A design method for lumped narrowband IPD filters based on N+2 coupling theory

Abstract

A design method for a lumped narrowband IPD filter based on N+2 coupling theory is presented. This invention addresses the problems of existing methods for calculating transmission zero locations being difficult to apply to IPD processes and for quickly providing component values. The design method comprises: 1. Performing bandpass frequency transformation on the admittance matrix equation; 2. Setting the cross-coupling factor between resonators i and k in the coupled filter network as M. ik The cross-coupling factor M is characterized by a PI-type capacitor network. ik ; 3. When M ik When it is positive, it belongs to magnetic coupling, M ik When the value is negative, it indicates electrical coupling. Fourth, the designed narrowband IPD filter circuit undergoes evolution and simplification processing, including source impedance transformation, narrowband approximation of magnetic coupling, and negative capacitance narrowband approximation, to solve for the component values ​​of each element in the circuit structure. This invention starts from the topology of the coupled filter and utilizes various narrowband filter analysis methods to achieve the evolution and simplification of the circuit structure.

Description

Technical Field

[0001] This invention relates to a design method for lumped element narrowband IPD filters based on an N+2 coupling matrix. This method can obtain high-performance narrowband filters without a complex optimization process and enables standardized and modular design. Background Technology

[0002] Over the past 20 years, with the invention of Integrated Passive Device (IPD) technology as an excellent manufacturing process, more and more microwave devices and modules have been presented to the world in a more compact form and with better characteristics, becoming one of the mainstream passive microwave device manufacturing processes. Numerous microwave filters based on IPD technology have also been continuously reported. Designing filter topologies with better rectangular coefficients and wider out-of-band suppression range at the same order, and the calculation methods for the values ​​of each component under this topology, have always been the focus of filter designers' research. Hybrid electromagnetic coupling, cross-coupling, and cascaded composite resonators are all common topologies for lumped filters. Their purpose is to form transmission zeros at the stopband, thereby obtaining better filtering effects. There are three types of methods for calculating the location of transmission zeros: microwave network method, electromagnetic coupling method, and odd-even mode impedance method. The latter two analysis methods are mainly applied to hybrid electromagnetic coupling filters. The microwave network method allows S... 21 The parameter is equal to zero, establishing a mathematical relationship between the component value and the transmission zero frequency. In addition, since the scattering matrix, impedance matrix, and admittance matrix have a transformation relationship according to equation (1), it can also be determined based on Z. 21 =0; Y 21=0 and other methods to solve. According to the characteristics of the topology, choose the matrix that is easy to solve for analysis. The electromagnetic coupling method is generally calculated by full-wave electromagnetic simulation to find the change of the strength of electric couple and magnetic coupling with frequency. The frequency point where the amplitudes of the two are equal is the frequency point where the electromagnetic coupling effect exactly cancels out, that is, the transmission zero frequency. The odd-even mode impedance method is analyzed from the perspective of the equivalent circuit of lumped elements. When the two-port network has strong symmetry, this method is very convenient and ingenious. Odd-mode impedance represents the output impedance of the two-port network when the input and output are connected to differential mode signals; even-mode impedance marks the output impedance of the two-port network when the input and output are connected to common mode signals. Calculate the reflection coefficient of the output port under these two excitations respectively, see equation (2) and equation (3). When these two reflection coefficients are exactly equal, it means that when the input port provides excitation, no energy flows out from the output port, and the two ports are in a completely isolated state. Therefore, it is only necessary to write out the odd-even mode impedance according to the topology and make them equal to solve the mathematical relationship between the transmission zero and the component value. These three methods are generally used to calculate transmission zeros when the topology is determined. When the filter order is less than the third order, these methods are relatively practical.

[0003]

[0004]

[0005]

[0006] Z 21 Z represents the forward transfer impedance when port 2 is open. outo Z represents the even-mode impedance. oute Z0 represents the odd-mode impedance, and Z0 represents the characteristic impedance of the resonant circuit.

[0007] Currently, there is an increasing number of topologies for high-performance filters, and the mechanisms for generating transmission zeros are becoming more sophisticated. However, among the numerous reported novel lumped filter topologies, some lack a uniquely definite mathematical relationship between the zeros and poles of the transmission characteristic function and component values. Others have complex mathematical relationships and topologies, relatively limited application scenarios, and are difficult to apply to IPD (Integrated Product Development) processes. This leads to a series of thorny problems when using novel filter topologies, such as the inability to quickly determine component values, the inability to predict filter performance in advance, and a limited optimization space for the topology. Furthermore, during filter design, the tuned and optimized filter results often fail to meet specifications, and it is difficult to quickly determine the specific reasons for this failure—whether it is due to insufficient resonator order, limitations of the topology itself, or room for further component value optimization. This complicates subsequent filter optimization. How to hierarchically, systematically, and conveniently optimize the topology based on technical specifications and quickly redetermine the values ​​of each component is another problem that this patent aims to solve. Summary of the Invention

[0008] The purpose of this invention is to address the problems that existing methods for calculating the transmission zero point location are difficult to apply to IPD technology, difficult to quickly provide component values, and unable to predict filter performance in advance. Instead, this invention provides a novel design method for lumped narrowband IPD filters based on N+2 coupling theory.

[0009] The design method of the lumped narrowband IPD filter based on N+2 coupling theory of this invention is implemented according to the following steps:

[0010] 1. Set the lumped topology of the narrowband IPD filter. For the N+2 type coupled filter network, the admittance matrix equation is [Y]=j[M]+j[s]+[G](4), where [M] represents the coupling matrix, the elements in the coupling matrix represent the coupling coefficients between resonators, [S] represents the identity matrix, and [G] represents the sparse matrix, where all elements are 0 except for the element in the upper left corner which is G1 and the element in the lower right corner which is Gn.

[0011] Then, a bandpass frequency transform is performed on the admittance matrix equation with a center frequency of f0 and a bandwidth of Δf. The source admittance of the bandpass filter is G. S Load impedance G L The admittance matrix equation after bandpass frequency transformation is obtained as follows:

[0012] [Y] = j[m] + [W] + [G](5a);

[0013] in

[0014] In the formula, ω0 is the center frequency of the bandpass filter, and C SSC is the coupling capacitance between the sources. LL C is the coupling capacitance between the loads. SL C is the coupling capacitance between the source and the load. NL Let C be the coupling capacitance between the Nth resonator and the load. 11 C is the coupling capacitance between couplers; S1 The coupling capacitance between the source and the first resonator;

[0015]

[0016] In the formula, C0 is the capacitance of the parallel resonant circuit, L0 is the inductance of the parallel resonant circuit, and ω is the center frequency of the parallel resonant circuit.

