Classifications

• • H—ELECTRICITY
  • H03—ELECTRONIC CIRCUITRY
  • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
  • H03H7/00—Multiple-port networks comprising only passive electrical elements as network components
  • H03H7/01—Frequency selective two-port networks
  • H03H7/0115—Frequency selective two-port networks comprising only inductors and capacitors
• • H—ELECTRICITY
  • H03—ELECTRONIC CIRCUITRY
  • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
  • H03H2260/00—Theory relating to impedance networks

Definitions

• the present invention relates to the field of bandpass filters.
• the present invention relates to a circuit transformation method intended for producing efficient filters or multiplexers under favorable technical and economic conditions.
• the method can be applied to filters or mixed multiplexers employing both inductors and dielectric resonators and / or piezoelectric resonators while obtaining the same advantages.
• the main object of the present invention is to enable efficient filters and multiplexers to be obtained under better technical and economic conditions than those of the state of the prior art.
• the design process proposed in the context of the present invention particularly concerns the classes of bandpass filters, in scale, with general response (characterized by a transfer function which is a rational fraction), capable of being obtained by synthesis ( or by a circuit transformation after synthesis) so as to have a minimum inductance topology (zigzag).
• These classes of filters are indeed essential, in practice, when one seeks the economic realization of efficient filters because they use the expensive elements of filters.
• the method also applies to other filter topologies, including those very conventionally used to produce polynomial filters.
• the technique proposed within the framework of the present invention, comprises three main variants applying more particularly to filters employing inductances and capacitors, filters with dielectric resonators and filters involving piezoelectric resonators with volume waves. or surface which will be described successively.
• Passive filters with LC circuit or with dielectric resonators, or with acoustic-electric resonators with surface or volume waves are widely used in telecommunications and particularly in radioelectric or cable transmissions to limit the spectrum of signals or to realize switches enabling the sending (and extraction) of several signals occupying different frequency bands on the same antenna or on the same transmission medium. In the majority of cases, these are filters used in very large numbers for which high performance is sought and at the lowest possible cost.
• inductances and dielectric resonators TEM most often have more dissipation than the capacitances, and that there exist for each frequency ranges of values or parameters which minimize their losses.
• field of feasibility of inductors or resonators having good characteristics is for a given technique much more restricted than that of the capacitors having favorable characteristics.
• inductors More precisely, for inductors and for frequency domains greater than about a few megahertz, it is only commercially available or inexpensive to realize that a fairly limited range of inductance values of good performance ( overvoltage, natural resonant frequency, etc.).
• Filters calculated by conventional methods usually have inductors of different values which are therefore unlikely to correspond to normalized trade values.
• inductors of different values which are therefore unlikely to correspond to normalized trade values.
• permittivity a small number of dimensions (sections) and therefore of the impedances characteristic of the resonators.
• the invention largely takes into account the classes of filters which use the inductors very well (or else the resonators of the various types); the efficiency being understood here as being characterized by the selectivity, for example measured by a form factor, obtained for a given number of inductors or resonators.
• the so-called minimum inductance filter classes which have a scale topology, are the most interesting.
• Z 0
• Y 0
• the dipoles located at the ends of the filter can include one, two or three elements L, C.
• Zigzag filters are considered to be technologically superior [1] [2] [3] to filters of more usual scale topologies (with some reservations for some , as well as with the possible exception of those having this same ladder shape and which would include irreducible dipoles more complex than those with three elements in each of their arms). These latter filters, little studied, rarely appear to be of additional interest. In addition, unlike the case of three-element dipoles, there are only a few distributed dipoles which can be represented by such equivalent schemes and which are of particular interest (in practice only multimode distributed resonators can be of significant interest).
• the zigzag topology is obtained by synthesis or from the more usual topologies by the transformation of Saal and Ulbricht [2]. It includes LC resonators with two elements of two different types at the two ends. Other types of filters with the same topology or neighboring topologies
• Ladder filters made entirely of three-element dipoles have the advantage of having the maximum number of attenuation poles at finite frequencies which can be achieved simply with a given number d 'inductances, the properties of the functions constituting their distribution matrix mean that they are sometimes credited with some minor theoretical and practical drawbacks compared to the previous ones (including a more complex calculation and implementation).
• the topologies made up only of such resonators and capacitors they are of essential interest for the realization of filters implementing representable distributed elements, at least in the vicinity of certain frequencies of their characteristic frequencies, by such patterns.
• Figure 1 shows an example of a minimum inductance filter (zigzag).
• this figure 1 there are two end quadrupoles A and B separated by four dipoles R 3 ⁇ , R 32 , R33, R34.
• Quadrupole A here includes an inductor and a capacitor placed in parallel between two horizontal conductive arms (two-element dipole).
• the quadrupole B here comprises on the upper horizontal strand an inductance and a capacity in series and a lower horizontal conductive arm (also a two-element dipole).
• the dipoles R 3 ⁇ and R 33 are placed in series on the upper horizontal arm between the two quadrupoles A and B.
• the dipole R 32 constitutes a vertical arm placed between the two dipoles R 31 and R 33 .
• the dipole R 34 constitutes another vertical arm placed between the dipole R3 3 and the quadrupole B.
• Each of the four dipoles R 3 - ⁇ , R 32 , R 33 and R 34 includes an inductor and two capacitors arranged (three-element dipole)
• Bandpass multiplexers are sets of filters having at least one common access (sometimes n) and p other accesses and performing selective switching of the signals contained in a given frequency band of an access (for example the single access common) to another.
• the known methods for calculating multiplexers are most often based on digital optimization techniques.
