CN102664301A - Direct integrated design method for random-bandwidth multi-pass-band generalized Chebyshev filter - Google Patents

Abstract

The invention relates to a direct integrated design method for a random-bandwidth multi-pass-band generalized Chebyshev filter. The method comprises the following steps of: 1, according to indexes of an analog filter to be integrated, performing independent integrated design on each pass band according to single-pass-band filters, and deriving a characteristic function and a polynomial, which correspond to each single-pass-band filter; 2, substituting the characteristic functions and the polynomials into a superposition relational expression, deriving the corresponding polynomials and determining final characteristic functions of the analog filter to be integrated; 3, converting a scattering matrix which is formed by the polynomials into a theoretic admittance matrix; and 4, performing partial fraction expansion on the theoretic admittance matrix which is obtained in the step 3, and thus obtaining a transverse network matrix of the analog filter to be integrated, which is represented in a global resonant mode. The direct integrated design method for the random-bandwidth multi-pass-band generalized Chebyshev filter has the advantages that network matrixes of various topological equivalent circuits for realizing the frequency response of the analog filter to be integrated can be directly derived, and final physical implementation is facilitated.

Description

Any direct comprehensive designing method of many passbands of bandwidth broad sense Chebyshev filter

Technical field

The present invention relates to a kind of filter synthesis method for designing of communication technical field; Specifically be a kind of any many passbands of bandwidth broad sense Chebyshev filter comprehensive designing method, can be used for many passbands broad sense Chebyshev filter of any bandwidth is carried out direct comprehensive Design based on rate addition method.

Background technology

In the last few years; Continue to bring out outstanding many wireless communication standard or agreement, for example global system for mobile communication (GSM) (800/900MHz), global positioning system (GPS) is (1575MHz); Wideband code division multiple access (WCDMA) (2.1GHz); Wi-Fi (802.11b/g/a, 2.4/5.2GHz), Bluetooth (2.4GHz); Wireless local-area network (WLAN) (2.4/5.2GHz), and Worldwide Interoperability for Microwave Access (WiMAX) is (3.5GHz) or the like.Current a kind of trend is that these application are incorporated among the triangular web, thereby can support the operation of multiple standards or agreement.This system can be called many pass-bands system, the single-pass band system that compares, and it has advantages such as high stability, high reliability and high centrality.Because these standards or agreement mainly concentrate in 0～6GHz frequency range.Therefore, comb filter is one of Primary Component in the multi-band communication systems, and it can realize effective division of frequency, simplifies whole system, reduces its volume and reduces its weight.

Existing many passbands broad sense Chebyshev filter comprehensive designing method belongs to indirect method, and they utilize the one or many frequency translation to obtain final many passband frequency response based on the notion of lowpass prototype filter again.For example, with document (Juseop Lee, Kamal Sarabandi; " A synthesis method for dual-passband microwave filters, " IEEE Transactions on Microwave and Techniques, vol.55; No.6; June 2007, pp.1163-1170.) are example, and the method for being introduced is low-pass prototype to be carried out double frequency translation obtain the frequency response of bilateral band.Other one piece of document (Yi-Ting, and Chi-yang Chang, " Analytical design of two-mode dual-band filters using e-shaped resonators "; IEEE Transactions on Microwave and Techniques; Vol.60, No.2, June 2012; Pp.250-260.) equally also be the low-pass prototype of setting up many passbands earlier, obtain final many passband responses through low pass to the logical frequency translation of band again.The deficiency that these existing comprehensive designing methods exist is that their resulting network matrixs are that the arrowband is approximate, mean the comb filter that cannot be used for comprehensive broadband.

Summary of the invention

Order of the present invention be to solve exist in existing many passbands broad sense Chebyshev filter comprehensive designing method can not be applicable to shortcomings such as wideband scenarios and process complicacy; The direct comprehensive designing method of any many passbands of bandwidth broad sense Chebyshev filter has been proposed targetedly; This comprehensive designing method can be directly in the logical territory of band each passband to comb filter carry out directly comprehensive; And then its superposition got up to obtain final many passband frequency response; This comprehensive designing method is a kind of direct method; Can be used to extract the network matrix that has any bandwidth and be positioned at many passbands broad sense Chebyshev filter of optional frequency place transmission zero, the network matrix of being derived has the actual physics meaning.