[0017]

[0018] (j[m * [Represents the coupling matrix between units]

[0019] Expanding the formula [Y]=j[m]+[W]+[G](5a), we get the formula (7), where S represents the source, L represents the load, and ν n Represents the source voltage or load voltage, C nj ν represents the coupling capacitance between the source or load and the j-th resonator. j ν represents the voltage of the j-th coupler. k C represents the voltage of the k-th coupler. kj i represents the coupling capacitance between the k-th coupler and the j-th coupler. j This represents the current of the j-th coupler;

[0020] II. Let M be the cross-coupling factor between resonator i and resonator k in the coupled filter network. ik The cross-coupling factor M is characterized by a PI-type capacitor network. ik The three capacitors in the PI-type capacitor network are C1, C2, C3, C4, C5, C6, m And 2 Cs a A capacitor connected in parallel in the resonant circuit characterizes the self-coupling M of resonator i. ii ;

[0021] III. When the cross-coupling factor M ik When positive, it belongs to magnetic coupling, and the series capacitor C in the PI-type capacitor network. m The value is negative, and the parallel capacitor C a It is positive; when the cross-coupling factor M is positive. ik When the value is negative, it indicates electrical coupling, and the series capacitor C in the PI-type capacitor network... m The parallel capacitor C is positive.a Negative;

[0022] Fourth, the narrowband IPD filter circuit is simplified by transformation, including source impedance transformation, narrowband approximation of magnetic coupling and narrowband approximation of negative capacitance. Finally, the component values ​​of each component in the circuit structure are solved according to the coupling matrix to complete the design of the lumped narrowband IPD filter.

[0023] The narrowband approximation process for the magnetic coupling is as follows:

[0024] When C m =-C ik C a =C ik At that time, C ik This represents the coupling capacitance between the i-th and k-th resonators. In this case, the PI-type capacitor network narrowband approximation is treated as a purely inductive PI-type narrowband approximation circuit. The purely inductive PI-type narrowband approximation circuit is composed of L... m * L1 * L2 * Composition, L m * L1 * and L2 * The calculation formula is shown in equation (10):

[0025]

[0026]

[0027]

[0028]

[0029] Where m ik ν represents the denormalized coupling coefficient between resonator i and resonator k. i ν represents the voltage of the i-th resonator. k C represents the voltage of the k-th resonator. ik This represents the coupling capacitance value between the i-th resonator and the k-th resonator, i i Represents the current of the i-th resonator, i k FBW represents the current of the k-th resonator;

[0030] The aforementioned narrowband approximation process for negative capacitance is as follows:

[0031] When the cross-coupling factor M ik When positive, it belongs to magnetic coupling, and the series capacitor C in the PI-type capacitor network. m Negative, -Cm Narrowband approximation as inductance L M Or inductor L′ M With capacitor C M Parallel circuit.

[0032] This invention starts with the topology of coupled filters and utilizes various proposed narrowband filter analysis (transformation) methods to achieve the evolution and simplification of the circuit structure. The component values ​​of each element are solved based on the numerical values ​​of the coupling matrix, completing the final circuit synthesis and implementation. Then, this method is used to design several typical narrowband bandpass filters, and schematic simulations are performed to verify the accuracy of the design method, making the design method for narrowband IPD filters more universal.

[0033] This invention proposes a design method for lumped element IPD bandpass filters with lumped narrowband high rectangular coefficients. In the filter design process, the filter topology and component values ​​are designed simultaneously based on technical specifications. Based on this, this invention proposes a prototype topology for analyzing narrowband coupled filters. Starting from the prototype topology, various topologies can be obtained, and component values ​​can be quickly calculated using simple formulas. This will create more opportunities to design IPD filters with superior performance and more reasonable design.

[0034] The method proposed in this invention avoids extensive tuning and optimization operations. It can quickly evaluate the design specifications of a filter and design the ideal component schematic in the shortest possible time. It can also be combined with programming, allowing users to input filter specifications into an interactive interface, and have the computer program synthesize the topology and determine the LC component values. This is a standardized and modular design method. Furthermore, the physical meaning of each component is very clear, facilitating layout parameter adjustments and significantly improving filter design efficiency. In actual layout design tolerances, designers can clearly identify which specific component has a greater impact on the result.

[0035] For asymmetric filters and the location of transmission zeros, this invention offers greater design flexibility. Designers can quickly pinpoint the location of transmission zeros by controlling their position when designing the coupling matrix, eliminating the need for further adjustments to the schematic. Further optimization of out-of-band rejection can be achieved by replacing the prototype resonator with a multi-frequency resonator.

[0036] The design method proposed in this invention has strong compatibility with many advanced high-performance filter design concepts. When a generalized Norton transform is used at the input and output ports, and the transformer turns ratio is complex, complex impedance matching can be achieved, making it more suitable for filtering active circuits. The method proposed in this invention can also be combined with surface acoustic wave (SAW) filters to form hybrid filters, achieving better filtering performance. Furthermore, extending the coupling matrix to the complex domain allows for the use of filter predistortion techniques.

[0037] The method proposed in this invention has strong compatibility with external packaging, which is not available in most circuit structures. This allows for the design of high-performance circuits without requiring overly stringent packaging processes. Attached Figure Description

[0038] Figure 1 This is a topology diagram of the coupling filter in step one of this invention;

[0039] Figure 2 This is a structural diagram of the PI-type capacitor network in step two of this invention;

[0040] Figure 3 This is a lumped topological structure diagram of the complex coupling matrix in a specific implementation method;

[0041] Figure 4 This is a schematic diagram of the filter source / load impedance in the second specific implementation method;

[0042] Figure 5 This is a schematic diagram of the capacitor tap impedance matching transformation in the third specific implementation method;

[0043] Figure 6 This is a schematic diagram of the impedance matching transformation of the inductor tap in Implementation Method 4;

[0044] Figure 7 This is an approximate schematic diagram of the narrow-band magnetic coupling in step four of this invention;

[0045] Figure 8 This is an approximate schematic diagram of the narrow band of negative capacitance in step four of the present invention;

[0046] Figure 9 This is a narrowband approximate schematic diagram of the negative capacitor, inductor, and parallel resonant circuit of the present invention for 'frequency invariant' coupling, where 1 represents -CM1 and 2 represents m. ij The inductance of 1 is equivalent to that of m. ij The parallel resonance equivalent of 1, 4 represents -CM2, and 5 represents m. ij The equivalent inductance of 2, 6 represents m ij Parallel resonance equivalent of 2;

[0047] Figure 10 This is a schematic diagram of the T / π transformation of the inductor section in specific implementation method seven;

[0048] Figure 11 This is a diagram of a commonly used IPD filter topology.