• the systematic and global process for transforming band pass filters with "minimum inductance" and several other topologies aims to obtain filters using only one (or few) value (s) ) predetermined inductance (s) or else using dielectric resonators of the same characteristic impedance or else using piezoelectric resonators having very substantially or exactly the same capacitance ratios and substantially or exactly the same inductances.
• This method also makes it possible to obtain, in addition to those indicated above, other advantages such as the choice of equal values for some of the capacities or else the choice of current commercial values for some of the latter.
• the method also applies under similar conditions to connection filters made up of filters of the technologies indicated above.
• three-element resonators can appear in one of the two forms illustrated in FIG. 2 comprising respectively a capacitance C sa in series with a parallel LC resonator formed by the capacitance C pa and the inductance M pa or in a dual manner by putting in parallel a capacitance C Pb and a serial resonator formed by the inductance L S b in series with the capacity C s t > -
• the first form a will have "series form” and the second form b "parallel form”.
• C sa C P b + C S b
• C pa C p b [1 + C P b / C S b]
• M pa L S b / [1 + C p b / C s b] 2
• These dipoles are characterized by three parameters which can be chosen in different ways.
• the capacity ratio is an interesting parameter because it is independent of the "impedance level" (for example characterized by the value of the inductance), and it simply depends on the ratio of the remarkable frequencies and their relative deviation.
• FIG. 3a Decomposition into three parts of the parallel capacitances C p or series C s , of the resonant circuits with two elements LC, parallel or series (located in this example at the ends of the filter), as illustrated for example in FIGS. 3a and 3b.
• the breakdown illustrated in FIG. 3a consists in replacing a parallel circuit comprising an inductance L p in parallel with a capacitance C p , by a circuit comprising an inductance L p in parallel with three
• the breakdown illustrated in FIG. 3b consists in replacing a series circuit comprising an inductance L s in series with a capacitance C s by a circuit comprising an inductance L s in series with three capacitors C su , C sv and Csw-
• the breakdown illustrated in FIG. 4a consists in replacing a circuit comprising a capacitance C s in series of a resonator formed of an inductance M p in parallel with a capacitance C p , by a circuit comprising two capacitors C su , C sv in series upstream of a resonator formed of an inductance M p in parallel with a capacity C p and a third capacity C s in series downstream of this resonator.
• Decomposition into three parts of the shunt capacitances C p associated with the resonators with three (vertical) elements of parallel shape for the resonator number r (as illustrated in FIG. 4b).
• Be: pr C C + C pru prv
• FIG. 7a The transformation illustrated in FIG. 7a consists in replacing a circuit comprising an upstream parallel capacity C p and a parallel downstream transformer, connected by a series capacity C s on the head arm, by a circuit comprising an upstream series capacity C s t and a parallel downstream capacity C p t.
• FIG. 7b The transformation illustrated in FIG. 7b consists in replacing a circuit comprising an upstream series capacity C ' s and a downstream capacity C' P in parallel with a parallel downstream transformer, by a circuit comprising a parallel upstream capacity C ' pt and a capacity downstream series C ' st .
• n ' is the transformation ratio
• n ⁇ 1 appears, ie mj ⁇ mj + ⁇ (if i is even and for a zigzag filter according to FIG. 1).
• the adaptation is carried out using two impedances Zi and Z2 arranged respectively in series on a horizontal branch, and in parallel on a vertical branch.
• the adaptation is carried out by the impedances Zi and Z 2 of opposite signs:
• FIG. 8b easily transposes from the previous one:
• the advantage of the method proposed in the context of the present invention lies largely in the use which can be made of these additional degrees of freedom to make the production of LC filters more economical or to allow use under conditions favorable of distributed dipoles which are known to be developed economically and / or which have more interesting characteristics in a given frequency range.
• the present invention proposes a method for optimizing the values of the elements of a narrow or intermediate band bandpass filter for which the LC prototype has been determined, characterized in that it comprises the steps consisting in i) breaking down into two or three of the parallel or series capacitances of the two or three element resonators, ii) insert pairs of transformers between the first separate element and the rest of the resonator, iii) move transformers to modify the impedance levels of the resonators, and iv) absorb residual transformers by transformation.
