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of Electronics
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METHODS OF MEASURING THE PROPERTIES
OF IONIZED GASES AT HIGH FREQUENCIES
I. MEASUREMENTS OF Q
SANBORN C. BROWN
DAVID J. ROSE
AO*~
TECHNICAL REPORT NO. 222
JANUARY 22, 1952
RESEARCH LABORATORY OF ELECTRONICS
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
CAMBRIDGE, MASSACHUSETTS
The research reported in this document was made possible
through support extended the Massachusetts Institute of Technology, Research Laboratory of Electronics, jointly by the Army
Signal Corps, the Navy Department (Office of Naval Research)
and the Air Force (Air Materiel Command), under Signal Corps
Contract No. DA36-039 sc-100, Project No. 8-102B-0; Department of the Army Project No. 3-99-10-022.
MASSACHUSETTS
INSTITUTE
OF
TECHNOLOGY
RESEARCH LABORATORY OF ELECTRONICS
January 22,
Technical Report No. 222
1952
METHODS OF MEASURING THE PROPERTIES
OF IONIZED GASES AT HIGH FREQUENCIES
I.
MEASUREMENTS OF Q
Sanborn C. Brown
David J. Rose
Abstract
Experimental methods are given for determining the Q of both high- and low-Q
resonant cavities at microwave frequencies.
The emphasis is placed on the practical
measurements necessary in determining the properties of ionized gases in the 3-cm and
10-cm wavelength range.
I
METHODS OF MEASURING THE PROPERTIES
OF IONIZED GASES AT HIGH FREQUENCIES
I.
I.
MEASUREMENTS OF Q
Introduction
The phenomena associated with electrical discharges in gases at microwave frequen-
cies are in general much simpler than the corresponding behavior of gases under the
action of a dc field.
On the other hand, microwave techniques are not as well known and
may therefore discourage workers from entering the field.
Experience has shown that
readily available texts on ultrahigh frequency measurements do not include the particular
calculations of the experimental parameters in a convenient form for gas-discharge
measurements.
The present series of reports has been prepared to fill this need.
For the sake of convenience, the range of frequencies is chosen so that cavity resonators may be employed which are relatively simple to construct and use, and where
power sources and measuring apparatus are available.
One of the important parameters
which control the physical behavior of the gas discharge is the value of the electric field
in which the electrons are accelerated.
Measurements of the field generally involve
the prior determination of the power absorbed in a resonant cavity and the determination of the characteristic of the cavity known as its Q, which is the ratio of the energy
stored by the cavity to the power dissipated in the cavity and certain associated components per radian of rf field.
In the study of ionization processes, breakdown, and low
current-density discharge phenomena, high-Q devices may be used.
density discharges, low-Q devices are necessarily used.
For high current-
Explicit use of the Q in cal-
culating electric fields is mainly confined to high-Q devices; thus this report is concerned principally with this case. However, certain calculations apply to low-Q cavities,
and we shall present these also.
In the problem of calculating the Q of resonant cavities used in gas-discharge measurements, the necessary accuracy is not achieved if one neglects the series losses in
the coupling circuit between cavity and transmission line.
Since the total loading of the
cavity determines the width of the resonance curve, a quantity known as the loaded Q
gives the best coverage of the parameters.
For gas-discharge work, the Q with the
series loss included is calculated in terms of the loaded Q.
This method extends the
work of Lawson (1) in which the calculations neglected the series loss, and differs from
that developed by Slater (2) which included the series loss but was calculated in terms
of an external Q.
II.
The Lumped Circuit Representation of a Cavity
A cavity may be represented as an element in a microwave circuit as shown in
the circuits of Fig. 1.
The cavity system consists of a cavity and a part of the in-
put line to which the cavity is coupled by loops through vacuum-tight, glass seals.