[0049] Figure 12 This is a circuit derivation diagram of the resonator-load coupling section in the embodiment;

[0050] Figure 13 This is a schematic diagram of the complex LC resonant structure in the embodiment;

[0051] Figure 14 For the example Figure 13 The admittance function test diagrams of the prototype resonator are shown in the order of the arrows: complex LC resonant structure a, complex LC resonant structure c, prototype resonator, and complex LC resonant structure b.

[0052] Figure 15 This is a schematic diagram of the input and output capacitors in the embodiment;

[0053] Figure 16 This is a schematic diagram of the topology of Case 1, designed based on the method proposed in this invention, in the embodiments.

[0054] Figure 17 This is a schematic diagram of the Case 2 principle topology designed based on the method proposed in this invention in the embodiment.

[0055] Figure 18 This is a schematic diagram of the Case 3 principle topology designed based on the method proposed in this invention in the embodiments.

[0056] Figure 19 The image shows the scattering parameter test diagram of the Case 1 filter designed based on the method proposed in this invention in the embodiment, where A represents S21 (prototype), B represents S21 (optimized), C represents S11 (prototype), and D represents S11 (optimized).

[0057] Figure 20 The image shows the scattering parameter test diagram of the Case 2 filter designed based on the method proposed in this invention in the embodiment, where A represents S21 (prototype), B represents S21 (optimized), C represents S11 (prototype), and D represents S11 (optimized).

[0058] Figure 21The image shows the scattering parameter test diagram of the Case 3 filter designed based on the method proposed in this invention in the embodiment, where A represents S21 (prototype), B represents S21 (optimized), C represents S11 (prototype), and D represents S11 (optimized).

[0059] Figure 22 The topology diagrams and transmission zeros of the three prototype filters designed using the method proposed in the embodiments are shown below. Detailed Implementation

[0060] Specific Implementation Method 1: This implementation method, based on the N+2 coupling theory, designs a lumped narrowband IPD filter according to the following steps:

[0061] 1. Set the lumped topology of the narrowband IPD filter. For the N+2 type coupled filter network, the admittance matrix equation is [Y]=j[M]+j[s]+[G](4), where [M] represents the coupling matrix, the elements in the coupling matrix represent the coupling coefficients between resonators, [S] represents the identity matrix, and [G] represents the sparse matrix, where all elements are 0 except for the element in the upper left corner which is G1 and the element in the lower right corner which is Gn.

[0062] Then, a bandpass frequency transform is performed on the admittance matrix equation with a center frequency of f0 and a bandwidth of Δf. The source admittance of the bandpass filter is G. S Load impedance G L The admittance matrix equation after bandpass frequency transformation is obtained as follows:

[0063] [Y] = j[m] + [W] + [G](5a);

[0064] in

[0065] In the formula, ω0 is the center frequency of the bandpass filter, and C SS C is the coupling capacitance between the sources. LL C is the coupling capacitance between loads. SL C is the coupling capacitance between the source and the load. NL Let C be the coupling capacitance between the Nth resonator and the load. 11 C is the coupling capacitance between couplers; S1 The coupling capacitance between the source and the first resonator;

[0066]

[0067] In the formula, C0 is the capacitance of the parallel resonant circuit, L0 is the inductance of the parallel resonant circuit, and ω is the center frequency of the parallel resonant circuit.

[0068]

[0069] (j[m * [Represents the coupling matrix between units]

[0070] Expanding the formula [Y]=j[m]+[W]+[G](5a), we get the formula (7), where S represents the source, L represents the load, and ν n Represents the source voltage or load voltage, C nj ν represents the coupling capacitance between the source or load and the j-th resonator. j ν represents the voltage of the j-th coupler. k C represents the voltage of the k-th coupler. kj i represents the coupling capacitance between the k-th coupler and the j-th coupler. j This represents the current of the j-th coupler;

[0071] II. Let M be the cross-coupling factor between resonator i and resonator k in the coupled filter network. ik The cross-coupling factor M is characterized by a PI-type capacitor network. ik The three capacitors in the PI-type capacitor network are C1, C2, C3, C4, C5, C6, m And 2 Cs a A capacitor connected in parallel in the resonant circuit characterizes the self-coupling M of resonator i. ii ;

[0072] III. When the cross-coupling factor M ik When positive, it belongs to magnetic coupling, and the series capacitor C in the PI-type capacitor network. m The value is negative, and the parallel capacitor C a It is positive; when the cross-coupling factor M is positive. ik When the value is negative, it indicates electrical coupling, and the series capacitor C in the PI-type capacitor network... m The parallel capacitor C is positive. a Negative;

[0073] Fourth, the narrowband IPD filter circuit is simplified by transformation, including source impedance transformation, narrowband approximation of magnetic coupling and narrowband approximation of negative capacitance. Finally, the component values ​​of each component in the circuit structure are solved according to the coupling matrix to complete the design of the lumped narrowband IPD filter.

[0074] The narrowband approximation process for the magnetic coupling is as follows:

[0075] When C m =-C ik C a =C ik At that time, C ikThis represents the coupling capacitance between the i-th and k-th resonators. In this case, the PI-type capacitor network narrowband approximation is treated as a purely inductive PI-type narrowband approximation circuit. The purely inductive PI-type narrowband approximation circuit is composed of L... m * L1 * L2 * Composition, L m * L1 * and L2 * The calculation formula is shown in equation (10):

[0076]

[0077]

[0078]

[0079]

[0080] Where m ik ν represents the denormalized coupling coefficient between resonator i and resonator k. i ν represents the voltage of the i-th resonator. k C represents the voltage of the k-th resonator. ik This represents the coupling capacitance value between the i-th resonator and the k-th resonator, i i Represents the current of the i-th resonator, i k FBW represents the current of the k-th resonator;

[0081] The aforementioned narrowband approximation process for negative capacitance is as follows:

[0082] When the cross-coupling factor M ik When positive, it belongs to magnetic coupling, and the series capacitor C in the PI-type capacitor network. m Negative, -C m Narrowband approximation as inductance L M Or inductor L′ M With capacitor C M Parallel circuit.

