CN104363004B - Filter direct synthetic method - Google Patents

Abstract

The invention discloses a filter direct synthetic method. By means of the filter direct synthetic method, the transmission zero points of filters can be flexible arranged, a smoothing polynomial of the filters can be led out, and the smoothing polynomial includes all information of the filters and can be directly used for achieving the filters. Effective connection is conduced through some basic structures which can achieve one or more transmission zero points, an achieving network of the filters is finally obtained, and modularization synthesis can be achieved; the method can be used for designing digital filters through bilinear transformation; the types of the filters comprise the low-pass type, the high-pass type, the band-pass type, the band elimination type and the like. The filter direct synthetic method has the advantages of being simple, fast and accurate.

Description

The direct integrated approach of wave filter

Technical field

The invention belongs to signal processing technology field, and in particular to a kind of design of the direct integrated approach of wave filter.

Background technology

Wave filter is one of Primary Component in radar, communication and measuring system, and its function is to allow that certain part frequency The signal of rate smoothly passes through, and allows the signal of another part frequency to be suppressed by larger, and its performance is for whole system Performance has important impact.Modern radar, communication and measuring system usually require that wave filter has good frequency selectivity The features such as.Divide according to target, wave filter can be divided into analog filter and the big class of digital filter two.Analog filtering Device is the signal for processing simulation or continuous time, and lumped parameter or distributed constant wave filter can be divided into again；In addition, root According to the component type for being adopted, analog filter can be divided into passive filter or active filter.Digital filter is used for locating Reason digital signal, can be divided into finite impulse response (FIR) digital filter and infinite impulse response (IIR) wave filter.According to Dividing, wave filter can be divided into low pass, high pass, band logical and band elimination filter to function.Divide according to type, conventional at present Filter type includes elliptic filter, Butterworth filter, Gaussian filter, Chebyshev filter and inverse Chebyshev Wave filter etc..Prior art selects some approximating functions to derive Filter polynomial, then comprehensively goes out low-pass prototype and (defines It is 1 ohm for singal source resistance, passband border angular frequency is the low pass filter of 1 radian per second), obtain low-pass prototype network；So Afterwards by low pass to high pass, low pass to band logical or low pass to frequency transformations such as band resistances, by low-pass prototype network transformation into corresponding Low pass, high pass, band logical or band elimination filter network.Prior art can be referred to as indirect method.Filter obtained by prior art The transmission zero of ripple device is usually located at zero frequency or infinite point, or fixed, it is impossible to freely place, it is impossible to which realization is more multiple Miscellaneous frequency response.In addition, prior art wave filter realize also lack motility in structure.

The content of the invention

The invention aims to solve prior art median filter and can not realize complex frequency response and realize structure A kind of the shortcomings of lacking motility, it is proposed that the direct integrated approach of wave filter.

Wave filter as two-port network, when passive lossless reciprocity condition is met, for describing its collision matrix [S] Can be write as following form：

Wherein, s is simulation complex angular frequencies variable；P (s) is referred to as transmission polynomial, and F (s) referred to as reflects multinomial, E (s) Multinomial is referred to as had, they are all the multinomials with regard to s, are referred to as Filter polynomial；Symbol * is represented and conjugation is taken to multinomial Computing；Symbol η is determined by the polarity of transmission polynomial P (s).When transmission polynomial P (s) is even function, η=+ 1；Work as biography When defeated multinomial P (s) is odd function, η=- 1.The map network of symbol up and down and its dual network in formula.Filter synthesis Basic thought be exactly to derive to disclosure satisfy that these Filter polynomials of Filter specification requirement, and find out appropriate network or knot Structure is realizing these Filter polynomials.

Based on above-mentioned thought, the technical scheme is that：A kind of direct integrated approach of wave filter, specifically includes following step Suddenly：

S1, the Filter polynomial that analog filter is derived according to analog filter characteristic parameter request；

S2, carry out that modularization comprehensive obtains analog filter to the Filter polynomial realize network, for simulating letter Number process；Or the transmission function that bilinear transformation obtains digital filter is carried out to the Filter polynomial, for numeral letter Number process.

The step of technology of the present invention, S1 was the Filter polynomial that analog filter is derived according to index request.Due to this Inventing the technology can cover the filter types such as low pass, high pass, band logical and band resistance, therefore will make introductions all round how to lead below Go out low pass, high pass, band logical and the Filter polynomial with analog filters such as resistances.

The method that the first derives the Filter polynomial of simulation low-pass filter：The passband for assuming simulation low-pass filter cuts Only frequency is ω_p, the return loss in passband represents with RL (unit be decibel, dB).Simulation low-pass filter is in finite frequency The transmission zero number at place is N_fIndividual, transmission zero number at infinity is N_iIt is individual, then the transmission zero in positive frequencies Sum be N=N_f+N_i.These transmission zeros are all with s_k(wherein k=1,2 ..., N) is representing.Simulation low-pass filter The derivation of Filter polynomial (is mapped corresponding from s planes (i.e. real physical frequencies plane) based on following this to g planes Changing the plane) between normalized mapping relation：

Wherein, g is interim complex variable.S=σ+j ω are simulation complex angular frequencies variables, and σ is complex angular frequencies variable Real part, the imaginary part (i.e. real physics angular frequency) of ω complex angular frequencies variables, j is imaginary unit.For convenience, Ke Yiren Meaning selects a characteristic angular frequency ω_cFor normalization.Complex angular frequencies variable-definition is simulated in normalizationSimulation The cut-off frequecy of passband ω of low pass filter_pRepresent, then normalization cut-off frequecy of passband is defined asBy this Individual mapping relations, transmission zero s in s planes_k(wherein k=1,2 ..., N_f+N_i) will be mapped to that g in g planes_k(wherein K=1,2 ..., N_f+N_i).Using these values g in g planes_k(wherein k=1,2 ..., N_f+N_i) can be in g plane configurations The function f of the characteristic of self-sustained oscillation is shown in some imaginary axis in g planes_l(g), for example：

Or

Wherein, Ev represents the computing that even portion is taken to multinomial.These functions show constant amplitude and shake in the imaginary axis in g planes The characteristic swung.When these functions are by above-mentioned normalized mapping relation transformation to s planes, then simulation low-pass filter is ensure that Logical passband fluctuation be self-sustained oscillation.Then, they can be used as the characteristic function of simulation low-pass filterMeanwhile, The characteristic function of simulation low-pass filterIt is defined as the reflection multinomial of simulation low-pass filterIt is multinomial with transmitting FormulaRatio, that is, have：

Wherein l=1 or 2.Finally, obtain determining the transmission polynomial of simulation low-pass filter and the polynomial formula of reflection It is as follows：

Work as N_iWhen being even number, M=N_f+N_i/2；Work as N_iWhen being odd number, M=N_f+(N_i-1)/2.M is also defined as analog low-pass The exponent number of wave filter.Coefficient a_2v(wherein v=1,2 ..., M) it is to formulaIdol is taken after expansion Determined by after portion.Choose multinomialMost high-order term coefficient as undetermined constant β value so that reflection it is multinomial FormulaMost high-order term coefficient be 1, so that it is determined that reflection multinomialUndetermined constant ε can be by passband Insertion loss or return loss at cut-off frequency determining, so that it is determined that transmission polynomialObtaining anti- Penetrate multinomialAnd transmission polynomialAfterwards, multinomial is hadCan be determined by law of conservation of energy.

