U.S. patent number 3,753,162 [Application Number 05/184,136] was granted by the patent office on 1973-08-14 for microstrip ferrite phase shifters having time segments varying in length in accordance with preselected phase shift characteristic.
Invention is credited to Donald A. Charlton, William P. Clark.
| United States Patent |
3,753,162 |
| Charlton , et al. |
August 14, 1973 |
MICROSTRIP FERRITE PHASE SHIFTERS HAVING TIME SEGMENTS VARYING IN
LENGTH IN ACCORDANCE WITH PRESELECTED PHASE SHIFT
CHARACTERISTIC
Abstract
An electronically controllable RF (radio frequency) phase
shifter that can be designed to provide either true time delay
characteristics or constant phase versus frequency characteristics.
The non-reciprocal microstrip phase shifters of the invention
utilize a ferrimagnetic substrate with a metallized strip conductor
on one face and a metallized ground plane on the other face. The
strip conductor has a plurality of adjacent line sections selected
to provide a circularly polarized RF magnetic field at a point
between each two adjacent conductors with the plane of the
circularly polarized magnetic field being orthogonal to the plane
of a DC magnetic bias field, the latter plane being provided
parallel to the face of the substrate. The circularly polarized RF
magnetic field is developed by selecting the line sections with a
length so that the signals in adjacent lines are 90.degree. out of
phase from each other. When either the level or direction of the DC
bias is changed, the permeability of the ferrimagnetic material
changes causing a change in the propagation constant and a
resultant phase shift change. To provide a relatively wide
bandwidth to the phase shifter and a desired delay characteristic,
the adjacent conductor sections have their line length varied so
that different portions of the line effects the phase shift for
different frequencies.
|
Inventors: |
Charlton; Donald A. (Huntington
Beach, CA), Clark; William P. (Orange, CA) |
| Family
ID: |
22675695 |
| Appl.
No.: |
05/184,136 |
| Filed: |
September 27, 1971 |
| Current U.S.
Class: |
333/24.1;
333/238; 333/156 |
| Current CPC
Class: |
H01P
1/19 (20130101) |
| Current International
Class: |
H01P
1/18 (20060101); H01P 1/19 (20060101); H01p
001/32 () |
| Field of
Search: |
;333/24.1,31R,29R,3R,84M |
References Cited
[Referenced By]
U.S. Patent Documents
Primary Examiner: Gensler; Paul L.
Claims
What is claimed is:
1. A wide bandwidth RF phase shifter responsive to applied control
signals, for phase shifting applied RF signals and wherein the
relative phase shift across the bandwidth is in accordance with a
preselected function of the frequency of the RF signals, said
device comprising:
a ferrimagnetic substrate having first and second surfaces;
a ground plane conductor on the first surface of said
substrate;
a continuous conductor on the second surface of said substrate said
conductor being a meander line having a plurality of equally spaced
substantially parallel adjacent line segments with the length of
the adjacent line segments varying log-periodically from one end to
the other end of said meander line; whereby the phase delay applied
to said RF signals is approximately a linear function of the
frequency of said RF signals.
means for applying said Rf input signals to a first end of said
conductor;
output means for receiving the RF signals from a second end of said
conductor; and
means for providing a DC magnetic bias field in said substrate in
response to the applied control signals;
whereby the value of phase delay applied to said RF signals is
controllable in response to said control signals, and the relative
phase shift across the bandwidth is in accordance with a
predetermined function of frequency established by said preselected
segment length distribution pattern.
2. A wide bandwidth RF phase shifter responsive to applied control
signals, for phase shifting applied RF signals and wherein the
relative phase shift across the bandwidth is in accordance with a
preselected function of the frequency of the RF signals, said
device comprising:
a ferrimagnetic substrate having first and second surfaces;
a ground plane conductor on the first surface of said
substrate;
a continuous conductor on the second surface of said substrate said
conductor being a meander line having a plurality of equally spaced
substantially parallel adjacent line segments with the length of
the adjacent line segments varying approximately linearly from one
end to the other end of said meander line,
means for applying said RF input signals to a first end of said
conductor;
output means for receiving the RF signals from a second end of said
conductor; and
means for providing a DC magnetic bias field in said substrate in
response to the applied control signals;
whereby the value of phase delay applied to said RF signals is
controllable in response to said control signals, and the relative
phase shift across the bandwidth is in accordance with a
predetermined function of frequency established by said preselected
segment length distribution pattern.
