US20010026200A1 - Filter and method and apparatus for manufacturing filters - Google Patents

Abstract

A method of producing filters using lower unloaded Q factor components than filters with the same performance characteristics but requiring higher unloaded Q factor components is disclosed. The method includes the steps of defining a desired filter characteristic and applying an algorithm which provides a filter having infinite Q factor elements and having a theoretical characteristic corresponding to the desired characteristic transformed to a compensate for the difference between finite Q factor and infinite Q factor elements.

Description

• 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. [0001]
• 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. [0002]
• 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. [0003]
• 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 FIG. 1. Each resonator couples loss into the system, giving rise to the problems outlined above. [0004]
• 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. [0005]
• Preferred embodiments of the present invention seek to provide a filter which, although constructed using finite Q elements, does not suffer from a reduction in selectivity as a result of resistive losses caused by these finite Q factor elements. [0006]
• 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. [0007]
• 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. [0008]
• 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. [0009]
• 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. [0010]
• 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. [0011]
• According to another aspect of the present invention, there is provided a: 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 having a theoretical characteristic corresponding to the desired characteristic transformed to compensate for the difference between infinite Q and finite Q factor elements. [0012]
• 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. [0013]
• 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. [0014]
• 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. [0015]
• In a preferred embodiment, the filter is a reflection mode filter. [0016]
• The filter is preferably a microwave filter. [0017]
• A filter may be a bandstop and/or a band pass filter. [0018]
• Preferably, the step of applying said algorithm comprises shifting the pole/zero plot of the desired filter characteristic by a constant amount.[0019]
• 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: [0020]
• FIG. 1 shows a conventional bandstop filter; [0021]
• FIG. 2 shows a reflection mode filter comprising a low loss circulator connected to an input of a microwave band pass resonator; [0022]
• FIG. 3 shows a lossless low pass ladder network; [0023]
• FIG. 4 shows a network comprising a resistive attenuator followed by a lossless ladder network in which N=3; [0024]
• FIG. 5 shows a complete synthesis cycle for a [0025] degree 4 network;
• FIG. 6 shows a network corresponding to the network of FIG. 5 modified by the replacement of the first four elements shown in FIG. 5 by a quadruplet of impedance inverters and two capacitors; [0026]
• FIG. 7 shows a reflection mode band stop microwave filter; [0027]
• FIG. 8 shows the simulated frequency response of the filter of FIG. 7; [0028]
• FIG. 9 shows a general Nth degree circuit for the band stop reflection mode filter of FIG. 7; and [0029]
• FIG. 10 shows the measured frequency response of an actual filter.[0030]
• Referring to FIG. 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 [0031] 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 [0032] 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 $\begin{array}{cc}\mathrm{Qu}=\frac{2\mathrm{fo}}{B}& \left(1\right)\end{array}$

  
• 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. [0033]
• 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 [0034] ${s_{11}\left(j\omega \right)}^2=\frac{F_{\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="US20010026200A1-20011004-D00001.png"\; state="\{\{state\}\}">N</figure-callout>}}^2\left(\omega \right)}{1+{\mathrm{<figure-callout\; id="2"\; label="F\; N"\; filenames="US20010026200A1-20011004-D00001.png"\; state="\{\{state\}\}">F</figure-callout>}}_N^{}\left(\omega \right)}$

  
• Where F[0035] _N(ω) 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 FIG. 3. In order to include eventual resonator losses we can multiply by an arbitrary constant K to yield; ${s_{11}\left(j\omega \right)}^2=\frac{{\mathrm{<figure-callout\; id="2"\; label="KF\; N"\; filenames="US20010026200A1-20011004-D00001.png"\; state="\{\{state\}\}">KF</figure-callout>}}_N^{}\left(\omega \right)}{1+{\mathrm{<figure-callout\; id="2"\; label="F\; N"\; filenames="US20010026200A1-20011004-D00001.png"\; state="\{\{state\}\}">F</figure-callout>}}_N^{}\left(\omega \right)}$

  
• 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 FIG. 4. [0036]
• 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. [0037]
• In order to achieve this, compensation is made for eventual resonator loss by shifting the poles and zeros of S[0038] ₁₁(p) towards the jω axis by a constant amount α, i.e. $\begin{array}{cc}p\to p-\alpha \mathrm{Thus}\mathrm{for}s_{11}\left(p\right)=\frac{\mathrm{KN}\left(p\right)}{D\left(p\right)}\mathrm{Then}s_{11}\left(p-\alpha \right)=\frac{\mathrm{KN}\left(p-\alpha \right)}{D\left(p-\alpha \right)}& \left(1\right)\end{array}$