Its two be derive mimic high pass filter Filter polynomial method：Make the plural angular frequency of simulation low-pass filter Rate represents that the complex angular frequencies of mimic high pass filter are represented with s with s '.If it has been found that simulation low-pass filter Reflection multinomial F_L(s '), and it can be expressed asWherein m represents reflection multinomial F_LThe highest of (s ') Number of times, u_pIt is reflection multinomial F_LThe expansion coefficient of (s '), p is integer variable；Transmission polynomial P_L(s ') can be expressed asWherein n represents transmission polynomial P_LThe highest number of times of (s '), d_qIt is transmission polynomial P_LThe expansion of (s ') Coefficient, q is integer variable.The characteristic function K of simulation low-pass filter_L(s '), it can be expressed as reflecting multinomial F_L(s ') and Transmission polynomial P_LThe ratio of (s '), i.e.,：

The derivation of the Filter polynomial of mimic high pass filter will based on it is following this from s ' plane (simulation low-pass filters Corresponding simulation complex angular frequencies domain) to s planes (the simulation complex angular frequencies plane corresponding to mimic high pass filter) it Between mapping relations：

Wherein, ω '_sIt is the passband cut-off angular frequency of simulation low-pass filter.ω_sIt is the passband section of mimic high pass filter Angle till frequency, andIt is the normalization passband cut-off angular frequency of mimic high pass filter, i.e.,Wherein ω_cIt is one It is individual can be with optional characteristic angular frequency, for normalization with Simplified analysis.Normalized simulation complex angular frequencies variable is determined Justice is

The characteristic function of mimic high pass filterIt is defined as the reflection multinomial of mimic high pass filterWith Transmission polynomialRatio, i.e.,The characteristic function of mimic high pass filterCan be by mould Intend the characteristic function of low-pass filtering derives through mapping relations above, i.e.,：

The characteristic function of mimic high pass filterMolecule multinomial useRepresent, denominator polynomials are used Represent, i.e.,：

Choose molecule multinomialMost high-order term coefficient as undetermined constant β value so that analog high-pass filtering The reflection multinomial of deviceMost high-order term coefficient be 1, so that it is determined that the reflection multinomial of mimic high pass filterUndetermined constant ε can by mimic high pass filter cut-off frequecy of passband insertion loss or echo damage Consume to determine, so that it is determined that the transmission polynomial of mimic high pass filterObtaining mimic high pass filter Reflection multinomialAnd transmission polynomialAfterwards, multinomial is hadCan be determined by law of conservation of energy.

Its three be derive analog band-pass filter Filter polynomial method：If an it has been found that analog low-pass filter The characteristic function K of ripple device_L(s '), it can be expressed as reflecting multinomial F_L(s ') and transmission polynomial P_LThe ratio of (s '), i.e.,：

Wherein, m represents reflection multinomial F_LThe highest number of times of (s '), u_pIt is reflection multinomial F_LThe expansion coefficient of (s '), p For integer variable, n represents transmission polynomial P_LThe highest number of times of (s '), d_qIt is transmission polynomial P_LThe expansion coefficient of (s '), q is Integer variable.The then derivation of the Filter polynomial of analog band-pass filter is based on the following from (the analog low-pass filter of s ' planes Simulation complex angular frequencies domain corresponding to ripple device) to s planes, (the simulation complex angular frequencies corresponding to analog band-pass filter are put down Face) between mapping relations：

Wherein, ω '_sRepresent the passband cut-off angular frequency of simulation low-pass filter.ω_uRepresent the logical of analog band-pass filter Border angular frequency is taken, a characteristic angular frequency ω is introduced_cAfterwards, normalized passband coboundary angular frequency is defined asω_dRepresent the passband lower boundary angular frequency of analog band-pass filter, normalized passband lower boundary angular frequency calibration Justice isω₀The center angular frequency of analog band-pass filter is represented, i.e.,Normalized central angle Frequency is defined asIt is normalized simulation complex angular frequencies variable-definition be

The characteristic function of analog band-pass filterIt is defined as the reflection multinomial of analog band-pass filterWith Transmission polynomialRatio, i.e.,The characteristic function of analog band-pass filterCan be by The characteristic function of analogue low pass filteringDerive through the mapping transformation of mapping relations recited above, i.e.,：

The characteristic function of analog band-pass filterMolecule multinomial useRepresent, denominator polynomials are usedRepresent, i.e.,：

Choose molecule multinomialMost high-order term coefficient as undetermined constant β value so that analog bandpass filtering The reflection multinomial of deviceMost high-order term coefficient be 1, so that it is determined that the reflection multinomial of analog band-pass filterUndetermined constant ε can by analog band-pass filter cut-off frequecy of passband insertion loss or echo damage Consume to determine, so that it is determined that the transmission polynomial of analog band-pass filterObtaining analog bandpass filtering The reflection multinomial of deviceAnd transmission polynomialAfterwards, multinomial is hadCan come true by law of conservation of energy It is fixed.

Its four be derive simulation band elimination filter Filter polynomial method：If an it has been found that analog low-pass filter The characteristic function K of ripple device_L(s '), it can be expressed as reflecting multinomial F_L(s ') and transmission polynomial P_LThe ratio of (s ').Here it is Distinguish, the simulation complex angular frequencies of simulation low-pass filter are represented with s ', simulate the simulation complex angular frequencies s of band elimination filter Represent.Then have：

Wherein, m represents reflection multinomial F_LThe highest number of times of (s '), u_pIt is reflection multinomial F_LThe expansion coefficient of (s '), p For integer variable, n represents transmission polynomial P_LThe highest number of times of (s '), d_qIt is transmission polynomial P_LThe expansion coefficient of (s '), q is Integer variable.The then derivation of the Filter polynomial of simulation band elimination filter is based on the following from (the analog low-pass filter of s ' planes Simulation complex angular frequencies domain corresponding to ripple device) to s planes, (the simulation complex angular frequencies corresponding to simulation band elimination filter are put down Face) between mapping relations：

Wherein, ω '_sRepresent the passband cut-off angular frequency of simulation low-pass filter.ω_uRepresent the upper of simulation band elimination filter Passband border angular frequency, introduces a characteristic angular frequency ω_cAfterwards, normalized upper passband border angular frequency is defined asω_dThe lower passband border angular frequency of simulation band elimination filter is represented, normalized lower passband border angular frequency is determined Justice isω₀The center angular frequency of simulation band elimination filter is represented, i.e.,Normalized central angle Frequency is defined asIt is normalized simulation complex angular frequencies variable-definition be

The characteristic function of simulation band elimination filterIt is defined as simulating the reflection multinomial of band elimination filterWith Transmission polynomialRatio, i.e.,The characteristic function of simulation band elimination filterCan be by mould Intend the characteristic function of low-pass filteringDerive through the mapping transformation of mapping relations recited above, i.e.,：

The characteristic function of analog band-pass filterMolecule multinomial useRepresent, denominator polynomials are used Represent, i.e.,：

Choose molecule multinomialMost high-order term coefficient as undetermined constant β value so that simulation bandreject filtering The reflection multinomial of deviceMost high-order term coefficient be 1, so that it is determined that simulation band elimination filter reflection multinomialUndetermined constant ε can by simulation band elimination filter cut-off frequecy of passband insertion loss or echo damage Consume to determine, so that it is determined that the transmission polynomial of analog band-pass filterObtaining simulating band elimination filter Reflection multinomialAnd transmission polynomialAfterwards, multinomial is hadCan be determined by law of conservation of energy.