[0083] The overall process of the design method of lumped narrowband IPD filter based on N+2 coupling theory in this embodiment is as follows: First, the coupling topology is determined by key technical indicators, and the N+2 coupling matrix is ​​listed. Then, it is simplified by characterizing it with a PI-type capacitor network and various narrowband filter approximation transformations. The prototype filter is improved with a complex resonator. Finally, the component values ​​are obtained.

[0084] In step two of this embodiment, the cross-coupling factor M is characterized by a PI-type capacitor network. ikThe derivation process is as follows: Considering the coupling between resonator i and resonator k, as well as their respective self-coupling, assuming that the coupling of other resonators to resonator i and resonator k is 0, write the Kirchhoff equation for the i / k-th coupler. In the Sub-6GHz band, the size of the integrated chip is small enough, belonging to the short-line model, and Kirchhoff's laws are applicable. Next, consider a circuit like... Figure 2 As shown, the left side represents the resonator, and the right side represents the resonator k,i. i ,v i i k ,v k Let C represent the node voltage and current of resonator i and resonator k, respectively. The node voltage equations are written, yielding equation (12). It is not difficult to deduce that when C... m =-C ik C a =C ik At this time, equations (11) and (12) are completely identical. This means that the PI-type capacitor network can characterize the coupling M between resonators. ik (i≠k), connecting a capacitor in parallel with the resonant circuit can characterize the self-coupling M of the resonator. ii Among them, the cross-coupling factor M ik >0, then C m <0, C a >0; and vice versa.

[0085]

[0086] Z oute =Z outo (12)

[0087] Following the same solution approach, the coupled topology of the load / impedance and resonator can be equivalent to a J-converter cascaded with resistors. It's easy to see that the Π-type topology always contains a negative capacitance; when the coupling is positive, the series capacitance is negative C. m When coupling is negative, the parallel capacitor C a It is negative.

[0088] In lossy filter predistortion techniques, the coupling matrix factor can become complex. This paper extends the coupling matrix to a complex matrix, providing further optimization space for the filter group delay characteristics. Let M... ij =A-jB, the circuit topology of lumped elements in this case is as follows: Figure 3 As shown. The imaginary part of the coupling matrix can be represented by a resistor. When B > 0, then G < 0; when B < 0, then G > 0. This results in a negative resistor that cannot be directly implemented from a passive device. Generally, a negative resistor can be constructed by building an active circuit.

[0089] The derivation process of the negative capacitor narrowband approximation circuit in step four of this embodiment is as follows: In the N+2 coupling matrix, there will always be coupling between the source / load and the resonator, as well as coupling between the source and the load. There are no capacitors or inductors at the source and load ends to absorb the negative capacitor in the coupling structure. The negative capacitor is directly transformed into an equivalent value without the need for external circuitry. The essence of the narrowband approximation is that at a single frequency point, the two circuits exhibit the same reactance characteristics, and are approximated as equivalent near this frequency point. The negative capacitors appearing in the circuit are used to achieve 'frequency-invariant' coupling; in fact, the negative capacitor itself is also a narrowband approximation. Therefore, the problem of the negative capacitor narrowband approximation is transformed into the 'frequency-invariant' coupling narrowband approximation. At the center frequency of the filter, its reactance value should be consistent with the 'frequency-invariant' coupling amount. Figure 8 Two feasible topologies are described, both of which achieve narrowband approximations using inductors and parallel resonant circuits. The effects of negative capacitance, inductance, and parallel resonant circuits on the 'frequency-invariant' coupling approximation are shown in [reference needed]. Figure 9 , Figure 9 In the diagram, -Cm1 and -Cm2 represent the coupling amount of the negative capacitor in any narrowband application. It's easy to see that the inductor's effect is similar to that of the negative capacitor, but superior to that of parallel resonance. In the figure, it's clear that various circuits affect m... ij2 The approximation is significantly better than m. ij1 The approximate bandwidth is wider.

[0090] This embodiment proposes a method for implementing a J-converter within the passband using physically realizable lumped passive components. A synthesis method for a series of LC resonators is introduced, which, based on the prototype filter, achieves superior out-of-band rejection.

[0091] Specific Implementation Method Two: This implementation method differs from Specific Implementation Method One in that the source-end impedance transformation in step four uses either capacitor tap impedance matching or inductor tap impedance matching.

[0092] Specific Implementation Method Three: This implementation method differs from Specific Implementation Method Two in that it uses a capacitor tap impedance matching method (such as...). Figure 5 As shown below:

[0093] In capacitor C and resistor R s An ideal transformer with a turns ratio of 1:n is inserted at both ends, and the capacitor C and resistor R are... s The Norton transformation of the parallel circuit is a circuit in which one end of capacitor C1′ is connected to one end of both R1′ and C2′, and the other ends of R1′ and C2′ are grounded respectively, where C1′=nC / (n-1), R1′=R s / n 2 , C2′=nC.

[0094] In this embodiment, an ideal transformer with a turns ratio of 1:N is inserted across the parallel capacitor and resistor. At this point, the resistor's value becomes 1 / N of its original value. 2 Next, we treat the capacitor and transformer as a whole and perform Norton substitution, resulting in circuit structure 5(c). Assuming N>1, the capacitor connected in series with the resistor is a negative capacitor. We approximate this negative capacitor as an inductor L in the narrow band at the center frequency f0. X When the impedance transformation ratio N is large, and the capacitance is relatively large compared to the narrow-band approximate frequency, the inductance L... X The smaller the value, the smaller the impact on the circuit, which can be approximated and ignored, thus yielding... Figure 5 (e). This diagram shows the most common impedance transformation circuit in high-frequency circuits, but only if it is near the center frequency and the inductor L... X It only holds true when the size is relatively small. Undoubtedly, it is clear... Figure 5 (d) has better circuit matching performance than Figure 5 The circuit in (e) is shown. In practical applications, capacitor-impedance networks will have more advantages. Inductors are easier to fabricate due to their smaller number, and more importantly, they have better compatibility with external parasitic effects, being almost unaffected by packaging parasitic effects. In fact, packaged test results may even be better than bare die test results. The Norton transform has an ideal transformer model, which facilitates impedance transformation and the integration of capacitor and inductor values, making the circuit easier to implement in IPD (Integrated Circuit Design) processes and enabling its repeated use in practical circuit transformations.