-1-
-
Oi
A
a
t-
-~-A2
~3s
:
i LINE
YC
i
PI
Gs
--- --- -- T
L
-_
I
(b)
P
E
P'
-
~~~--------~
(a)
p
CI~~~C
11
g$
t
G 'L
-_______T'
P'
(C)
t'
(d)
Fig. 1
Equivalent circuits for a resonant cavity.
Our calculations apply explicitly to the usual case in which the cavity terminates the
line, but certain cases in which additional elements are placed beyond the cavity are
susceptible to the same treatment.
The cavity can be represented by an impedance Z'
at TT' which is transformed by the loop circuit to the impedance Z at a reference plane
in the input line PP'.
We will develop methods for determining the impedance Z, the Q,
and the resonant wavelength X of the cavity system from measurements of the voltage
distribution on the line terminated by the cavity.
The measurements consist of deter-
mining the position of the voltage minima d and the voltage standing-wave ratio in decibels, as functions of the wavelength X.
The representation of the cavity and coupling
system by Z at PP' will only be valid as long as we stay outside of the reference plane,
that is, to the left of PP' of Fig. 1.
In order to be complete, the equivalent circuit should contain sufficient elements to
account for all phenomena represented by the cavity.
difficult to work with in detail.
Practically, such a circuit is very
First, therefore, we will concern ourselves with the
general characteristics of a fairly complete equivalent circuit, and then, following
certain restrictions, its simplification to usable form. Let us first consider the circuit
of Fig. la, where measurements are made at the points PP' on the line.
The resonant
cavity, across TT', can be characterized by parallel reactance L' and C', and conductance G', connected to the line by a transformer of admittance ratio A :1. This representation of a cavity with an isolated resonance can be justified by fairly rigorous
methods (2).
In order for the representation to be correct, it is necessary that the
reactive elements L' and C' refer only to the cavity in question. For example, the
coupling of a second cavity onto the first cannot generally be treated mathematically in
this manner.
However, the conductance Gt may well include the effect of nonresonant
elements coupled to the cavity as outputs.
To this extent, then, the cavity need not
-2-
terminate the transmission line.
The
reactance of the loop is represented by
the lossless network X 5 which is often
treated as a series inductance;
and the
losses in the loop, seals, and line back
to PP' are represented by the conductance Gs.
s
In the following analysis, it
is assumed that the line of characteristic
admittance Y c is matched at PP' looking
toward the generator.
Following the general method given
1,,
C1-+
&J/
.
ctg
x
(..f,4
\kl.
?
a,
I.,
p..-d.
R1,_AQ
Qn
-
n
.
V11
-o.r
aj
demonstrate the characteristics of this
circuit.
Fig. 2
For the sake of discussion, the
network Xs is replaced by a series
inductance L . If the series reactance
s
jLsw is a much more slowly varying
Approximate impedance diagram
for circuit of Fig. la.
function of frequency than the cavity reactance, the impedance Z at PP' is approximately a circle in the complex impedance plane as shown in Fig. 2.
We get this circle
by splitting the complex function Z, derived for circuit la, into the real and imaginary
parts and by elimination of
resonance, at
= o'.
from these two parts.
Point B, nominally at
Point A corresponds to the cavity
= 0 and
= oo, may be approached very
closely, a few percent off resonance; its position is at Z = 1/G
Awc'
s
+ jLsW', insofar as
throughout the range of interest.
A simple analysis near resonance is possible only if the energy storage in the loop
circuit is negligible compared with that in the cavity at resonance.
If the loop is non-
resonant, an approximately equivalent criterion is that the ratio of energy stored off
resonance to energy stored on resonance is negligible; or equivalently, that the cavity
resonance curve (described in detail below) shows no signs of additional resonant frequencies near the main one.
Under these assumptions, the loop elements are a small
perturbation and may be taken into account in the following manner.
The lossless net-
work X s is replaced by a length of line, a transformer, and a susceptance B s , which is
The elements are then transformed to
always possible, giving the circuit of Fig. lb.
those of Fig. lc in which the loop reactance, which is the principal complication to
further analysis, has been combined with the other cavity parameters. This simplified
circuit is the basis for all subsequent analysis.