Its five be derive simulation band elimination filter Filter polynomial method：If it is known that the filter of analog band-pass filter Ripple multinomial, then can be the reflection multinomial of analog band-pass filterTransmission as simulation band elimination filter is multinomial FormulaThe transmission polynomial of analog band-pass filterAs the reflection multinomial of simulation band elimination filterThen further according to law of conservation of energy, using the transmission polynomial of simulation band elimination filterWith reflection multinomialDerive total multinomial

Preferably, the derived multinomial of institute is all real number multinomial, is realized with lumped LC match network；Institute is derived more Xiang Shineng is used for the design of microwave/radio-frequency filter.

Preferably, the transmission zero of wave filter can be flexibly placed at zero frequency, infinity or finite frequency, for harmonic wave Suppression either improves band connection frequency selectivity or improves group delay, realizes complicated frequency response.

The step of technology of the present invention, S2 was that the Filter polynomial to analog filter carries out modularization comprehensive and obtains mould That intends wave filter realizes network for processing analogue signal, or carries out bilinearity to these Filter polynomials of analog filter Conversion obtains the transmission function of digital filter to be used to process digital signal.

Modularization comprehensive is carried out if necessary to the Filter polynomial to analog filter, obtain analog filter realizes net Network is used to process analogue signal, then according to lower relation of plane by two port scattering matrix [S (s)]：

It is converted into transmission matrix [A (s)]：

For simplicity, above formula can be write as following form：

Wherein：

The root of transmission polynomial P (s) is defined as transmission zero；The comprehensive thought of filter moduleization be find some can Realizing the basic structure of one or several transmission zeros carries out effectively connection so as to which final network structure can realize wave filter Transmission matrix.Here the transmission matrix of wave filter is usedRepresent, the transmission matrix of transmission zero basic structure is usedTo represent, then can be by the transmission matrix of each transmission zero basic structure using relationship belowDraw the transmission matrix of wave filterSo as to realize the modularization comprehensive of wave filter：

Wherein, N is the total number of required basic structure, P_k(s)、a_k、b_k、c_kAnd d_kIt is the biography of k-th basic structure Constitution element in defeated matrix, is all the multinomial with regard to complex angular frequencies s；In addition, meeting condition

The transmission matrix of the basic structure of above-mentioned transmission zero can be determined by method below：Hypothesis treats comprehensive biography Defeated matrixIt is known, transmission polynomial P that these transmission zeros are constituted_kS () is also known；Transmission zero The transmission matrix of point basic structure is usedTo represent, wherein a_k、b_k,、c_kAnd d_kIt is unknown multinomial, it is remaining Transmission matrixIt is also unknown, then the relation of three is as follows：

After mathematical operation, can obtain：

Above-mentioned formula is investigated in transmission polynomial P_kRoot (i.e. the transmission zero to be realized of this basic structure) place of (s) Value, and compare both members, it may be determined that the multinomial a of this basic structure_k、b_k、c_kAnd d_kAnd remaining transmission square Battle array

If carrying out bilinear transformation to these Filter polynomials of analog filter, it is possible to obtain digital filter Transmission function, for processing digital signal.Setting analog filter (for example low pass, high pass, band logical and band hinder etc. type) biography Defeated multinomial is P_aS (), the total multinomial of analog filter is E_a(s), the then transfer function H of analog filter_aS () defines For transmission polynomial P of analog filter_aThe total multinomial E of (s) and analog filter_a(s) ratio.If transmission polynomial P_aS () can be expressed asWherein n represents transmission polynomial P_aThe highest number of times of (s), d_qIt is transmission polynomial P_aThe expansion coefficient of (s)；Total multinomial E_aS () can be expressed asWherein m represents total multinomial E_a The highest number of times of (s), u_pIt is total multinomial E_aThe expansion coefficient of (s).The then transfer function H of analog filter_aS () can be write Into following form：

The transmission function of digital filter is to carry out being obtained after bilinear transformation by the transfer function to analog filter Arrive.Normalization bilinear transformation contextual definition is：

Wherein, ω is simulation angular frequency, and s is simulation complex angular frequencies, and T is sampling period, f_sFor sampling frequency, z=e^{j ωT}, constant c=2/T=2f_s.For the sake of simplicity, reference frequency f can be selected_s0It is normalized, thenWithThe then transfer function H of analog filter_aS () obtains the transmission letter of digital filter after bilinear transformation Counting H (z) is：

Finally, the transfer function H (z) for obtaining digital filter is：

The invention has the beneficial effects as follows：

(1) transmission zero of wave filter can be flexibly placed at zero frequency, infinity or finite frequency, humorous for improving Ripple suppression, band connection frequency selectivity or group delay etc., the frequency response for making wave filter has great motility；

(2) Filter polynomial of wave filter can directly be derived for synthesis, can realize modularization comprehensive, so that Realize that network agile is various；

(3) technology involved in the present invention can be not only used for analog filter synthesis, and digital filter design can be used for again.

Description of the drawings

Fig. 1 is the FB(flow block) of method involved in the present invention.

Fig. 2 is the frequency response of three simulation low-pass filters in the embodiment one provided in the present invention.

Fig. 3 is that simulation low-pass filter A in the embodiment one provided in the present invention realizes network.

Fig. 4 is that simulation low-pass filter B in the embodiment one provided in the present invention realizes network.

Fig. 5 is that simulation low-pass filter C in the embodiment one provided in the present invention realizes network.

Fig. 6 is the frequency response of the mimic high pass filter in the embodiment two provided in the present invention.

Fig. 7 is that mimic high pass filter in the embodiment two provided in the present invention realizes one of network.

Fig. 8 is that mimic high pass filter in the embodiment two provided in the present invention realizes the two of network.

Fig. 9 is the frequency response of the analog band-pass filter in the embodiment three provided in the present invention.

Figure 10 is that analog band-pass filter in the embodiment three provided in the present invention realizes network.

Figure 11 is the frequency response of the simulation band elimination filter in the example IV provided in the present invention.

Figure 12 is that the simulation band elimination filter in the example IV provided in the present invention realizes network.

Figure 13 is the frequency response of the simulation band elimination filter in the embodiment five provided in the present invention.

Figure 14 is that the simulation band elimination filter in the embodiment five provided in the present invention realizes network.

Figure 15 is the frequency response of the digital filter in the embodiment six provided in the present invention.

Figure 16 is the microstrip filter structural representation in the embodiment seven provided in the present invention.

Figure 17 is the contrast of the synthesis in theory result in the embodiment seven provided in the present invention and the simulation results.