[0095] Specific Implementation Method Four: This implementation method differs from Specific Implementation Method Two in that it uses the inductor tap impedance matching method (e.g., ...). Figure 6 As shown below:

[0096] Inductor L and resistor R s An ideal transformer with a turns ratio of 1:n is inserted at both ends, LR s The Norton transform of a parallel circuit is a circuit in which one end of inductor L1″ is connected to both one end of R1″ and one end of L2″, where L1″ = L(n-1) / n, L2″ = L / n, and R1″ = R s / n 2 .

[0097] Specific Implementation Method Five: This implementation method differs from Specific Implementation Method One or Two in that step two uses a PI-type capacitor network to characterize the cross-coupling factor M. ik The condition is that it is under the Sub-6G frequency band.

[0098] In the Sub-6GHz band, the size of the integrated chip is small enough, which is a short-line model, and Kirchhoff's laws apply.

[0099] Embodiment Six: The difference between this embodiment and any one of Embodiments One to Five is that the evolution simplification process described in Step Four further includes T / π circuit transformation.

[0100] Embodiment Seven: The difference between this embodiment and Embodiment Six is that the T-type pure inductance circuit is transformed into two-section PI-type circuits through Norton transformation.

[0101] In this embodiment of cross-magnetic coupling, the circuit structure as shown in Figure 7 (c) inevitably appears. The middle series circuit is inversely proportional to the square of the de-normalized magnetic coupling factor, so its inductance value is generally relatively large, about dozens of nH (self-resonance frequency is relatively low). It is necessary to take effective measures to reduce its inductance value. This embodiment uses T / π transformation to reduce the inductance. However, in many cases, it is not desired to involve all the parallel inductors on both sides in the transformation. Only a part of the inductance is expected to participate in the transformation, as shown in Figure 10 (a). Especially when the series inductor is much larger than the pull-down inductors on both sides, it will cause the inductance value after transformation to be too small, and the circuit performance is sensitive to its inductance value, which is also not conducive to the implementation of IPD process. This embodiment determines the component values according to the inductance reduction factor to achieve the method of partial T / π transformation.

[0102] First, divide the middle series inductor into two halves and add two completely symmetric ideal transformers in the middle, as shown in Figure 10 (b). To reduce L m , generally N>1 is taken. Norton transformation is performed on the two shaded areas respectively to obtain the circuit shown in Figure 10 (c). At this time, L3 is a negative inductor. However, as long as L3 < L0, the negative inductor can be absorbed by the inductor of the parallel resonance circuit. When L3 = L0, the circuit transformation at this time is a complete T / π transformation. The calculation formulas for the component values after transformation are shown in Equation (13), where 2N is the reduction factor of the series inductor L m .

[0103]

[0104] Embodiment Eight: The difference between this embodiment and any one of Embodiments One to Seven is that in Step Four, when -C m is approximately processed as an inductor L M (as shown in Figure 8 c),

[0105] Embodiment Nine: The difference between this embodiment and any one of Embodiments One to Eight is that in Step Four, when -C m is approximately processed as a parallel circuit of an inductor L′ M and a capacitor C M (as shown in Figure 8 d),

[0106] This implementation method Figure 8 In the circuit diagram of d, C0|M ij |=C a , Figure 8 'a' represents the electrical coupling situation, in which the negative capacitance to ground can be absorbed.

[0107] Example 1: The design method of the lumped narrowband IPD filter based on the N+2 coupling theory in this example is implemented according to the following steps:

[0108] I. Prototype Filter Synthesis: In this embodiment, a parallel LC structure is used as the resonant unit, and only the cross-coupling between resonators, the self-coupling of resonators, and the coupling between the first resonator and the load are involved. The circuit diagram is as follows. Figure 12 As shown in (a). In this embodiment, these three types of coupling are considered and calculated separately.

[0109] Coupling Method 1: First, only consider the coupling between resonators and the self-coupling of the resonators. Since most of the negative capacitance in these two circuit parts will be absorbed by the surrounding parallel capacitors or form a magnetic coupling circuit, the circuit structure does not need to be changed; only the values ​​of each component need to be calculated. In this case, the coupling of resonator i is divided into electrical coupling m. ek With magnetic coupling m mk Assume there are Q electrical cross-couples and P magnetic cross-couples involving resonator i. After circuit simplification and rearrangement, the following expressions (14-18) are obtained. Where C... i ,L i These represent the capacitance and inductance of the resonant circuit, C. eik L mik C represents the capacitance and inductance values ​​connected between resonator i and resonator k, respectively. ik C is the capacitance between the i-th resonator and the k-th resonator. ii It is the capacitance value of the i-th resonator itself, m ii L is the coupling coefficient of the i-th resonator itself. ik L is the inductance value between the i-th resonator and the k-th resonator. mik M is the inductance value between the i-th resonator and the k-th resonator. ek It is the electrical coupling of the k-th resonator, M mk It is the magnetic coupling of the k-th resonator, M ii It is the coupling of the i-th resonator itself;

[0110]

[0111]

[0112] C eik =C0m ek (16)

[0113]

[0114] m ek =M ek ×FBW;m mk =M mk ×FBW;m ii =M ii ×FBW (18)

[0115] Both coupling capacitors and self-coupling capacitors are M of the resonant capacitor. ek ×FBW times, while M ek The values ​​are generally less than 1, and the relative bandwidth of narrowband filters is less than 10%. Therefore, when the number of negative capacitors that need to be canceled is less than 10, the cross-coupled and self-coupled negative capacitors will not completely cancel the resonant capacitor or even make it negative.

[0116] Coupling Method Two: Next, we will analyze the relevant circuitry for the coupling between resonator 1 and the load. The circuitry related to this part will be simplified as follows: Figure 12 As shown in (a). In the previous discussion of the narrow-band approximation of negative capacitance, it was concluded that the smaller the 'frequency-invariant' reactance, the larger the negative capacitance, and the better the approximation using an inductor. Therefore, the Norton transform will be used. Inserting two ideal transformers into the circuit yields... Figure 12 (b) Perform the Norton transform to obtain Figure 12 (c) At this point, the reactance of the negative capacitor is reduced to 1 / N1, and the load impedance becomes the original N1. 2 One-third. To make the output port impedance equal to 50 ohms, the turns ratio of the transformer can be calculated by equation (19). The calculation formulas for all component values ​​are shown in equation (20). The negative capacitor is replaced by an inductor, and the formula for calculating the equivalent inductance is shown in equation (21), where M 3L This represents the coupling coefficient between the third resonator and the load that does not change with frequency.

