Ferromagnetic resonant devices include special coupling loops formed of multi-conductor transmission lines to increase the RF electromagnetic coupling to the ferromagnetic resonators, while decreasing coupling to spurious resonant modes.

BACKGROUND 
1. Field 
This invention relates to improvements in ferromagnetic filters and, in 
particular, to a method for increasing the bandwidth while reducing 
spurious responses in such filters. 
2. Prior Art 
A ferromagnetic filter in its rudimentary form, consist of a coupling loop 
positioned close to a sphere of a ferromagnetic material located in a 
magnetic field. The ferromagnetic material, usually yttrium-iron-garnet 
(YIG), can be made to produce a principal resonance at a frequency 
determined by the strength of the magnetic field. The resonant frequency 
is given by fo=.gamma.Ho where Fo is the resonant frequency, .gamma. is 
the gyromagnetic ratio, 2.8 MHz/oersteds, and Ho is the applied magnetic 
field in gauss. 
Bandwidths of such devices are usually small, typically less than 35 MHz 
about the center frequency. Increasing the bandwidth of these filters has 
been a long-standing objective. In prior art approaches to produce wider 
bandwidths, the coupling between the loop and the sphere has been 
increased by bringing the loop closer to the sphere or a strap with lower 
inductance has been substituted for the more commonly used single wire 
loop. These approaches have resulted in an increase in both crossing and 
tracking spurious responses. Tracking spurious are spurious responses 
which follow the principal resonance of the sphere as it is tuned across a 
frequency range. Crossing spurious are those which do not tune at the same 
rate as the principal resonance mode and therefore cross through the 
principal resonance mode as it is tuned through a frequency range. 
Prior approaches designed to reduce the spurious responses have included 
decreasing the unloaded Q of the YIG sphere by means of roughening the 
surface of the sphere; however, this process increases the insertion loss 
at the principal resonance. 
There are a number of additional problems associated with prior art YIG 
filters which may be explained with reference to a rudimentary YIG filter, 
such as that shown in FIG. 4. In this Figure, an input port 401 is 
connected to an output port 402 by way of a coupling loop 403, which 
surrounds a YIG sphere 404. Note that in all figures, dots on a line about 
a YIG sphere represent the initiation or termination of a coupling loop. 
For example, in FIG. 4B, the dots represent the initiation and termination 
of loop 403. In the operation of this device, a signal placed on the input 
port is transmitted to the output port. Signals which are at the principal 
resonance of the sphere are rejected and returned to the input port. In 
this mode of operation, the device functions as a band-stop filter. 
The length of the line from the input port to the output port forms an 
inductance that is an integral part of the band-stop filter. This 
inductance limits the range over which the band-stop filter can operate 
because it functions as a portion of a separate low-pass filter structure. 
Increasing the inductance reduces the high frequency cutoff of the 
low-pass filter which, in turn, limits the high frequency response of the 
YIG filter. 
One prior art approach, intended to increase the bandwidth of the YIG 
filter at its principal resonance, is to lower the external Q of the 
sphere and loop by increasing the coupling between the two. This is done 
by increasing the turns of the coupling loops about the sphere. The 
disadvantage of this approach is it increases the series inductance of the 
line between the input and output ports and consequently reduces the high 
frequency cutoff off the low-pass filter section formed by this line. 
The desirability of reducing the line inductance in band-stop filters has 
been generally recognized; however, it has not been as well recognized for 
bandpass filter. Attempts to reduce the line inductance by again 
substituting a wide strap for the usual single wire loop has resulted in 
the increases spurious response described previously. As an alternative to 
the strap, a number of parallel, closely spaced or touching wires has also 
been used with similar unsatisfactory results. 
Practical prior art ferromagnetic resonator filters, which have been, for 
the most part, band-pass filters, usually make use of the same components 
described in connection with the band-stop filter of FIG. 4. That is, they 
make use of a coupling wire for coupling to the ferromagnetic material, 
which is typically in the shape of a sphere. The coupling wire is often 
formed into a loop around the sphere for increased coupling to the sphere. 