Specific embodiment

With reference to the accompanying drawings and examples the present invention is further illustrated.

As shown in figure 1, technology of the present invention includes two key steps：

S1, the Filter polynomial that analog filter is derived according to index request；

S2, these Filter polynomials are carried out with modularization comprehensive obtains analog filter realize network, for simulating letter Number process；Or these Filter polynomials are carried out with the transmission function that bilinear transformation obtains digital filter, for numeral letter Number process.

Embodiment one is the synthesis with regard to simulation low-pass filter, here by taking three simulation low-pass filters as an example, i.e. mould Intend low pass filter A, simulation low-pass filter B and simulation low-pass filter C.The passband cut-off of these three simulation low-pass filters Frequency is set to 4GHz, and the return loss in passband is less than -20dB.In order to illustrate the superiority of the method for the invention, i.e., The performance of simulation low-pass filter can be changed by arranging transmission zero in specified position so as to which can be flexibly met will Ask, three simulation low-pass filters have different frequency responses, as shown in Figure 2.In simulation low-pass filter A, can be by All of transmission zero is all placed in infinite point, so as to have good high-frequency suppressing.Its Filter polynomial is as follows：

Transmission matrix can be derived by these filter polynomials, so as to obtain its circuit realiration network, as shown in Figure 3. Component value in Fig. 3 is as follows：

R_S=R_L=50 Ω, C₁=0.7745pF, L₂=2.7301nH, C₃=1.4349pF, L₄=2.7301nH, C₅= 0.7745pF。

In simulation low-pass filter B, one of transmission zero can be moved to finite frequency such as from infinite point At 5GHz, to improve the frequency selectivity of passband.Its Filter polynomial is as follows：

Transmission matrix can be derived by these filter polynomials, so as to obtain its circuit realiration network, as shown in Figure 4. Component value in Fig. 4 is as follows：

R_S=R_L=50 Ω, C₁=0.2831pF, L₂=1.0788nH, C₂=0.9392pF, C₃=1.1536pF, L₄= 2.8354nH, C₅=0.8008pF.

In simulation low-pass filter C, there are two transmission zeros to be located at finite frequency 5GHz and 6GHz, so as to further The frequency selectivity and near-end for improving passband suppresses.Its Filter polynomial is as follows：

Transmission matrix can be derived by these filter polynomials, so as to obtain its circuit realiration network, as shown in Figure 5. Component value in Fig. 5 is as follows：

R_S=R_L=50 Ω, C₁=0.2996pF, L₂=1.1682nH, C₂=0.8673pF, C₃=0.9723pF, L₄= 1.8051nH, C₄=0.3898pF, C₅=0.5078pF.

Embodiment two is the synthesis with regard to mimic high pass filter.For example, a mimic high pass filter, its passband are designed Initial frequency is appointed as 5GHz, and the return loss in passband is less than -20dB, and transmission zero is located at zero frequency, and in addition one Individual transmission zero is arranged at 2GHz, and its frequency response is as shown in Figure 6.By the method for the invention, analog high-pass filter can be derived The Filter polynomial of ripple device is as follows：

Transmission matrix can be derived by these filter polynomials, so as to obtain its circuit realiration network, as shown in Figure 7. Component value in Fig. 7 is as follows：

R_S=R_L=50 Ω, L₁=2.1477nH, L₂=9.0781nH, C₂=0.6976pF, L₃=2.1477nH.

In addition, being presented in Fig. 8 its dual network.Component value in Fig. 8 is as follows：

R_S=R_L=50 Ω, C₁=0.8591nH, L₂=1.7439nH, C₂=3.6312pF, C₃=0.8591nH.

Embodiment three is the synthesis with regard to analog band-pass filter.For example, a comprehensive three rank analog band-pass filters, its Passband is located at [3.0,5.0] GHz, and the return loss in passband is less than -20dB, and a transmission zero is located at zero frequency, one Transmission zero is located at 2.5GHz, and a transmission zero is located at 6.0GHz.These are located at the transmission zero at finite frequency can change The frequency selectivity of kind wave filter, its frequency response is as shown in Figure 9.By the method for the invention, this analog band can be derived The Filter polynomial of bandpass filter is as follows：

Transmission matrix can be derived by these filter polynomials, so as to obtain its circuit realiration network, as shown in Figure 10. Component value in Figure 10 is as follows：

R_S=R_L=50 Ω, L₁=2.9570nH, L₂=1.1561nH, C₂=3.5057pF, L₃=0.8761nH, C₃= 1.9257pF, L₄=0.4822nH, C₄=1.4593pF, C₅=0.5685pF.

Example IV is the synthesis with regard to simulating band elimination filter.For example, comprehensive three order modes intend band elimination filter, its Cut-off frequecy of passband on the left of stopband is 3.0GHz, and the passband initial frequency on the right side of stopband is 5.0GHz, in passband Fluctuation be less than 0.04dB, its frequency response is as shown in figure 11.If using in technology of the present invention by analogue low pass filtering The method that device is converted into simulation band elimination filter, the Filter polynomial that can derive this simulation band elimination filter is as follows：

Transmission matrix can be derived by these filter polynomials, so as to obtain its circuit realiration network, as shown in figure 12. Component value in Figure 12 is as follows：

R_S=R_L=50 Ω, L₁=4.8083nH, C₁=0.3512pF, L₂=0.5905nH, C₂=3.1628pF, L₃= 0.5339nH, C₃=2.8598pF, L₄=4.8083nH, C₄=0.3512pF.

Can see from example IV, the passband initial frequency of the simulation band elimination filter can be distribution accurately controlled.

Embodiment five is the synthesis with regard to simulating band elimination filter.For example, comprehensive three order modes intend band elimination filter, its Stopband is located at [3.0,5.0] GHz, and insertion loss in stopband (i.e. | S₂₁|) it is more than 20dB, its frequency response is as shown in figure 13.This In using in technology described in this method, simulation band elimination filter is derived by the filter polynomial of exchange analog band-pass filter Filter polynomial method.The Filter polynomial that this simulation band elimination filter can be derived is as follows：

Transmission matrix can be derived by these filter polynomials, so as to obtain its circuit realiration network, as shown in figure 14. Component value in Figure 14 is as follows：

R_S=R_L=50 Ω, L₁=2.4475nH, C₁=0.6900pF, L₂=0.8388nH, C₂=3.1794pF, L₃= 0.5311nH, C₃=2.0132pF, L₄=2.4475nH, C₄=0.6900pF.

Can see from embodiment five, the stopband initial frequency of the simulation band elimination filter can be distribution accurately controlled.

Embodiment six is the design with regard to digital filter.Above derive various analog filters Filter polynomial it Afterwards, by bilinear transformation, the transmission function of corresponding digital filter can be obtained, is available for Digital Signal Processing.Here with As a example by one three rank digital high-pass filter, if sampling frequency is 1000, its passband initial frequency is in j0.4 π, a transmission zero O'clock 0, one in j0.2 π, one is set to 0.1dB in j0.3 π, the fluctuating in passband.Can be led by technology of the present invention The Filter polynomial for going out mimic high pass filter is：

After bilinear transformation, the transmission function for obtaining digital high-pass filter is

Corresponding frequency response is as shown in figure 15.