The new cavity parameters are L, G,
and C; and the new transformer admittance ratio, obtained from combining the two
transformers, is a :1. It is seen that the principal effect of the loop is to shift the resonant frequency to
, where
between the cavity and PP'.
and to change the effective line length
= 1/(LC) /2,
The effective line length is defined as the electrical distance
between TT' (the points at which the cavity alone could be represented by a single
-3-
impedance) and PP' (the points at which the cavity plus loop circuit may be represented
TT' would stay
Thus if only the coupling loop were changed,
by a single impedance).
fixed but PP' would change.
The points PP' are determined on a lossless line only to
integral multiples of X/2.
For many purposes, this circuit may again be replaced by that of Fig.
gs
At resonance,
LYc
Gs
y
c
I-- =
,
g
a
a2 G
--- ,
c
=
. and
c
Ca
2
It is now con-
the resonant conductance across PP' as g,
g
g
(1)
.
c
the susceptance of the parallel l-c combination is zero.
venient to define two quantities:
wherein
Here
the line admittance is normalized to unity.
=
d,
where
(2)
g
l+
gs
and a dimensionless quantity
, akin to susceptance,
(
'(u)
=
given by
.
(3)
Yc
The line is terminated at PP' with the normalized impedance
1
z =-+
g,
1
g+
jb
(4)
jb
where
(5)
b = wc At resonance b -O
and zo = 1/g
s
+ l/g = l/g
if 1/g o > 1 and undercoupled if l/g
o
o.
We call the cavity system overcoupled
< 1.
Let us now determine the relations between the experimentally measured position
of the voltage minima and the voltage-standing-wave ratio, and the cavity parameters
enumerated above.
Assume a voltage wave A = Aexp j(wt - 2rx/Xg)
traveling from the
generator along the positive x axis toward the cavity represented by the normalized
is the guide wavelength and t is the time. The position
g
x = 0 can be chosen at any fixed point on the line; it is most convenient to choose it at
impedance z at PP'.
PP'.
Here, X
There is also a reflected wave B = Bexp j(wt + 2wx/Xg).
all complex quantities.
these two waves.
A, A o , B, and B
are
The voltage at any point on the line at any time is the sum of
A probe inserted into a slotted line and connected to a proper receiver
measures a quantity proportional to the time average of the power at that point, that is,
proportional to the absolute magnitude of the square of the voltage A + B.
The resulting
quantity varies down the line as a sin2 curve displaced above the axis (see Fig. 3).
The complex ratio of incident to reflected waves is
which is seen to be
-4-
the reflection coefficient
r,
B Bo j4rx/g
=p
e
r' = =--
j
6)
(6)
.
o
Here, p =
Ir I
is the modulus of the reflection coefficient, a quantity which is always
real and positive;
The standing-wave ratio R V , that is, the ratio
is the phase angle.
of the maximum to minimum voltage on the line, is seen to be
RV
(7)
p
1
As mentioned above, relative power is usually the quantity measured.
The decibel
power standing-wave ratio R is given by
R = 20 logl0Rv.
(8)
The experimental procedure consists in setting the wavelength, measuring the
standing-wave ratio R in db, and also measuring the position d of a voltage minimum.
The ordinates are found by varying X and
The curve of Fig. 4 is plotted point by point.
setting the probe for each X value first at a minimum and then at a maximum.
With the
probe at a minimum, the input attenuation of the receiver is set at a given value.
With
the probe at a maximum we bring the signal back to the same level by increasing the
input attenuation.
The ratio of these two attenuator settings gives R.
A phase curve
which will resemble either Fig. 5a or 5b, depending on whether the cavity is undercoupled or overcoupled, is obtained by plotting the position of the voltage minimum.
The asymptotes of Fig. 5 are the actual positions of the points PP', determined within
multiples of Xg/2.