  
• 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 α, so that the resultant network is passive and has minimum loss for a given value of α. [0039]
• The specific frequencies ω[0040] _o and values of K are then determined such that: ${s_{11}\left(p-\alpha \right)}^2=1$ $\mathrm{and}\frac{}{\omega }{s_{11}\left(p-\alpha \right)}^2=0$

  
• are simultaneously satisfied with the minimum value of K. [0041]
• Having found the values ω[0042] _o and α then formulate $s_{11}\left(p-\alpha \right)=\frac{\mathrm{KN}\left(p-\alpha \right)}{D\left(p-\alpha \right)}=\frac{\mathrm{N1}\left(p\right)}{\mathrm{D1}\left(p\right)}$

  
• The input impedance Zin (p) may now be found from [0043] $\mathrm{Zin}\left(p\right)=\frac{{\mathrm{<figure-callout\; id="1"\; label="D"\; filenames="US20010026200A1-20011004-D00001.png,US20010026200A1-20011004-D00002.png"\; state="\{\{state\}\}">D</figure-callout>}}_1\left(p\right)+{\mathrm{<figure-callout\; id="1"\; label="N"\; filenames="US20010026200A1-20011004-D00001.png,US20010026200A1-20011004-D00002.png"\; state="\{\{state\}\}">N</figure-callout>}}_1\left(p\right)}{{\mathrm{<figure-callout\; id="1"\; label="D"\; filenames="US20010026200A1-20011004-D00001.png,US20010026200A1-20011004-D00002.png"\; state="\{\{state\}\}">D</figure-callout>}}_1\left(p\right)-{\mathrm{<figure-callout\; id="1"\; label="N"\; filenames="US20010026200A1-20011004-D00001.png,US20010026200A1-20011004-D00002.png"\; state="\{\{state\}\}">N</figure-callout>}}_1\left(p\right)}$

  
• Zin has a transmission zero at ω[0044] _o 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 [0045] no 3, 1931, p 191. $\mathrm{Given}\mathrm{Yin}\left(p\right)=\frac{1}{\mathrm{Zin}\left(p\right)}\mathrm{and}\mathrm{evaluating}$ $\mathrm{Yin}\mathrm{at}p=j{\omega }_o\mathrm{it}\mathrm{is}$

  
• 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. [0046]
• Yin (jωo)=−jB
• Extracting a shunt negative capacitor of value −C[0047] ₁ from Yin provides
• Y ₁(p)=Yin(p)+C ₁ p
• Observing that Y[0048] ₁ is one degree higher in p than Yin then since Yin (jω_o) was purely imaginary, Y₁ must be equal to zero at this frequency. Consequently Y₁ (p) must have a quadratic factor at p=±jω_o. ${\mathrm{<figure-callout\; id="1"\; label="Y"\; filenames="US20010026200A1-20011004-D00001.png,US20010026200A1-20011004-D00002.png"\; state="\{\{state\}\}">Y</figure-callout>}}_1\left(p\right)=\left({\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="US20010026200A1-20011004-D00001.png"\; state="\{\{state\}\}">p</figure-callout>}}^2+{\omega }_o^2\right)\frac{N\left(p\right)}{P\left(p\right)}$

  
• Inverting Y[0049] ₁(p) to form Z₁(p) a series branch composed of a parallel tuned circuit can be extracted, ie $Z_{}$ ${}_1\left(p\right)=\frac{D\left(p\right)}{\left({\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="US20010026200A1-20011004-D00001.png"\; state="\{\{state\}\}">p</figure-callout>}}^2+{\omega }_o^2\right)N\left(p\right)}=\frac{\mathrm{<figure-callout\; id="2"\; label="Ap\; p"\; filenames="US20010026200A1-20011004-D00001.png"\; state="\{\{state\}\}">Ap</figure-callout>}}{p^{}}={\mathrm{<figure-callout\; id="2"\; label="Z"\; filenames="US20010026200A1-20011004-D00001.png"\; state="\{\{state\}\}">Z</figure-callout>}}_2\left(p\right)$