Embodiment seven is typical case's application with regard to technology of the present invention in microwave/radio-frequency filter design, with Illustrate the superiority of technology of the present invention.Design an analog band-pass filter, it is desirable to which its bandwidth covers [2.0,4.0] GHz, i.e. relative bandwidth are about 67%, and the return loss in passband is less than -20dB, at least suppression of 15dB at 6GHz. Here, realized using a microstrip filter, its structural representation as shown in figure 16, it by a parallel connection short circuit minor matters, one The three part cascades of individual series-connected transmission minor matters and a parallel connection short circuit minor matters are formed.If Z₁It is the feature of two parallel connection short circuit minor matters Impedance, θ is its electrical length, can select to determine θ at mid frequency here；Z₂It is the feature resistance of middle series-connected transmission minor matters Anti-, its electrical length is the twice of parallel connection short circuit minor matters.The transmission matrix [A] of the microstrip filter_C(θ)It is as follows

The transmission matrix [A] of microstrip filter_C(θ)Through following mapping

S=jtan θ

Wherein, the complex angular frequencies of s correspondences mimic high pass filter, θ is the electrical length variable of microstrip filter.Through upper After stating conversion, the transmission matrix [A] of microstrip filter_C(θ)It is changed into

From the property of above-mentioned mapping relations, above-mentioned transmission matrix [A]_C(s)Correspond to an analog high-pass response.Cause This, can by technology of the present invention according to wave filter index request, derive response mimic high pass filter filtering it is many Item formula, and thus obtain following transmission matrix

Wherein, Z₀It is the input of microstrip filter or the characteristic impedance of output feeder, Z is taken here₀=50 Ω.By the present invention Transmission matrix derived from the technology is contrasted with the transmission matrix of microstrip filter, i.e.,

[A]_T=[A]_C(s)

Can determine that the unknown parameter in microstrip filter.In the present embodiment, can obtain

Z₁=48.12 Ω, Z₂=63.02 Ω

After simulation optimization, the parameter of final determination is

Z₁=53.21 Ω, Z₂=61.80 Ω

The microstrip filter is finally processed test.In fig. 17, give the synthesis result of technology of the present invention with The contrast of the simulation results of microstrip filter, three coincide preferable.This illustrates that technology of the present invention is applicable to Among the design of microwave/radio-frequency filter.Unlike the prior art, the derived filter polynomial of technology institute of the present invention, Can directly with microwave/radio-frequency filter, with more physical significance.

One of ordinary skill in the art will be appreciated that embodiment described here is to aid in reader and understands this Bright principle, it should be understood that protection scope of the present invention is not limited to such especially statement and embodiment.This area It is each that those of ordinary skill can make various other without departing from essence of the invention according to these technologies enlightenment disclosed by the invention Plant concrete deformation and combine, these deformations and combination are still within the scope of the present invention.

Claims (9)

1. the direct integrated approach of a kind of wave filter, it is characterised in that specifically include following steps：

S1, the Filter polynomial that analog filter is derived according to analog filter characteristic parameter request；

S2, carry out that modularization comprehensive obtains analog filter to the Filter polynomial realize network, at analogue signal Reason；Or the transmission function that bilinear transformation obtains digital filter is carried out to the Filter polynomial, at digital signal Reason；

When analog filter in step S1 is simulation low-pass filter, its concrete grammar for deriving Filter polynomial is： The cut-off frequecy of passband for assuming simulation low-pass filter is ω_p, the return loss in passband represents with RL, and the unit of RL is dB； Transmission zero number of the simulation low-pass filter at finite frequency is N_fIndividual, transmission zero number at infinity is N_iIt is individual, Then the sum of the transmission zero in positive frequencies is N=N_f+N_i；These transmission zeros are with s_kTo represent, wherein k=1,2 ..., N；The Filter polynomial of simulation low-pass filter derivation based on it is following this from s planes to the normalized mapping g planes Relation, wherein s planes are real physical frequencies plane, and g planes are the corresponding changing the plane of mapping：

$g^2=\frac{{\stackrel{\‾}{s}}^2+{\stackrel{\‾}{\mathrm{\ω}}}_p^2}{{\stackrel{\‾}{s}}^2}$

Wherein, g is interim complex variable；S=σ+j ω are simulation complex angular frequencies variables, and σ is the reality of complex angular frequencies variable Portion, the imaginary part of ω complex angular frequencies variables, i.e., real physics angular frequency, j is imaginary unit；Arbitrarily select a feature angular frequency Rate ω_cFor normalization；Complex angular frequencies variable-definition is simulated in normalizationThe passband cut-off of simulation low-pass filter Frequency ω_pRepresent, then normalization cut-off frequecy of passband is defined asBy this mapping relations, in s planes Transmission zero s_kWill be mapped to that the g in g planes_k, wherein k=1,2 ..., N_f+N_i；Can be with using these values gk in g planes The function f of the characteristic of self-sustained oscillation is shown in some imaginary axis in g planes of g plane configurations_l(g), when these functions By in above-mentioned normalized mapping relation transformation to s planes, then the logical passband fluctuation that ensure that simulation low-pass filter is constant amplitude Vibration；Then, they can be used as the characteristic function of simulation low-pass filterMeanwhile, the spy of simulation low-pass filter Levy functionIt is defined as the reflection multinomial of simulation low-pass filterAnd transmission polynomialRatio, i.e.,：

$K_L\left(\stackrel{\‾}{s}\right)=\frac{F_L\left(\stackrel{\‾}{s}\right)}{P_L\left(\stackrel{\‾}{s}\right)}=f_l\left(g\right){|}_{g^2=\frac{{\stackrel{\‾}{s}}^2+{\stackrel{\‾}{\mathrm{\ω}}}_p^2}{{\stackrel{\‾}{s}}^2}}$

Finally, obtain determining that the transmission polynomial of simulation low-pass filter and the polynomial formula of reflection are as follows：

$Ev\left\{\underset{k=1}{\overset{N_f}{\Π}}{(g_k-z)}^2\underset{k=1}{\overset{N_i}{\Π}}(-1-g)\right\}=\underset{v=0}{\overset{M}{\Σ}}{a}_{2v}{g}^{2v}$

$F_0\left(\stackrel{\‾}{s}\right)=\underset{v=0}{\overset{M}{\Σ}}{a}_{2v}{({\stackrel{\‾}{s}}^2+{\stackrel{\‾}{\mathrm{\ω}}}_p^2)}^v{s}^{N-2v}$

$P_0\left(\stackrel{\‾}{s}\right)=\underset{k=1}{\overset{N_f}{\Π}}({\stackrel{\‾}{s}}^2-{\stackrel{\‾}{s}}_k^2)$

Work as N_iWhen being even number, M=N_f+N_i/2；Work as N_iWhen being odd number, M=N_f+(N_i-1)/2；M is also defined as analogue low pass filtering The exponent number of device；Coefficient a_2vIt is to formulaTake after expansion and determined after polynomial even portion , wherein v=1,2 ..., M, Ev is represented and is taken polynomial even portion's computing；Choose multinomialMost high-order term coefficient make For the value of undetermined constant β, so that reflection multinomialMost high-order term coefficient be 1, so that it is determined that reflection multinomialUndetermined constant ε can determine by the insertion loss of cut-off frequecy of passband or return loss, so that it is determined that Transmission polynomialObtaining reflecting multinomialAnd transmission polynomialAfterwards, multinomial is hadCan be determined by law of conservation of energy.