The coupling loops and spheres are housed in a structure which provides RF 
shielding between stages, but which allows the coupling wires to pass from 
stage to stage through the shield. A stage, as used herein is a basic 
filter section comprising for example one YIG sphere and its associated 
circuitry which is typically one or more coupling loops positioned about 
the sphere. In FIG. 2, loop 206 positioned about YIG sphere 201 comprise a 
first stage, loop 207 and sphere 202 comprise a second, and loop 208 and 
sphere 203 comprise a third. 
Interstage coupling is accomplished with a wire with two loops formed along 
it, both ends of this wire being electrically connected to the RF housing 
or ground. Input and output coupling is accomplished with a wire loop 
connected from the input or output transmission line to the RF housing or 
ground. The coupling loops in each stage are positioned orthogonally with 
respect to one another to minimize coupling from one loop to another. 
It is generally known that a band-pass filter can be designed by using 
input and output stage external Q and interstage coupling coefficients 
because the internal Q is relatively high in comparison to the Q of the 
external circuitry. The coupling values required are available from 
published tables and are related to the basic filter network. Thus, it is 
possible to attain the band-pass filter response desired from a 
ferromagnetic filter by adjusting the coupling loops close to the sphere, 
or by using a sphere which is large compared to the diameter of the 
coupling loop. Unfortunately, the spurious problem encountered with 
band-stop filters is present in band-pass filters as well. Both of these 
approaches to wide bandwidths lead to increased coupling to spurious 
modes. The spurious modes are undesirable in a band-pass filter because 
the tracking spurious modes produce additional passbands which degrades 
the filter out-of-band rejection and the crossing spurious modes produce 
additional passband insertion loss. Coupling to these spurious modes can 
be reduced by decreasing the unloaded Q of the ferromagnetic sphere, but 
this also causes increased passband insertion loss and a reduction in 
filter bandwidth. Thus, increased bandwidth in prior art devices results 
in degraded filter performance. 
SUMMARY 
In the present invention, spurious responses have been reduced and 
bandwidth has been increased in YIG filters without increasing loss by 
means of a multi-conductor loop in which the multi-conductors are 
separated from one another.

DETAILED DESCRIPTION OF THE INVENTION 
In the band-stop filter of FIG. 1, a drive circuit 101 supplies a drive 
signal to a winding 103 located about a core 102, to produce a magnetic 
field 109 directed to pass through a ferromagnetic sphere 106. An input 
port 104 is connected to an output port 105, by way of a loop 107 which 
encircles sphere 106. The sphere and loop are located in a cavity 108 of a 
frame 109. 
FIG. 1A represents a cross sectional view of the side of the band-stop 
filter, while FIG. 1B represents a top view. It can be seen in FIG. 1B 
that the coupling loop is divided into two separate conductors, 107A and 
107B. 
In the operation of the device in FIG. 1, a signal placed on the input port 
104 is delivered to the output port 105. Energy at the frequency of the 
resonant sphere is reflected by the sphere back to the input port, 
creating a band-stop filter action at the principal resonance frequency of 
the sphere. 
The conductors 107A and 107B are separated by at least the thickness of one 
of the conductors. The two conductors provide a reduction in the 
inductance in the line between ports 104 and 105 over a single conductor 
line, while providing a lower spurious response than is usually 
encountered with either a strap or a single conductor loop, for the same 
equivalent coupling bandwidth. The reduced inductance of the multiple 
conductors produces a lower external Q device and, therefore, increases 
the bandwidth. With the present invention, bandwidths have been increased 
by approximately 50 percent over that achieved with prior art devices. 
