CN104900969B

CN104900969B - Power splitter design method

Info

Publication number: CN104900969B
Application number: CN201510317826.5A
Authority: CN
Inventors: 肖飞
Original assignee: University of Electronic Science and Technology of China
Current assignee: University of Electronic Science and Technology of China
Priority date: 2015-06-11
Filing date: 2015-06-11
Publication date: 2018-06-08
Anticipated expiration: 2035-06-11
Also published as: CN104900969A

Abstract

Power splitter/combiner is the important devices in communication or radar system.The present invention provides a kind of N etc. to divide power splitter (N is natural number, and N >=2) design method, including two steps：The first step is required according to the transmission characteristic of power splitter, and first integrating a transmission network TN (can be by multiple transmission network TN₁、TN₂、…、TN_nCascade), make its meet port 0 and port k (k=1,2 ..., N) between transmission characteristic requirement.Second step merges the left end of N number of transmission network TN, and as the port 0 of power splitter, remaining port and selects appropriate matching network MN respectively as the port k of power splitter₁、MN₂、…、MN_mAccess, according to the strange mould equivalent circuit of power splitter, adjustment matching network MN₁、MN₂、…、MN_mIn component value, and then change strange mould reflectance factor Γ_o, it is made to approach even mould reflectance factor Γ_e(ideally Γ_o=Γ_e), so as to ensure that the isolation between the return loss of port k and other ports is met the requirements.Entire method is simply accurate.

Description

Design method of power divider

Technical Field

The invention belongs to the technical field of communication, and particularly relates to a design method of a power divider with a signal processing function.

Background

The power divider is called a power divider, and is an important device in a communication or radar system. The device divides one path of input signal energy into two paths or multiple paths of input signal energy which are output with equal or unequal energy, and can also synthesize the multiple paths of signal energy into one path of output in turn, and at the moment, the device can also be called a combiner. Since the power divider can be used in reverse as a combiner, the following discussion takes the power divider as an example. Certain isolation degree should be guaranteed between output ports of one power divider. The main technical parameters of the power divider are insertion loss, return loss, isolation between power distribution ports, pass band width and the like.

Disclosure of Invention

The existing power divider lacks a simple and accurate design method. The invention aims to overcome the defects of the prior art and provides a design method of a power divider with a signal processing function. Different from the traditional power divider, the power divider realized by the method not only can realize accurate equal division of input power, but also has a signal processing function on input signals, and can synthesize corresponding circuits according to actual requirements.

The general structure diagram of the power divider is shown in fig. 1, and the power divider can realize N equal division (N is a natural number, and N is more than or equal to 2) of an input signal. The network in FIG. 1 is a network with NA network of +1 ports is described as port 0, port 1, port 2, …, port N, respectively. For an N-equal power divider, when energy is fed from port 0, it will be equally divided into port 1, port 2, …, and port N output. Therefore, the electrical performance of port 1, port 2, …, port N is symmetrical. A plurality of two-port networks TN are respectively arranged between the port 0 and the port k (wherein k is 1,2, …, N)₁、TN₂、…、TN_n(where n is a natural number greater than 1) are connected in a cascade, these two-port networks being referred to as transport networks; in order to ensure isolation among ports 1,2, …, and N, which are output ports, a plurality of two-port networks MN are connected between port k and port j (where k is 1,2, …, and N, j is 1,2, …, and N, and j is not k)₁、MN₂、…、MN_m(where m is a natural number greater than 1), these two-port networks are referred to as matching networks; r is characteristic impedance at port 0₀The characteristic impedances at port 1, port 2, …, and port N are represented by R₁And (4) showing.

The electrical characteristics between the ports of the N-equal power divider can be described by a scattering matrix [ S ], which is defined as

The elements in the scattering matrix [ S ] are scattering parameters and are defined as

(where j ≠ k) is 0, 1, …, N, k ═ 0, 1, …, N)

Wherein, a_kIs the normalized incident wave of port k, b_kIs the normalized outgoing wave of port k, b_jIs the normalized outgoing wave for port j.