2. the direct integrated approach of wave filter according to claim 1, it is characterised in that the analog filtering in step S1 When device is mimic high pass filter, its concrete grammar for deriving Filter polynomial is：Make the plural angular frequency of simulation low-pass filter Rate represents that the complex angular frequencies of mimic high pass filter are represented with s with s '；If it has been found that simulation low-pass filter Reflection multinomial F_L(s '), and it can be expressed asWherein m represents reflection multinomial F_LThe highest of (s ') Number of times, u_pIt is reflection multinomial F_LThe expansion coefficient of (s '), p is integer variable；Transmission polynomial P_L(s ') can be expressed asWherein n represents transmission polynomial P_LThe highest number of times of (s '), d_qIt is transmission polynomial P_LThe expansion of (s ') Coefficient, q is integer variable；The characteristic function K of simulation low-pass filter_L(s '), it can be expressed as reflecting multinomial F_L(s ') and Transmission polynomial P_LThe ratio of (s '), i.e.,：

$K_L\left(s^{\′}\right)=\frac{F_L\left(s^{\′}\right)}{P_L\left(s^{\′}\right)}=\frac{\underset{p=0}{\overset{m}{\Σ}}{u}_p{\left(s^{\′}\right)}^p}{\underset{q=0}{\overset{n}{\Σ}}{d}_q{\left(s^{\′}\right)}^q}$

The derivation of the Filter polynomial of mimic high pass filter will be closed from s ' planes based on following this to the mapping s planes System, wherein s ' planes are the simulation complex angular frequencies domain corresponding to simulation low-pass filter, and s planes are mimic high pass filter institute Corresponding simulation complex angular frequencies plane：

$s^{\′}=\frac{{\mathrm{\ω}}_s^{\′}{\stackrel{\‾}{\mathrm{\ω}}}_s}{\stackrel{\‾}{s}}$

Wherein, ω '_sIt is the passband cut-off angular frequency of simulation low-pass filter；ω_sIt is the passband angle of cut-off of mimic high pass filter Frequency, andIt is the normalization passband cut-off angular frequency of mimic high pass filter, i.e.,Wherein ω_cBe one can be with Optional characteristic angular frequency, for normalization with Simplified analysis；It is normalized simulation complex angular frequencies variable-definition be

The characteristic function of mimic high pass filterIt is defined as the reflection multinomial of mimic high pass filterAnd transmission MultinomialRatio, i.e.,The characteristic function of mimic high pass filterCan be by analog low-pass The characteristic function of filtering is derived through mapping relations above, i.e.,：

$K_H\left(\stackrel{\‾}{s}\right)=K_L{\left(s^{\′}\right)}_{s^{\′}=\frac{{\mathrm{\ω}}_s^{\′}{\stackrel{\‾}{\mathrm{\ω}}}_s}{\stackrel{\‾}{s}}}$

The characteristic function of mimic high pass filterMolecule multinomial useRepresent, denominator polynomials are usedTable Show, i.e.,：

$F_0\left(\stackrel{\‾}{s}\right)=\underset{p=0}{\overset{m}{\Σ}}{u}_p{\left({\mathrm{\ω}}_s^{\′}{\stackrel{\‾}{\mathrm{\ω}}}_s\right)}^p\×{\stackrel{\‾}{s}}^{m-p}$

$P_0\left(\stackrel{\‾}{s}\right)={\stackrel{\‾}{s}}^{m-n}\underset{q=0}{\overset{n}{\Σ}}{d}_q{\left({\mathrm{\ω}}_s^{\′}{\stackrel{\‾}{\mathrm{\ω}}}_s\right)}^q\×{\stackrel{\‾}{s}}^{n-q}$

Choose molecule multinomialMost high-order term coefficient as undetermined constant β value so that mimic high pass filter Reflection multinomialMost high-order term coefficient be 1, so that it is determined that the reflection multinomial of mimic high pass filterUndetermined constant ε can by mimic high pass filter cut-off frequecy of passband insertion loss or return loss To determine, so that it is determined that the transmission polynomial of mimic high pass filterObtaining mimic high pass filter Reflection multinomialAnd transmission polynomialAfterwards, multinomial is hadCan be determined by law of conservation of energy.

3. the direct integrated approach of wave filter according to claim 1, it is characterised in that the analog filtering in step S1 When device is analog band-pass filter, its concrete grammar for deriving Filter polynomial is：If an it has been found that analog low-pass filter The characteristic function K of ripple device_L(s '), it is expressed as reflecting multinomial F_L(s ') and transmission polynomial P_LThe ratio of (s '), i.e.,：

$K_L\left(s^{\′}\right)=\frac{F_L\left(s^{\′}\right)}{P_L\left(s^{\′}\right)}=\frac{\underset{p=0}{\overset{m}{\Σ}}{u}_p{\left(s^{\′}\right)}^p}{\underset{q=0}{\overset{n}{\Σ}}{d}_q{\left(s^{\′}\right)}^q}$

Wherein, m represents reflection multinomial F_LThe highest number of times of (s '), u_pIt is reflection multinomial F_LThe expansion coefficient of (s '), p is whole Number variable, n represents transmission polynomial P_LThe highest number of times of (s '), d_qIt is transmission polynomial P_LThe expansion coefficient of (s '), q is integer Variable；Then the derivation of the Filter polynomial of analog band-pass filter is based on the following from s ' planes to reflecting s planes Relation is penetrated, wherein s ' planes are the simulation complex angular frequencies domain corresponding to simulation low-pass filter, and s planes are analog bandpass filtering Simulation complex angular frequencies plane corresponding to device：

$s^{\′}=\frac{{\mathrm{\ω}}_s^{\′}}{{\stackrel{\‾}{\mathrm{\ω}}}_u-{\stackrel{\‾}{\mathrm{\ω}}}_d}\·\frac{{\stackrel{\‾}{s}}^2+{\stackrel{\‾}{\mathrm{\ω}}}_0^2}{\stackrel{\‾}{s}}$

Wherein, ω '_sRepresent the passband cut-off angular frequency of simulation low-pass filter；ω_uRepresent on the passband of analog band-pass filter Border angular frequency, introduces a characteristic angular frequency ω_cAfterwards, normalized passband coboundary angular frequency is defined as ω_dThe passband lower boundary angular frequency of analog band-pass filter is represented, normalized passband lower boundary angular frequency is defined asω₀The center angular frequency of analog band-pass filter is represented, i.e.,Normalized center angular frequency is determined Justice isIt is normalized simulation complex angular frequencies variable-definition be

The characteristic function of analog band-pass filterIt is defined as the reflection multinomial of analog band-pass filterAnd transmission MultinomialRatio, i.e.,The characteristic function of analog band-pass filterCan be by simulating The characteristic function of low-pass filteringDerive through the mapping transformation of mapping relations recited above, i.e.,：