3. A wide bandwidth RF phase shifter responsive to applied control
signals, for phase shifting applied RF signals and wherein the
relative phase shift across the bandwidth is in accordance with a
preselected function of the frequency of the RF signals, said
device comprising:
a ferrimagnetic substrate having first and second surfaces;
a ground plane conductor on the first surface of said
substrate;
a continuous conductor on the second surface of said substrate said
conductor having a generally spiral-shaped configuration from one
end to the other end thereof with each turn of said spiral forming
a conductor section and with adjacent conductor sections varying in
length from a first end to a second end of said spiral in
accordance with a log-periodic distribution pattern; whereby the
phase delay applied to said RF signals is approximately a linear
function of the frequency of said signals;
means for applying said RF input signals to a first end of said
conductor;
output means for receiving the RF signals from a second end of said
conductor; and
means for providing a DC magnetic bias field in said substrate in
response to the applied control signals;
whereby the value of phase delay applied to said RF signals is
controllable in response to said control signals, and the relative
phase shift across the bandwidth is in accordance with a
predetermined function of frequency established by said preselected
segment length distribution pattern.
Description
BACKGROUND OF THE INVENTION
1. Field of the Invention
This invention relates to RF phase shifters and particularly to an
electronically controlled RF phase shifter having a wide bandwidth
and having desired phase shift characteristics such as true time
delay or constant phase versus frequency.
2. Description of the Prior Art
Two basic families of wide bandwidth RF phase shifter devices would
be desirable for different applications, with the first family
having the characteristic of true time delay and the second family
having the characteristic of constant phase versus frequency. The
true time delay phase shifters could be employed in antenna array
applications, and the constant phase versus frequency phase
shifters could be employed as the active phasing device in Butler
matrix applications, in Blass matrices and in switchable four-port
differential phase shift circulators. Suitable phase shifters with
true time delay characteristics are presently not known, and prior
art phase shifters with a constant phase versus frequency
characteristic have bandwidth limitations. In the past, systems and
devices have been limited to the bandwidth of the phase shifters,
approximately 12 percent, thus providing a substantial limitation
to the system operation. Another substantial requirement for phase
shifters in certain operations is that the amount of phase shift be
electronically controllable.
SUMMARY OF THE INVENTION
Briefly, the phase shifters in accordance with the invention are
non-reciprocal, microstrip ferrite phase shifters fabricated by
using a ferrimagnetic substrate with a metallized conductor line on
one face or surface, positioned to form a plurality of adjacent
line segments and with a metallized ground plane on the other face.
The devices develop a circularly polarized RF magnetic field
between adjacent line segments in a plane orthogonal to the plane
of a DC magnetic bias field, the latter plane being perpendicular
to the plane of the substrate. The circularly polarized RF magnetic
field is generated by selecting the length of the line segments to
provide the RF signal 90.degree. out of phase in the adjacent line
segments. In response to a DC magnetic bias applied to the
substrate, either the level or direction of the DC magnetic field
or magnetic bais field is changed so that the permeability of the
substrate material is controlled with a resultant desired phase
shift. Due to the closed magnetic path in the substrate, the DC
magnetic field remains constant without a continuously applied
external driving source. Any desired number of phase shift
conditions may be selected by controlling the DC magnetic bias. In
order to provide a phase shift versus frequency characteristic that
is either true time delay or constant phase, the length of the line
segments are varied with a distribution along the plurality of line
segments such that phase shift only occurs in the group of lines
whose length is approximately equal to a quarter wavelength of the
operating frequency. Also, the variation of line length provides a
desired wide bandwidth to the phase shifter.
It is therefore an object of this invention to provide an improved
microstrip RF phase shifter having desired time delay
characteristics.
It is another object of this invention to provide an improved RF
phase shifter device having a substantially wide bandwidth.
It is another object of this invention to provide an improved
electronically controllable phase shifter for reliably selecting
desired phase shift characteristics.
It is another object of this invention to provide RF phase shifters
that can be developed to provide a characteristic of true time
delay or to provide a characteristic of constant phase versus
frequency.
It is still another object of this invention o provide an
electronically controlled microstrip RF phase shifter that has a
wide bandwidth and that has a desired time delay
characteristic.