Technical scheme of the present invention is: any direct comprehensive designing method of many passbands of bandwidth broad sense Chebyshev filter comprises the steps:

Step S1: according to the index of treating the comprehensive simulation filter; Each passband is carried out independent comprehensive Design according to the single-pass band filter, derive each single-pass band filter characteristic of correspondence function

and multinomial

and

separately

Step S2: with these characteristic functions

And multinomial

With

Among the substitution superposition relational expression and derive corresponding multinomial

With

Confirm the characteristic function of treating that the comprehensive simulation filter is final $C\left(\stackrel{\‾}{s}\right)=F\left(\stackrel{\‾}{s}\right)/P\left(\stackrel{\‾}{s}\right);$

Step S3: by polynomial and posed by the scattering matrix

into theoretical admittance matrix

Step S4: carries out residue with the theoretical admittance matrix that obtains among the step S3; And with horizontal equivalent electric circuit in corresponding equivalent electric circuit admittance matrix

compare, thereby confirm to treat resonance frequency

and admittance inversor parameter

and

of each resonator in the comprehensive simulation filter thus obtain treating the horizontal network matrix of representing with overall mode of resonance

of comprehensive simulation filter

The invention has the beneficial effects as follows: compare with the prior art scheme and have following remarkable advantage: 1. can directly derive the network matrix that is used to realize treat the various topoligical equivalence circuit of comprehensive simulation filter freguency response, be convenient to final physical and realize; 2. the bandwidth of treating each passband of comprehensive simulation filter can and can be the broadband by accurate control; 3. in the network matrix that comprehensively obtains by the method for the invention; The resonance frequency of each resonator that is comprised and the admittance inversor parameter that is used to describe coupled relation between them have physical significance, and comprehensively to obtain the low pass arrowband of network matrix approximate and the network matrix based on low-pass prototype that art methods derived can be regarded as the method for the invention; 4. scheme involved in the present invention can be applied in the comprehensive Design of many stopbands broad sense Chebyshev filter easily; 5. scheme involved in the present invention is compared with art methods, has advantage simply fast and accurately.

Description of drawings

Fig. 1 is a FB(flow block) of the present invention.

Fig. 2 is the bandpass response figure of six rank bilateral band filtering in the embodiment of the invention one.

Fig. 3 is the low-pass prototype frequency response chart of six rank double-passband filters in the embodiment of the invention one.

Fig. 4 is the bandpass response figure of seven rank double-passband filters in the embodiment of the invention two.

Embodiment

Below in conjunction with accompanying drawing and embodiment the present invention is described further.

Before scheme of the present invention is described in detail.At first hypothesis is only considered lossless situation, supposes to treat that comprehensive many passbands broad sense Chebyshev filter has M (M is the natural number more than or equal to 2) passband, and this M passband lays respectively at [ω _{D, i}, ω _{U, i}] (i=1 ..., M), ω _{U, i}And ω _{D, i}Be respectively the coboundary angular frequency and the lower boundary angular frequency of i passband, the return loss in each passband is RL _i

As shown in Figure 1, the direct comprehensive designing method of many passbands of bandwidth broad sense Chebyshev filter comprises the steps: arbitrarily

Step S1: according to the index of treating the comprehensive simulation filter; Each passband is carried out independent comprehensive Design according to the single-pass band filter; Derive each single-pass band filter characteristic of correspondence function

and multinomial

and

i=1 wherein separately;, M;

At first, define one and be used for normalized characteristic angle frequencies omega for for simplicity _c, ω generally speaking _cValue for example treats that the frequency range of comprehensive simulation filter drops within the GHz arbitrarily, can choose ω _c=2 π 10 ⁹Rad/s.The amplitude of a complex number frequency variable is defined as s=j ω, and wherein j is an imaginary unit, and ω is the angular frequency variable, and then normalization amplitude of a complex number frequency variable does

Because hypothesis treats that the comprehensive simulation filter has M passband, considers i passband [ω at present _{D, i}, ω _{U, i}], become after its normalization

(wherein

).If counting, the repellel in this passband is N _iIndividual, we can regard this passband as a N _iRank single-pass band filter, and near the transmission zero this passband regard as this single-pass band filter all.Suppose to have p at the zero frequency place at this single-pass band filter _iIndividual transmission zero (p _iBe odd number), the place has m in limited positive frequency _iIndividual transmission zero has l in just infinite distant place _iIndividual transmission zero as transmission zeros all on the positive negative frequency is taken into account, is considered symmetry, and all total transmission zero numbers of this single-pass band filter are n _i=p _i+ 2m _i+ (2l _i+ p _i)=2N _i(wherein need at infinity to replenish p _iIndividual transmission zero is to remedy the p at the zero frequency place _iThe caused polarity problems of individual transmission zero), use complex frequency here