  
• A is the residue of Z[0050] ₁(p) at p=jω_o. Inverting Z₂(p) to obtain Y₂(p) then a shunt capacitor may be extracted from Y₂(p) as follows: ${\mathrm{<figure-callout\; id="3"\; label="C"\; filenames="US20010026200A1-20011004-D00001.png,US20010026200A1-20011004-D00007.png"\; state="\{\{state\}\}">C</figure-callout>}}_3=\frac{{\mathrm{<figure-callout\; id="2"\; label="Y"\; filenames="US20010026200A1-20011004-D00001.png"\; state="\{\{state\}\}">Y</figure-callout>}}_2\left(p\right)}{p}p=\infty$ $\mathrm{and}{\mathrm{<figure-callout\; id="3"\; label="Y"\; filenames="US20010026200A1-20011004-D00001.png,US20010026200A1-20011004-D00007.png"\; state="\{\{state\}\}">Y</figure-callout>}}_3\left(p\right)={\mathrm{<figure-callout\; id="2"\; label="Y"\; filenames="US20010026200A1-20011004-D00001.png"\; state="\{\{state\}\}">Y</figure-callout>}}_2\left(p\right)-{\mathrm{<figure-callout\; id="3"\; label="C"\; filenames="US20010026200A1-20011004-D00001.png,US20010026200A1-20011004-D00007.png"\; state="\{\{state\}\}">C</figure-callout>}}_3p$ $\mathrm{Forming}{\mathrm{<figure-callout\; id="4"\; label="Z"\; filenames="US20010026200A1-20011004-D00001.png"\; state="\{\{state\}\}">Z</figure-callout>}}_4\left(p\right)+\frac{1}{{\mathrm{<figure-callout\; id="3"\; label="Y"\; filenames="US20010026200A1-20011004-D00001.png,US20010026200A1-20011004-D00007.png"\; state="\{\{state\}\}">Y</figure-callout>}}_3\left(p\right)}.$

  
• A series resistor equal in value to the minimum real part of Z[0051] ₄ (p) must now be extracted. This may be evaluated from the minimum value of the even part of Z₄(p).
• Thus Z₅(p)=Z₄(p) −R
• where R=min Ev(Z₄(p))
• In most cases the minimum value of Z[0052] ₄(p) will occur at ω=∞ and the remaining network may be synthesised as a lossy ladder network.
• The complete synthesis cycle is shown for a [0053] degree 4 network in FIG. 5.
• It is important to note that the network shown in FIG. 5 is not immediately suitable for realisation using microwave resonators. However, it may readily be transformed into the network of FIG. 6 which consists entirely of inverters, capacitors and resistors. [0054]
• The capacitors shown in FIG. 6 are initially lossless but are transformed into finite Q elements by the final simple modification. [0055]
• 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. [0056]
EXAMPLE
• The procedure outlined has been applied successfully to the design of a bandstop filter with specification as outlined above. [0057]
• A fourth degree Elliptic Function Filter was synthesised. The choice of α was 0.093 corresponding to approximately 6 dB out of band loss. The resultant network is shown in FIG. 7. The simulated response of this network is shown in FIG. 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 FIG. 10 and are in excellent agreement with theory. [0058]
• 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. [0059]

Claims (15)

1. A method of designing a filter, comprising the steps of:

(i) defining a desired filter characteristic; and

(ii) applying an algorithm to the desired filter 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.

2. A method of manufacturing a filter, comprising the steps of:

(i) designing a filter according to the method of

claim 1

; and

(ii) constructing using finite Q factor elements a filter corresponding to the theoretical filter.

3. A method according to

claim 1

or

claim 2

, in which the algorithm includes the step of shifting a pole/zero plot of the desired filter characteristic by a constant amount.

4. A filter manufactured according to the method of any of claims 1-3.

5. Apparatus for use in manufacturing filters, 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 having a theoretical characteristic corresponding to the desired characteristic transformed to compensate for the difference between infinite Q and finite Q factor elements.

6. Apparatus according to

claim 5

, in which the algorithm includes the step of shifting the pole/zero plot of the desired filter characteristic by a constant amount.

7. A filter manufactured using the apparatus of

claim 5

or

claim 6

.

8. 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.

9. A filter according to

claim 8

, which is a reflection mode filter.

10. A filter according to

claim 8

or

claim 9

, which is a microwave filter.

11. A filter according to any of claims 8-10, which is a bandstop filter.

12. A filter according to any of claims 8-10, which is a band pass filter.

13. A method of designing a filter substantially as hereinbefore described with reference to the accompanying drawings.

14. Apparatus for manufacturing a filter substantially as hereinbefore described with reference to the accompanying drawings.

15. A filter substantially as hereinbefore described with reference to the accompanying drawings.

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