A WIDEBAND POWER MIJCER TUBE •

Horace Richard Johnson Electron Tiibe Laboratory-

Hughes Research and Development Laboratories Culver City, California

Summary

The use of a traveling-nave tube^ as a power mixer employing phase modu­lation at a single frequency has been described by W. J. Bray.2 To use the same modulation principle with a wide band of modulation frequencies (hundreds of megacycles), excessive modulating power would be needed. Ihis paper presents theory and experimental data for a broad-band traveling-wave type mixer requiring low modxilating power. It consists of an input helix, a drift tube and an output helix arranged successively along a beam. Low modulating voltage is realized by operating the drift tube at low potential; the output helix is operated at h i ^ potential so the required power output can be obtained.

Introduction

A traveling-wave tube amplifierl can be used as a mixer by applying a modulating voltage to the cathode, as described by Bray.2 since the helix-to-cathode voltage is first adjusted to naximize the power output, there is little amplitude modulation; and since the transit angle of the electrons through the tube is many cycles, and the electron velocity is being varied, nearly pure phase modulation results. This sdieme already has considerable practical imp­ortance when a fixed modulation frequency is used.

A mixer capable of accepting a wide band of modulating frequencies (hundreds of megacycles) is also of practical importance. Ihe tube Just described could be made broadband by connecting a resistor between cathode and ground. If a resist­ance low enough to give several hundred megacycles bandwidth is used, the h i ^ modulating voltage necessitates prohibitively large modulating power for appreci­able power output. Low modulating voltage could be obtained in an electrically long low-voltage tube. High power output, on the other hand, implies a short, high-voltage tube.

It is the object of this paper to describe an experimental mixer tube that combines low modulating power with high power output. Sufficiently complete theory to enable tube design and experimental verification of the theory are presented.

• Presented at the Conference on Electron Tube Research at Stanford University, Stanford, California, June, 1953·

1 For book or article designated by this and the following footnote numbers, see List of References at the end of this paper.

1 5

This mixer tube consists of an input helix, a drift tube and an output helix arranged successively along an electron beam. The input helix and drift tube are maintained at low potential relative to the cathode, and the output helix is operated at higher voltage; the low-voltage drift tube results in the low modulating voltage, and the output section enables the high power output. The input helix is short, merely introducing the carrier signal to the beam. The low modulating voltage results from three effects, listed below in order of importance. First, a small change in cathode potential produces a large frac­tional change in beam velocity in the drift tube because it is operated at low voltage. Second, the change in jiiase velocity of the space-charge wave in the drift tube is nearly the full change in electron velocity — a greater change than in a helix section. In the helix case some of the energy propagates along the circuit, and the i*iase velocity of the circ\iit part is not much affected by electron velocity. Third, the electrical length of the drift tube is large be­cause of the low voltage. The cumulative effect can be a 20 - 30 decibel reduc­tion in conversion loss from modulating power to sideb€Uid output power.

The task of the theory for a mixer tube of this kind is to predict the carrier input power, sideband output power, and modulating power for the tube. Mks units and the following symbols will be used.

A Initial loss, defined by Pierce,^ decibels. Β Gain factor for gro?ring wave, defined by Pierce.^ b Radius of electron beam in drift tube [Eq.(4) and Figs. 4 and 5]j

also, velocity parameter defined by Eq.(8). C Piercel gain parameter, c Velocity of light in vacuum, d Loss parameter defined by Pierce.1

e/m Charge-to-mass ratio of the electron, f Frequency of signal, fp plasm frequency, fq Reduced plasma frequency, lo Beam current. i Alternating component of beam current.

First order Bessel function.

Κ Helix impedance at the beam E ^ 2 ^ P, discussed by Pierce .- k Efficiency factor, k = Pq/cioV2. Ay Length of a helix section,

-^d Length of drift tube, m Mass of the electron. Ν Transit angle of electrons through the helix, cycles. Nd Electron transit angle through drift tube, cycles. P q Sideband output power. Pq Carrier output power for zero modulation. QC Space-charge parameter, defined by Pierce.^ U q Average electron velocity. V Potential difference between cathode and drift tube [Eqs.(4) and (6)

and Figs. 4 and 5] or between cathode and helix [Eqs.(7), (8), (9)]. V q Voltage to accelerate electrons to a velocity equal to the helijc phase

velocity in absence of electrons. V2 Average potential difference between cathode and output helix. Vm Peak value of sinusoidal modulating voltage.

