A novel method called "Dynamic Velocity Taper' to linearize the Pout versus Pin transfer characteristic that does not require any extraneous circuitry or tuning, has large bandwidth capabilities ( 10 percent) and offers also an increase in the intrinsic traveling wave tube (TWT) efficiency by 1 to 2 dB is described. In addition, the method permits the TWT to be operated at or near the synchronous voltage (b plus or minus o) which produces a flat small and large signal gain responses and low AM to PM conversion. The physics of the method and experimental verification are given. The implementation should have a significant impact on TWT performance and increase the channel capacity of communication satellites

Kosmahl, H. G.

Peterson, J. C.

English

NASA Technical Reports Server

NASA Technical Memorandum
A TWT Amplifier With a Linear Power
Transfer Characteristic and
Improved Efficiency
iSA-TM- & *« AMELIFIZE WITH A S84-2 1803
LINEAR POMER TRANSFER CHARACI ERISTIC AND
""""
 (BASS)
 '
2 P
101 G3/33
Henry G. Kosmahl
Lewis Research Center
Cleveland, Ohio
and
John C. Peterson
Hughes Aircraft Company
Torrance, California
Prepared for the
Tenth Communications Satellite Systems Conference
sponsored by the American Institute of Aeronautics and Astronautics
Orlando, Florida, March 18-22, 1984
NASA
https://ntrs.nasa.gov/search.jsp?R=19840013735 2020-03-20T23:46:04+00:00Z
ERRATA
NASA Technical Memorandum 83590
A TWT AMPLIFIER WITH A LINEAR POWER TRANSFER
CHARACTERISTIC AND IMPROVED EFFICIENCY
Henry G. Kosmahl and John C. Peterson
March 1984
Cover: The TM number should be 83477.
Report documentation page, block 1: The TM number should be 83477.
OF POOR QUALITY
A TWT AMPLIFIER WITH A LINEAR POWER TRANSFER CHARACTERISTIC AND
IMPROVED EFFICIENCY
Henry G. Kosmahl*
National Aeronautics and Space Administration
Lewis Research Center
Cleveland, Ohio 44135
and
John C. Peterson
Hughes Aircraft Company, EOD
Torrance, California 90509
Abstract
A novel method to linearize the POU* versus
P,n power transfer characteristic of TWTs by
strictly internal modifications to the phase
velocity of the slow wave circuit is described.
The AM to AM characteristic approaches then that
of a hard limiter and with a significantly
improved intrinsic efficiency (1 to 2 dB) while
the AM to PM conversion is not much different from
that in an unmodified TWT, e.g. not exceeding
3°/dB. Work is in progress to develop techniques
that will reduce this AM to PM conversion to
smaller values. The theory of the "Dynamic
Velocity Taper" (DVT) is introduced and applied to
compute two different TWT's. The computed and
measured power transfer characteristics of these
two TWT's - one a Ku Band and the other a Ka Band
TWT for broadcasting from space - are shown in
their unmodified and modified form with their
respective DVTs. The basic scheme of the DVT is
the continueous and dynamic synchronization of the
phase velocity on the TWT circuit with the
conditions on the spent beam accomplished
internally in the TWT.
A 4-minute movie contrasting the bunching
phenomena in a TWT without and with a DVT will be
shown.
An attempt is made to compare the advantages
of an internal Velocity Taper - perhaps in
combination with an external and simple phase
linearizer-against active or passive predistortion
techniques.
Theory of the Dynamic Velocity Taper
The idea and pursuit of a linear and
distortion free amplifier is obviously not new.
Until now, most attempts to eliminate or to reduce
the nonlinearities in the AM to AM and AM to PM
transfer characteristics were directed to
techniques external to the TWTs by passive
predistortion techniques or active feedbacks. A
few cases were reported, without however much
detail, about discretely placed positive and
negative velocity tapers* such as to obtain
improved intrinsic efficiencies associated with
low distortions without achieving linearity. The
method to be described in this paper addresses
directly the problem of achieving internally a
linear power transfer characteristic approaching
that of an ideal hard limiter, together with an
efficiency improvement by 1 to 2 dB. Thee
resulting AM to PM conversion of about 30° can be
accepted in some applications or be combined with
a much simpler phase equalizer that provides an
almost negligible phase shift. In addition,
efforts are being made to develop new techniques
that will retain the hard limiter characteristics
with increased efficiency but reduce the total AM
to PM conversion to small values.