In order to explain the benefit of the invention, the mathematics which 
describe its operation are introduced below. The external coupling to a 
YIG shpere is expressed by: 
##EQU1## 
Where: Qe=external Q of the resonator 
r=radius of the coupling loop in meters 
Ra=external load impedance in ohms 
N=number of turns 
.mu..sup.o =permeability of free space, 1.256.times.10.sup.-6 henries/meter 
Vm=volume of the YIG sphere in meters.sup.3 
.gamma.=gyromagnetic ratio, 1.759.times.10.sup.11 (MKS units) 
Ms=saturation magnetization of the material (MKS units) 
.omega..sup.o =resonant frequency of the resonator in radians/second 
Ls=self inductance of the coupling loop in henries 
The derivation of the above expression is based on the representation of 
the YIG resonator as an equivalent lumped parallel resonate circuit, 
formed of conventional inductors and capacitors, separate from the 
coupling loop inductance. The quantity in the first bracket then 
represents an equivalent circuit for the YIG resonator. The equivalent 
circuit values for the inductor and capacitors can be obtained by setting 
L.sub.s equal to zero in Equation 1. 
##EQU2## 
An equivalent circuit for an input stage is shown in FIGS. 5A and B, while 
an equivalent circuit for two YIG resonators coupled by wire loops is 
shown in FIGS. 6A and B. 
The schematic circuit of FIG. 5A comprises a generator 501, a generator 
source impedance 502, a ferromagnetic sphere 504, and a loop 503 coupled 
to the ferromagnetic sphere. 
FIG. 5B is a lumped element equivalent of the circuit shown in FIG. 5A. 
This circuit comprises a generator 501, a generator source impedance 502, 
a self-inductance of the loop 504, an equivalent inductance of the 
ferromagnetic sphere 506, and an equivalent capacitance of the 
ferromagnetic sphere 505. 
FIG. 6A is a schematic of the interstage coupling of a band-pass filter. 
This circuit comprises a first loop 601, a first ferromagnetic sphere 602, 
a second loop 604, and a second ferromagnetic sphere 603. 
FIG. 6B is a lumped element equivalent circuit for the circuit of FIG. 6A, 
wherein inductor 605 and capacitor 606 represent the resonance of sphere 
602 and the inductor 608 and capacitor 609 represents the resonant circuit 
of sphere 604. The inductance 607 represents the combined series 
inductance of loops 601 and 604. 
It can be seen that the equivalent circuit for a YIG band-pass filter is an 
inductively coupled filter. The coupling between stages of an inductively 
coupled filter is given by: 
##EQU3## 
Where: L.sub.i, i+1 =coupling inductance between stages i and i+1 
L.sub.i =inductance of the inductor in the i.sup.th stage 
L.sub.i+1 =inductance of the inductor in the i.sup.th +1 stage 
BW=bandwidth of the filter in radians/second 
The inductance L.sub.i, i+1 is the self inductance of the coupling wire. At 
microwave frequencies this coupling wire has electrical length and its 
inductance is expressed by: 
EQU L.sub.i, i+1 =(Zo/.chi..sub.o) sin (.beta..lambda.) Equation (4) 
Where: 
Zo=equivalent characteristic impedance of the coupling wire within the 
structure chosen 
.beta.=propagation constant in radians/meter 
.lambda.=length of the coupling wire in meters 
It now becomes apparent that the interstage coupling in a loop coupled YIG 
filter is highly dependent upon the characteristic impedance and length of 
the coupling loop. Prior art devices typically use a single 0.003 inch 
diameter wire in a 0.060 inch diameter cavity, and this structure has a 
characteristic impedance of approximately 160 ohms. Attempts to increase 
the coupling in prior art devices consisted of bringing the coupling wire 
closer to the sphere. This resulted in increased coupling to spurious 
responses. Since the above mathematical explanation of the parameters 
involved in the coupling to YIG resonators is not generally available, 
designs of prior art devices have not made use of all of the coupling 
parameters involved. In fact, most prior art design practice is based, 
primarily, upon previous experience of the practitioner and upon an 
empirical approach, rather than a mathematical or quantitive one. The 
mathematics presented provides a method for designing the filter input and 
output couplings, as well as interstage couplings which are required for a 
particular filter passband response. These equations show the importance 
of the coupling loop length and characteristic impedance on filter 
bandwidth. 
This invention effectively increases the coupling to YIG resonators by 
providing a decrease in the characteristic impedance of the coupling 
structure. This is accomplished through a construction which uses multiple 
and parallel conductors. These conductors are spread apart, which further 
reduces the characteristic impedance, but with an accompanying decrease in 
the coupling to spurious modes compared to close space conductors. 