Occasionally the resonance curve is too broad to enable one to reach
these asymptotes conveniently, and yet it may be desirable to determine them.
In such
a case, the cavity should be short-circuited in its high-field region with a substantial
metallic conductor.
The resonance is then far removed from ao, and the position of
the standing-wave minimum follows the asymptotes through the region near wo.
The
decibel standing-wave ratio so obtained with this arrangement is R, (Fig. 4).
Before performing the specific algebraic manipulations involved in finding the cavity
Q, it remains to relate the reflection coefficient
to the cavity impedance Z.
It can
be shown in general that the reflection coefficient at any point is given by
r=
z- I
I-
= 1
y(9)
(9)
where z is the normalized impedance at the point in question on the line; y = l/z is the
corresponding normalized admittance.
0 of
varies with position on the line; the associated impedance z varies correspond-
ingly.
Henceforth, the calculations will deal entirely with conditions at the point PP'.
It is understood that F and
r
As may be seen from Eq. 6, the phase angle
and
refer to that point.
Since z at PP' is given by Eq. 4,
at PP', and p, R V , and R are all determined.
One can obtain a geometrical representation of Eq. 9, similar to Fig. 2, when the
series impedance is neglected,
by splitting it into real and imaginary parts and
-5-
Fig. 3
Superposition of the incident
and reflected waves.
3
0
0a
PP'
9
0
!a
o
Fig. 4
Typical exI)erimental
resonanc e curve.
3:
to
-Rh
z
(n
WAVELENGTH
w
0
w
.4
4
I0
z
2
I2
i
2
Z
Fig. 5
Typical phase curves.
U0o
z
0
I-
a
0
0
o
0
X,
WAVELENGTH
a) UNDERCOUPLED
Xo WAVELENGTH X
b) OVERCOUPLED
-6-
X
Fig. 6
Smith chart.
Circles of constant go and b in the r
eliminating the reactive element b in the admittance.
The r
plane.
circles are the conduct-
ance circles of a Smith (3) impedance chart and the tip of the r vector determines the
susceptance circle.
Thus a Smith chart yields p and
given y or z at PP'.
according to Eq. 9 for every
This is shown in Fig. 6.
At PP', Eqs. 4, 6 and 9 can be combined to yield
14b
+ [2(l
g2(.
tan
c~ =
undercoupled
From Fig. 3, and the definition of
-I)
+
2(1
Po
=
+ b2(
)
(10)
+ b(gL +
9
b 2 ~
l
(go - 1)/(go + 1)
(12)
~'
4o = r.
, it is seen that the position d of the standing-wave
-7-
minimum is given by
d = (2k-
1)-
(13)
+
where k is an integer, indicating that the kth minimum to the left of PP' is being measured.
This variation gives the curves of Fig. 5.
The slope of the dotted asymptotes is
due to the first term in Eq. 13, as X increases with X. In the undercoupled case,
has
the value r both at resonance and far from resonance. In the overcoupled case,
is
zero at resonance,
-r
at the lower asymptote, and +w at the upper one.
overcoupled
undercoupled
upper asymptote
d = 2kXg/4
resonant line
d = (k
lower asymptote
d = (2k - 2)\g/4
asymptote
d = 2kXg/4.
One further convention will be mentioned.
Thus
- 1)\g/4
(14)
Although RV is always greater than unity
and therefore R is always greater than zero, it is useful,
in order to distinguish
between the undercoupled and overcoupled cases, to define formally R < 0 for the
undercoupled and R > 0 for the overcoupled cavity systems.
III.
The Measurement of Q
The quantity Q is defined as
oU
Q
oP
where U is the energy stored, and P is the energy dissipated per second.
(15)
It may be
noted that the concept of a cavity Q is valid only if the stored energy takes many cycles
to decay after excitation is removed, i. e. only if Q >> 1.
Various kinds of Q's may be
discussed, depending on where, in a particular problem, it is convenient to consider
the energy to be dissipated.