[0117]

[0118] C 3L '=C 3L N1 (20a)

[0119] C 1L '=C 1L N1 (20b)

[0120]

[0121] C3'=C3+(N1-1)C 3L (20d)

[0122] C y =N1 2 C y +N1(N1-1)(C 1L -C 3L (20e)

[0123] C1'=C1-(N1-1)C 1L (20f)

[0124]

[0125] Coupling Method 3: The above-described capacitor network is used to achieve impedance matching at the input port. Its topology is shown below. Figure 12 (d) The matching capacitor can be determined by equations (22)-(23), where M S1 The coupling coefficient between the source and the first resonator does not change with frequency.

[0126] C S1 * =PC1'(22a)

[0127]

[0128]

[0129] II. Synthesizing composite LC resonators: To further improve the out-of-band rejection and frequency selectivity of the filter based on the prototype filter, transmission poles are generated not only in the passband but also transmission zeros in the stopband, effectively attenuating certain sensitive frequencies. For information on filters using complex resonant units, please refer to documents such as "Multilayer LTCC bandpass filter design with enhanced stopband characteristics," "A high stopband-rejection LTCC filter with multiple transmission zeros," "Design and simulation of a 2.4GHz bandpass filter on silicon substrate," and "A highly selective and compact 5G n77 bandpass filter based on HRS IPD technology." Figure 13In (a), (b), and (c), the composite LC resonator can simultaneously provide both transmission zeros and transmission poles. Introducing these resonators into existing prototype filter synthesis systems can further improve filter performance. On one hand, based on technical specifications, starting from a series of existing mathematical prototype curves (generalized Chebyshev, generalized Butterworth, generalized elliptic, etc.), the mathematical equation for the optimal S-scattering parameters is calculated, and the two-port admittance matrix is ​​obtained through the mathematical transformation relationship between scattering parameters and admittance matrices; on the other hand, based on… Figure 1 Given the circuit topology diagram, calculate the admittance matrix containing coupling matrix information. By making the two admittance matrices equal, the coupling matrix can be calculated.

[0130] During frequency transformation, only a narrow-band approximation was performed on the coupling matrix, not on the admittance matrix of the parallel LC resonant unit. In other words, the equivalent of the resonant unit can no longer be approximated using a narrow-band approximation similar to that of a negative capacitor; a wider-bandwidth and more rigorous equivalence is required. This does not mean that the coupling matrix synthesis method does not support other types of resonators; it is sufficient to find an admittance function for a certain resonant structure that is equivalent to the admittance function of a parallel LC resonator over a wide frequency band. For G... LC Perform a Taylor expansion, as shown in equation (24), where L i C i Let ω represent the inductance and capacitance of resonator i, respectively. i Let represent the resonant frequency of resonator i. A broadband approximation is achieved by ensuring that the admittance functions and first-order partial derivatives of other types of resonant units are identical at the center frequency to those of the parallel resonant circuit. From another perspective, the previously introduced 'frequency-invariant' narrowband approximation is equivalent to the zeroth-order Taylor expansion. The resonator is equivalently approximated using the first-order Taylor expansion, while the equivalent transformation in circuit theory is the infinite-order Taylor expansion approximation, where the functions on both sides are completely equal. Theoretically, the higher the order of the approximation, the better the approximation effect. Conversely, the more components used, the wider the approximation bandwidth.

[0131]

[0132] Next, regarding Figure 13 Analyzing the topology of (a), we obtain equations (25-26), where ω0 / N represents the series resonant frequency of the resonator. The component values ​​equivalent to an LC parallel circuit are calculated, as shown in equation (27). Structure Figure 13 The transmission zero generated by the resonator in (a) is in the low-frequency range.

[0133]

[0134]

[0135]

[0136] L1C2=N 2 / ω i 2 (26c)

[0137]

[0138] Here, N > 1, N ∈ R

[0139] When an L i C i When a parallel resonator is equivalent to a certain resonator structure, the effectiveness of the equivalent is determined. The absolute value ε of the difference between the second derivatives of the two resonators is used to measure the approximation effect. Continuing with... Figure 13 Taking the resonator of structure (a) as an example, we obtain equation (28). It is found that only when... hour, at this time Figure 13 Structure (a) will completely degenerate back into an LC parallel resonant circuit. It can be concluded that replacing the resonator will inevitably affect the in-band transmission characteristics, and the smaller N is, the greater the impact; at the same center frequency, the smaller the original capacitor used, the smaller the impact.

[0140]

[0141] In addition, for Figure 13 In terms of structure (a), when equation (29) is satisfied, the inductor will be in a differential excitation state. At this time, by optimizing the spiral structure of the inductor, the impedance between the inductor and the dielectric substrate can be effectively improved, thereby improving the quality factor and self-resonant frequency of the inductor.

[0142] C1 = C2 (29)

[0143] Using the same comprehensive method, it is also possible to target Figure 13 Structure (b) yields the following formulas (30-32), where Nω i This is the series resonant frequency of L1C2. Therefore, we can conclude that... Figure 13 Structure (b) can generate high-frequency transmission zeros.

[0144]

[0145] (L1+L2)C2=L i C i (31a)

[0146]

[0147]

[0148]

[0149] Here, N > 1, N ∈ R

[0150] Similarly, Figure 13 Structure (c) can also be calculated similarly, resulting in equation (33), where N1 / ω i With N2 / ω i These represent the resonant frequencies of the series resonators L1C1 and L2C2, respectively. The introduction of this structure can generate a transmission zero in both the low-frequency and high-frequency bands. Figure 13 Structure (c) is different Figure 13 Structures (a) and (b) together have four elements, which means that its approximation can be extended to the second derivative. In this case, ε is given by equation (34). It is not difficult to deduce that when equation (35) is satisfied, ε equals 0. Figure 13 The resonator (c) provides the best approximation of the prototype resonant structure within the passband.

[0151]

[0152] Here, N1 > 1 > N2 or N2 > 1 > N1.

[0153]

[0154] N1N2=1 (35)

[0155] Figure 14 It showed Figure 13 The structures (a), (b), and (c) and the admittance of the prototype resonator vary with frequency. This example is designed with a resonant frequency of 3.56 GHz. It can be seen that... Figure 13 The resonator (c) can not only increase the out-of-band transmission zeros, but also improve the approximation of the admittance function in the passband.

[0156] III. Other Effective Methods for Generating Transmission Zeros Sometimes, in order to improve the rectangularity factor and out-of-band rejection, additional components are added, which often leads to a deterioration of the in-band performance. This embodiment proposes some simple and quick methods to introduce transmission zeros, improve high-frequency out-of-band rejection, and at the same time, not affect the in-band performance.