• FIG. 1 represents an example of a conventional minimum inductance (zigzag) filter
• FIG. 2 represents two topologies of dipoles with three elements belonging to this filter
• FIGS. 3a and 3b represent the decomposition of the capacities of the dipoles with two elements LC respectively for a parallel configuration and a series configuration
• FIGS. 4a and 4b respectively represent the breakdown of the capacities of the three-element dipoles of the series form and of the parallel form
• FIG. 5 shows diagrammatically the step of inserting transformers
• FIG. 6 shows diagrammatically the step of moving the transformers
• FIG. 7a and FIG. 7b schematically represent the step of eliminating the internal transformers, for two configurations of the capacities
• FIG. 8 shows diagrammatically the step of eliminating transformers at the ends of the filter, respectively for Z * > Zo in FIG. 8a and Z * ⁇ Zo for FIG. 8b,
• FIG. 9 represents the diagram of a prototype zigzag filter obtained by synthesis
• FIG. 10 represents the corresponding electrical diagram of the transformed filter
• - Figure 11 represents the responses of the prototype filter compared to those of the transformed filter
• - Figure 12 represents the diagram of a filter to which the process according to the present invention is applicable, (it will be noted that it includes "sub" circuits of different topologies),
• FIG. 13 represents the diagram of a prototype filter of order 12
• FIG. 14 represents the diagram of a transformed filter of ATNTNB topology, (note: the topology is identified from the end A of the filter going to the end B, by letters N or T which indicate that the shape of the three-element dipoles has been preserved (N) or transformed (T)),
• - Figure 15 represents the diagram of a transformed filter of topology ANTTNB
• - Figure 16 represents the diagram of a transformed filter of topology
• FIG. 17 represents the diagram of a transformed filter of ATNTTB topology
• - Figure 18a represents the response of the prototype filter and the aforementioned transformed filters without losses
• - Figure 18b represents the detail of the bandwidth response of the prototype filter and the aforementioned transformed filters (it will be observed that the curves are exactly superimposed)
• FIG. 19 represents a prototype diagram used for a transformation
• FIG. 20 represents the structure of a first resonator for this diagram
• FIG. 21 represents the transformation structure for a second resonator
• FIG. 22 represents the structure of a third resonator
• FIG. 23 represents the structure of a last resonator
• FIG. 24 represents an example of a complete solution after transformation
• - figure 25 represents the response of the transformed filter for lines of equal characteristic impedance
• - figure 26 represents the diagram of a prototype zigzag filter of order
• FIG. 27 represents the response of such a prototype zigzag filter
• - Figure 28 represents the diagram of a transformed filter with adaptation by two impedances
• - Figure 29 represents the response of the transformed filter for TEM resonators
• Zc 11.5 Ohm (adaptation for inductances on both sides)
• FIGS. 30a and 30b respectively represent the responses of the transformed filter with adaptation by capacitors, in bandwidth for FIG. 30a and the whole of the response for FIG. 30b,
• FIG. 31 represents a diagram equivalent to a lithium tantalate resonator
• FIG. 32 represents the diagram of an initial zigzag filter
• FIG. 33 represents the diagram of the transformed filter
• FIG. 34 represents the response of a crystal filter obtained by transformation (without losses)
• FIGS. 35a and 35b respectively represent the response of a transformed filter taking into account the losses and the response of the transformed filter taking into account the losses in bandwidths,
• - Figure 36 represents the diagram of the transformed filter
• - Figure 37 represents the response of a transformed filter of order 8 to two L-SAW resonators and inductors (with losses and without taking losses into account (this last response is confused) with that of the prototype))
• FIG. 38a, 38b and 38c show three usual topologies for resonator filters, The following figures relate to the production of duplexer according to the invention (connection filter with two inputs to an output).
• FIG. 39 represents the response of two prototypes taken in isolation
• FIG. 40 represents the evolution of the passband responses during the optimization (the two filters then have a common end),
• FIG. 41 represents the responses finally obtained for the duplexer
• FIG. 42 represents the impedance transformation at the end common to the two filters
• FIG. 43 represents the transformed diagram of a duplexer
• FIG. 44 represents the electrical response of a duplexer after the transformation of the diagram illustrated in FIG. 43
• FIG. 45 represents the transformed diagram of a duplexer
• FIG. 46 represents a diagram comprising connection filters that can be produced according to the present invention (for application in mobile radiotelephony to equipment having to operate in multiple frequency bands),
• FIG. 47 represents another exemplary embodiment in accordance with the present invention indicating the functions which can be performed in a mobile terminal or in a multi-frequency and multi-standard base station,
• FIG. 48 diagrams the transformation of sub-circuits which include T or ⁇ respectively into T or ⁇
• the indices a and b relate respectively to the form a and to the form b defined in FIG. 2.
• L 2 *, L 3 * and L 4 * provides 4 relationships (L * are the transformed values).
• the shape chosen for the filter requires m2 ⁇ m 3 ; the 2N-1 degrees of freedom (here 7 degrees of freedom) allow to set the 4 values of the inductors and the values of three capacitors (for example C sa 2 w and C P 3 and another). Multiple choices are of course possible including, for example, that made in the following example. It is also possible to ensure that certain capacitances (three here at most if the inductances are fixed) take defined values corresponding to current normalized values.
• FIG. 11 represents the responses of the prototype filter and of the filter transformed according to the method of the present invention.
• the great advantage of the process according to the invention is that it can take into account all the possibilities and generalize to a significant number of filter topologies.
• the analysis of the transformation process shows that it applies to ladder filters comprising at most one inductance per arm (or transformable so as to verify this condition) such that a pair of transformers can be introduced. by inductance and eliminate after displacement one of these transformers by Norton transformation.
• This supposes the existence of two capacities (one in series in a horizontal arm and one in parallel in a vertical arm) resulting from the division of the capacities in the arms containing resonators with two or three elements or which preexist in the diagram (capacity series or shunt) and which are located in the direction of movement of the transformer after the inductor to be transformed and before the next one (to be able to transform all the inductors independently).
• condition is also fulfilled if one or both of the preceding conditions are replaced by the condition that after any dipole containing a single inductance there is found a ⁇ or a T of preexisting capacities.
• FIG. 12 This is illustrated in FIG. 12 which brings together sub-circuits employing various current topologies.
• the adaptation components, inductance or capacitance, added modify the behavior outside bandwidth input or output impedances of the filter, in different ways, but which can be very favorable for certain applications (for example in the production of duplexers, the choice between modifying the response at zero frequency or at infinite frequency may be important).
• the adaptation to narrow band leads to very satisfactory solutions for bandwidths very much larger than those which are usually called narrow. In practice, no performance limitation has been encountered as a result in all the cases treated (ie for relative bandwidths of up to approximately 30%). It was mentioned above that other adaptation techniques could be used for the case of wider relative bands.
• the degrees of freedom introduced in the proposed transformation process allow, in practice, the realization of the filter with completely equal inductances, which is the most interesting case economically.