In the N-equal power divider, the electrical performance of the port 1, the port 2, the port … and the port N are symmetrical. Therefore, the symmetry between ports is described by the following symmetric transformation matrix [ F ], i.e

To derive a scattering matrix [ S ] of an N-equal power divider]According to the definition of the scattering parameters, incident waves are sequentially applied to a port k (wherein k is 1,2, … and N)Excited while keeping the voltage incident wave at the other port at(where j ≠ k) is 1,2, …, N. By analysing a symmetric transformation matrix [ F ]]Knowing the eigenvalues and eigenvectors of these incident wave excitations can be decomposed into even mode excitations and odd mode excitations, i.e.

Wherein the even mode excitation is

The odd mode is excited as

When the even-mode excitation is applied to the N equal-division power divider, the port 0 is open-circuited, and the matching network MN between the port k and the port j is connected₁、MN₂、…、MN_mIgnored because of even mode excitation. The resulting even-mode equivalent circuit network for port k is shown in fig. 2. In the even-mode equivalent network, the characteristic impedance at port 0 becomes N · R₀The characteristic impedance at port k is still R₁. Therefore, the even-mode equivalent network is substantially degraded to a characteristic impedance N.R₀For a single port network of the load, the transmission characteristics between port 0 and port k are described. As shown in FIG. 2, in the even-mode equivalent network, there are a plurality of transport networks TN₁、TN₂、…、TN_nAnd (4) cascading. The plurality of cascaded transport networks TN₁、TN₂、…、TN_nMay be represented by an equivalent transport network TN as shown in fig. 3. In practice, a power divider is required to have a corresponding signal processing function. The transmission network TN can thus be synthesized according to the actual requirements (for example bandwidth, in-band fluctuations, return loss of port 0, out-of-band rejection, phase or group delay, etc.), noting that the characteristic impedance at the left end is N · R₀And the characteristic impedance at the right end is R₁. Under even mode excitation, let the even mode input admittance as seen from port k into transport network TN be Y_eThe corresponding even mode reflection coefficient is gamma_eThe outgoing wave of port k is

When odd mode excitation is applied to the N-equally divided power divider, port 0 is shorted. In addition, for a matching network MN connected between port k and port j_i(i ═ 1,2, …, m), it can be decomposed into two networks MN_i' and MN_i"to make the potential at its intermediate junction zero. One example is shown in FIG. 4, where Z is the impedance and the port voltage at the left end isPort voltage at right end isUnder the excitation of the odd mode, the corresponding zero potential can be found out, as shown in the figure. Therefore, under the excitation of the odd-mode, the analysis of the N-equal power divider can be simplified into the analysis of the single-port network for the port k, and finally the odd-mode equivalent circuit is obtained as shown in fig. 5. Under odd mode excitation, the odd mode input admittance looking into the transport network TN from port k is assumed to be Y_oThe corresponding odd mode reflection coefficient is gamma_oThe outgoing wave of port k is

By using the superposition theorem, the total outgoing wave b of the port k is known_kIs composed of

Outgoing wave b of other port j_jIs composed of

According to the definition of the scattering parameters, the scattering coefficient corresponding to each port can be obtained as

Therefore, to ensure isolation between port k and port j, it is necessary to select an appropriate matching network MN₁、MN₂、…、MN_mTo adjust the odd mode reflection coefficient to gamma_oTo approach the even mode reflection coefficient of gamma_eIdeally, the condition is

Γ_o＝Γ_e(10)

Thereby making the

S_k,k＝Γ_eAnd S_j,k＝0 (11)

In summary, it can be seen from the foregoing analysis that the design method of the N-level power divider of the present invention includes two steps. Firstly, according to the transmission characteristic requirements (such as bandwidth, fluctuation in pass band, return loss of port 0, out-of-band rejection, phase or group delay and the like) of the N-equal power divider, a transmission network TN (which can be composed of a plurality of transmission networks TN) is synthesized₁、TN₂、…、TN_nCascaded) so that it satisfies the transmission characteristics between port 0 and the other ports k (where k is 1,2, …, N). Second, the left ends of the N transmission networks TN are merged to be used as the port 0 of the power divider, and the other ports are respectively used as the port k of the power divider, and a proper matching network MN is selected₁、MN₂、…、MN_mAccessing to the space between the port k and the port j (wherein k is 1,2, …, N, j is 1,2, …, N, and j is not equal to k), and adjusting the matching network MN according to the odd-mode equivalent circuit of the power divider₁、MN₂、…、MN_mFurther, the odd-mode reflection coefficient gamma corresponding to the odd-mode equivalent circuit of the power divider is changed_oTo make it approach the even mode reflection coefficient gamma corresponding to the even mode equivalent circuit of the power divider_e(ideally, Γ_o＝Γ_e) Thereby meeting the return loss requirement of the port k and the isolation requirement between the port k and the port j.