[0157] Observe the circuit at this time. Figure 15The capacitors at the input and output ports are split into two parts in parallel: one slightly larger and one slightly smaller. A low-quality-factor inductor is connected in series with the smaller capacitor to form a low-quality-factor series resonant circuit. Its resonant frequency is the frequency that needs to be suppressed. It is not difficult to find that this method generally produces transmission zeros in the high-frequency range. When the resonant frequency of this series resonance is much higher than the passband frequency, its impact on the passband will be very small. This step should be performed after the capacitor and impedance matching is completed.

[0158] IV. Specific Circuit Design: A third-order bandpass filter with an input / output impedance of 50 ohms, a center frequency of 3500MHz, and a bandwidth of 200MHz is designed. Considering the filter's group delay characteristics and the deterioration caused by in-band ripples at the passband edges, as well as the frequency deviation caused by the 5% irreversible and unavoidable manufacturing error in actual production, a bandwidth of 400MHz is chosen for the design. Based on the design method proposed in this invention, three representative filters are designed. Their coupling structures and coupling matrices are shown below. Figure 22 As shown in the diagram. First, a prototype filter is designed, selecting a resonant inductance of 2nH. Then, the resonator is improved to achieve better out-of-band rejection. The completed schematic topology and component values ​​are shown in the diagram. Figure 16-18 See Table 1-3. Test results are shown in Table 1-3. Figure 19-21 Curve A represents the scattering parameters of the prototype filter using LC parallel resonance, while curve B represents the scattering parameters of the bandpass filter after out-of-band suppression optimization. Upon finalizing all component values ​​and performing an overall analysis, it was found that the out-of-band suppression was essentially as expected, but the in-band return loss increased slightly. This is to be expected given the extensive use of narrowband approximations in this invention. In this case, only the input and output capacitor matching networks need to be adjusted to optimize the return loss, while other components require minimal adjustment. The closer the transmission zero is to the passband, the better the filter's rectangular coefficient, but the out-of-band suppression effect will decrease.

[0159] By introducing a low-quality-factor series resonator and a multi-frequency resonator, not only were the technical indicators such as in-band ripple, bandwidth, center frequency, and transmission zero position of the prototype filter not affected, but the out-of-band rejection was also improved, verifying the correctness of the previous calculation formula and proposed method.

[0160] The design process of this novel lumped narrowband IPD filter based on N+2 coupling theory is summarized as follows:

[0161] Step 1: Using full-wave electromagnetic simulation software, input the center frequency, bandwidth, in-band return loss, and other key technical parameters. Based on the requirements of the rectangular coefficient, flexibly determine the location and number of out-of-band transmission zeros. For an N+2 coupled matrix filter, an Nth-order filter can generate at most N transmission zeros. Pay attention to the trade-off between the rectangular coefficient and out-of-band rejection.

[0162] Step 2: Select a suitable coupling topology and obtain the corresponding N+2 coupling matrix. At this stage, ensure the coupling structure is easy to implement. Furthermore, the coupling matrix should primarily consist of electrical coupling. In IPD technology, the footprint and insertion loss of a metal-dielectric-metal capacitor are much smaller than those of a spiral inductor.

[0163] Step 3: Based on the location of the filter's center frequency, select an inductor with a high quality factor as the resonant inductor. In IPD technology, for spiral inductors, the inductance value is generally related to its quality factor at a specific frequency. Ideally, the inductor's quality factor should be as high as possible at the center frequency to improve the resonator's no-load quality factor and reduce the filter's insertion loss. Generally, based on design experience, a 1nH inductor is optimal for around 5GHz, and a 2.5nH inductor performs best at 3.5GHz.

[0164] Step 4: Construct the basic topology of the LC bandpass filter and calculate the values ​​of each component. If the capacitance is too small or the inductance is too large, use the T / π transform to make the component values ​​more suitable for the frequency band. In this step, Norton transform and a series of narrowband approximations can be used to integrate the component values;

[0165] Step 5: Based on the out-of-band rejection requirements, select and design a multi-band resonator (high-order resonator) to replace the LC parallel resonant structure in the prototype, obtain more out-of-band transmission zeros, and improve out-of-band rejection;

[0166] Step 6: Impedance transformation. Design filters with different load impedances and source impedances as needed to realize the function of variable impedance filters.

[0167] Step 7: Schematic simulation, make appropriate adjustments to component values ​​to optimize return loss;

[0168] Step 8: Finally, perform electromagnetic simulation of the layout and external packaging. Build and test the physical prototype, and observe the actual results.

[0169] Table 1 shows the component values ​​of the Case 1 filter designed based on the method proposed in the embodiments.

[0170] C1 C2 C3 C5 C6 1.15pF 1.04pF 0.92pF 0.75pF 98fF C7 C8 C9 C10 C11 98fF 0.77pF 87fF 0.35pF 0.21pF C12 C13 L1 L2 L3 2.53pF 0.87pF 1nH 3.18nH 2nH L4 L5 R1 R2 RS / L 5.38nH 1nH 3Ω 3Ω 50Ω

[0171] Table 2 shows the component values ​​of the Case 2 filter designed based on the method proposed in the embodiments.

[0172] C1 C2 C3 C5 C6 1.6pF 1.23pF 103fF 103fF 0.76pF C7 C9 L1 L2 L3 2.04pF 1.33pF 6.89nH 2nH 4.96nH L4 L5 L6 C10 C11 0.82nH 3.94nH 3.94nH 1.63pF 4.19pF

[0173] Table 3 shows the component values ​​of the Case 3 filter designed based on the method proposed in the embodiments.

[0174] C1 C2 C3 C4 C5 0.83pF 1.03pF 115fF 50fF 130fF C6 C7 C9 C10 C11 0.82pF 0.153pF 0.217pF 1pF 1.21pF C12 C13 L1 L2 L3 3.77pF 0.35pF 4.4nH 2nH 3.17nH L4 L5 L6 RS RL 3.68nH 1nH+3Ω 1.5nH + 3Ω 50Ω 50Ω

[0175] This invention proposes a design method for lumped LC narrowband IPD filters based on N+2 coupling matrix theory. It presents the topology of RLC lumped filters under complex coupling matrices, summarizes a complete set of calculation formulas, circuit evolution methods, and a relatively complete design flow. Using existing software, a coupling matrix that meets technical specifications is synthesized, and the equivalent circuit method is used to... Figure 1 The topological structure was physically realized, establishing the coupling matrix and the mathematical relationship between each component. A relatively complex LC resonator was used as the resonant unit, and out-of-band rejection was improved according to design requirements. Even after the design is complete, out-of-band rejection can be further improved by appropriately introducing a small number of components at the input and output ports.