• the remaining degrees of freedom can be used in different ways. We have indicated above the interest of choosing trade values for capacities.
• Another possibility of particular interest is to fix the capacity ratios of the three-element resonators, since it allows the production of filters employing resonators piezoelectric with volume or surface waves. This possibility of the process will be discussed further below.
• the capacity ratio of three-element resonators also has interesting fundamental properties: it is a simple function of the relative separation of the remarkable frequencies of these dipoles and, therefore, it strongly conditions the maximum bandwidth that a filter using such resonators can have. It is easy to show that this parameter has, in the transformations carried out, the important property of being able only to decrease. It can therefore take after transformation, for each three-element resonator, only values located in the interval between zero and its value in the prototype scheme.
• This example relates to the transformation according to the proposed method of a zigzag filter of order 12 calculated to have a pass band going from 51.0 to 59.0 MHz with a ripple of 0.3 dB and a rejection in attenuated band 70 dB.
• the diagram of the prototype filter considered is shown in Figure 13.
• the ATNTNB configuration is made up of three-element resonators all in the form (b) of FIG. 2 (made up of an LC series resonant arm placed in parallel with a capacitance (called static capacitance)).
• this topology is useful for example to comply with the use of the representation of piezoelectric resonators when we want to constitute filters based on these elements (the capacitance and inductance values "equivalent" to the resonators given by resonator manufacturers correspond to this form).
• FIGS. 18a and 18b respectively illustrate the response of the prototype filter and of the transformed filters (without losses) and the detail of the bandwidth response of the prototype filter and the transformed filters (the curves are exactly superimposed) ( Figures 18a and 18b below).
• the components added for narrowband matching slightly improve the response to very low frequencies in the above case.
• Dielectric resonators are characterized by their length or by one of their (theoretical) no-load resonance frequencies (inversely proportional to the length), these quantities being adjustable by mechanical means (or by adding discrete adjustable components), and by their characteristic impedance Z because which is determined by the geometric characteristics of the resonator and the dielectric permittivity of the material used.
• the characteristic impedance is most often between 6 Ohm and 16 Ohm depending on the relative permittivity of the material and the cross-section of the bar, but other slightly higher or lower values can be achieved in special cases.
• the degrees of freedom will therefore be used, under the constraint of a characteristic impedance, to identify the impedances of the resonator alone or of the resonator and of its coupling elements (serial and / or shunt capacitors) so as to obtain a good approximation of the 'impedance 2 or 3 element resonators.
• a characteristic impedance to identify the impedances of the resonator alone or of the resonator and of its coupling elements (serial and / or shunt capacitors) so as to obtain a good approximation of the 'impedance 2 or 3 element resonators.
• LC resonators are identified with coaxial resonators with ⁇ / 4 or ⁇ / 2 lines.
• the present invention can implement at least one diagram where some of the resonators are produced not by taking the dielectric resonator in shunt (in dipole, the other end of the resonator being either grounded or in open circuit), but in series, one of the accesses being on the central core of the resonator, the other access of the quadrupole being on the external metallization of the resonator.
• the first 2-element resonator illustrated in FIG. 19 can be transformed as illustrated in FIG. 20.
• the parallel resonator L p ⁇ -C p ⁇ of FIG. 19 can be transformed either into a parallel resonator, into ⁇ / 4 in short circuit, on a vertical branch or into a parallel resonator, into ⁇ / 2 in open circuit , on a vertical branch.
• the resonant frequency of the residual shunt LC circuit ⁇ L p - ⁇ , C p ⁇ v ⁇ is quite above the resonance of ⁇ L p ⁇ C p ⁇ . Strictly speaking, it would be necessary to identify in the middle m 0 of the passband the values of the admittance and its derivative on the one hand for the form L p ⁇ C p ⁇ v and on the other hand for the realization with coaxial resonator. To simplify, we will identify the anti-resonance frequency f
• the second resonator illustrated in FIG. 19 (with three elements located in a horizontal arm) can be transformed as illustrated in FIG. 21.
• the resonator of FIG. 19 comprising a capacity C s 2 v in series with a circuit comprising in parallel an inductance M pa 2 and a capacity C pa 2 can be transformed either into a series resonator on a horizontal branch in ⁇ / 4 to short circuit associated with a series capacitor C c 2 , or in a series resonator on a horizontal branch in ⁇ / 2 in open circuit associated with a capacitor C c 2 .
• the infinite weakening frequency (anti-resonance) ⁇ a2 must be preserved, the resonance frequency ⁇ > b2 is a priori in the passband and the slope of the impedance must be preserved at this point.
• 9 (Z) / 9 ⁇ in ⁇ > b2 from the responses of equivalent schemes with discrete elements and with resonator.
• the impedance of the dipole with line ⁇ / 2 and capacity is:
• the identification of the slope at ⁇ b2 can be done as follows.
• L Sb 2 equiv is the inductance of the three-element resonator put in the form b of figure 2.
• the third resonator illustrated in FIG. 19 (three elements in a vertical arm) can be transformed as illustrated in FIG. 22.
• the resonator of FIG. 19 comprising a capacitance C Pb 3 V in parallel with a branch formed of an inductance Ls in series with a capacitance C s can be transformed either into a parallel resonator on a vertical branch in ⁇ / 4 short-circuit in series with a capacity C c 3 , or in a parallel resonator on a vertical branch in ⁇ / 2 in open circuit in series with a capacity C c 3 .
• m 3 2 (2 Z because ⁇ b3 C sb3 / ⁇ ) (1 + t) 3 / (t 2 (2 + t) 2 ).