The Q of principal interest in this report is that obtained
by considering the cavity represented in Fig. ld to be excited externally, and calculating the ratio of energy stored in the cavity to that dissipated in gs and g.
determines the unloaded Q, QU' which is,
at resonance,
1/2
QU =
Since the quantities gs and g
2
()1/'
(I)
P(gs - go
-
+
This ratio
ss
(g
g'
) 2
g )
(16)
can be expressed directly in terms of the resonant decibel
standing-wave ratio R and the off-resonance ratio Roo, the calculations of
closely allied. Two methods are now presented for determining QU
-8-
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A.
Resonance Curve Method
This method is
applicable if the resonance curve is
sufficiently sharp so that a
certain width AX as shown in Fig. 4 can conveniently be measured on it.
this width may be measured where the curve is,
In order that
in general, most accurately known, the
calculation of QU is broken into two parts.
It is convenient to define a loaded Q, QL'
in terms of the ratio of energy stored and
energy dissipated through the parallel conductances
and line are viewed from the terminals tt'.
g and g/(g
Theri in trms
s
+ 1),
when the cavity
of the quantities gs and go
given by Eq. 2
L
(gs - go)(gs + 1)
5
2
gs(g° + 1)
This relation also defines the width AX to be measured.
X°
(17)
Now the
-c susceptance at tt'
is
jb = j)
-
and at AX/2 off resonance, the quantity Iw/wo -
(18)
o/wl is equal to AX/Xo; at these points,
the susceptance is equal to the conductance across tt'.
Under these conditions, the
impedance zh at PP' is
Zh
+
(19)
g+
The reflection coefficient
r
g2(g ° + 1)
(gs - go)(gs + 1)
for the circuit of Fig.
ld is given by Eq. 9; thus, using
Eq. 10
Ph =
2 2
2
2
1/2
(gogs + go + gs - 4gogs + 1)1/2
(20)
(gs + l)(go + 1)
Rh is
then found from Eqs. 7 and 8.
yield values of go and gs.
is to be measured.
Measurements of the db ratios R
and RO
The value of Rh so determined is that at which the width AX
These results may be put into the form of Fig. 7 where curves of
Rh vs Ro are plotted for various values of R.
These curves are identical for posi-
tive and negative values of Ro
0
The value of QL is then determined in the following manner.
Ro,,
The ratios R
and
and the resonant wavelength Xo , are found from the experimental resonance curve
as in Fig. 4; then from Fig. 7, the value of Rh is determined.
nance curve at R = Rh is the required quantity AX,
and QL is found from Eq. 17.
From Eqs. 16 and 17, the unloaded Q is seen to be
-12-
The width of the reso-
- go)(go +
go(g 5 + )
(g
U
)QL
(21)
for various values of R o.
The required ratio QU/QL may thus be plotted vs R
shown in Fig. 8.
It is
Comparison of the phase curve with Fig. 5 will determine the proper
sign of R o .
The quantity
is most conveniently calculated from Eq. 16 as
___= gs(g+
QL
1)
~(g~~ ~(22)
0 +l)~
gs
(gs - go)(gs + 1)'
is determined
is plotted for various values of Ro, in Fig. 9; then
from these curves and the value of QL. If the series loss can be neglected, the calcuThe ratio
/QL VS R
lations are greatly simplified, for the ratio Ro is essentially infinite.
Q
L
g
In such a case
( 17a)
+
and
(go
QU
B.
+
1)QL
(21 a)
Phase Curve Method
When
above.
it is often difficult to perform the measurements indicated
is quite low,
is 5, the required wavelength separation AX is enormous and
If, for example,
may easily fall outside the wavelength range of the oscillator used.
In this case, it is
sufficient to measure the slope of the phase curve and the standing-wave ratio on resonance. It will turn out that g << 1, so that it is permissible near resonance to neglect
the series resistance l/g
s
If desired, the value of gs may be found by
and set go = g.
the method used for determining the reference points PP'.