BRIEF DESCRIPTION OF THE DRAWINGS
These and other objects, features and advantages of the invention
itself will become apparent to those skilled in the art in the
light of the following detailed description taken in consideration
with the accompanying drawings wherein like reference numerals
indicate like or corresponding parts throughout the several
parts:
FIG. 1 is a schematic diagram of a simplified microstrip phase
shifter utilizing a meander line for explaining the operation
thereof in accordance with the principles of the invention;
FIG. 2 is a schematic sectional drawing taken at line 2--2 of FIG.
1 for explaining the theory of operation thereof;
FIG. 3 is a schematic diagram of vectors useful in explaining the
operation of the phase shifters by reference to FIG. 2;
FIG. 4 is a schematic diagram of a microstrip phase shifter
utilizing a meander line with a log-periodic line length
distribution and indicating other possible line length
distributions in accordance with the invention;
FIG. 5 is a schematic diagram of hysteresis curve of magnetic flux
density versus current for explaining the DC magnetic bias utilized
to provide the electronically controlled phase shifts in accordance
with the invention;
FIG. 6 is a schematic plan view of a single conductor microstrip
phase shifter in a circular or spiral format in accordance with the
invention;
FIG. 7 is a schematic diagram of phase shift versus frequency for
explaining the characteristics and the selection of characteristics
of the phase shifters in accordance with the invention; and
FIG. 8 is a curve of phase shift versus frequency showing
experimental results from the performance of a phase shifter in
accordance with FIG. 4 having a log-periodic line length
variation.
DESCRIPTION OF THE PREFERRED EMBODIMENT
Referring now to FIGS. 1 and 2, a simplified ferrimagnetic phase
shifter 10 in accordance with the invention may be fabricated by
using a ferrimagnetic substrate 12 which may be of any suitable
material such as ferrite or garnet with a metallized strip
conductor 14 on one face and a metallized ground plane 18 on the
other face. The conductors utilized in the phase shifters of the
invention may be of any suitable conductive material such as
aluminum, copper, silver, gold, for example, and may be deposited
or mounted on the substrate by any suitable technique. For example,
the conductor may be a thin film deposited by vapor deposition or
by sputtering, or may be a film placed on the substrate by a thick
film process in which a mixture including silver and glass
particles are painted on the substrate and then fused in an oven. A
source of RF input signals 20 applies RF (radio frequency) signals
to the line 14 to excite line segments 15, 16 and 17. Each line
segment such as 16 has a line length or line segment length between
points such as 23 and 25 or between similar points. Coupled to the
lead 14 at the output of the phase shifter 10 is a utilization unit
28. For electronically controlling the DC (direct current) magnetic
field in the substrate 12, a pulse control source 30 is provided
for appplying current pulses of a waveform 31 through a lead 32
which is wound through an opening or hole 36 in the substrate, to
establish the DC magnetic field or magnetic state therein indicated
by a dashed line 33. The pulse control source 30 is a suitable
voltage driving source controlled to selectively provide current
pulses of the waveform 31 with a predetermined amplitude and of a
predetermined duration. The control source 30 in some arrangements
in accordance with the invention for a digital source, may include
a current source, a switch such as a single pole double throw
switch selectively passing positive or negative current pulses from
the source through a gate to the drive line 32, with a peak current
sensor controlling the gate in response to the drive line current
reaching a predetermined level, as is well known in the art. The
control source 30 for some arrangements in accordance with the
invention for an analog source, may include a voltage source,
switch such as a single pole double throw switch selectively
passing either positive or negative current pulses to a gate and a
controllable counter closing the gate for selected periods of time
to pass pulses to the drive line 32. It is to be understood that
the control source 30 is not limited to any particular arrangement
but may include any suitable mechanization in accordance with the
invention.
A first requirement for the non-reciprocal phase shifter in
accordance with the invention is that the RF magnetic field be
circularly polarized at a point A in the material. The line length
of line segments such as 15 and 16 is equal to a quarter wavelength
of the RF signal frequency so that adjacent signals are 90.degree.
out of phase from each other to develop the circularly polarized
region. The line length for the effected signal is .lambda./4 or
.eta..lambda. + .lambda./4 where .eta. is any integer and .lambda.
is the wavelength of the RF signal effected or phase shifted at
that line area. The second requirement for the phase shifter of the
invention is that a DC magnetic field be produced orthogonal to the
plane of the circularly polarized field developed at point A and a
third requirement is that the RF signal must pass through that RF
circular polarized region A. The DC magnetic field H.sub.DC is
shown passing into the paper in the region of the line segments in
FIG. 2 by arrowheads 48 and 50 and coming out of the paper in a
region away from the meander line by an arrow point 47, as
developed by the conductor 32.