• the resonator of figure 19 comprising a capacitance C s in series of an inductance L s can be transformed either into a serial resonator on a horizontal branch in ⁇ / 4 short circuit with input on the central core and output on the external metallization of the resonator, either as a series resonator on a horizontal branch in ⁇ / 2 in open circuit, or in a series resonator on a horizontal branch in ⁇ / 4 in short-circuit in series with an inductance L sw .
• a 4 1 for a half-wave resonator in open circuit
• a 4 2 for a quarter-wave resonator.
• C p1w C p1 - (R ⁇ 0 ) "1 ( r ⁇ n 2 -1) 1/2 - C p1v .
• C pb 3w C p b3 - C sa 2w (m3 / m 2 -1) - C p b3v m is determined by comparison of:
• the prototype is a filter of the same topology as that of Figure 19 but here it is a filter synthesized to have specified infinite attenuation frequencies (888 MHz and 899 MHz) very close to the passband which goes from 890 to 897 MHz.
• the bandwidth ripple is 0.2 dB.
• the rejection of the attenuated bands (not equal in this case) is of the order of a little less than 30 dB.
• Table 8 The values of the elements of the prototype equivalent scheme are shown in the following table. Table 8
• FIG. 24 An example of a solution thus obtained is illustrated in FIG. 24.
• the values of the elements of the TEM line diagram thus illustrated for a particular solution are indicated below in table 9.
• This example relates to the transformation of a zigzag order 12 LC elliptical prototype, of central frequency 520 MHz having a bandwidth of 40 MHz with a ripple of 0.3 dB and a rejection in attenuated band of 70 dB (see diagram given in figure 26 and the answer given in figure 27).
• the strong inductances of the prototype scheme are difficult to achieve (self-resonance too low) and, on the other hand, the dielectric resonators allow an appreciable gain in performance, in particular in terms of insertion loss due to their high overvoltage.
• the principle set out above for order 8 easily extends to higher orders by iteration on the pairs of three-element resonators.
• n-2 4 capacity ratios of the three-element resonators (in the final transformed state)
• C s4v C S bv-
• the first case can be useful in particular for making multiplexers.
• the program determines the domain of existence of the solutions (by the variation of C sbv in its range of possible variation and by variation of the 4 capacity ratios between their initial values and approximately 1/20 of these (we avoid values too close to zero (this is the minimum allowed) which lead to values too extreme for capacities.
• a solution exists for given values of the parameters when all the inequalities indicated more high are respected and when all the calculated values of the elements of the filter are positive.
• the domain of existence is more complicated (fragmented) than these simplified data reveal.
• adaptation to the ends by two capacities or by an inductance and a capacity one observes that the field of existence remains rather close to that indicated above.
• One of the advantages of this analysis of the domain of existence of the solutions is to show that one can in addition obtain a diagram using 5 judiciously predetermined values of the capacities of the final diagram (for example values of the standard series) and to provide a systematic method for obtaining solutions of this type.
• the characteristics of the targeted filter are as follows: - Central frequency 520 MHz,
• the transformation is carried out as described above.
• the advantage of including inductors at the ends of the filter is important. On the one hand, they greatly reduce the unwanted responses in attenuated band due to the multi-mode nature of the resonators. On the other hand, their losses do not influence the response of the filter if care is taken to take them into account in the source and load resistances.
• FIGS. 30a and 30b Verification by simulation of the response of the transformed filter with adaptation by capacitors has been made, this response is given in FIGS. 30a and 30b respectively for the bandwidth and the entire response.
• the present invention can also find application in the design of tunable filters.
• the degrees of freedom available can (also) be used to reduce the number of variable capacities in tunable filters for which it is desired to keep, for example, the bandwidth more or less constant over the entire tuning range.
• Piezoelectric crystal resonators have unequaled characteristics of overvoltage (up to several million and typically hundreds of thousands for quartz) and stability as a function of temperature and time which allow the production of efficient filters with relative bands narrow or very narrow. They use electromechanical waves propagating in the volume or on the surface of monocrystalline solids (quartz, lithium tantalate, lithium niobate, langasite (lanthanum silico-gallate), gallium phosphate, etc.) or piezo ceramics -electric (lead titano-zirconate, etc.).
• volume wave resonators in the frequency range 10 kHz-10 GHz and surface wave resonators in the range 10 MHz-10 GHz (resonance frequencies are very complex functions of parameters characterizing the material and geometric parameters characterizing the resonators. Dependence on the latter is often dominated by that of only one of the parameters (the thickness for many wave resonators of volume and pitch of the interdigitated combs for surface wave resonators).
• these resonators are characterized by a capacitance ratio substantially fixed by the material, the type of wave and the crystal orientation (for example of the order of 0.52% for the wave of slow shear volume AT cut quartz), moreover for a given frequency, the achievable values of the inductors, under "good conditions” (of performance, undesirable responses and cost), lie within a generally very narrow range of values (for example towards the center of the 5.7 mH to 10.9 mH range for AT quartz at 20 MHz).
• the filters being very narrow, the most "easily achievable" values of the equivalent inductances of the different resonators are very close (frequencies close) and it is quite often possible to impose without difficulty having them all equal.
• the filters involving these devices are taking on great importance at present because of the advantage of reducing the volume and cost of components in equipment and particularly in subscriber terminals. For example at the frequencies involved in personal terrestrial and satellite radiocommunications their size is extremely reduced (a few mm 3 ) and one can envisage making banks of filters or multiplexers integrated on the same substrate to produce multi-standard and multi-frequency terminals.
• the principle is to use the degrees of freedom introduced in the general method of transformation to reveal here resonators having both a given inductance and a given capacity ratio.