The circuit takes the form
of Fig. 10.
In the vicinity of resonance, the susceptance b (Eq. 18) will be much smaller than g.
It is then permissible to neglect all second order terms in subsequent manipulations.
Near resonance, the reflection coefficient r
1 - g - jb
is then
(1-
1+ g+jb'
The small phase angle
g2)
-
j2b
(23)
(l + g)2
b is very closely
<,
2b
2b
g -1
The slope of the phase curve d(d)/dX from Eq. 13 is
-13-
(24)
-dX
4
This derivative is to be evaluated at
dX
TV a+
'
-- -
= 0 (minimum position at resonance), X =
(25)
0o,
kg = kgo, using the relation
Thee eslt
s3
=
There results
d(d)
dX
+
2k-1 (go
4
Xo
=0
go db db
4rr d U=-
(26)
But
db
db (+=0
is given by Eq. 24, and
db
dX=
0
With these insertions
is simply -2p/ko by definition of b (Eq. 18).
d(d)
TX
2k - 1go
=O
=
go
4~-~-o/
(27)
ir(1 - g )X 0
whence
2k - 1
o d(d)
Here, g is the reciprocal of RVo
(1
go(28)
the voltage standing-wave ratio on resonance;
the
g2) term is usually a minor correction when P is small;
d(d)
dk
=0
is simply the slope of the phase curve at resonance; the factor (2k - 1)/4 can usually
be found by measuring the physical distance in guide wavelengths between the cavity
and the point of measurement.
The unloaded Q is given in this case by
QU = .
U
(29)
g
Fig. 10
Equivalent circuit for gs- oo.
-14-
I
C.
High-Frequency Bridge Method
At somewhat lower frequencies (of the order of 100 Mc/sec) standing waves still
exist on the transmission line and must therefore be taken into account.
However, the
use of slotted sections is physically impractical, and it becomes desirable to use the
high-frequency impedance bridge (4).
This instrument is employed commercially in
high-frequency power and impedance measuring equipment.
Essentially it consists of
two bridge circuits constructed so that one of them is sensitive to power incident on the
load, and the other to power reflected from the load.
Together they indicate the true
absorbed power and, indirectly, the absolute value of the reflection coefficient and
standing-wave ratio of the load.
Since the ratio of reflected power Pr to incident power Pi can be read, it is,
in prin-
ciple, possible to plot a resonance curve for the cavity for
p
IrI
=
(P
1/2
)
*
RV and R are determined from p in the usual manner.
(30)
All of the calculations of the
preceding section apply, except that since the position of standing-wave minimum cannot
be plotted as a function of wavelength, a phase curve similar to Fig. 5 cannot be
obtained.
coupled.
Thus it remains to be determined whether the cavity is undercoupled or overThis coupling condition can be determined by a knowledge of loop orientation
and the variation of p0 at resonance as the coupling is altered.
If p
decreases as the
coupling is increased, the cavity is undercoupled; if p0 increases as the coupling is
increased, the cavity is overcoupled.
For the undercoupled case, go = RVo > 1; and
for the overcoupled case, go = 1/RVo < 1.
It often happens that the frequency cannot be perturbed sufficiently to make the
required excursions.
In that case, the Q can be determined by measurements near
resonance in the following manner.
Since Ro, cannot be measured now, it is necessary to make some assumptions about
the series loss gs.
as is done here.
In most cases at these frequencies, it is justifiable to neglect it,
Thus QU is given by Eq. 29; and since g = go is determined at reso-
nance, only the measurement of
remains.