K transmission zero representing this single-pass band filter.Carry out comprehensively according to single-pass band broad sense Chebyshev filter integrated approach below, derive its characteristic function

and derive multinomial and

by characteristic function

again because characteristic function

then can be confirmed multinomial

and

through following relation of plane

${\mathrm{\β}}_i\·F_i\left(\stackrel{\‾}{s}\right)=F_{0i}\left(\stackrel{\‾}{s}\right)=\underset{v=0}{\overset{N_i}{\mathrm{\Σ}}}{a}_{2v}{({\stackrel{\‾}{s}}^2+{\stackrel{\‾}{\mathrm{\ω}}}_{u,i}^2)}^v{({\stackrel{\‾}{s}}^2+{\stackrel{\‾}{\mathrm{\ω}}}_{d,i}^2)}^{N_i/2-v}$ Formula 1

${\mathrm{\ϵ}}_i\·P_i\left(\stackrel{\‾}{s}\right)=P_{0i}\left(\stackrel{\‾}{s}\right)={\stackrel{\‾}{s}}^{p_i}\·\underset{k=1}{\overset{m_i}{\mathrm{\Π}}}({\stackrel{\‾}{s}}^2-{\stackrel{\‾}{s}}_{0k}^2)$ Formula 2

Wherein, factor beta _iBe taken as multinomial

The coefficient of high-order term so that multinomial

The coefficient of high-order term be 1; V is that span is 0 to N _iIntermediate variable; a _2vBe

Expansion coefficient, operator Ev representes right

Get even portion, z is an intermediate variable, and intermediate variable z is in the respective value of k transmission zero

In the formula

Be k transmission zero

Pairing angular frequency; ω _{U, i}And ω _{D, i}Be respectively the coboundary angular frequency and the lower boundary angular frequency of i passband.Constant ε _iCan (cut-off frequency can be from optional one of the coboundary angular frequency of passband or lower boundary angular frequency, and present embodiment is chosen the coboundary angular frequency of passband at cut-off frequency by given

) on reflection coefficient ρ _iObtain

${\mathrm{\ϵ}}_i=\frac{1}{\sqrt{{10}^{{\mathrm{RL}}_i/10}-1}}\·{\left|\frac{P_{0i}\left(\stackrel{\‾}{s}\right)}{F_i\left(\stackrel{\‾}{s}\right)}\right|}_{\stackrel{\‾}{s}=j{\stackrel{\‾}{\mathrm{\ω}}}_{u,i}}$ Formula 3

RL _iBe the return loss in the passband (dB); Multinomial in the formula

Multinomial $F_i\left(\stackrel{\‾}{s}\right)=F_{0i}\left(\stackrel{\‾}{s}\right)/{\mathrm{\β}}_i.$

Multinomial

is confirmed by following relational expression

$E_i\left(\stackrel{\‾}{s}\right)E_i^{*}\left(\stackrel{\‾}{s}\right)=F_i\left(\stackrel{\‾}{s}\right)F_i^{*}\left(\stackrel{\‾}{s}\right)+P_i\left(\stackrel{\‾}{s}\right)P_i^{*}\left(\stackrel{\‾}{s}\right)$ Formula 4

Subscript * representes to get conjugation.

Step S2: with these characteristic functions

(i=1 wherein ..., M) and multinomial

With

Among the substitution superposition relational expression (formula 5 with formula 6) and derive corresponding multinomial

With

Confirm the characteristic function of treating that the comprehensive simulation filter is final $C\left(\stackrel{\‾}{s}\right)=F\left(\stackrel{\‾}{s}\right)/P\left(\stackrel{\‾}{s}\right).$

M passband treating the comprehensive simulation filter in front respectively carry out comprehensive after; Obtained the pairing characteristic function of each passband

(i=1 wherein; M) and multinomial and again with these characteristic functions

(i=1 wherein; M) be updated among the following superposition relational expression, confirm to treat the final multinomial of comprehensive simulation filter

and

$F\left(\stackrel{\‾}{s}\right)=\underset{i=1}{\overset{M}{\mathrm{\Π}}}{F}_i\left(\stackrel{\‾}{s}\right)$ Formula 5