The invention has the beneficial effects that:

the ① power divider can divide input signals by N (N is a natural number, and N is more than or equal to 2) equally or synthesize N paths of input signals;

② the characteristic impedance of port 0 of the power divider may be different from the characteristic impedance of other ports, i.e. the power divider also has the function of impedance transformation;

③ the transmission characteristics of port 0 and other ports of the power divider can have signal processing function;

④ the design method of the power divider of the invention has the characteristics of simplicity, rapidness and accuracy.

Drawings

Fig. 1 is a general structural schematic diagram of an N-equal power divider according to the present invention.

Fig. 2 is an even-mode equivalent network of the N-equal division power divider obtained under the excitation of the even mode.

Fig. 3 is a simplified even-mode equivalent network of an N-equal division power divider obtained under even-mode excitation.

Fig. 4 illustrates, by way of example, the determination of a zero potential plane by a network equivalent transformation.

Fig. 5 is an odd-mode equivalent network of the obtained N-equal power divider under odd-mode excitation.

Fig. 6 is a general structure diagram of a halving power divider.

Fig. 7 is an even mode equivalent network of a halving power divider under even mode excitation.

Fig. 8 is an even-mode equivalent circuit of the halving power divider in the first embodiment.

Fig. 9 is a frequency response of an even-mode equivalent circuit of the halving power divider in the first embodiment.

Fig. 10 is an implementation network of a halving power divider in the first embodiment (without adding a matching network).

Fig. 11 is a frequency response of a halving power divider (without adding a matching network) in the first embodiment.

Fig. 12 is a network for implementing the halving power divider according to the second embodiment.

Fig. 13 is an odd-mode equivalent network of the halving power divider in the second embodiment.

Fig. 14 is a frequency response of the halving power divider in the second embodiment.

Fig. 15 is an implementation network of a halving power divider in the third embodiment.

Fig. 16 is an odd-mode equivalent network of the halving power divider in the third embodiment.

Fig. 17 is a frequency response of the halving power divider in the third embodiment.

Fig. 18 is an even mode equivalent network of the halving power divider of the fourth embodiment under the excitation of the even mode.

Fig. 19 is an implementation network of a halving power divider in the fourth embodiment.

Fig. 20 is an odd-mode equivalent network of the halving power divider under odd-mode excitation in the fourth embodiment.

Fig. 21 is a frequency response of the halving power divider in the fourth embodiment.

Fig. 22 is an implementation network of a halving power divider with a high-order bandpass response in the fifth embodiment.

Fig. 23 is a frequency response of a halving power divider with a higher-order bandpass response in the fifth embodiment.

Fig. 24 is a general structure diagram of a trisection power divider.

Fig. 25 is an even-mode equivalent network of the trisection power divider in the sixth embodiment under the excitation of the even mode.

Fig. 26 is an implementation network of a power divider trisection in the sixth embodiment.

Fig. 27 is an odd-mode equivalent network of the trisection power divider in the sixth embodiment under the excitation of an odd mode.

Fig. 28 is a frequency response of the trisection power divider in the sixth embodiment.

Detailed Description

The present invention will be further described with reference to the following drawings and specific examples, but the embodiments of the present invention are not limited thereto. Summarizing the above analysis, the design method of the power divider of the present invention includes two steps. First, according to the transmission characteristic requirements (such as bandwidth, fluctuation in pass band, return loss of port 0, out-of-band rejection, phase or group delay, etc.) of the power divider, a transmission network TN (which may be composed of multiple transmission networks TN) is synthesized₁、TN₂、…、TN_nCascaded) so that it satisfies the transmission characteristics between port 0 and the other ports k (where k is 1,2, …, N). Second, the left ends of the N transmission networks TN are merged to be used as the port 0 of the power divider, and the other ports are respectively used as the port k of the power divider, and a proper matching network MN is selected₁、MN₂、…、MN_mAccessing to the space between the port k and the port j (wherein k is 1,2, …, N, j is 1,2, …, N, and j is not equal to k), and adjusting the matching network MN according to the odd-mode equivalent circuit of the power divider₁、MN₂、…、MN_mFurther, the odd-mode reflection coefficient gamma corresponding to the odd-mode equivalent circuit of the power divider is changed_oTo make it approach the even mode reflection coefficient gamma corresponding to the even mode equivalent circuit of the power divider_e(ideally, Γ_o＝Γ_e) Thereby meeting the return loss requirement of the port k and the isolation requirement between the port k and the port j.