It is now believed that coupling to spurious modes is enhanced by a 
conductive surface near the YIG sphere, such that an image of the YIG 
sphere can exist in this conductor. Crossing spurious responses are 
observed only at the main resonance. That is, they are not excited at 
frequencies away from the main resonance. It would appear that the main 
resonance mode couples to the spurious responses, rather than the coupling 
loop itself coupling directly to the spurious modes. An explanation for 
this phenomenon is provided by an image surface which allows an image 
resonator to exist. It is generally known that an additional sphere in a 
coupling structure will cause coupling to spurious modes. This explains 
why prior art devices, which use coupling ribbons, straps, large diameter 
wire, or other large conductors, also have strong coupling to crossing 
spurious modes. 
This invention effectively reduces or eliminates coupling to crossing 
spurious modes, as well as other spurious modes. The use of multiple 
conductors spread apart, in effect, breaks up the image plane and reduces 
the coupling to spurious modes. 
The benefit of the invention is apparent in the design and performance of 
YIG band-pass filters. Prior art devices, using single wire conductors, 
and doped material to avoid low-level coincidence limiting provide a 
maximum filter bandwidth of 25 to 4 MHz over a 2 to 18 GHz tuning range. 
With the present invention, filter bandwidths of greater than 50 MHz are 
consistently attained, along with reduced spurious responses. 
The new invention is also a benefit in the performance of YIG band-stop 
filters. The coupling to a YIG band-stop filter section is also given by 
equation 1, but the term Ra becomes equal to twice the system impedance 
because the coupling loop is in series with the source and load impedance. 
Since the coupling loop self-inductance is in series with the transmission 
path, one of the primary design problems is the attainment of a wide 
impedance match in a band-stop filter. In general, this requires coupling 
loops with less self-inductance, and a lower characteristic impedance for 
the coupling loop structure than is used in band-pass filters. Prior art 
devices typically use a large conductor cross-section, such as relatively 
large diameter wire, for the coupling loop, but this approach contributes 
to the coupling to spurious modes, as explained by the image surface 
concept. 
The use of the multiple, and separated, conductor coupling loop structure 
provides the reduced coupling loop self-inductance required in a band-stop 
filter along with reduced coupling to spurious responses. 
FIG. 2 is a drawing of a multistage band-stop filter in which FIG. 2A 
illustrates a side view of this filter, while FIG. 2B illustrates a top 
view. In these figures, an input port 204 is coupled to an output port 205 
by means of cascaded coupling loops 206, 207, and 208, which encircle 
ferromagnetic spheres 201, 202, and 203, respectively. It can be seen in 
FIG. 2B that loop 207 is comprised of conductors 207A and 207B, and 
coupling loop 208 is comprised of conductors 208A and 208B. 
In the operation of this filter, a signal placed on port 204 arrives at 
port 205, except for power reflected at the resonant frequency of three 
spheres. 
It is possible to combine single solid wire loops with multiple conductor 
loops, as can be seen in this Figure. The use of different number of 
conductors in a loop varies the inductance of the loop. This adjustment in 
the inductance can be used as an aid in varying the impedance of each 
section as required. 
FIG. 3A illustrates a side view of a simple bandpass filter employing the 
present invention, while FIG. 3B illustrates a top view of this filter. In 
these Figures, input port 301 is connected to ground by way of loop 302, 
which encircles YIG sphere 305. Output port 303 is connected to ground by 
way of loop 304. In FIG. 3B, it can be seen that both loops 304 and 302 
each comprise two conductors, A and B, and that loop 302 passes over the 
top of the sphere, while loop 304 passes beneath the sphere. The two loops 
are oriented in a generally orthogonal manner. A signal supplied to input 
port 301 is fed to loop 302 where it is coupled through the sphere at the 
principal resonance frequency to the output loop 304 and then is fed to 
the output port 303. Typically two conductor loops are used and the 
conductors are spaced apart by at least the thickness of one of the 
conductors. A method for predictably producing the proper spacing in 
production is to use a strip conductor and by means of photo etching 
techniques divide the strip into multiple conductors.