$P\left(\stackrel{\‾}{s}\right)=\underset{i=1}{\overset{M}{\mathrm{\Σ}}}[P_i\left(\stackrel{\‾}{s}\right)\·\underset{j\≠i}{\overset{M}{\underset{j=1}{\mathrm{\Π}}}}{F}_j\left(\stackrel{\‾}{s}\right)]$ Formula 6

expression is even taken the opportunity and is not considered this (promptly the company of participation does not take advantage of) that j=i is corresponding in the formula.

can be confirmed by following formula as for the another one multinomial:

$E\left(\stackrel{\‾}{s}\right)E^{*}\left(\stackrel{\‾}{s}\right)=F\left(\stackrel{\‾}{s}\right)F^{*}\left(\stackrel{\‾}{s}\right)+P\left(\stackrel{\‾}{s}\right)P^{*}\left(\stackrel{\‾}{s}\right)$ Formula 4

So, treat the transfer function

of comprehensive simulation filter and the ratio that reflective function

(transfer function

and reflective function

are the element of collision matrix

) can be expressed as two N (wherein ) rank multinomial:

${\stackrel{\‾}{S}}_{21}\left(\stackrel{\‾}{s}\right)=\frac{P\left(\stackrel{\‾}{s}\right)}{E^{\′}\left(\stackrel{\‾}{s}\right)},$ ${\stackrel{\‾}{S}}_{11}\left(\stackrel{\‾}{s}\right)=\frac{F\left(\stackrel{\‾}{s}\right)}{E^{\′}\left(\stackrel{\‾}{s}\right)}$

In the formula, In the ordinary course of things, coefficient ε _R=1.When whole transmission zeros all are positioned at the finite frequency place,

wherein is any transmission zero of treating the comprehensive simulation filter.

Above-mentioned formula 5, formula 6 are used for evaluator

and are collectively referred to as the superposition relational expression in this step.

Step S3: by polynomial

and posed by the scattering matrix

into theoretical admittance matrix

Polarity according to multinomial

and

; Can with collision matrix

be converted into theoretical admittance matrix

since in the method for the invention the multinomial of deriving be real coefficient, and the transmission zero that is positioned at the zero frequency place is necessary for odd number.Generally speaking; Adopt symmetrical structure more to correspond to actual needs, so the form below adopting is converted into theoretical admittance matrix

with collision matrix

( is strange, and

is even) formula 7

In the formula; E ' writing a Chinese character in simplified form for

; F writing a Chinese character in simplified form for

; P is the writing a Chinese character in simplified form of

, up and down number (± or

) pairing network antithesis each other; Subscript e representes to get polynomial even portion, and subscript o representes to get polynomial strange portion.

Step S4:

carries out residue with the theoretical admittance matrix that obtains among the step S3; And with horizontal equivalent electric circuit in corresponding equivalent electric circuit admittance matrix

compare, thereby confirm to treat resonance frequency

and admittance inversor parameter

and

of each resonator in the comprehensive simulation filter thus obtain treating the horizontal network matrix of representing with overall mode of resonance

of comprehensive simulation filter

carries out residue with the theoretical admittance matrix that obtains among the step S3; Compare with the pairing equivalent electric circuit admittance matrix of the horizontal equivalent electric circuit of treating the comprehensive simulation filter

then, promptly

${\left[\stackrel{\‾}{y}\right]}_{\mathrm{circuit}}=\left[\begin{array}{cc}{\stackrel{\‾}{B}}_S+\underset{k=1}{\overset{N}{\mathrm{\Σ}}}\frac{\stackrel{\‾}{\mathrm{\ω}}{\stackrel{\‾}{J}}_{\mathrm{Sk}}^2}{j({\stackrel{\‾}{\mathrm{\ω}}}^2-{\stackrel{\‾}{\mathrm{\ω}}}_k^2)}& {\mathrm{jJ}}_{\mathrm{SL}}+\underset{k=1}{\overset{N}{\mathrm{\Σ}}}\frac{\stackrel{\‾}{\mathrm{\ω}}{\stackrel{\‾}{J}}_{\mathrm{Sk}}{\stackrel{\‾}{J}}_{\mathrm{Lk}}}{j({\stackrel{\‾}{\mathrm{\ω}}}^2-{\stackrel{\‾}{\mathrm{\ω}}}_k^2)}\\ j{\stackrel{\‾}{J}}_{\mathrm{SL}}+\underset{k=1}{\overset{N}{\mathrm{\Σ}}}\frac{\stackrel{\‾}{\mathrm{\ω}}{\stackrel{\‾}{J}}_{\mathrm{Sk}}{\stackrel{\‾}{J}}_{\mathrm{Lk}}}{j({\stackrel{\‾}{\mathrm{\ω}}}^2-{\stackrel{\‾}{\mathrm{\ω}}}_k^2)}& {\stackrel{\‾}{B}}_L+\underset{k=1}{\overset{N}{\mathrm{\Σ}}}\frac{\stackrel{\‾}{\mathrm{\ω}}{\stackrel{\‾}{J}}_{\mathrm{Lk}}^2}{j({\stackrel{\‾}{\mathrm{\ω}}}^2-{\stackrel{\‾}{\mathrm{\ω}}}_k^2)}\end{array}\right]$

