. source conductance were made for a number of different grid biases and from these curarves the minimum obtainable noise factor was determined for each value of grid bias. Fig. 3.L shows the results of these tests, indicating the undesirability of operating the tube at maximm-plate current, The conclusion to be drawn from the above discussion is that a reduction of grid bias and the consequent increase in i will not always reduce the noise factor of an amplifier. If the plate current and consequently gm are increased by increasing the plate voltage,

-20Ao 4 6 / Plate Current, Ib' in Milliamperes Figure 3.4* Minimum noise factar as a function of plate current for a 30 mc. cascode amplifier employing a triodeconnected 6AG5 as the input tube. leaving the grid bias unchanged, then as shown by Fig, 3.1, there will be relatively little increase in grid noise and a lower noise figure will be obtained because of the reduction in Req. For example, referring to Fig. 3.4, if the plate voltage were increased 50 volts or so, the minimum of the curve would shift to the right and down slightly provided the grid bias were left unchanged. There appears to be an optimum combination of plate voltage and grid bias which will provide the lowTest possible noise factor for an amplifier. Unfortunately it is not possible to specify these operating conditions precisely forthoh they depend on characteristics of the circuit as well as the tube. Although the optimum operating point must ultimately be

-21determined by trial and error, the above comments should be helpful in predicting which changes can be expected to lead to an improvement in noise factor. The reader is referred to References 2 and 6 for more complete discussions on the characteristics and design of low-noise amplifiers...Descrintion of the Measurng Euipment This section presents descriptions and details of the circuits used in constructing the apparatus with which grid noise neasuremnts were made. The circuit represented by each of the blocks in Fig. 1.1 is presented and discussed, and the unusual features in its design and construction are pointed out. The circuit used to supply the required voltages to the tube under test is shown in Fig. 4.1. The terminal labeled "at' connects directly to the input of the amplifier described on succeeding pages. The heater conmctions are not shown —one side of the heater is connected to ground and the other connection is made through an r.f. filter to an adjustable source of heater voltage.

Figure h.1. Circuit used to supply operating voltages to tube under test. The capacitor C was made series resonant with its leads (by adjusting the lead lengths) in order to provide as good an r.f. shortcircuit as possible between plate and cathode. The capacitors labeled C are conventional by-pass capacitors (10000OOOOfd.). C2 is the coupling capacitor to the amplifier input —its nominal value is 560 ~sjfd. All capacitors are of the ceramic type. The inductance L is essentially an r.f. choke but it is wound so as to be self-resonant with its distributed capacitance at about 30 mc., thus increasing its impedance to r.f. currents. It is desirable to use a choke for the filter in the plate lead so that the plate voltage can be conveniently measured without connecting an additional lead directly to the plate. It is not necessary to use an inductance in the filter to the grid lead because no d.c. current flows in this circuit. Indeed, it is desirable to avoid the use of an inductance in this filter, for no matter

-23how carefully the plate and grid leads may be shielded there is always a possibility that a small amount of coupling could exist through the medium of a mutual inductance between the grid and plate chokes. In this event, any plate noise which succeeds in avoiding the by-pass capacitor C, would calesa some additional noise in the grid circuit, leading to experimental error s. The resistance R1 loads the input circuit of the amplifier and its effect must be taken into account in determining the magnitude of the correction term in Eq (1.7). It should be of relatively high resistance to avoid unnecessary loading of the amplifier input. The plate supply, Eb, and the grid bias supply, E c both contain milliammeters: one to measure plate current and the other to monitor the grid circuit for possible grid current which wouldi be indicative of a gassy tube. Such a tube would have abnormally large grid noise. Fig. 4.2 shows the circuit used for the standard noise generator. It is of conventional design and a complete description of the construction of a similar noise source can be found in Chapter 1l of Reference 6. The plate of the noise diode (point "al") isconrected directly to the input coil of the amplifier and the d.c. plate current of the diode flows through this coil. It is shown dotted in Fig. 4.2. The cathode of the diode is made negative with respect to ground since the plate is at d.c. ground potential. The diode (a Sylvania type 5722 noise diode) is operated temperature-limited and a simple measurement of its d.c. plate current enables us to determine the noise current added to the amplifier input circuit.