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ν Alternating component of beam velocity, v . Phase velocity of fast space-charge wave. v_ Phase velocity of slow space-charge wave.

Rate of phase shift as cathode potential is changed, radians/volt. Rate of phase shift in drift tube, radians/volt.

^sx^-^Jy^^ Quantity defined by Pierce,^ Equation (7.11), p.ll3j his equation contains a misprint — C should be replaced by C

€ Q Permittivity of free space. Ψ Total phase shift in a helix section, radians.

Phase shift of space-diarge wave in a drift tube, radians. Q Radian frequency of signal, radians/sec.

If a carrier power Pq is sinusoidally phase modulated, the output power in each of the first order sidebands is

and they occur at frequencies higher and lower than the carrier frequency by an amount equal to the modulation frequency.

Prediction of P Q and the carrier drive power is the problem of predicting gain and power out put 1,3 of a traveling-wave tube. Nothing further will be said regarding gain except that Figs. 2 and 3 (kindly supplied to the author by Η · C. Poulter) with the aid of Pierce's appendix enable accurate small-signal computa­tion of this quantity. Large-signal gain is lower, sometimes by 10 decibels or more. Power output is

Pq = l^CIoV2 , (2)

where k is a factor usually of the order of 1 or 2.

This section will be devoted to computation of Δ · The three main contribu­tions to , which will be discussed here in order of importance, are the change in phase shift of the slow-space charge wave in the drift tube, the change in the phase shift in the helix sections, and the change in phase shift at the section boundaries.

First, we calculate the ciiange in phase shift of a signal on an electron stream passing through a drift tube as voltage between cathode and drift tube is changed. A drifting stream of electrons of radius* b passing through a conduct­ing tiobe of radius a was demonstrated by Hahn and Ramo4. to be capable of propa­gating space-charge waves in the direction of the stream (small signal). Vari­ations from d-c conditions of uniform velocity U Q and ciirrent I Q were assumed to be small quantities. The two lowest modes have velocities

^1 = (11 fq/f) , (3)

* The symbol b is customarily used for beam radius and for the velocity parameter defined by Eq.(8). It is hoped that the appropriate definition will be clear in each equation.

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-where fq is the "reduced plasma frequancy" and f is the signal frequency; fq depends on the plasma frequency

f2 lo Ρ 47/3 g b2 V e/m tv (4)

through the reduction factor^ fq/fp shorni in Fig. 5; V is cathode and drift tube. Fig. 4 is a nomograph of Eq.(4).

the voltage between

Suppose the waves in the drift tube are excited by a helix and, further, that at the end of the exciting helix the growing wave predominates. The alter­nating current and velocity associated with that growing helix wave must be matched to the alternating current and velocity at the input to the drift tube. This results in the conclusion that for QC>»0.2, the slow wave in the drift tube is excited much more strongly than the fast wave. The proof appears in the appendix.

Thus, we can approximate the phase shift in the drift tube with

V d = 2tffXd (5) Uo(l-fq/f)

The rate of phase shift is

A o - ^ Ψ d - tfNd V(l-fq/f) C6)

Next, we treat the problem of calculating the phase shift of the growing wave in a helix section of the tube. A similar calculation in the literature contains an error.^ The total phase shift \p in a l e n g t h o f the growing wave is

- " 2 — mc /2e [1-

KIQ

4V 3/3

Ύ ά ϊ β τ θ is a function of b and therefore of V throu^

V 3 Í ^1/2 b s

1/2 - 1

Equations (7) and (8) imply that

3V V o 3 ^ 3 ( v o ) " f ^ ^ b

(7)

(8)

( 9 )

1 8

Eq.C9) contains knomi or easily calculable quantities irLth the exception of yi, 3 y i / 3 ^ and V / V Q * we have nvimerically evaluated the first two with results presented in Figs. 6 and 7. Fig. 6 shows y^ as a fianction of ^ when b is chosen equal to bopt for maximum x^ (maximum gain of the growing wave). The variation of yi for b = bopt with circuit loss d over the range O^d ^1 is less than + 8 percent for QC = 0 and decreases as ^ increases. The plot of /4QC in Fig. δ" shows that it is an excellent approximation to yi for QC-^ 0.2. Fig. 7 shows contours of constant dvi/3b on the d-vs. iC plane; 7> Τ]/Τί b was estimated graphically from published curves^ and is probably accurate to about +10 percent; V / V Q can be obtained from the curve of bopt Fig.8) , used in conjunction with Eq.(8).