In the formula, the angular frequency variable after expression normalization.Theoretical admittance matrix

compares with equivalent electric circuit admittance matrix

; Can confirm in the equivalent electric circuit admittance matrix

each resonator resonance frequency

and admittance inversor parameter

and

wherein

be the admittance inversor parameter between source end and k the resonator;

is the admittance inversor parameter between load end and k the resonator; Admittance inversor parameter between expression source end and the load end); Thereby the normalized reactance

that obtains being connected source end or load end is after obtaining these parameters, just can write out the horizontal network matrix of representing with overall mode of resonance

Wherein, G _sAnd G _LBe respectively the characteristic admittance of input port and output port, be normalized to 1 usually.

Further, take advantage of through number and rotate first conversion that disappears and can the aforementioned horizontal network matrix of representing based on overall mode of resonance

be transformed into desired sparse topological structure network matrix (for example foldable structure etc.).Because the enforcement of this step can be able to implement to those skilled in the art through prior art, therefore is not described in detail.

Through above-mentioned specific descriptions to the present invention program; Scheme of the present invention has been proved to be has exploitativeness; And because in the above-mentioned technical description process; Abstract to the quantity of passband is M (M for more than or equal to 2 natural number), and therefore scheme of the present invention can be adapted to passband quantity more than or equal to 2 situation.

In order to make those of ordinary skill in the art can get more information about scheme of the present invention; The present invention chooses the situation of passband quantity M=2 the present invention is done further description; But passband quantity is chosen M=2 just in order to simplify computational process; Can not be regarded as the restriction of passband quantity of the present invention, the enforcement of the inventive method that aforementioned content is verified, irrelevant with passband quantity.

Below in conjunction with accompanying drawing and two embodiment the present invention is described further.

Embodiment one: as shown in Figures 2 and 3, present embodiment is with document (Yi-Ting, and Chi-yang Chang; " Analytical design of two-mode dual-band fi lters using e-shaped resonators "; IEEE Transactions on Microwave and Techniques, vol.60, No.2; June 2012, and the example 2 in pp.250-260.) is comprehensive object.This example is one six rank double-passband filter (being passband quantity M=2), and the centre frequency of first passband is at 1.79GHz, and second passband be at 2.265GHz, the return loss RL in the passband _iBe all 15dB.The low-pass prototype network matrix [M] that is provided in this article does

$\left[M\right]=\left[\begin{array}{cccccccc}-j& 0.4873& 0& 0& 0.4214& 0& 0& 0\\ 0.4873& \mathrm{\Ω}+0.7689& 0.2247& 0& 0& 0& 0& 0\\ 0& 0.2247& \mathrm{\Ω}+0.7435& 0.2247& 0& 0& 0& 0\\ 0& 0& 0.2247& \mathrm{\Ω}+0.7689& 0& 0& 0& 0.4783\\ 0.4214& 0& 0& 0& \mathrm{\Ω}-0.8282& 0.1729& 0& 0\\ 0& 0& 0& 0& 0.1729& \mathrm{\Ω}-0.8025& 0.1729& 0\\ 0& 0& 0& 0& 0& 0.1729& \mathrm{\Ω}-0.8282& 0.4214\\ 0& 0& 0& 0.4783& 0& 0& 0.4214& -j\end{array}\right]$

Wherein, Ω is a normalized frequency.