• One of the resonance or anti-resonance frequencies is free.
• the other is imposed by the position of the infinite points.
• the material chosen is lithium tantalate with a cut very close to X which give resonators with a much larger theoretical capacity ratio than quartz (C p / C s # 8k 2 / n 2 ⁇ 2 + ⁇ (k 4 ) with k # 44% against # 8% for quartz).
• quartz C p / C s # 8k 2 / n 2 ⁇ 2 + ⁇ (k 4 ) with k # 44% against # 8% for quartz.
• inductances of the order of 40.0 ⁇ H are obtained for resonant frequencies close to 68.5 MHz and a dynamic capacitance Cs of the order of 0.135 pF.
• the experimental static capacity is of the order of 1.5 pF. It includes an overall stray capacitance of the order of 0.65 pF, itself comprising capacitances relative to the housing and a very low capacitance between the accesses.
• the diagram of the filter allows these parasitic capacities to be taken into account. We preferred here to simplify the presentation, take them globally into account and consider the total "static" capacity (which corresponds to the case where the case is left “in the air”).
• the overvoltage of these resonators is of the order of 2500.
• the overvoltage of these elements is not very critical and it is possible to choose inductors on a toroid of carbonyl iron powder of very small dimensions.
• the resonator can be likened to a capacitor C 0 'placed in parallel with a branch comprising in series a capacitor C s and an inductance L s .
• the resonator can also be assimilated to a circuit comprising in addition to the components which have just been described, two additional capacitances C p ⁇ and C p2 which respectively connect the input and the output of the circuit to the box and a capacitance between the input and the output C p o.
• C p o, C p ⁇ , C P 2 representing the parasitic capacities between the input and the output and between these accesses and the box.
• the diagram of the initial zigzag elliptical prototype of degree 12 is indicated on figure 32.
• the only free variable is C Sb v which one chooses so as to have a low frequency resonance.
• the transformation method has the advantage of allowing filters to be taken into account taking into account the parasitic capacities of the crystals in the case where the case is “grounded” (with some additional calculations). This possibility is useful if it is sought to obtain relative bandwidths close to half of the theoretical value of the capacity ratio.
• the transformation process also has the advantage of being the only one allowing the production of filters with general response using crystals without the use of balanced transformers.
• the diagram of the filter transformed to include crystal resonators with lithium tantalate is given in FIG. 33.
• the characteristics of the TaLi03 resonators of section X are those indicated above.
• FIG. 34 The response of the transformed crystal filter calculated without losses is shown in FIG. 34.
• the response of the transformed filter by considering the losses is indicated in FIGS. 35a and 35b.
• the overvoltages considered are indicated in the table above (after the values of inductances). It is observed that the method provides a filter of excellent form factor with few resonators which differ in practice only by a different final frequency adjustment (step anyway essential and automated).
• a confinement is also (generally) obtained thanks to the discontinuities of the speed produced by the presence of the "rails" of current supply bordering the transducers (and if necessary the reflecting networks) and of free space outside.
• the principle and the calculation of these devices are described in recent literature (see for example the references [16 and 22]).
• Various types of surface waves are commonly involved in devices. The most common are Rayleigh waves (pure or generalized), transverse or quasi-transverse waves (SSBW, STW) and pseudo longitudinal surface waves (L-SAW).
• the waves of the last two types are schematically, almost waves of volume which are more or less guided (maintained) close to the surface by modifications of this one (corrugations or metallizations) which locally modify their speed. Their decrease in the thickness of the plate can be slower than that (exponential) of Rayleigh waves (this is an advantage for the realization of filters supporting a certain power because it reduces the density of acoustic energy at equal power).
• transverse wave resonators lead to better overvoltages than those involving Rayleigh waves. It then closely approaches the intrinsic material (at the central frequency). It is recalled that the overvoltage varies in 1 / Fc so that Qin t in sè qu e -Fc ⁇ constant # 1.5 .10 13 for quartz and probably # 2. 10 13 for lithium tantalate, for example. Rayleigh wave devices themselves, generally also, have better overvoltages than those using pseudo longitudinal surface waves (these waves are, inherently slightly dissipative).
• the central frequency of this filter is fixed at 900 MHz, it must be terminated at 50 Ohm, and have a bandwidth of 20 MHz (ripple 0.3 dB), a loss of 20 dB at + and - 5 MHz from the corners of the bandwidth and 30 dB from ⁇ 7.5 MHz of the bandwidth.
• the prototype diagram chosen to satisfy this template is that of an elliptical zigzag filter of order 8 (same type of diagram as in FIG. 19), the values of the elements of the initial diagram are indicated in table 18 below.
• these resonators In the vicinity of the chosen central frequency, it is known to make these resonators in the form of a long transducer having a high number of fingers (a little more than a hundred) on lithium tantalate of cut Y + 48 ° or Y + 52 °.
• the values of the other production parameters can be chosen for get a good response, a good overvoltage (700-800) and a small footprint.
• these resonators are characterized, at the central frequency, by an equivalent inductance equal to 104.5 nH, an overall static capacity close to approximately 3.6 pF, a coupling coefficient of approximately 10.57%, and a capacity ratio of C O / C ⁇ I 1, 696.
• Topology ATNB (L-SAW) retained a priori (inequalities)
• Topology ANTB eliminated (inequalities)
• Figure 37 shows the responses calculated without taking into account the losses of the resonators and inductors, for the prototype and transformed filters of order 8 with 2 L-SAW resonators (the responses are then combined), and taking them into account, for the transformed filter. It will be noted that the insertion loss remains reasonable under these conditions for a filter of small width. As in the previous case, the parasitic capacities were taken into account overall.