We now come to the problem of changes in phase shift between sections, which changes will be shown to be negligible. The total phase shift consists of changes in the phase of the growing wave in helix sections and of the slow space-charge wave in the drift section. Simple addition of the phase changes of these principal waves in each section will generally result in little error for the total phase change of an electrically long tube. The approximation involved in this procedure can best be illustrated by the simple example of a drift tube propagating only the slow space-charge wave. At the point where this drift tube suddenly ends and a helix section begins, the total helix voltage must be zero, and the appropriate current and velocity modulation are determined from the space-charge wave. Three helix waves are excited. Only the growing wave is important at the end of the helix section; its i*iase, referred to the helix input, does not, in general, agree with the phase of the space-charge wave. This phase difference changes as the cathode potential is altered, but the change is generally small for electrically long tubes with few discontinuities, and becomes relatively smaller as the length of the sections is increased. A special case appropriate to the experimental tube was computed, and the unimportance of the additional term verified.

Construction Of Mixer Tube

Several experimental tubes similar to Fig. 1 were constructed to operate near 3000 mc/sec (see Figs. 9, 10, 11). The special L-type cathode has an emit­ting diameter of 0.070 inch. The Pierce-type gun (Figs. 12 and 13) has a per-veance of about 40 percent of the value calculated from the parallel plane formula, 0.036 inch between planes; = 5 was observed for the grid. The input helix, wound with tungsten wire of diameter 0.006 inch, has 86 turns/inch, is 0.75 inch long and, like the drift tube and output helix, is 0.120 inch o.d. The drift tube is 303 nonmagnetic stainless steel, 2.00 inches long and 0.100 Inch i.d. The second helix is of 0.010 inch tungsten wire, 44 turns/inch and is 4.00 inches long. The helices are wound on centerless-ground molybdenum mandrels and hydrogen fired for 15 minutes at 1000^ C. Ihe barrel is Corning 7070 glass vacuum-shrunk on an 0.120-inch water-hardened steel drill rod and etched to have an 0.020-inch wall. The collector is air-cooled copper brought out through a gold-copper braze to Kovar.

For the input and output helices, the values of -^a (pierce notation) a»re about 2.4 and 1.4, respectively. Maximum gain for the two helices occurs at frequencies some-rfiat lower and higher, respectively, than the design frequency of 3000 mc/sec. The input helix is terminated with colloidal carbon (Dixonac and diatomaceous earth diluted with distilled water) painted on the outside of the glass; an appropriate amount of loss is placed on the second helix similarly.

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The first helix is just long enou^ (CN = 0.38) to set up the growing wave on the electron stream; the second helix is long enough so that the calculated over-^11 sirall-signal gain of the tube as an amplifier is about 32 db with a beam current of 20 ma. Gain calculations yrere made as outlined by Pierce^ and using curves obtained due to Η· C Poiilter (Figs. 2 and 3)·

Experimental Results

Operation of the L-cathode at 1070^0 brightness easily enables the necessary 21 ma to be emitted from the cathode. 7iith a magnetic field of 1000 gauss, about 0.6 ma strikes the second helix, 0.4 ma strikes the anode, and negligible current is intercepted on first helix and drift tube.

The gain of this tube as an amplifier was measured as 30 db at 20 ma. The phase shift of the tube operated as an amplifier was measured with 20 ma beam cur­rent. The voltages between the cathode and input helix and between the cathode and second helix were varied independently for a more detailed check on the theory. Results and comparison with theory are listed in Table I; for the experimental points, see Fig. 14. The agreement with theory is considered good.

TABLE I

^ , radians/volt Calctilated Measured Error, percent

Total -0.205 -0.229 11

First helix and drift tube

-0.161 -0.185 13

Second helix -0.0Λ3 -Ο.0Λ5 5

Fig. 15 shows the maximum upper sideband output (modulation voltage adjusted for maximum output at each frequency). It is constant within HH 2·3 db. Ihe VSWR of the modulation input, -which is also shown, is good except in the vicinity of 155 mc, where there is a pronounced resonance caused by series resonance of cathode-lead inductance and stray capacitance (see Fig. 16 ). The modulating voltage nece­ssary to obtain maximum power in the upper sideband is shown in Fig. 17. Below 150 mc good agreement with the static phase-shift measurement was obtained; the rising characteristic above 150 mc is associated with the low-pass character of the equivalent circuit of Fig. 16. From Fig. 15^ the efficiency constant k of Eq.(2) is found to lie between 0.24 and 0.72. The carrier drive was about 30 milliwatts for the tests, so the conversion gain from carrier to upper sideband was 10 db. The output is quite insensitive to the drive power (saturation is very broad). The output does vary periodically + 1.5 db for small variations of the magnetic field, presumably because of beam scalloping. The focusing field is 1000 gauss.