By method of the present invention; Can obtain following multinomial

and

(detailed calculated process can with reference to abovementioned steps S1 and step S2), promptly

$P\left(\stackrel{\‾}{s}\right)=0.0276{\stackrel{\‾}{s}}^7+0.3344{\stackrel{\‾}{s}}^5+1.4200{\stackrel{\‾}{s}}^3+2.1056\stackrel{\‾}{s}$

$F\left(\stackrel{\‾}{s}\right)={\stackrel{\‾}{s}}^{12}+24.8856{\stackrel{\‾}{s}}^{10}+255.2756{\stackrel{\‾}{s}}^8+1381.1749{\stackrel{\‾}{s}}^6$

$+4156.4499{\stackrel{\‾}{s}}^4+6596.7865{\stackrel{\‾}{s}}^2+4314.9106$

$E^{\′}\left(\stackrel{\‾}{s}\right)={\stackrel{\‾}{s}}^{12}+0.4821{\stackrel{\‾}{s}}^{11}+25.0018{\stackrel{\‾}{s}}^{10}+10.0343{\stackrel{\‾}{s}}^9+257.2144{\stackrel{\‾}{s}}^8$

$+82.5745{\stackrel{\‾}{s}}^7+1393.1881{\stackrel{\‾}{s}}^6+335.7138{\stackrel{\‾}{s}}^5+4189.2062{\stackrel{\‾}{s}}^4+674.1271{\stackrel{\‾}{s}}^3$

$+6629.9299{\stackrel{\‾}{s}}^2+534.8140\stackrel{\‾}{s}+4314.9106$

Be converted into theoretical admittance matrix to these collision matrixes

that constitute by multinomial

and and carry out residue; And compare with the equivalent electric circuit admittance matrix

that horizontal equivalent electric circuit is derived; Just can confirm that ( and

wherein

is the admittance inversor parameter between source end and k the resonator to each resonator resonance frequency in the horizontal equivalent electric circuit

admittance inversor parameter;

is the admittance inversor parameter between load end and k the resonator; Admittance inversor parameter between expression source end and the load end) and to be connected the normalized reactance of source end or load end final, the horizontal network matrix

that obtains representing with overall mode of resonance as follows

$\left[\stackrel{\‾}{A}\right]=\left[\begin{array}{cccccccc}-j& 0.1804& 0.2489& 0.1714& 0.1670& 0.2419& 0.1752& 0\\ 0.1804& \stackrel{\‾}{\mathrm{\ω}}-\frac{2.8917}{\stackrel{\‾}{\mathrm{\ω}}}& 0& 0& 0& 0& 0& 0.1804\\ 0.2489& 0& \stackrel{\‾}{\mathrm{\ω}}-\frac{3.1863}{\stackrel{\‾}{\mathrm{\ω}}}& 0& 0& 0& 0& -0.2489\\ 0.1714& 0& 0& \stackrel{\‾}{\mathrm{\ω}}-\frac{3.5093}{\stackrel{\‾}{\mathrm{\ω}}}& 0& 0& 0& 0.1714\\ 0.1670& 0& 0& 0& \stackrel{\‾}{\mathrm{\ω}}-\frac{4.7504}{\stackrel{\‾}{\mathrm{\ω}}}& 0& 0& 0.1670\\ 0.2419& 0& 0& 0& 0& \stackrel{\‾}{\mathrm{\ω}}-\frac{5.1302}{\stackrel{\‾}{\mathrm{\ω}}}& 0& -0.2419\\ 0.1752& 0& 0& 0& 0& 0& \stackrel{\‾}{\mathrm{\ω}}-\frac{5.4759}{\stackrel{\‾}{\mathrm{\ω}}}& 0.1752\\ & 0.1804& -0.2489& 0.1714& 0.1670& -0.2419& 0.1752& -j\end{array}\right]$

Top horizontal network matrix

counted take advantage of and rotation disappears after first conversion; Obtain and document (Yi-Ting; And Chi-yang Chang; " Analytical design of two-mode dual-band fi lters using e-shaped resonators "; IEEE Transactions on Microwave and Techniques; Vol.60; No.2, June 2012, and pp.250-260.) the corresponding to network matrix of median filter topological structure