To understand the technique it is useful and
necessary to briefly review the small signal
theory of TWT's, that Pierce developed and
described with the help of several fundamental
parameters listed below?:
- gain and efficiency parameter
- velocity parameter
uQ, vQ - initial electron and circuit phase
velocities, respectively
b(z) u - v(z)Cv(z) - dynamic velocity parameter
Observe that one dimensional theories, such as
small signal theory of Pierce, use differently
defined values for b, C, and Z from those used
in multidimensional programs.
Consider now a typical AM to AM power transfer
curve of a communication - type TWT such as the
curves 1n fig. 1 marked w/o taper. The straight
line region from origin up to about 6 to 10 dB
below saturation covers a range of at least 25 dB
of small signal gain. In this region a bunch has
been formed and assumed a favorable phase location
for production of power. However, in every small
signal region both the amount of energy extraction
and the velocity spread within the bunch are, by
definition, negligible; the small signal gain is
precisely predictable and corresponds directly to
the velocity parameter b0. As the small signal
region ends the bunch begins to lose slowly energy
to the wave. Looking at b it may be
b0 decreases
neTTow IEEE.
seen readily that as u0 decreases
too, the favorable synchronization between beam and
wave deteriorates, the gain slope decreases more
and more until saturation is reached. Another
reason for this behavior is, of course, the
development of an increasing velocity spread in
the bunch. To prevent the small signal gain slope
from falling we have to keep b0 constant.
ORISiNAL
OF POOR QUAUTV"
Obviously, since one cannot prevent UQ from
decreasing (we want the electrons to give up their
energy), v must be decreased such as to keep b0
approximately constant. We thus write
u - v(z) (1)
This nonlinear TWT interaction Eq. (1) can be
solved only with a modern high speed computer: As
the internal conversion efficiency increases with
distance, u decreases but this decrease is
compensated by a reduction in v(z).
Mathematically, this is implemented by making b
variable:
Since the electron velocity distribution as a
function of energy extraction (distance) is known
in the program we select the parameter a such as
is necessary to maintain the gain linear by
slowing the velocity v(z) in a relation to the
loss of energy or increase in efficiency. The
computed and typical dependence of n(z) on the
location Z along the (unmodified) TWT with the
input power as parameter is shown in Fig. 4.
Were n(z) a strickly exponential function of Z,
as it is in the small signal region, we would
obtain straight lines. Since the deviations from
linearity are small, except at saturation, we are
justified to put
n(z)*e
r(Z-Z
-l r(Z-Z0)
(3)
Z0 is the value of z at which the intended taper
is to begin. From Eq. (2) and (3) we can write
(4)
And from Eq. (1) we get
1 + Cbo dv/dz 1 dv/dz
- UT T -777
Equating Eq. (4) and (5) and multiplying by
dz
/c>{5)
dzorC(Z - Z0)fl +£ (Z - Z0)
The integration of Eq. (6) gives
v(z) = voexp -a rC(Z - ZQ)
dv_
v
- Z
(6)
(7)
Now, in the nondispersive region of a helix or
other periodic slow wave structures we may write,
approximately
(8)
where c is the speed of light, p the pitch and
a the helix radius.
From Eq. (7) and (8) it follows
p = P0 exp ]- orC(Z - ZQ)H - Zo> + "I(9)
for 2 > 10 and p = p0 at Z = Z0.
Approximately we get from Eq. (9) for
a r C ( Z - Z0) « 1
f 2 2
P = P0 1 - arC(Z - ZQ) - «c£ (Z - Z0)
+ a2C2r2(Z - Z)2 + -
The taper should be placed after the small
signal region, because too "early" a placement is
distructive to the performance.
It is useful to calculate two other quantities
of interest in designing tapers for linearized TWTs.
From Eq. (8) it follows directly for the local
change in pitch
dp = =2?- dv •= - —• Cv db = - ^  2itaCadn = - p.CadnC C C 0
The total change in the pitch 1s:
v.
(10)
/
s odp = - 2»a —— Ca f dn
P0 n(Zo)
= -2na — Ca(n - n0)
where saturation occurs at Z = Zc
The number of turns in the tapered section is
given by
and
Obviously, N - N0 is the difference in the
number of turns
with v = VQ at Z = ZQ.
ORIGINAL'
OF POOR QUALITY
Discussion of Results
Figures 1, 2, and 5 show AM to AM and AM to PM
transfer curves for the H8802 and H918 TWTs at 50
watts/12 GHz and at 75 W/20 GHz, respectively.
For the unmodified and tapered TWTs measured
curves are shown and compared with computed
results on the H8802 experimental TWT built with a
DVT. The existing discrepancy between the
predicted and measured power for both cases - with
and without the DVT - is largely due to the use of
"cold" measured helix loss values for the
computation of losses in the operational ("hot")
TWT instead of actual, "hot" loss values. The
latter are best determined by pulsed, low duty
cycle RF power measurements against CW
measurements. The heating up of the output
section of helices causes appromixately 0.5 dB
reduction in power output of 12 GHz.