Noise and spurious signals do not exceed the level of 60 db below the side­band output in this tube. In an earlier model considerable noise, and occasion-

20

ally sharp sidebands several megacycles removed from the carrier, were observed. Ihey were eliminated in later models by using the high-perveance gun (Fig. 12) so that no ion trap exists along the beam, and by baking the tube for 12 hours at 3500 c and for half an hour at 400© C , then operating it with 60 percent over-voltage and 250 percent of normal current while on the pump for 7 hours more. Two getters were used.

None of these tubes has failed yet, and one has been operated for more than 300 hours.

Appendix

This appendix shows that, under average or large sp>ace-charge conditions, the wave excited in a drift tube by an incident growing wave is largely the slew Hahn-Ramo space-charge wave.

The input boundary conditions, which must be matched are the alternating components of beam current and velocity i and v, respectively. If the ratio of these quantities for the input growing wave matches the ratio associated with the slow space-charge wave, this wave alone (with proper amplitude) will satisfy the boundary conditions. Eqs.(7.18) and (7.19) in Piercel give for the ratio

where 8 is defined, for C ^ ^ l , by the appropriate root of

For the growing wave with QC 0.2,

$ = xi - Ó^JW^¡ (3) and for large gC,

- j 4QC. (4)

Eq.(2) for the traveling-wave tube may be applied to the drift tube if b-i>oo (circuit far from synchronism). This gives for the drift tube,

6 = ± J V ^ Q c ~ (5)

the negative sign corresponding to the slow wave. Since S for the growing wave, from (4), is approximately equal to i> for the slow wave in the drift tube, from (5), it follows from (1) that the ratio of current to velocity for these two waves will ma teil.

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Aclalowledgement

The author profited frol7l many helpful discussions with Dr. J. R. Whinnery and other colleagues. The tubes were constructed by J. A. Dallons, A. M. Anderson, G. Lee and several other members of our engineering section.

List of References

1. J. R. Pierce, Traveling-wave tubes. D. Van Nostrand, New York; 1950.

2. W. J. Bray, "Traveling-wave valve as a microwave phase-shifter and frequenoy­modulator, II proe. Inst. Elec. Eng., Vol.99, Part III, p.15, London; January, 1952.

3. A. Nordsieck, "Theory of the large-signal behavior of traveling-wave amplifier," Proc. I.R.E., Vol.41, p.630; May, 1953.

4. S. Ramo, "Space-charge and field waves in an electron beam," Phys. Rev., Vol.56, p.267; August, 1939.

5. D. A. Watkins, "Traveling-wave tube noise figure,n Froc. I.R.E., Vol.40, p.65j January, 1952.

6. H. R. Johnson and J. R. Whinnery, "Traveling-wave tube oscillators," Trans. I.R.E. Prof. Group on Electron Devices, Vol.II; November, 1952.

? L. D. Smullin and W. R. Coffey, "The Use of a silicon point-contact rectifier for modulating microwave signals," Technical Report No .83, Research .Ia.b. of Electronics, M.I.T.; November 12, 1948.

8. SpeCifications, for V[estern Electric Tube Type 416A.

9. W. H. Forster, "6000 megacycle television relay system," Electronics, Vol.22, p.80; January, 1949.

10. V. Learned, "The Klystron mixer applied to television relaying," Proc. I.R.E., Vol.38, p.l033; september, 1950.

li. I. D. Olin, "The Behavior of the klystron amplifier as an electronic phase­shifting elelOOnt," N .R. L. Report 3895; November 30, 1951.

12. J. T. Mendel, "Grid-modulated traveling-wave tube for low-pass amplification," Stanford University, E.R.L. Technical Report No.4?; July 31, 1952.

13. J. R. carson, "Notes on the theory of modulation," Proc. I.R.E., Vol.lO, p.5?; February, 1922.

14. A. V. Haeff, "Space-charge effects in electron beams," Proc. I.R.E., vol.2?, p.586; september, 1939.

15. L. P. Smith and p. L. Hartman, "The Formation and maintenance of electron and ion beams," Jour. Appl. Phys., Vol.ll, p.220; March, 1940.