is promptly

$\left[{\stackrel{\‾}{A}}^{\′}\right]=\left[\begin{array}{cccccccc}-j& 0.3520& 0& 0& 0.3423& 0& 0& 0\\ 0.3520& \stackrel{\‾}{\mathrm{\ω}}-\frac{3.1855}{\stackrel{\‾}{\mathrm{\ω}}}& \frac{0.2181}{\stackrel{\‾}{\mathrm{\ω}}}& 0& 0& 0& 0& 0\\ 0& \frac{0.2181}{\stackrel{\‾}{\mathrm{\ω}}}& \stackrel{\‾}{\mathrm{\ω}}-\frac{3.2163}{\stackrel{\‾}{\mathrm{\ω}}}& \frac{0.2181}{\stackrel{\‾}{\mathrm{\ω}}}& 0& 0& 0& 0\\ 0& 0& \frac{0.2181}{\stackrel{\‾}{\mathrm{\ω}}}& \stackrel{\‾}{\mathrm{\ω}}-\frac{3.1855}{\stackrel{\‾}{\mathrm{\ω}}}& 0& 0& 0& 0.3520\\ 0.3423& 0& 0& 0& \stackrel{\‾}{\mathrm{\ω}}-\frac{5.1303}{\stackrel{\‾}{\mathrm{\ω}}}& \frac{0.2562}{\stackrel{\‾}{\mathrm{\ω}}}& 0& 0\\ 0& 0& 0& 0& \frac{0.2562}{\stackrel{\‾}{\mathrm{\ω}}}& \stackrel{\‾}{\mathrm{\ω}}-\frac{5.0958}{\stackrel{\‾}{\mathrm{\ω}}}& \frac{0.2562}{\stackrel{\‾}{\mathrm{\ω}}}& 0\\ 0& 0& 0& 0& 0& \frac{0.2562}{\stackrel{\‾}{\mathrm{\ω}}}& \stackrel{\‾}{\mathrm{\ω}}-\frac{5.1303}{\stackrel{\‾}{\mathrm{\ω}}}& 0.3422\\ 0& 0& 0& 0.3520& 0& 0& 0.3422& -j\end{array}\right]$

The pairing frequency response of network matrix

that comprehensively obtains by the method for the invention; With document (Yi-Ting; And Chi-yang Chang; " Analytical design of two-mode dual-band filters using e-shaped resonators ", IEEE Transactions on Microwave and Techniques, vol.60; No.2; June2012, pp.250-260.) described in the pairing bandpass response of low-pass prototype network matrix [M] that obtains of method synthesis, in Fig. 2, provide.It is thus clear that both coincide better, explain that the network matrix that the method for the invention comprehensively obtains has broad sense Chebyshev character.

If; The network matrix

that the method for the invention is comprehensively obtained filter transforms to low pass, then can obtain following low-pass network matrix [M ']:

$\left[M^{\′}\right]=\left[\begin{array}{cccccccc}-j& 0.4795& 0& 0& 0.4136& 0& 0& 0\\ 0.4795& \mathrm{\Ω}+0.7556& 0.2018& 0& 0& 0& 0& 0\\ 0& 0.2018& \mathrm{\Ω}+0.7241& 0.2018& 0& 0& 0& 0\\ 0& 0& 0.2018& \mathrm{\Ω}+0.7556& 0& 0& 0& 0.4795\\ 0.4136& 0& 0& 0& \mathrm{\Ω}-0.8254& 0.1874& 0& 0\\ 0& 0& 0& 0& 0.1874& \mathrm{\Ω}-0.8031& 0.1874& 0\\ 0& 0& 0& 0& 0& 0.1874& \mathrm{\Ω}-0.8254& 0.4135\\ 0& 0& 0& 0.4795& 0& 0& 0.4135& -j\end{array}\right]$

With this low-pass network matrix [M '] and document (Yi-Ting; And Chi-yang Chang, " Analytical design of two-mode dual-band filters using e-shaped resonators ", IEEE Transactions on Microwave and Techniques; Vol.60; No.2, June 2012, pp.250-260.) described in the low-pass prototype network matrix [M] that obtains of method synthesis compare; It is thus clear that both difference is very little, pairing low-pass prototype frequency response provides in Fig. 3.A kind of low pass that this explanation, the integrated approach in the document can be regarded as the method for the invention is approximate.Therefore, the network matrix that the inventive method comprehensively obtained

has the actual physics meaning.