$K_{BP}\left(\stackrel{\‾}{s}\right)=K_L\left(s^{\′}\right){|}_{s^{\′}=\frac{{\mathrm{\ω}}_s^{\′}}{{\stackrel{\‾}{\mathrm{\ω}}}_u-{\stackrel{\‾}{\mathrm{\ω}}}_d}\frac{{\stackrel{\‾}{s}}^2+{\stackrel{\‾}{\mathrm{\ω}}}_0^2}{\stackrel{\‾}{s}}}$

The characteristic function of analog band-pass filterMolecule multinomial useRepresent, denominator polynomials are usedTable Show, i.e.,：

$F_0\left(\stackrel{\‾}{s}\right)=\underset{p=0}{\overset{m}{\Σ}}{u}_p{\left(\frac{{\mathrm{\ω}}_s^{\′}}{{\stackrel{\‾}{\mathrm{\ω}}}_2-{\stackrel{\‾}{\mathrm{\ω}}}_1}\right)}^p{({\stackrel{\‾}{s}}^2+{\stackrel{\‾}{\mathrm{\ω}}}_0^2)}^p{\stackrel{\‾}{s}}^{m-p}$

$P_0\left(\stackrel{\‾}{s}\right)={\stackrel{\‾}{s}}^{m-n}\underset{q=0}{\overset{n}{\Σ}}{d}_q{\left(\frac{{\mathrm{\ω}}_s^{\′}}{{\stackrel{\‾}{\mathrm{\ω}}}_2-{\stackrel{\‾}{\mathrm{\ω}}}_1}\right)}^q{({\stackrel{\‾}{s}}^2+{\stackrel{\‾}{\mathrm{\ω}}}_0^2)}^q{\stackrel{\‾}{s}}^{n-q}$

Choose molecule multinomialMost high-order term coefficient as undetermined constant β value so that analog band-pass filter Reflection multinomialMost high-order term coefficient be 1, so that it is determined that the reflection multinomial of analog band-pass filterUndetermined constant ε can by analog band-pass filter cut-off frequecy of passband insertion loss or echo damage Consume to determine, so that it is determined that the transmission polynomial of analog band-pass filterObtaining analog band-pass filter Reflection multinomialAnd transmission polynomialAfterwards, multinomial is hadDetermined by law of conservation of energy.

4. the direct integrated approach of wave filter according to claim 1, it is characterised in that the analog filtering in step S1 To simulate during band elimination filter, its concrete grammar for deriving Filter polynomial is device：If an it has been found that analog low-pass filter The characteristic function K of ripple device_L(s '), it can be expressed as reflecting multinomial F_L(s ') and transmission polynomial P_LThe ratio of (s ')；Here it is Distinguish, the simulation complex angular frequencies of simulation low-pass filter are represented with s ', simulate the simulation complex angular frequencies s of band elimination filter Represent, then have：

$K_L\left(s^{\′}\right)=\frac{F_L\left(s^{\′}\right)}{P_L\left(s^{\′}\right)}=\frac{\underset{p=0}{\overset{m}{\Σ}}{u}_p{\left(s^{\′}\right)}^p}{\underset{q=0}{\overset{n}{\Σ}}{d}_q{\left(s^{\′}\right)}^q}$

Wherein, m represents reflection multinomial F_LThe highest number of times of (s '), u_pIt is reflection multinomial F_LThe expansion coefficient of (s '), p is whole Number variable, n represents transmission polynomial P_LThe highest number of times of (s '), d_qIt is transmission polynomial P_LThe expansion coefficient of (s '), q is integer Variable；The derivation of Filter polynomial of band elimination filter is then simulated based on the following from s ' planes to reflecting s planes Relation is penetrated, wherein s ' planes are the simulation complex angular frequencies domain corresponding to simulation low-pass filter, and s planes are simulation bandreject filtering Simulation complex angular frequencies plane corresponding to device：

$s^{\′}={\mathrm{\ω}}_s^{\′}\·({\stackrel{\‾}{\mathrm{\ω}}}_u-{\stackrel{\‾}{\mathrm{\ω}}}_d)\frac{\stackrel{\‾}{s}}{{\stackrel{\‾}{s}}^2+{\stackrel{\‾}{\mathrm{\ω}}}_0^2}$

Wherein, ω '_sRepresent the passband cut-off angular frequency of simulation low-pass filter；ω_uRepresent the upper passband of simulation band elimination filter Border angular frequency, introduces a characteristic angular frequency ω_cAfterwards, normalized upper passband border angular frequency is defined as ω_dThe lower passband border angular frequency of simulation band elimination filter is represented, normalized lower passband border angular frequency is defined asω₀The center angular frequency of simulation band elimination filter is represented, i.e.,Normalized center angular frequency is determined Justice isIt is normalized simulation complex angular frequencies variable-definition be

The characteristic function of simulation band elimination filterIt is defined as simulating the reflection multinomial of band elimination filterAnd transmission MultinomialRatio, i.e.,The characteristic function of simulation band elimination filterCan be low by simulating The characteristic function of pass filterDerive through the mapping transformation of mapping relations recited above, i.e.,：

$K_{BS}\left(\stackrel{\‾}{s}\right)=K_L{\left(s^{\′}\right)}_{s^{\′}={\mathrm{\ω}}_s^{\′}({\stackrel{\‾}{\mathrm{\ω}}}_u-{\stackrel{\‾}{\mathrm{\ω}}}_d)\frac{\stackrel{\‾}{s}}{{\stackrel{\‾}{s}}^2+{\stackrel{\‾}{\mathrm{\ω}}}_0^2}}$

The characteristic function of analog band-pass filterMolecule multinomial useRepresent, denominator polynomials are usedTable Show, i.e.,：

$F_0\left(\stackrel{\‾}{s}\right)=\underset{p=0}{\overset{m}{\Σ}}{u}_p{\[{\mathrm{\ω}}_s^{\′}({\stackrel{\‾}{\mathrm{\ω}}}_2-{\stackrel{\‾}{\mathrm{\ω}}}_1)\]}^p{\stackrel{\‾}{s}}^p{({\stackrel{\‾}{s}}^2+{\stackrel{\‾}{\mathrm{\ω}}}_0^2)}^{m-p}$

$P_0\left(\stackrel{\‾}{s}\right)={({\stackrel{\‾}{s}}^2+{\stackrel{\‾}{\mathrm{\ω}}}_0^2)}^{m-n}\underset{q=0}{\overset{n}{\Σ}}{d}_q{\[{\mathrm{\ω}}_s^{\′}({\stackrel{\‾}{\mathrm{\ω}}}_2-{\stackrel{\‾}{\mathrm{\ω}}}_1)\]}^q{\stackrel{\‾}{s}}^q{({\stackrel{\‾}{s}}^2+{\stackrel{\‾}{\mathrm{\ω}}}_0^2)}^{n-q}$

Choose molecule multinomialMost high-order term coefficient as undetermined constant β value so that simulation band elimination filter Reflection multinomialMost high-order term coefficient be 1, so that it is determined that simulation band elimination filter reflection multinomialUndetermined constant ε can by simulation band elimination filter cut-off frequecy of passband insertion loss or echo damage Consume to determine, so that it is determined that the transmission polynomial of analog band-pass filterObtaining simulating band elimination filter Reflection multinomialAnd transmission polynomialAfterwards, multinomial is hadCan come true by law of conservation of energy It is fixed.