Figure 3 shows the RF basic efficiency poltted
versus the helix (cathode) voltage for the H8802
with and w/o the DVT. Note that higher voltage
corresponds to higher beam velocity, higher b
value and consequently higher power output. Note
also that the TWT with DVT shows 16 percent
efficiency - that is 5 p.c. points more than the
TWT w/o DVT because higher efficiencies than in
tubes w/o DVT are being achieved at lower voltages
and lower b values, b » o, which produce smaller
phase shift and a flatter, 0 slope gain response
while the TWT w/o DVT shows a S.S. gain slope of
1.6 dB/GHz, as shown in Fig. 6. Note also that
the improvement in efficiency that is due to the
DVT is very significant and amounts at a given
voltage to about 1.5 dB for the H8802 TWT. The
degree of improvement depends, of course, on
several design parameters.
The computed linearity of the AM to AM plots
can be seen to approach the shape of a hard
limiter. The AM to PM conversion is shown
computed and measured for the H8802 only that was
augmented with DVT. We know that, as may be
expected, the helix with the DVT has a phase delay
of about 30° but the total gain is also larger and
the measured curves never exceed the 3.0°/dB
slope. Another interesting point in this context
is the question where to place the saturation on
the curve approaching the flat top of a hard
limiter. If that point were moved close to the
knee the phase shift would become smaller.
At this time, a brief discussion of merits and
disadvantages of predistortion techniques and/or
active feedback alternatives to the velocity taper
seems appropriate. Some points are obvious: the
velocity taper, being an internal modification to
the TWT, adds no weight or complexity, does not
increase the cost and offers substantial bandwidth
(> 10 percent) without any tuning. All properly
designed negative velocity tapers (that is v(z)
decreasing with distance), produce an efficiency
improvement - an important benefit not available
from any feedback system. In the case of a DVT a
closely linear AM to AM characteristic may be
obtained together with an improvement of 1 to 2 dB
in efficiency. With an RF efficiency above 16
percent, a well designed multistage Depressed
Collector (MDC) that has graphite, very low
secondary emission electrodes, should raise the
overall efficiency above the 50 percent level. A
future replacement of BeO rods with Diamond 2A
rods is likely to result in overall efficiencies
around 65 percent since both losses are reduced
and the impedance much increased.
Such improvements will make future TWTs as
linear as Solid States Amplifiers but with an
efficiency far above any present and potential
ability of FETS.
Figures 7 and 8 shows the pitch variation
the DVT computed for the H8802 and H918 TWTS,
respectively.
in
An expansion of the present method to include
a simple passive phase cancellation devices, in
addition to the DVT in the output section, is
under study at Hughes EDD. Some results of this
work may be available for the March AIAA
presentation.
A 4-minute movie that visualizes the bunching
phenomena in untapered TWT's and in those having a
DVT will be shown.
References
1. Collomb, J., Gosset, P., and Raye, H.: "A New
Generation of Satellite Traveling-Wave Tubes
for TV-Broadcasting and Telecommunications,"
AIAA Paper 80-0485, April 1980.
2. Pierce, J.R., Traveling Wave Tubes, Van
Nostrand, New York, 1950.
Op POOR QUALITY
o:
LU
I
^—
o.
i—
O
0
-5
-10
-15
-20
-25
-30
-35
S1
•o
o
CO
<:
Q.
UJ
25
0
-25
-50
-75
-100
-125
-150
-175
-200
MEASURED
WITH DVT7
COMPUTED /
WITHDVT-7/
 14dB
3.2dB-,/ r
'OUT'
PHASED
*- WITHOUT DVT
H WITH DVT
POWER TRANSFER
-50 0 5-40 -30 -20 -10
INPUT POWER. P(N. dB
Figure 1. -Hughes 8802 experimental 12 GHz TWT. AM/AM and
AM/PM conversion on a double decibel scale with and without
DVT.
ORSGPAL W
OF POOR QUALITY
20
18
16
14
^
£ 12
i
CJi 10
D TWT WITHOUT DVT
(OPERATING AT 3% OVER VOLTAGE)
O TWT WITH DVT
(OPERATING AT 0% OVER VOLTAGE)
I I
-18 -14 -10 -6 -2 SAT 2
RF INPUT POWER. dB
10
Figure 2. - Basic efficiency measured versus power input
with and without DVT, for the Hughes 880a
ORIGINAL
OF POOR QUALITY
o
18
16
14
12
§ 10
o
o
CO
D TWT WITHOUT DVT
O TWT WITH DVT MEASURED
SYNCHRONOUS
VOLTAGE
BOTH CASES
I I I
4/100 -5500 -5600 -5700 -5800 -5900 -6000
CATHODE POTENTIAL. V
Figure 3. - Basic efficiency versus voltage with and
without DVT for the Hughes 8802, measured.