Claims

1. A design method for lumped narrowband IPD filters based on N+2 coupling theory, characterized in that... This design method is implemented according to the following steps:

1. Set the lumped topology of the narrowband IPD filter. For the N+2 type coupled filter network, the admittance matrix equation is [Y]=j[M]+j[s]+[G](4), where [M] represents the coupling matrix, the elements in the coupling matrix represent the coupling coefficients between resonators, [S] represents the identity matrix, and [G] represents the sparse matrix. Then, a bandpass frequency transform is performed on the admittance matrix equation with a center frequency of f0 and a bandwidth of Δf. The source admittance of the bandpass filter is G. S Load impedance G L The admittance matrix equation after bandpass frequency transformation is obtained as follows: [Y] = j[m] + [W] + [G](5a); In the formula, ω0 is the center frequency of the bandpass filter, and C SS C is the coupling capacitance between the sources. LL C is the coupling capacitance between the loads. SL C is the coupling capacitance between the source and the load. NL Let C be the coupling capacitance between the Nth resonator and the load. 11 C is the coupling capacitance between couplers; S1 The coupling capacitance between the source and the first resonator; In the formula, C0 is the capacitance of the parallel resonant circuit, L0 is the inductance of the parallel resonant circuit, and ω is the center frequency of the parallel resonant circuit. (j[m * [Represents the coupling matrix between units] Expanding the formula [Y]=j[m]+[W]+[G](5a), we get the formula (7), where S represents the source, L represents the load, and ν n Represents the source voltage or load voltage, C nj ν represents the coupling capacitance between the source or load and the j-th resonator. j ν represents the voltage of the j-th coupler. k C represents the voltage of the k-th coupler. kj i represents the coupling capacitance between the k-th coupler and the j-th coupler. j This represents the current of the j-th coupler; II. Let M be the cross-coupling factor between resonator i and resonator k in the coupled filter network. ik The cross-coupling factor M is characterized by a PI-type capacitor network. ik The three capacitors in the PI-type capacitor network are C1, C2, C3, C4, C5, C6, m And 2 Cs a A capacitor connected in parallel in the resonant circuit characterizes the self-coupling M of resonator i. ii ; III. When the cross-coupling factor M ik When positive, it belongs to magnetic coupling, and the series capacitor C in the PI-type capacitor network. m The value is negative, and the parallel capacitor C a It is positive; when the cross-coupling factor M is positive. ik When the value is negative, it indicates electrical coupling, and the series capacitor C in the PI-type capacitor network... m The parallel capacitor C is positive. a Negative; Fourth, the narrowband IPD filter circuit is simplified by transformation, including source impedance transformation, narrowband approximation of magnetic coupling and narrowband approximation of negative capacitance. Finally, the component values ​​of each component in the circuit structure are solved according to the coupling matrix to complete the design of the lumped narrowband IPD filter. The narrowband approximation process for the magnetic coupling is as follows: When C m =-C ik C a =C ik At that time, C ik This represents the coupling capacitance between the i-th and k-th resonators. In this case, the PI-type capacitor network narrowband approximation is treated as a purely inductive PI-type narrowband approximation circuit. The purely inductive PI-type narrowband approximation circuit is composed of L... m * L1 * L2 * Composition, L m * L1 * and L2 * The calculation formula is shown in equation (10): Where m ik ν represents the denormalized coupling coefficient between resonator i and resonator k. i ν represents the voltage of the i-th resonator. k C represents the voltage of the k-th resonator. ik This represents the coupling capacitance value between the i-th resonator and the k-th resonator, i i Represents the current of the i-th resonator, i k FBW represents the current of the k-th resonator; The aforementioned narrowband approximation process for negative capacitance is as follows: When the cross-coupling factor M ik When positive, it belongs to magnetic coupling, and the series capacitor C in the PI-type capacitor network. m Negative, -C m Narrowband approximation as inductance L M Or inductor L′ M With capacitor C M Parallel circuit.

2. The design method of the lumped narrowband IPD filter based on N+2 coupling theory according to claim 1, characterized in that... In step four, the source-end impedance transformation uses either capacitor tap impedance matching or inductor tap impedance matching.

3. The design method of the lumped narrowband IPD filter based on N+2 coupling theory according to claim 2, characterized in that... The impedance matching method for capacitor taps is as follows: In capacitor C and resistor R s An ideal transformer with a turns ratio of 1:n is inserted at both ends, and the capacitor C and resistor R are... s The Norton transformation of the parallel circuit is a circuit in which one end of capacitor C1′ is connected to one end of both R1′ and C2′, and the other ends of R1′ and C2′ are grounded respectively, where C1′=nC / (n-1), R1′=R s / n 2 , C2′=nC.

4. The design method of the lumped narrowband IPD filter based on N+2 coupling theory according to claim 2, characterized in that... The impedance matching method for capacitor taps is as follows: Inductor L and resistor R s An ideal transformer with a turns ratio of 1:n is inserted at both ends, LR s The Norton transform of a parallel circuit is a circuit in which one end of inductor L1″ is connected to both one end of R1″ and one end of L2″, where L1″ = L(n-1) / n, L2″ = L / n, and R1″ = R s / n 2 .

5. The design method of the lumped narrowband IPD filter based on N+2 coupling theory according to claim 1, characterized in that... In step two, the cross-coupling factor M is characterized using a PI-type capacitor network. ik The condition is that it is under the Sub-6G frequency band.

6. The design method of the lumped narrowband IPD filter based on N+2 coupling theory according to claim 1, characterized in that... The evolution simplification process described in step four also includes T / π circuit transformation.

7. The design method of the lumped narrowband IPD filter based on N+2 coupling theory according to claim 6, characterized in that... The T-type pure inductor circuit is converted into a two-stage PI-type circuit through Norton transformation.

8. The design method of the lumped narrowband IPD filter based on N+2 coupling theory according to claim 1, characterized in that... In step four, when -C m Narrowband approximation as inductance L M hour, 9. The design method of the lumped narrowband IPD filter based on N+2 coupling theory according to claim 1, characterized in that... In step four, when -C m Narrowband approximation as inductance L′ M With capacitor C M Parallel circuits,

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