From the knowledge of the two-port network, the scattering matrix S of the transport network TN in fig. 3 is known]_TNIt can be expressed as follows.

Wherein,andare scattering parameters defined for the two-port network, and the corresponding superscript e indicates for the even mode. The return loss of port 0 is completely determined byThe transfer characteristic between port 0 and port k is determined byOrAnd (6) determining. The scattering matrix [ S ] is known from the property of a passive lossless reciprocal network]_TNCan be expressed as a ratio of two real coefficient polynomials, i.e.

Wherein, s is a complex angular frequency variable, and represents the conjugate operation. F(s) is called reflection polynomial, p(s) is called transmission polynomial, e(s) is called common polynomial, which are collectively called filter polynomial. When the polarity of the transmission polynomial P(s) is odd (i.e. P)^*(s) ═ P (s)), η ═ 1, when the polarity of transmission polynomial P(s) is even (i.e. P)^*(s) ═ p (s)), η ═ 1. therefore, in the even-mode equivalent circuit, the even-mode reflection coefficient Γ is_eCan be expressed in the following forms

In practice, a power divider is required to have a corresponding signal processing function. Therefore, the corresponding scattering matrix [ S ] can be derived according to actual needs]_TNAnd further synthesize the transmission network TN. For example, when the power divider is required to have a filtering function, a Butterworth (Butterworth) type, an Elliptic (elliptical) type, a Bessel (Bessel) type, or a generalized tangent ratio can be selectedThe transport network TN is integrated by existing filter integration methods of the General Chebyshev type. Without loss of generality, a synthesis method of a generalized Chebyshev band-pass filter is here chosen to synthesize the transmission network TN. Depending on the transmission characteristic requirements between port 0 and port k, for example, the passband frequency range is designated as [ omega ]_d,ω_u]Wherein ω is_dIs the lower boundary angular frequency, omega, of the passband_uIs the passband upper boundary corner frequency. The return loss in the passband is greater than RL (units: dB). In addition, the corresponding transmission zero point can be set as required to control the performance outside the passband. For example, N may be placed at zero frequency_pA transmission zero point for placing N at finite positive frequency_mA transmission zero point, N is placed at infinite frequency_lAnd if there are transmission zeros, the total number M of transmission zeros (including the whole frequency axis) is: m is equal to N_p+2N_m+(2N_l+N_p) And use in combination of s_i(wherein i is 1,2, …, M). These transmission zeros may be mappedMapping the s plane to the g plane to obtain a corresponding point g_i. Let M be 2N, then N is defined as the order of the filter. The filter polynomial of a generalized Chebyshev (General Chebyshev) band-pass filter can then be derived from the following equation:

where s is a complex angular frequency variable, g is a temporary complex variable, Ev represents the operation on the even part of the polynomial, and the coefficient d_2iBy pairsCoefficient β is used to ensure that the coefficient of the first term of the reflection polynomial F(s) is normalized, and that the coefficient ε is determined by the return loss RL in the specified pass-band, i.e., theThe common polynomial e(s) is derived from the reflection polynomial f(s) and the transmission polynomial p(s) by the energy conservation equation.

Taking a halving power divider as an example, an implementation block diagram thereof is shown in fig. 6. When a signal is fed from port 0, it will be equally divided into port 1 and port 2 outputs. The electrical performance of port 1 and port 2 is symmetrical. A plurality of transport networks TN are respectively arranged between the port 0 and the port k (where k is 1 and 2)₁、TN₂、…、TN_nTo connect; in order to ensure the isolation between the output ports, i.e. port 1 and port 2, a plurality of matching networks MN are connected between port 1 and port 2₁、MN₂、…、MN_m(ii) a R is characteristic impedance at port 0₀The characteristic impedance at port 1 and port 2 is denoted by R₁And (4) showing. Under the excitation of the even mode, the equivalent network of the even mode of the halving power divider is shown in fig. 7. In the even-mode equivalent network, the characteristic impedance at port 0 becomes 2R₀The characteristic impedance at port 1 (or port 2) is still R₁. Therefore, the even-mode equivalent network is substantially degraded to a characteristic impedance 2R₀For a single-port network of loads, the transmission characteristics between port 0 and port k (where k is 1,2) are described. In practice, a power divider is required to have a corresponding signal processing function. Therefore, the corresponding scattering matrix [ S ] can be derived according to actual needs]_TNAnd further synthesize the transmission network TN.