• the proposed embodiment is not currently used, several advantages have been indicated above. Another results from the technology used to make the resonators. It will indeed be noted that the majority of the capacitors introduced into the transformation have low values, so that they can be produced directly on the substrate used for the production of the L-SAW resonators which further reduces the cost of production (the Lithium tantalate has fairly high dielectric constants ( ⁇ r of the order of 40) stable as a function of temperature and excessively low dielectric losses, which leads to very high quality capacities.
• FIG. 38a corresponds to a configuration comprising only resonators, both on the horizontal branches, and on the vertical branches.
• FIG. 38b corresponds to a configuration comprising resonators on the horizontal branches and capacitors on the vertical branches.
• FIG. 38c corresponds to a configuration comprising resonators on the vertical branches and capacitors on the horizontal branches.
• the proposed transformation process makes it possible to reduce to a small number of types of resonator (one or two also in practice) achievable with good performances on known materials but by preserving the totality of the possibilities of responses allowed by this topology (and especially the high number of possible different infinite attenuation frequencies). This should lead to much better performance and also make it possible to correct imperfections, currently difficult to avoid, of certain types of surface wave resonators.
• the n to p connection filters consist of filters connecting n accesses (inputs) to p accesses (outputs) and allowing only a finite number of frequency bands to pass from one input to an output (generally only one). Quite often, there is only one input access (one channel to p) or output (n channels to one), the connection filter used to send to a transmission medium (or to extract) several signals located in different frequency bands.
• These filters are generally calculated by digital optimization techniques starting from synthesized filters, to have, when taken alone, the desired response and a topology favorable to the pooling of one or more accesses.
• optimization generally based on the minimization of an expression representing according to a certain criterion (least squares, least k th ) the difference to the desired responses. It can also be based on a Remetz type method in the case of an approximation in the sense of Tchebitchev. In all cases, it modifies the values of the components, generally without changing the topology of the various filters, so as to obtain the set of desired responses of the branch, for example characterized generally by its distribution matrix (Sij). In some cases, it may be useful to introduce one or more additional dipoles at the common point (s).
• connection filters we give here a simple example relating to the case of a duplexer (2 channels to one or else one way to 2).
• these filters are connected so that they have the common end B.
• the corresponding input (output) impedance has characteristics favorable to this connection, and it is not necessary to use a compensation dipole.
• the values of the components of the two filters are varied without modifying the topology, so that the response of each of the filters having a common access approaches at best, in bandwidth the previous response of the filters considered in isolation and that the rejection condition is fulfilled.
• Zigzag filter order 6 bp6 5152.
• opt Zigzag filter order 6 bp6_5552.opt
• connection filters The application of the method of the invention to the case of connection filters meets the criteria below.
• the steps indicated above for the "simple" filters apply to branch filters made up of filters of topologies with minimum inductances or using other topologies fulfilling the criteria defined above.
• the different technologies of coil filters, dielectric resonators and piezoelectric resonators can be used, optionally by combining them in the same connection filter.
• there are a few additional considerations to take into account In particular, it is necessary to take into account the very fact that the two filters have a common end and, if necessary, to choose carefully the solution to be adopted for the impedance transformations at the common end. If one chooses the narrow band adaptation, the choice of the type of the adaptation reactances can be important, but one can be brought to choose, in certain cases, a broadband adaptation because the filters of connection to a lot of channels quite often operate on a broad spectrum.
• connection filter from one channel to two channels so that it uses TEM dielectric resonators of the same characteristic impedance (the most efficient solution in this frequency range).
• This deliberately simplified example is given here to describe the principle of the process.
• additional refinements using the free parameters
• termination resistors equal to the common access after schema transformation (for example by additional division of component - the inductance Lb in cases similar to this one).
• the final step is the narrow band adaptation modifying the level of the termination resistance at the common point, which leads to the final diagram illustrated in FIG. 45.
• Table 22 Values of the elements of the transformed diagram up to the common point (side B)
• the resonator 1 is a ⁇ / 4 CC and the resonator 6 is a ⁇ / 4 CO).
• the first variant consists in replacing, when necessary, the narrow band adaptation by a wider band adaptation technique involving known techniques which lead to the use of more complex quadrupoles than those with two elements employed above. above (it is quite common for connection filters to operate over a very wide frequency band).
• Another advantage of broadband adaptation is to allow better taking into account the reactive part of the input impedance at the common point and also to provide additional filtering outside the passbands of the filters constituting the connection. High pass, low pass or band pass structures can be used for this purpose.
• a second useful variant in the case of complex branching filters consists in carrying out the different operations in a different order. This variant is based, on the one hand, on the fact that the phase of optimizing the responses of the branching filters makes it possible, practically without altering the responses, to modify, even notably, the termination resistors.
• This variant therefore consists (in the case of dielectric resonators but it is possible to transpose for cases where one would like to use a small number of inductances or piezoelectric resonators) to directly transform the diagrams of the filters taken alone by introducing adaptation elements (by not seeking to minimize the number of components by recombination), then to optimize the connection response by leaving the resonators mentioned above fixed and by fixing limits to the values of the inductances of the resonators ends (to be able to show dielectric resonators of a suitable characteristic impedance). In this case, it is possible not to introduce a lot of additional elements and not to have selective elements between the access and the point common to the different filters, which is essential when the connection includes a high-pass filter. , band pass and low pass.
• connection filters are of particular interest in the current context.