-24The filament current and hence the emission of the noise diode is varied by means of the resistance R in series Tudith the filament supply battery. This is a storage battery and arrangements were made to put it on "trickle" charge when not in use for noise measuremnts. The use of a transformer for the filament supply was found to be unsatisfactory because Xqi if &r COZ4 4,-= IuI' I I\ L 4A ij - Figure 4.2. Circuit of the noise generator. of variations in line voltage which could not be reduced sufficiently even when a constant voltage transformer was employed. It is necessary to carefully shield the circuits of Figs. L.1 and 4.2, as well as the input circuit of the amplifier to which they are connected. If even a slight amount of coupling should exist between the output of the amplifier and either of these circuits) regeneration could take place and produce disturbing effects on noise mrasurementso Fig. L.3 shows the shielding of thetube under test and the diode noise generator as well as the input circuit of the amplifiero The filters in the leads of the diode and the tube under test can be seen clearly and the input coil and neutralizing coil of the casode amplifier

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-26described below are also visible. The soc-keet for.t.he tube under test is mounted on a plate enabling it to be removed easily and replaced by a holder for a set of plug-in resistors for use in measuring the amplifier noise factor. Switches, controls and plugs for measuring currents and voltages are mounted on a larger chassis to which the two smaller ones shown in Fig, )4X are fastened, The ampifier used for the noise rreasurements reported here consists of a' cascode-input three-stage preamplifier coupled by a short coaxial link to a 30 mc. radar iif, amplifier, modified slightly to make it more suitable for the present application. The circuits of the two components are shown in Fig. 4.4. Since most of the circuit is conventional, only certain details are pointed out here, References 2 and 6 contain excellent discussions on the design, construction and adjustment of amplifiers of this type and the reader is referred to these references for further information pertaining to the circuit details. As indicated in Fig. 4.4 a small (ceramic) variable capacitor, Ct, is mounted in parallel with the input coil of the preamplifier. The sum of this capacitance, Ct, the capacitance of the tube under test and the capacitance of the preamplifier input circuit must be such as to resonate with the coil L1. If the capacitance presented by the tube under test should change then Ct will permit retuning the input circuit to the correct frequency, The output of the preamplifier is coupled by a short length of coaxial cable to the input of the modified radar i.fo amplifier, Most of the r.f. plate current of the final stage of the preamplifier flows into this coaxial cable and through the 50sohm resistor which terminates the cable. The voltage developed across this resistor is thy used to erxcite

-27the input tank of the i.f. amplifier. The use of coil LS, resonating with C5 plus the input capacitance, provides a step-up in voltage from the coaxial input to the 6AK5 grid~ The gainof the amplifier is controlled by varying the grid bias of the second t'o 6AK~ stages. As the grid bias is varied on either of these tubes their input capacitance changes, detuning the input circuit (coil L6 or L7). To prevent this variation in input capacity, part of the cathode-bias resistor is left unby-passed. The amount of unby-passed resistance to byused, 47 ohms, was determined by trial and error, observing the change in resonant frequency of the input circuit as the gain control was varied. In the development of Eq (1.7) for the measurement of induced grid noise it is necessary to assume that the bandwidth of the amplifier does not change when the tube under test is turned on and adds its input conductance to that of the cascode input circuit. In order to be certain that the bandwidth of the.complete amplifier remains the same regardless of tbe.loading of the input circuit, it is necessary to make the overall bandwidth of the amplifier less than one-half the bandwidth of the input circuit. With the input fed from a 50-ohm source the half-power bandwidth of the complete amplifier plus the detector circuit was found to be approximately 200 KC. Calculations showed that the bandwidth of the case code input circuit is greater than 500 KC for all possible corditions of loading so that the assumption of constant amplifier bandwidth is justified. The amplifier was carefully tested for evidences of regeneration sinceof the presence of evien a small amount of feedback to the input circute of the amplifier would be detrimental to its noise factor0 The importance

-28of avoiding feedback coupling to the circuits of the tube under test and the noise diode has been pointed out previously, but it is mentioned again here for emphasis. On the other hand, regeneration within the amplifier itself, if it is not excessive, willZ have no disastrous effects on the measurement of roise from the tube under test since noise from this tube and noise from the comparator diode are affected identically by such regeneration. The amplifier was tested for regeneration (1) by the temporary application of plate voltages considerably higher than normal while advancing the gain control as far as possible and trying to detect a tendency for oscillation, (2) by observing the plate current of the first stages while varying the gain control, and (3) by trying to detect changes in the conductance of the input circuit as the gain control was advanced. After considerable time spent shielding components, adjusting by-passes, filtering leads to common supply voltages, etc., regeneration was finally eliminated or reduced to negligible proportions. Subsequent

