Note: Descriptions are shown in the official language in which they were submitted.
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FILTER AND METHOD AND APPARATUS FOR MANUFACTURING FILTERS
The present invention relates to filters and to a method
and apparatus for manufacturing filters, and relates
particularly, but not exclusively, to microwave filters and a
method and apparatus for manufacturing microwave filters.
Microwave filters are often constructed from networks of
coupled passive resonators, each passive resonator having a
finite unloaded Q factor. In narrow bandwidth applications,
the resistive loss associated with this finite unloaded Q
factor can lead to significant reduction in achievable
performance, and in bandpass applications, designs with a good
input and output reflection coefficient will exhibit
significant bandpass loss variation.
In the narrow band bandstop case the resistive loss
manifests itself as a roll off of insertion loss into the pass
band, and also limits the achievable notch depth. The
combination of these two effects limits the achievable
selectivity from a bandstop filter designed using previously
available techniques.
In an existing bandstop filter, resonators are coupled
off from a main through transmission line with an electrical
separation of an odd number of quarter wavelengths, as shown in
Figure 1. Each resonator couples loss into the system, giving
rise to the problems outlined above.
In various applications of microwave filters, such as in
base stations for cellular telecommunications, the above
difficulties are addressed by using components having very high
Q factors, typically up to 40, 000. However, this increases the
physical size of the devices involved, whereas it is usually
desirable in such applications to make the devices as compact
as possible.
Preferred embodiments of the present invention seek to
provide a filter which, although constructed using finite Q
-dements, does not suffer from a reduction in selectivity as a
result of resistive losses caused by these finite Q factor
elements.
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Preferred embodiments of the present invention also seek
to achieve a desired filter characteristic using components
having lower unloaded Q factor than in the case of the prior
art.
Preferred embodiments of the present invention also seek
to provide a bandstop/pass filter having a steep transition
between the stop and pass band and using lower value unloaded
Q factor components than in the case of the prior art.
According to an aspect of the present invention, there is
provided a method of designing a filter, the method comprising
defining a desired filter characteristic, and applying an
algorithm to the desired characteristic to provide a filter
having infinite Q factor elements and having a theoretical
characteristic corresponding to the desired characteristic
transformed to compensate for the difference between finite Q
factor and infinite Q factor elements.
According to another aspect of the present invention,
there is provided a method of manufacturing a filter, the
method comprising the steps of designing a filter according to
a method as defined above, and constructing using finite Q
factor elements a filter corresponding to the theoretical
filter.
This provides the advantage of a filter design technique
which takes resistive losses of the individual components, such
as inductors and capacitors, of the filter into account, and
therefore enables a filter having a desired characteristic to
be designed using finite Q value components. This in turn
enables a filter having a particular characteristic to be
realised using lower unloaded Q factor components than in the
case of the prior art, which in turn enables the filter to be
constructed more compactly than in the case of the prior art.
According to another aspect of the present
invention, there is provided an apparatus for use in
manufacturing filters, the apparatus comprising an input means
..in which a desired filter characteristic is defined in use, and
means for applying an algorithm to the desired characteristic
to provide a filter having infinite Q factor elements and
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having a theoretical- characteristic corresponding to the
desired ,characteristic transformed to compensate for the
difference between infinite Q and finite Q factor elements.
According to a further aspect of the invention, there is
provided a filter manufactured according to a method or using
an apparatus as defined above.
This has the advantage of enabling the realisation of a
filter having lower Q value components than in the case of the
prior art, which in turn enables the construction of a more
compact filter.
According to a further aspect of the invention, there is
provided a filter comprising first and second resonators
interconnected by a quadruplet of impedance inverters, a ladder
network connected to the quadruplet of impedance inverters via
a series resistor and comprising a plurality of further
resonators, wherein adjacent further resonators of the ladder
network are coupled to each other by respective impedance
inverters.
In a preferred embodiment, the filter is a reflection
mode filter.
The filter is preferably a microwave filter.
A filter may be a bandstop and/or a band pass filter.
Preferably, the step of applying said algorithm comprises
shifting the pole/zero plot of the desired filter
characteristic by a constant amount.
A preferred embodiment of the invention will now be
described, by way of example only and not in any limitative
sense, with reference to the accompanying drawings, in which:
Figure 1 shows a conventional bandstop filter;
Figure 2 shows a reflection mode filter comprising a low
loss circulator connected to an input of a microwave band pass
resonator;
Figure 3 shows a lossless low pass ladder network;
Figure 4 shows a network comprising a resistive
-.attenuator followed by a lossless ladder network in which N=3 ;
Figure 5 shows a complete synthesis cycle for a degree 4
network:
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Figure 6 shows a network corresponding to the network of
Figure 5 modified by the replacement of the first four elements
shown in Figure 5 by a quadruplet of impedance inverters and
two capacitors;
Figure 7 shows a reflection mode band stop microwave
filter;
Figure 8 shows the simulated frequency response of the
filter of Figure 7;
Figure 9 shows a general Nth degree circuit for the band
stop reflection mode filter of Figure 7; and
Figure 10 shows the measured frequency response of an
actual filter.
Referring to Figure 2, there is shown a resonant circuit
with finite loss which is coupled to one of the ports of a
circulator. The transmission characteristic from ports 1 to 3
is the reflection coefficient from the network connected at
port 2. If the input coupling to the resonant circuit is
adjusted so that the resistive part of its input impedance is
matched to the circulator, then at resonance all power supplied
at port 1 will emerge at port 2 and be absorbed in the
resistive part of the resonator.