16. D. A. Watkins and A. E. Siegman, I~elix impedance measurements using an electron beam," Jour. APpl. ~. [To be published].

I ,^η,,τ > ^ « E S I S T I V E -

P M O O U L A T E O / O U T P U T

C A T H O O C , I I f , " ^ ' - ' /

0

" Τ Υ Β Ε ^

J T P U T - . I L E L I X \ f

L O O O Q O Q Q Q Q

M A G N E T I C F I E L D

Fig. 1. Schematic drawing of mixer tube.

0 01 0 2 0 3 0.4 0.5 0.6 0.7 O.i OS 1.0 I.I 12 1.3 1.4 1.5 1.6 1.7 1.8 Fig. 2. Β = const, on d vs. QC plane, b chosen for maximum χχ·

Fig. 3 . A = const, on d vs. QC plane, b chosen for maximum x^.

2 3

1 , 0 0 0 , 0 0 0

1 0 0 , 0 0 0

1 0 , 0 0 0

1 , 0 0 0

3 5 0 0 -

3 0 0 0

2 5 0 0 -

2 0 0 0

1 8 0 0 ·

1 6 0 0

1 4 0 0

1 2 0 0

1000

9 0 0

\ 8 0 0

\ 7 0 0

\ \

6 0 0

5 0 0

4 0 0

3 5 0

3 0 0

MC

Fig. 4 · Nomograph of Eq . ( 4 ) giving plasma frequency in terms of voltage, current, and diameter of an electron base.

Fig. 5· Plasma frequency reduction factor vs.JS^b = 2itfb/u^ with ratio of beam radius to tube radius b/a as parameter.

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Λ c

θ 10 1.2 14 1.6 I.θ

oc

Fig. 6 Plot of 71 and V l i o T b s QC ^ e n b is Approximate contours of con-chosen for maxlimim gain of the *- g- ' ^ g ^ ^ ¿ growing wave. ^ plane when b is cEosen

TOR MAXIRAUM GASII X^ OF THE GROWING WAVE (bsb^jp^.),

Λ /

/ / \

/ / /

\ / V

\ / / J /

7 — /

/ / J /

/

/ / . >

/ /

/ > f

, f 1 . J / /

/ n— -(d>0 C 1 W- 0

\ .25)

1 / 1 I

1 \ 5

QC 1 1 0

2 / w-o 5)

3

Fig. 9. Photograph of ndJcer tube.

Fig. 8. Plot of bopt vs. QC for d'O, 0.25 and 0.50j-s/4QC vs. Q C

25

Fig. 10. Photograph of mixer tube, magnet and package assembly.

i Fig. 11. Photograph of open mixer tube package.

T A N T A L U M A N O D E

L - C A T H O D E 0 . 0 7 0 E M I T T I N G D I A M E T E R

Fig. 12. Drawing of Pierce gun*

2 6

Fig. 13· Photograph of parts for Pierce gun.

5 10 15 2 0

VOLTAGE I N C R E A S E . V O L T S

Fig. Ik Measured phase shift of mixer tube vs. helix and drift tube potentials.

4 0 0

I 300

o Q

< 200

£ 100

X

-

- POWER -Η J V _ Ρ tí Ρ V.S.W.R.

3 G

< O O 2 U .

o

( O

>

50 100 150 200 250

MODULATING FREQUENCY, MC.

300

Fig. 15 Measured maximum upper sideband power output vs. frequency and cathode modulation input VSWE vs. frequency.

5 0 OHM RESISTOR

50 OHM CABLE / I / / '

/ / ' I

/ CATHODE LEAD ' ^ INDUCTANCE

^MODULATION INPUT

3 - M I X E R T U P E

/ CATHODE-TO-GRID PLUS CATHODE-TO-ANODE STRAY CAPACITANCE

GRID LEAD

-ANODE LEAD

Fig. 16 Schematic drawing of the equi­valent circuit for cathode modulation.

15

o < 10

Γ 5

3 Q O

- V -

•

i < x ^ 1 — ^ THEORETICAL

SHIFT MEASL .FROM PH/ REMENT

\SE -

Fig. 17

<

O Α .

0.5 ζ

o 2

< - J

O O 2

50 100 150 2 0 0 250

MODULATING FREQUENCY MC.

300

Measured modulating voltage for máximum sideband output vs. fjre-quency; theoretical curve from phase-shift measurements.

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