OAKS Co o 1/2 JO SC 0a_. -! _ (150LV + FIG. 4.4o. coscode preamplifier CISAKS SAKS CI AK C Or C 120 C'12TO 50..M 12 OXa C C IlL C - WO Lo TO FIG. 4.4b modified radar i.f. amplifier

-.30o i" measurements of the amplifier's noise factor bore out the conclusion of negligible regeneration by yielding results which were equal within experimental errors to the noise factor calculated from directly-measured values of grid and plate noise. In the original radar i.f. amplifier the coil labeled L8 in Fig. 4.4 was connected to the grid of the next 6AK5 stage. By designing an adapter wrhich plugs into the socket of this stage a simple means was provided for obtaining an output connection from the amplifier. The detector, whose circuit is shown in Fig. h.5, is actually built into this plug as close as possible to the amplifier output. The small 3^36W capacitor in Fig. 4.5, together with stray capacitance, resonates with the coil L8 in the anplifier, providing maximum signal for the detector. low'To I _tRO//#fUv7- J.3zutw4. C 4 4~ CIA Figure 4.5. Circuit of the detector built into the adapter plug sho-m in Figure 4.6.

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-3aFig. 4.6 shows the mechanical construction of the adapter plug: two capacitors, a coil and the crystal fit inside a brass sleeve which is soldered to the end of a shielded cable leading to the microameter. The large pin on thc end of the plug fits as a guide into the center hole of a miniature socket,and the small pin fits as a tube prong into the proper socket contact. The microammeter which is used as an output indicator is of a rather unusual type, consisting of a photoelectric tube mounted on a sensitive mirror galvanometer andoonnected in the feedback loop of a d.c. amplifier. Fig. 4.7 shows a photograph of the complete microammeter, including the galvanometer, phototube mount, amplifier, indicating meter and power supply. The sensitivity of this microammeter ranges from 0.5 to 10.0 microamperes full scale, depending on the position of the range switch. The advantages of this type of microammeter over an ordinary galvanometer are chiefly its rapid response and is extremely low input resistance. If the crystal detector istohave a good square -law response)it must operate into nearly a d.c. short-circuit and the device used here is ideally suited for such an application. The circuit described below has an input resistance of about 00.4 ohm. The electrical circuit of the microammeter is shown in Fig. 4.8. It consists essentially of a modification of the circuit shown on pace L90 of Reference 6 which also contains a discussion of the principle of oneration of this type of feedback system. The modification embodied in the

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circuit of Fig. 4.8 consists of the addition of a cathode follower stage to supply the current forthe feedback loop instead of obtaining this feedback directly from the plate circuit of the 6SF5. The additional stage was found necessary to insure good linearity for such a small full-scale current. The 920 phototube and the 6SF5 are mounted on the front of the galvanometer (see Fig. 4,7) and connected by a shielded cable to the remainder of the circuit. The operation of the circuit of Fig. 4.8 is as follows: the introduction of a small current to the input terminals results in a current through the galvanometer coil and deflects the light spot which is focused on the photoelectric tube. The phototube is of the differential type and the deflection of the spot causes more light to fall on one cathode than on the other. This causes a change in the grid voltage of the 6SF 5and hence a change in its plate current. This current change is amplified by the cathode follower and a small portion, determined by the range switch, is fed back to the galvanometer coil and used to counteract the effect of the original input current. Thus the light spot is kept focused on the phototube and the amount of current which must be fed back to keep it there is a measure of the input current which produced the original unbalance. The linearity of the complete system was tested by plotting a curve df output current as measured by the microammeter vs. the plate current of the temperature-limited diode. As discussed in Section 1.1 this plot should be a straight line if the amplifier is linear, if the crystal possesses a good square-law characteristic and if the microammeter is linear. That all of these conditions are satisfied for the apparatus

150V OOK 3. 5K o.,,4 INPUT 1800.r —----- I 6SF I 5K 4 5K 4-1 - I ur10.0 GALV. 1920 i s80of SWITCH i 4 7 1.0 IK I LAMPI,KOJL 47K 47K ICROAMMETER 0-100 Figure 4.8. Circuit diagram of the feedback microammeter pictured oin Figure 4..