Slightly off resonance, the cavity admit-
tance is
y = g + jb
g + 2jAco
(31)
co
Here it is assumed that the frequency excursion Aw << oo so that
to 2Aw/co0 very closely.
and 9 as
/wo -
o /o
is equal
The modulus of the reflection coefficient p is given by Eqs. 6
P
2
=
(1 - g) + b
2
(1 + g)2 + b2
-15-
(32)
where
b2= p (l+g) - (l-g)
1 -p
+
R(g
[R-
g
+
RV
Pr(1+g)2
-
V
~~~~~~(33)
Pi(l'g)2
Pi-Pr
r
Thus b may be calculated using the most convenient form of Eq. 33.
calculated by reference to Eq. 31 and QU by Eq. 29.
Then 1 is
For example,
Pr ( l+g) - Pi ( l-g)
r
Pi - Pr
o
Q U g02gAo
(34)
Pi and Pr are to be measured at the frequency excursion corresponding to Ah.
g = 1 and Eq. 34 becomes
cavity is critically coupled at resonance,
W
U
If the
P
0
r
(34a)
Jr
- P ir
The solution for b may be carried out graphically using a normalized admittance
chart containing circles of constant reflection coefficient.
As seen from the above dis-
cussion, there are two possible values of g, and the proper one is chosen by a knowledge
of the condition of the coupling.
Graphically, it can be shown that the two values of g
are the two intercepts on the g axis of the circle of constant reflection coefficient po.
At a frequency slightly different from resonance,
mines a second circle on the chart.
the new value of p = (P/Pi)1/2
deter-
The intersection of this circle with the appropriate
line g = constant determines b.
In practice, several readings are made at different frequency excursions and corresponding values of Pi and Pr.
The various calculated values of QU are then averaged.
It has been assumed that gs was infinite; whether this is indeed the case depends on
construction of the coupling device.
If frequency and power output of the signal source
are stable and the cavity is reasonably rigid, good results are obtained within 5 percent
accuracy.
Care must be exercised in choosing the frequency excursion so that Pr or
Pi - Pr can be measured accurately.
approximately.
A wise choice can be made if the Q is
known
Generally, measurements of Pr and Pi can easily be made, but meas-
urements of the frequency excursion may be troublesome;
of 1000, variations of one part in 105 must be measured.
-16-
for if the QU is of the order
IV.
Measurement of a Steady-State Discharge
The introduction of a steady-state discharge into the cavity is equivalent to the addi-
tion of an admittance gd
+
jbd in parallel with the cavity elements g + jb, that is,
parallel with the parallel elements of Fig.
d.
in
It is convenient to determine all the
quantities except gd and jbd on the empty cavity prior to the initiation of the discharge.
Theoretically two measurements will then suffice to determine these quantities and a
complete resonance curve of the cavity containing the plasma need not be measured.
The discharge tends to undercouple the cavity, to lower its Q, and to change its resonant frequency.
Thus the db standing-wave ratio Ro at resonance Wo can be considered
as changed to RI0 at w', and these new quantities are measured.
0CO
Since
and gs do not
change, measurement of R' yields the unloaded Q of the cavity with the discharge going
as
Q =
-,
From these plotted ratios (using R o , and the known
.
and Ro)
(35)
QU can be determined.
Such measurements involve frequency excursions of the applied field of the order
of one percent.
This has a negligible effect on the discharge except insofar as the
amount of power transmitted to the discharge by the cavity is concerned.
It is there-
fore useful to monitor the light output of the discharge so that the input power can be
adjusted for constant light intensity, and hence constant discharge density as the frequency is varied.
Acknowledgment
The authors wish to acknowledge the valuable assistance of Dr. Melvin A. Herlin
and Dr. Edgar Everhart in the preparation of Technical Reports No. 66 and No. 140.
The techniques presented in this report were taken in part from these two reports.
References
1.
2.
G. B. Collins: Microwave Magnetrons, Sec. 18.5, McGraw-Hill Book Company,
Inc., New York, 1948
J. C. Slater: Rev. Mod. Phys. 18, 473, 1946
3.
P. H. Smith:
4.
J. F.
Electronics, Jan. 1939 and Jan. 1944
Morrison, E. L. Younker:
Proc. Inst. Radio Engrs. 36, 212, 1948
-17-