Referring now also to FIG. 3, the RF signal passing through line
segments 15 and 16 shown as I.sub.rf for each line segment at a
time t = 0 are respectively maximum in the line segment 15 with
current conducting into the plane of the drawing and has a value of
zero in the line segment 16. The magnetic field h .sub.rf at point
A has the direction and magnitude of a vector 36 resulting from
magnetic fields 34 and 35 (when current flows through the
conductors). At a second time t = T/4 where T is the period of a
cycle of the RF signal, the RF current is at a zero level through
the line segment 15 and is passing with a maximum amplitude through
the line segment 16 in a direction into the paper. As a result, the
magnetic field has a valve and amplitude of a vector 38. At a time
t = T/2, RF current passes through the line segment 15 with a
maximum amplitude in a direction out of the paper and zero current
passes through the line segment 16 to provide a magnetic vector 40
at point A. At a fourth time t = 3T/4 zero current passes through
the line segment 15 and current of maximum amplitude passes through
the line segment 16 in a direction out of the paper, resulting in a
magnetic vector 41 at point A. Thus, a circular polarized condition
is developed at the point A and an elliptically polarized condition
is developed in adjacent regions such as 44 and 46. It is to be
noted that the interaction which provides the phase shift in
accordance with the invention is developed in the elliptically
polarized regions as well as at the circularly polarized region or
point A. Less interaction is provided in the elliptical polarized
regions than in the circularly polarized regions. It is to be noted
that a similar circularly polarized point A is developed between
each pair of conductors for acting on the RF phase such as between
conductors 16 and 17 as well as between conductors 15 and 16.
The operation of the DC magnetic bias field H.sub.DC orthogonal to
the plane of the circular polarization will now be further
explained. The ferrite material 12 may be considered as being
divided into magnetic domains, each domain having its atoms with a
certain moment and a certain direction and angle of precession. The
electrons spin in each domain with a certain moment as determined
by that group of atoms. When a DC magnetic field is provided, all
of the domains align so that the atoms have the same direction of
moment and the same precession angle. The RF magnetic field changes
the precession angle of the atom due to the interaction of the
magnetic forces. A change of the precession angles of the atoms
changes the effective permeability of the ferrite material and in
turn the amount of time delay provided therethrough, resulting in a
different phase shift. For example, an increase of the precession
angles of the spinning atom, increases the effective permeability
of the ferrite, slows down the transfer of the RF signal
therethrough and provides a larger phase shift. The DC field which
is orthogonal to the plane of the RF field controls the direction
of the magnetic moment and therefore the direction of the
precessional spin relative to the direction of the circularly
polarized magnetic field, thus changing the effective permeability
of the ferrite. For example, if the DC field changes to its
opposite direction of polarity, the precession is in the opposite
direction and the precession angle will be smaller which results in
a reduction of the RF energy density. Since the group velocity of
RF energy passing through the ferrite type material is equal to the
power flow density divided by the energy density in the ferrite, a
reduction of energy density will cause an increase in group
velocity. Thus, the phase shifter of the invention provides an
effective change in the material so that the energy passes through
the ferrite at selected speeds, the change in material being a
change in the RF permeability of the ferrimagnetic material.
Referring now to FIG. 4 which shows a phase shifter 60 having a
single conductor 64 as a meander line and which is formed of a
ferrimagnetic substrate 68 on which the conductor 64 is deposited
or positioned to establish the meander line generally indicated as
70. A ground plane (not shown) is provided as shown in FIG. 2. In
the illustrated arrangement, the line length defined as the
distance between points 72 and 74, for example, is varied along the
meander line in accordance with selected characteristics such as
log-periodically so that the longer lines on the left-hand side of
the device provides a phase shift at the lower operating
frequencies and the shorter lines at the right-hand side of the
device provides a phase shift at the higher operating frequencies.