Embodiment two: as shown in Figure 4, treat that the comprehensive simulation filter is seven rank filters with two asymmetric passbands.Two passbands lay respectively at [2.5,3.0] GHz and [5.0,6.0] GHz, and the return loss in the passband is made as 20dB.Comprehensively obtaining horizontal network matrix

by the method for the invention does

$\left[\stackrel{\‾}{A}\right]=\left[\begin{array}{ccccccccc}-J& 0.2907& 0.4469& 0.4155& 0.2534& 0.4995& 0.8330& 0.4478& 0\\ 0.2907& \stackrel{\‾}{\mathrm{\ω}}-\frac{5.8303}{\stackrel{\‾}{\mathrm{\ω}}}& 0& 0& 0& 0& 0& 0& 0.2907\\ 0.4469& 0& \stackrel{\‾}{\mathrm{\ω}}-\frac{6.6807}{\stackrel{\‾}{\mathrm{\ω}}}& 0& 0& 0& 0& 0& -0.4469\\ 0.4255& 0& 0& \stackrel{\‾}{\mathrm{\ω}}-\frac{8.4583}{\stackrel{\‾}{\mathrm{\ω}}}& 0& 0& 0& 0& 0.4155\\ 0.2534& 0& 0& 0& \stackrel{\‾}{\mathrm{\ω}}-\frac{9.3885}{\stackrel{\‾}{\mathrm{\ω}}}& 0& 0& 0& -0.2534\\ 0.4995& 0& 0& 0& 0& \stackrel{\‾}{\mathrm{\ω}}-\frac{23.3803}{\stackrel{\‾}{\mathrm{\ω}}}& 0& 0& 0.4995\\ 0.8330& 0& 0& 0& 0& 0& \stackrel{\‾}{\mathrm{\ω}}-\frac{32.2987}{\stackrel{\‾}{\mathrm{\ω}}}& 0& -0.8330\\ 0.4478& 0& 0& 0& 0& 0& 0& \stackrel{\‾}{\mathrm{\ω}}-\frac{38.6940}{\stackrel{\‾}{\mathrm{\ω}}}& 0.4478\\ 0& 0.2907& -0.4469& 0.4155& -0.2534& 0.4995& -0.8330& 0.4478& -j\end{array}\right]$

The resulting frequency response of horizontal network matrix

provides in Fig. 4 thus.It is thus clear that the method for the invention can be used for directly comprehensive many passbands of bandwidth broad sense Chebyshev filter arbitrarily; And resulting network matrix

has the actual physics meaning, and entire method is simple, quick and accurate.

Those of ordinary skill in the art will appreciate that embodiment described here is in order to help reader understanding's principle of the present invention, should to be understood that protection scope of the present invention is not limited to such special statement and embodiment.Those of ordinary skill in the art can make various other various concrete distortion and combinations that do not break away from essence of the present invention according to these teachings disclosed by the invention, and these distortion and combination are still in protection scope of the present invention.

Claims (4)

1. any direct comprehensive designing method of many passbands of bandwidth broad sense Chebyshev filter comprises the steps:

Step S1: according to the index of treating the comprehensive simulation filter; Each passband is carried out independent comprehensive Design according to the single-pass band filter, derive each single-pass band filter characteristic of correspondence function

and multinomial

and

separately

Step S2: these characteristic function? and polynomial?

and?

into superposed relationship among and derive the corresponding polynomial? and?

integrated analog filter to be the ultimate determining the characteristic function?

Step S3: by polynomials?

and?

posed by the scattering matrix?

into theoretical admittance matrix?

Step S4:

carries out residue with the theoretical admittance matrix that obtains among the step S3; And with horizontal equivalent electric circuit in corresponding equivalent electric circuit admittance matrix

compare, thereby confirm to treat resonance frequency

and admittance inversor parameter

and

of each resonator in the comprehensive simulation filter thus obtain treating the horizontal network matrix of representing with overall mode of resonance

of comprehensive simulation filter

2. the direct comprehensive designing method of any many passbands of bandwidth broad sense Chebyshev filter according to claim 1; It is characterized in that the concrete computational process of multinomial described in the step S2 is:

3. the direct comprehensive designing method of any many passbands of bandwidth broad sense Chebyshev filter according to claim 1; It is characterized in that the concrete computational process of multinomial described in the step S2

is:

where?

means that even by not considered when j = i corresponds to this.

4. the direct comprehensive designing method of any many passbands of bandwidth broad sense Chebyshev filter according to claim 1; It is characterized in that the following formula simultaneous that passes through of multinomial described in the step S2

calculates:

In the above-mentioned formula, in the ordinary course of things, coefficient ε _R=1; When whole transmission zeros all are positioned at the finite frequency place,

Wherein

It is any transmission zero of treating the comprehensive simulation filter.

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