-36employed here is clearly shown by Fig. 4.9. 4.2 o 20 40 60 80 / Diode Current in Microamperes Figure 4.9. The results of a linearity test on the complete measuring apparatus, The microanmeter output current is plotted as a function of the plate current of the temperature-limited diode.

-375. Justification for Neglecting the Effect of Cathode Lead Inductance on Induced Grid Noise The effect. of inductance in the cathode lead can be quantitatively investigated by reference to Fig. 5.1. A current i is assumed to flow in p the plate circuit and the grid current, ig produced by this plate current is calculated. The impedance of the tuned circuit connected to the grid is represented by R in Fig. 5.1, being a pure resistance when the circuit g is in resonance as assumed here. The other symbols are self-explanatory...... LA Figure 5.l. Equivalent circuit used to calculate the effects of cathode lead inductance. Through the use of simple circuit theory it is easily shown that ig = l2 Cgk (5.1)'g!; jaC- R. gk g The largest that ig could ever become is thus i = 2 Cgk k ip (5.2) We prdoeed to calculate the mean square grid noise current produced through lead inductance effects by fluctuations in the plate current:

-38i2 gkLk)2 ip2 (5*3) Taking generous estimates of Cgk and Lk, for a 6AG5 Lk =.01/6hy we find that at a frequency of 30 mc. ig — = 2.5 x 10'27 (amperes)2 per unit bandwidth. _ f This is about one one-hrandredth of rrasured grid noise values so that our assumption that grid noise produced by lead inductance effects is negligible seems completely justified. An experimental check was also obtained using a 6J6 and inserting a piece of wire one inch long (Calculated to have an inductance of about 0.02A4hy) in series with the cathode lead. No noticeable increase in grid noise could be detected.

BIBLIOGRAPHY 1. W. Schottky, "Spontaneous Currert Fluctuations in Various Conductors", Ann_. Physik, Vol. 57, pp. 541*567 (1918). 2. H. Wallman, A.B. Macnee, C. P. Gadsen, t"A Loz-Noise Amplifier", Proc. IR.E,, Vol. 36, pp. 700-708 (1948). 3. C. J. Bakker, "Fluctuations and Electron Inertia", Physica, Vol. 8, pp. 23-43 (19L1). 4* E J. Schremp, "Amplifier Sensitivity", Chapter 12, Vacuum Tube Amplifiers, Vol. 18, M.I.T. Rad. Lab. Series, McGraw-Hill, New York (1948). 5. D. 0. North and W, R. Ferris, "Fluctuations Induced in Vacuum Tube Grids at High Frequencies", Proc. I.R.E., Vol. 29, pp. 49-50 (1941). 6* R. Q. Twiss and Y. Beers, "Minimal Noise Circuits", Chapter 13, Vacuum Tube Amplifiers, Vol. 18, M.I.T. Rad. Labo Series, McGraw-Hill, New York (1948). 7. R. L. Bell, "Induced Grid Noise", Wireless Eng,, Vol 27, pp. 87-94 (1950). 8. S. Ballentine, "Schrot-effect in High Frequency Circuits1t, Jour. Franklin Inst., Vol. 206, pp. 159-167 (1937). 9. G. E, Duvall, "The Effects of Transit Angle on Shot Noise in Vacuum Tubes"t, M.I.T. Res, Lab, of Electronics, Tech. Rep* No. 82, Sept. 8, 1948. 10* E. Spenke, "Die Frequenzabhangigkeit der Schroteffektes", Wiss. Veroffent. Siemens-Werken, Vol. 16, pp. 127-136 (1937) 11. A. J. Rack, "tEffect of Space Charge and Transit Time on the Shot Noise in Diodes", BSTJ, Vol. 17, pp. 592-619 (1938)* 12. W. Schottky and E, Spenke, "Die Raumladungsschwachung des Schroteffektes", Wiss. Veroffent. Siemens-Werken, Vol. 16, pp.' 1-41"(137) — 13, D. 0. North, "Fluctuations in Space-Charge-Limited Currents at Moderately High Frequencies, Part II, Diodes and Negative Grid Triodes", RCA Rev,, Vol. 4, ppo 441-472 and Vol. 5, pp. 106-12L4 (1940. —. -39

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