The meander line 70 is shown with a log-periodic distribution of
line length to provide a true time delay phase shift
characteristic. Other variations are linear having a configuration
of dotted lines 78 and 79 and a variation of lines 80 and 81 which
may be selected to provide a constant phase characteristic. The
variation of the line length is such that a phase shift only occurs
in the group of lines whose length is approximately equal to a
quarter wavelength of the operating frequency because this is the
only frequency at which a circular polarized condition is developed
at the point A and other similar points as explained relative to
FIG. 2. For the log-periodic line length distribution, every
frequency is effected by an equal number of lines, but not by the
same ones, and a wide bandwidth operation is achieved as well as
the desired phase shift versus frequency characteristic. For line
length distributions other than log-periodic for providing other
desired phase shift versus frequency characteristics, different
frequencies are effected by different numbers of lines but a
substantially wide bandwidth is achieved. When the line length is
varied log-periodically, as shown in FIG. 4, for example, and the
line spacing such as 75 is held constant, a true time dealy
characteristic is achieved. A log-periodic distribution means that
for adjacent line segments equally spaced along the meander line,
each adjacent line segment length varies as a constant, K, times
the length of the previous adjacent line segment. The DC magnetic
field is provided by passing conductor 86 through openings 88 and
90 in the substrate 68 so that the DC magnetic fields are all in
the same direction, and applying a DC control current therethrough
from a DC control source 94. The line 64 has an input port 98 and
an output port 100 thus requiring only a single strip conductor
being placed upon the substrate 68.
When the line segments of the meander line of FIGS. 2 and 4 have a
length .eta..lambda. + .lambda./4 and .eta. is an integer greater
than zero, some additional loss may be developed. In this condition
with additional wavelengths, there are additional circular
polarized points along the center between adjacent conductor
segments. The RF rotation changes direction between adjacent
circular polarized points by a change from a circular polarization
point to elliptical and then to linear and then back to elliptical
and a circular polarized point. For a line length of .lambda. +
.lambda./4 there are five points (like point A) between adjacent
segments with three providing a positive phase shift and two
providing a negative phase shift to develop a net positive phase
shift, for example. For a line length of 2.lambda. + .lambda./4
there are nine points with five providing a positive phase shift
and four providing a net positive phase shift, for example.
Referring now also to FIG. 5 which shows the hysteresis curve of
the ferrimagnetic material 68, the control source 94 may provide
digital control so that the material is in either state 103 or 105
resulting in a reversal of the polarity of the magnetic moment.
Also within the scope of the invention, the control source 94 may
select any analog magnetic state such as 107 to 110 for respective
phase shifts of 45.degree., 90.degree., 180.degree. or 270.degree.,
for example. The DC source 94 may be a suitable circuit for digital
or analog operation as discussed relative to FIG. 1. For analog
operation the source 94 may be any suitable voltage source circuit
as well known in the art for providing a predetermined voltage for
a predetermined time for each controlled phase shift state.
Referring now to FIG. 6 which shows a single conductor microstrip
phase shifter 120 employing a circular or spiral format and which,
for example, may have a log-periodic variation of circular line
segment length of a plurality of adjacent line segments. The spiral
phase shifter includes a ferrimagnetic substrate 122 and a spirally
arranged strip conductor 124 having a first port 126 and a second
port 128 either of which may be the input or output ports. A ground
plane (not shown) is provided as shown in FIG. 2. The spiral is
arranged so that the distance around any circular portion or line
segment of the conductor such as portions 130 and 132 from a
position of a line 134 is 90.degree. less for the signal in the
inner portion 132 than in the outer portion 130. The line segments
are spaced from each other as a function of the selected line
length distribution. The length of each portion further out from
the next inner portion is .lambda./4 more than the adjacent inner
segment. The k.sup.th spiral segment has a length
.eta..lambda..sub.k + .lambda..sub.k /4 where .eta. is 0 or any
integer and .lambda..sub.k is the wavelength which receives a
maximum phase shift in this segment. Thus, for each line segment,
l.sub.k, a different frequency as defined by the expression
.eta..lambda.+ .lambda./4 = l.sub.k receives the maximum phase
shift. The length of adjacent segments is varied as a selected
function (such as log-periodic) so that the 90.degree. phase
difference is provided between adjacent segments and so that
frequencies are effected in each line as defined by the .lambda. of
that line. Each of the circular line segments may control only the
RF signal at a single frequency (as defined by the .lambda. used in
the line length) or narrow band of frequencies in the phase shifter
bandwidth. In the spiral configuration a continuous line of the
point A circularly polarized condition is provided between the
conductors. A DC conductor 136 passes through the opening 141 to
provide a DC magnetic field of dotted lines 137 and may be
controlled by a suitable digital or analog pulse control source
such as source 30 of FIG. 1 or source 94 of FIG. 4.