5. the direct integrated approach of wave filter according to claim 3, it is characterised in that the analog filtering in step S1 To simulate during band elimination filter, its concrete grammar for deriving Filter polynomial is device：If it is known that the filter of analog band-pass filter Ripple multinomial, then can be the reflection multinomial of analog band-pass filterTransmission as simulation band elimination filter is multinomial FormulaThe transmission polynomial of analog band-pass filterAs the reflection multinomial of simulation band elimination filterThen further according to law of conservation of energy, using the transmission polynomial of simulation band elimination filterWith reflection multinomialDerive total multinomial

6. according to the arbitrary described direct integrated approach of wave filter of claim 1-5, it is characterised in that：The derived multinomial of institute is all It is real number multinomial, is realized with lumped LC match network；Derived multinomial can be used for setting for microwave/radio-frequency filter Meter.

7. according to the arbitrary described direct integrated approach of wave filter of claim 1-5, it is characterised in that：The transmission zero of wave filter Can flexibly be placed at zero frequency, infinity or finite frequency, for harmonics restraint either improve band connection frequency selectivity or Improve group delay, realize complicated frequency response.

8. according to the arbitrary described direct integrated approach of wave filter of claim 1-5, it is characterised in that to filter in step S2 Ripple multinomial carries out the concrete grammar of modularization comprehensive：By two port scattering matrix [S (s)]：

It is converted into transmission matrix [A (s)]：

For simplicity, above formula can be write as following form：

$\[A\left(s\right)\]=\frac{1}{P\left(s\right)}\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]$

Wherein：

$a=\frac{1}{2}\left(E\right(s)+{\mathrm{\ηE}}^{*}(s\left)\right)\±\frac{1}{2}\left(F\right(s)+{\mathrm{\ηF}}^{*}(s\left)\right)$

$b=\frac{1}{2}\left(E\right(s)-{\mathrm{\ηE}}^{*}(s\left)\right)\±\frac{1}{2}\left(F\right(s)-{\mathrm{\ηF}}^{*}(s\left)\right)$

The root of transmission polynomial P (s) is defined as transmission zero；The transmission matrix of wave filter is usedRepresent, transmission zero The transmission matrix of point basic structure is usedTo represent, then can be basic by each transmission zero using relationship below The transmission matrix of structureDraw the transmission matrix of wave filterSo as to realize the module of wave filter Change comprehensive：

$\frac{1}{P\left(s\right)}\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]=\underset{k=1}{\overset{N}{\Π}}\frac{1}{P_k\left(s\right)}\left[\begin{array}{cc}{a}_k& b_k\\ c_k& d_k\end{array}\right]$

Wherein, N is the total number of required basic structure, P_k(s)、a_k、b_k、c_kAnd d_kIt is the transmission square of k-th basic structure Constitution element in battle array, is all the multinomial with regard to complex angular frequencies s；In addition, meeting condition

The transmission matrix of the basic structure of above-mentioned transmission zeroCan be determined by method below：Hypothesis is treated Comprehensive transmission matrixIt is known, transmission polynomial P that these transmission zeros are constituted_kS () is also known 's；The transmission matrix of transmission zero basic structure is usedTo represent, wherein a_k、b_k、c_kAnd d_kIt is unknown multinomial Formula, remaining transmission matrixIt is also unknown, then the relation of three is as follows：

$\frac{1}{P_b\left(s\right)}\left[\begin{array}{cc}{a}_b& b_b\\ c_b& d_b\end{array}\right]=\frac{1}{P_k\left(s\right)}\left[\begin{array}{cc}{a}_k& b_k\\ c_k& d_k\end{array}\right]\·\frac{1}{P_a\left(s\right)}\left[\begin{array}{cc}{a}_a& b_a\\ c_a& d_a\end{array}\right]$

After mathematical operation, can obtain：

$\left[\begin{array}{cc}{d}_k& -b_k\\ -c_k& a_k\end{array}\right]\left[\begin{array}{cc}{a}_b& b_b\\ c_b& d_b\end{array}\right]=P_k^2\left(s\right)\left[\begin{array}{cc}{a}_a& b_a\\ c_a& d_a\end{array}\right]$

Above-mentioned formula is investigated in transmission polynomial P_kTaking at the root of (s), the i.e. transmission zero to be realized of this basic structure Value, and compare both members, it may be determined that the multinomial a of this basic structure_k、b_k、c_kAnd d_kAnd remaining transmission matrix

9. according to the arbitrary described direct integrated approach of wave filter of claim 1-5, it is characterised in that obtain in step S2 The concrete grammar of the transmission function of digital filter is：The transmission polynomial of analog filter is set as P_a(s), analog filter Total multinomial be E_a(s), the then transfer function H of analog filter_aS () is defined as transmission polynomial P of analog filter_a The total multinomial E of (s) and analog filter_a(s) ratio；If transmission polynomial P_aS () can be expressed asWherein n represents transmission polynomial P_aThe highest number of times of (s), d_qIt is transmission polynomial P_aThe expansion coefficient of (s)； Total multinomial E_aS () can be expressed asWherein m represents total multinomial E_aThe highest number of times of (s), u_pIt is Total multinomial E_aThe expansion coefficient of (s)；The then transfer function H of analog filter_aS () can be write as following form：

$H_a\left(s\right)=\frac{P_a\left(s\right)}{E_a\left(s\right)}=\frac{\underset{q=0}{\overset{n}{\Σ}}{d}_q{s}^q}{\underset{p=0}{\overset{m}{\Σ}}{u}_p{s}^p}$

Wherein, p is integer variable, and q is integer variable；The transmission function of digital filter is by the transmission to analog filter Function carries out what is obtained after bilinear transformation；Normalization bilinear transformation contextual definition is：

$\stackrel{\‾}{s}=\stackrel{\‾}{c}\frac{1-z^{-1}}{1+z^{-1}}$

Wherein, ω is simulation angular frequency, and s is simulation complex angular frequencies, and T is sampling period, f_sFor sampling frequency, z=e^jωT, often Number c=2/T=2f_s；For the sake of simplicity, reference frequency is set as f_s0And be normalized, thenWithThen The transfer function H of analog filter_aS () after bilinear transformation, the transfer function H (z) for obtaining digital filter is：

$H\left(z\right)=H_a\left(s\right){|}_{s=c\frac{1-z^{-1}}{1+z^{-1}}}$

Finally, the transfer function H (z) for obtaining digital filter is：

$H\left(z\right)=\frac{\underset{q=0}{\overset{n}{\mathrm{\Σ}}}{d}_q\·c^q{(1-z^{-1})}^q{(1+z^{-1})}^{m-q}}{\underset{p=0}{\overset{m}{\mathrm{\Σ}}}{u}_p\·c^p{(1-z^{-1})}^p{(1+z^{-1})}^{m-p}}.$