• the method according to the invention makes it possible to produce branching filters using dielectric resonators of the same characteristic impedance and having the most general responses allowed by the different zigzag filter topologies.
• FIG. 46 shows schematically three antennas.
• the first antenna is connected via a “band 1r” connection filter to the input of an LNA converter / amplifier, which is connected to a receiver stage, via a network comprising in parallel three filters, called "band 1r", “band 2r” and "band 3r”.
• the second antenna is connected on the one hand to the input of LNA, via a “2r band” connection filter, on the other hand to the output of a PA converter / amplifier, via a “2nd band” connection filter.
• the PA element has its input connected to a transmitter stage via a network comprising in parallel two connection filters "band 2nd", "band 3rd”.
• the third antenna is connected on the one hand to the input of LNA, via a “band 3r” connection filter, on the other hand to the output of PA, via a filter of "3rd band” connection.
• This method also allows connection filters to be produced using piezoelectric resonators with volume or surface waves and / or dielectric resonators.
• piezoelectric resonators piezoelectric resonators
• the maximum use of the first of these technologies is the most promising to obtain both performance gains and space thanks to the "natural" dimension of these resonators and also thanks to the possibilities of integration of complex functions on the same substrate (several filters constituting all or part of a branching filter).
• the method also makes it possible to produce filters with several bandwidths which are disjoint or not (filter connections at both ends), for example by using surface wave resonators of a single type (per bandwidth) which can lead to space-saving and inexpensive integrable solutions for interstage filtering in multi-band terminals.
• the particular case of contiguous or overlapping bandwidths may be in the case of surface wave or thin piezoelectric film technologies, one of the means allowing the production of filters accepting more power while retaining high performance, very small footprint. and low cost. This means can be combined with already known solutions (use of structures with strong parallelism) to further increase the power admissible by these filters.
• FIG. 47 Another example indicating the functions which could be carried out by implementing these concepts in a mobile terminal or in a multi-frequency and multi-standard base station is given in figure 47.
• UHF radio frequency
• a dual-band antenna connected to a receiver stage by means of a circuit comprising two branches in parallel, one comprising in series a connection filter “band 1r”, a converter / amplifier LNA1 and a branch filter forming a "band 1r” duplexer, the other comprising in series a branching filter "band 2r”, an LNA2 converter / amplifier and a branching filter forming a "band 2r” duplexer.
• the antenna is connected to a transmitting stage by means of a circuit comprising two branches in parallel, one comprising in series a connection filter forming a “band 1e” duplexer, a PA1 converter / amplifier and a filter.
• connection forming multiplexer "band 1e” the other comprising in series a connection filter "band 2e", a PA2 converter / amplifier and a connection filter forming duplexer "band 2e”.
• the various means thus described constitute an integrable UHF subset.
• the method according to the present invention can in particular be implemented on filters with volume or surface wave crystal resonators or with a thin piezoelectric layer, or with piezoelectric resonators using non-crystalline materials, in order to ensure that the ratios elements C parallel / C series of the equivalent diagram of the resonators remain in a given range or take a given value, and that the inductances of these resonators take a given value adapted to the economic, easy and efficient realization of these resonators.
• the present invention can also be implemented for the design of tunable filters for which it is desired to limit the variation in coupling capacities between resonators while retaining a band approximately constant value (in MHz and not in relative value in%).
• topology of the transformed filters in accordance with the present invention is characterized in particular by the systematic presence of a T or a ⁇ of capacitances between the resonators.
• the topology of the circuit obtained can be changed, by simple additional transformations which may be of real interest in certain cases of filters with inductances and capacities.
• the advantage of these transformations is to modify the values of the capacities in a favorable direction.
• Ca has the capacity of a first vertical branch, Cb the capacity of a horizontal branch, and Cc the capacity of a second vertical branch of ⁇ .
• the two capacities of the horizontal branch are referenced C1 and C2 and C3 the capacity of the vertical branch of a T.
• Ci (C a C b + C b C c + C a C c ) / C a
• the transformation method described above has the maximum interest in cases where the dipoles constituting the arms of the filter on a prototype scale are resonators comprising at most only one inductance (of which the value to obtain a desired value).
• the present invention applies to prototype filters whose arms comprise only one element (a capacitance, except at the ends), or only comprise a resonator with two or three elements and with a single inductance.
• FIGS. 49 and 50 show schematically equivalent transformations which can be used in the context of the present invention. In the case where these transformations reveal negative capacities, it is advisable to recombine these with neighboring positive capacities.
• Figure 49 shows schematically the transformation of a circuit comprising an impedance Z in parallel on the input of a transformer of ratio 1 / n into a T-circuit comprising in its horizontal branch a first impedance (1-n) Z and a second impedance n (n-1) Z and in its vertical branch an impedance nZ.
• FIG. 50 shows diagrammatically the transformation of a circuit comprising an impedance Z in series on the input of a transformer of ratio n / 1 into a circuit in ⁇ comprising in its first vertical branch an impedance Z / (1-n), in its horizontal branch an impedance Z / n and in its second vertical branch an impedance Z / n (n-1).
• the present invention applies in particular to the design of components for mobile and satellite radiocommunications in the frequency range 0.5-3 GHz (filters and multiplexers implementing surface wave resonators or dielectric resonators in particular) and cable transmission.
• filters and multiplexers implementing surface wave resonators or dielectric resonators in particular filters and multiplexers implementing surface wave resonators or dielectric resonators in particular
• cable transmission it makes it possible to find new solutions for filtering in terminals that must be multi-band or multi-standard.
• Dielectric resonators in particular TEM or quasi-TEM resonators, as well as filters using them for cellular applications:

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