Referring now also to FIG. 7, the selection of the line length
distribution along the length of the conductor will be further
explained. Synthesis has shown that the line lengths can be varied
to provide a desired phase shift versus frequency characteristic
that is consistent over an extremely wide band of operation. If the
line length distribution of FIGS. 4 or 6 varies with a log-periodic
line variation, a true time delay of a curve 69 is provided over a
relatively wide frequency band. If the distribution of the length
of the line segments is selected to provide a constant phase shift
versus frequency characteristic, a wide frequency band of operation
is provided as shown by a curve 71. One arrangement for determining
the line length distribution of the conductor segments is to draw
from calculated or experimental phase shift amplitudes, curves such
as 70, 72 and 74, each for a portion of the conductor segments
between the input and output terminals. Longer line length at the
input provides a phase shift at lower frequencies as shown by the
curve 70 and the shorter line lengths at the output provides a
phase shift at higher frequencies as shown by a curve 74. The curve
72 may represent the phase shift at the central portion along the
length of the conductor. Any number of curves may be utilized to
provide this graphical distribution of line lengths. The combined
result, when the line length distribution is properly selected to
provide proper curves such as 70, 72 and 74, is the resultant phase
shift curve 69, for example, when the line length between the two
adjacent conductor segments is log-periodic, that is, the line
length for each segment is a constant times the line length of the
previous segment (for equal line spacing). Thus, any desired phase
shift versus frequency curve such as 69 or 71 may be provided in
accordance with the invention. It has been determined in accordance
with the invention, that for a true time delay the variation in
line length is typically log-periodic. For a log-periodic
variation, the amount of line segments utilized for the different
frequencies is less for the lower frequencies and substantially
more for the higher frequencies. For a constant phase shift versus
frequency characteristic the distribution of the line lengths is
more line segments for the low frequencies and less line segments
for the high frequencies. The distribution may be determined, for
example, either by computer simulation, by graphical simulation as
explained relative to FIG. 7, or by calculation or
experimentally.
Referring now to FIG. 8 which shows an experimental curve 170 of
phase shift versus frequency developed from the phase shifter of
FIG. 4 having a log-periodic line distribution. The constructed
phase shifter provided approximately one wavelength or 360.degree.
or true time delay phase shift over the frequency band of 5.0 to
6.0 GHz (gigahertz). The length of the lines were varied
log-periodically and the spacing was held constant to provide a
true time delay. The device performance was in accordance with the
solid curve 170 and the frequency band of operation represents a
bandwidth of 18 percent. It is to be noted that this achieved
bandwidth is not an inherent limitation to the device but rather
resulted from a particular design. Broken lines 171 and 173 show a
theoretical perfect true time delay characteristic. The solid
experimental line 170 varies a relatively small amount from the
theoretically perfect characteristic. In addition to this wide
bandwidth performance, the device could be switched from one phase
state to a second within five microseconds. The energy required to
perform the switching operation was 20 microjoules. The size of the
constructed device was 1.0 .times. 2.0 .times. 0.025 inches with a
weight of 4.6 grams (0.010 lbs.).
Thus there has been provided electronically controllable RF phase
shifters which may develop over a 360.degree. phase shift, a
characteristic of true time delay or which may be designed to
provide a constant phase versus frequency characteristic. The phase
shifters in accordance with the invention provide a bandwidth
substantially greater than any similar type devices known in the
art today. The phase shifters of the invention operate with either
terminal or port being the input so that the input RF signal can be
applied initially to either the short or the long line segments.
The principles of the invention include controlling the phase shift
electronically and varying the line length in the configuration of
a meander line or other arrangements having adjacent line segments.
The phase shifter devices which employ log-periodic line spacing
develop a true time delay in accordance with the principles of the
invention. However, it is to be understood that phase shifters
having a line spacing other than log-periodic such as to develop a
constant phase versus frequency characteristic are within the scope
of the invention.
* * * * *