Hence there is no transmission to port 3 and the 1-3
transmission characteristic is that of a resonator with
infinite unloaded Q. For a resonator of centre frequency fo
and 3 dB bandwidth B the unloaded Q is given by
Qu _ 2~ C1)
B
For example, if B = 250 KHz and fo=1 GHz, then Qu = 8000.
It can therefore be seen that the previously considered
specification can be met with much lower Q resonators, with a
consequent reduction in physical size, provided that a design
procedure for multi-element filters is available.
In order to provide such a design procedure, the
magnitude squared of the input reflection coefficient of a
lossless lowpass prototype filter may be expressed as
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Sm (Jw),I2- - FN2 (w)
1+FNZ ( w )
Where FN(w) is the characteristic function for a
Butterworth, Chebychev, Elliptic Function or other prototype
network. This reflection coefficient may readily be
synthesised as a lossless lowpass ladder network which is
terminated in a resistor as shown in Figure 3. In order to
include eventual resonator losses we can multiply by an
arbitrary constant K to yield;
4 Sm( jw) I 2 - KFN2(w)
1 + FN2(w)
This may now be synthesised as a resistive attenuator
followed by a lossless ladder network which in turn is
terminated in a resistor, as shown in Figure 4.
The resultant network now contains dissipative elements.
However, these are not distributed throughout the Nth degree
network but remain concentrated at the input. A network
containing lossy elements is required so that the required
response can be achieved using finite Q resonators.
In order to achieve this, compensation is made for
eventual resonator loss by shifting the poles and zeros of
S11(p) towards the jw axis by a constant amount a, i.e.
p -~ p - a
Thus for Sll(p) - K Nfp)
D (p)
-" Then S11 ( p-a ) - K N (p-a 1
(1)
D (p-a)
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The reflection coefficient given in (1) may now be
synthesised as one port impedance function. First the maximum
value of K must be uniquely determined for any specific value
of a, so that the resultant network is passive and has minimum
loss for a given value of a.
The specific frequencies ~o and values of K are then
determined such that:
I Sll ( P-a ) I 2 - 1
and d I S11 ( P-a ) I
do
are simultaneously satisfied with the minimum value of K.
Having found the values coo and a then formulate
S11 ( p-a ) - K N p-a~ - N1
D (p-a) D1(p)
The input impedance Zin (p) may now be found from
Zin(P) - _D~lP) + N~-LPG
' D~(P) - N~ (P)
Zin has a transmission zero at coo and thus cannot be
synthesised as a ladder network.
However any positive real function may be synthesised
using Brunes' Procedure as set out in O Brune. "Synthesis of a
Finite Two-Terminal Network whose Driving Point Impedance is a
Prescribed Function of Frequency". Journal of Maths and
Physics, Vol X no 3, 1931, p 191.
Given Yin(p) - 1 and evaluating Yin at p = j~o it is
Zin(p)
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found that this is a pure susceptance. This is a consequence
of the network being purely reflective at that frequency. This
susceptance will be negative i.e.
Yin (j~o) - -jB
Extracting a shunt negative capacitor of value -Cl from Yin
provides
Yl(p) - Yin(p) + Clp
Observing that Yl is one degree higher in p than Yin then since
Yin ( jc~o) was purely imaginary, Yl must be equal to zero at this
frequency . Consequently Yl ( p ) must have a quadratic f actor at
p = ~
Thus Y,(P) - (PZ + X02) N(p)
P(P)
Inverting Yl ( p ) to form Z1 ( p ) a series branch composed of a
parallel tuned circuit can be extracted, ie
Z~(P) - ~(P) - AP - ZZ(P)
( PZ+~o2 ) N ( P ) p2+~o2
A is the residue of Zl ( p ) at p =jwo . Inverting Z2 ( p ) to obtain
Y2 ( p ) then a shunt capacitor may be extracted from Y~ ( p ) as
follows:
C3 - Yz(P)
P p=°°
~. and Y3 ( P ) - Yz ( P ) -C3P
i i i i
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Forming Z, ( p ) + _ 1
Y3(p)
A series resistor equal in value to the minimum real part of
Z,(p) must now be extracted. This may be evaluated from the
minimum value of the even part of Z, ( p ) .
Thus Z5(p) - Z,(p) -R
where R - min Ev(Z,(p))
In most cases the minimum value of Z,(p) will occur at c~
- ~ and the remaining network may be synthesised as a lossy
ladder network.
The complete synthesis cycle is shown for a degree 4
network in Figure 5.
It is important to note that the network shown in Figure
is not immediately suitable for realisation using microwave
resonators. However, it may readily be transformed into the
network of Figure 6 which consists entirely of inverters,
capacitors and resistors.
The capacitors shown in Figure 6 are initially lossless
but are transformed into finite Q elements by the final simple
modification.
p ~ p + a
The resultant lowpass prototype network may then be
converted into a bandpass network by applying the appropriate
transformation for any particular type of resonator.
Example
The procedure outlined has been applied successfully to
the design of a bandstop filter with specification as outlined
above.
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A fourth degree Elliptic Function Filter was synthesised.
The choice of a was 0.093 corresponding to approximately 6 dB
out of band loss. The resultant network is shown in Figure 7.
The simulated response of this network is shown in Figure 8,
from which it can be seen that the response achieves the
desired specification. This actual filter has been constructed
using coaxial resonators. The measured performance
characteristics are shown in Figure 10 and are in excellent
agreement with theory.
It will be appreciated by persons skilled, in the art that
the above embodiment has been described by way of example only,
and not in any limited sense, and that various alterations and
modifications are possible without departure from the scope of
the invention as defined by the appended claims.