ORSG3NAL PAGE EU
OF POOR QUALITY
10
a. i
cc l
er
.1
r r
^OUTPUT
/ COUPLER
4 6
Z, in.
10
Figure 4 - Basic efficiency versus distance along the helix
with power input as parameter.
ORIGINAL PA l^ E3
OF POOR QUALITY
76 W
WITH DVT
WITHOUT TAPER
I I
10 60 7020 30 40 50
P|NPUT. RELATIVE UNITS
Figures. - Power transfer characteristic for the Hughes 918
with and without the DVT. (Computed.)
ORIG5NAL
OF POOR QUALITY
CO
P|NPUT=27-9dBm
''OUTPUT02-85'18"1
-TWT WITH DVT
11.7
-TWT WITHOUT DVT
0.2dB
P.MR. -7.2dBm
0.2 dB
vz
P.MR. -8.0dBm
12.2
FREQUENCY. GHz
Figure 6. - Gain variation for the Hughes 8802 with and
without the DVT. (Measured.)
.0225
.0220
~- .0215
B
O_
.0210
. 0205.5.0
-Z0 = 5.5 in.
P0 • 0.0225 in.
UP TO Z0 -5.5 in.;
"- ",021 in.
e - aCy(Z-Z 0 )
P(ZS) • 0~. 021 in.
Z 0 = 5 . 5 i n .
END OF INTERACTING
HELIX.
-BEGINNING OF TAPER, 5.5 \
1 I I
5.5
^n
6.0
Z
6.5 6.67 7.0
Zc
Figure 7. - Pitch variation in the DVT for the Hughes 8802.
.0320
/-START OF TAPER
.0315
.0310
o o
-n 3)
•0 O
§820 f
•O ig
c &
— Pn - 0.032 UP TO Z • 5.5 in.; P(Z.) • 0.03115
-OUTPUT COUPLER.
END OF TAPER, 7.2
.5 6.0 6.5 7.0 7.5
Z, in.
Figure a - Pitch variation in the DVT
for the Hughes 91&
1 Report No NASA TM- *&3 // f "Sovernment Accession No
AIAA-84-0762 I
3 Recipient's Catalog No
4 Title and Subtitle 5 Report Date
A TWT Amplifier With a Linear Power Transfer
Characteristic and Improved Efficiency 6 Performing Organization Code
506-62-52
7 Author(s)
Henry G. Kosmahl and John C. Peterson
8 Performing Organization Report No
E-1793
10 Work Unit No
9 Performing Organization Name and Address
National Aeronautics and Space Administration
Lewis Research Center
Cleveland, Ohio 44135
11 Contract or Grant No
12 Sponsoring Agency Name and Address
National Aeronautics and Space Administration
Washington, D.C. 20546
13 Type of Report and Period Covered
Technical Memorandum
14 Sponsoring Agency Code
15 Supplementary Notes
Henry G. Kosmahl, NASA Lewis Research Center; John C. Peterson, Hughes Aircraft
Company, EDO, Torrance, California 90509. Prepared for the Tenth Communications
Satellite Systems Conference sponsored by the American Institute of Aeronautics
and Astronautics, Orlando, Florida, March 18-22, 1984.
16 Abstract
A novel method called "Dynamic Velocity Taper" to linearize the Pout versus
Pin transfer characteristic that does not require any extraneous circuitry
or tuning, has large bandwidth capabilities (> 10 percent) and offers also an
increase in the intrinsic TWT efficiency by 1 to 2 dB is described. In
addition, the method permits the TWT to be operated at or near the synchronous
voltage (b = o) which produces a flat small and large signal gain responses
and low AM to PM conversion. The physics of the method and experimental
verification are given. The implementation should have a significant impact
on TWT performance and increase the channel capacity of communication
satellites.
17 Kay Words (Suggested by Authors))
TWT
Li nearized
Higher efficiency
IB Distribution Statement
Unclassified - unlimited
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Unclassif ied
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Unclassified
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'for sale by the National Technical Information Service, Springfield, Virginia 22161
National Aeronautics and
Space Administration
Washington, D.C.
20546
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A TWT amplifier with a linear power transfer characteristic and improved efficiency

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