In order to simplify and clarify the method of the present invention, the design of the halving power divider will be described in detail with reference to the following examples. If a halving power divider with bandpass filtering function is to be designed, the characteristic impedance at port 0, port 1 and port 2 is set to 50 ohms. The transmission characteristic between port 0 and port 1 (or port 2) is required to be the frequency response of a band pass filter with a passband set to [0.9,1.1] GHz, a return loss at port 0 of less than-20 dB, an out-of-band rejection at 0.6GHz of at least-20 dB, and an out-of-band rejection at 2.0GHz of at least-15 dB. The realization networks meeting the performance requirements of the power divider are various, and in the invention, a plurality of embodiments are considered to realize the halving power divider, thereby showing the flexibility of the method of the invention. According to the method of the invention, a first step is to synthesize a transport network TN such that it satisfies the transport characteristics between port 0 and port k (where k is 1, 2). Since the transmission characteristic between the port 0 and the port k is a frequency response of a band pass filter, a generalized Chebyshev (Chebyshev) band pass filter synthesis method may be selected to synthesize the transmission network TN as required. To this end, a filter polynomial may be derived from the transmission characteristics between port 0 and port k as

P(s)＝1.2505·10⁹·s³+4.9366·10²⁴·s (18)

F(s)＝s⁴+7.8558·10¹⁹·s²+1.5123·10³⁹(19)

E(s)＝s⁴+3.9323·10⁹·s³+8.5508·10¹⁹·s²+1.4498·10²⁹·s²+1.5123·10³⁹(20)

Since the polarity of the transmission polynomial P(s) is odd (i.e. P)^*(s) ═ p (s)), η ═ 1, and the polarity of reflection polynomial F(s) is even (i.e., F)^*(s) ═ f (s)). From a scattering matrix [ S ]]_TNVarious TN meeting the requirements can be comprehensively obtained. For example, a transmission network TN as shown in fig. 8 can be obtained, the characteristic impedance of port 0 of which is 2R₀The characteristic impedance of port k is R₁. The component values in the two-port network TN are: r₀＝R₁＝50Ω，L₁＝4.7939nH，C₁＝3.1140pF，C₂＝2.5440pF，L₃＝2.3973nH，C₃8.7699 pF. The frequency response of the transmission network TN is shown in fig. 9, and it can be seen that the transmission network TN completely meets the transmission characteristic requirement between the port 0 and the port k. From the foregoing analysis, it can be seen that the even mode reflection coefficient Γ of the even mode equivalent circuit_eIs composed of

According to the design method of the power divider of the present invention, the second step is to merge the left ends of the two transmission networks TN to be the port 0 of the halving power divider, and the other two ports are respectively the port 1 and the port 2 of the halving power divider, so that the halving power divider in the first embodiment shown in fig. 10 can be obtained. The corresponding frequency response is shown in fig. 11, and it can be seen that the transmission characteristics of the halving power divider are accurately controlled, but the return loss of the port 1 and the port 2 and the isolation between the port 1 and the port 2 are not good.

To improve the return loss of the output ports and the isolation between the output ports in the first embodiment, an appropriate matching network MN is selected₁、MN₂、…、MN_mAccessing, adjusting the matching network MN according to the odd-mode equivalent circuit of the power divider₁、MN₂、…、MN_mFurther change the odd mode reflection coefficient gamma_oTo make it approximate to even mode reflection coefficient gamma_e(ideally, Γ_o＝Γ_e) Thereby ensuring that the return loss of the port 1 (or the port 2) and the isolation between the port 1 and the port 2 meet the requirements. In the second embodiment, first, a resistance R is selected_mAs a matching network MN₁Connected between port 1 and port 2. An implementation network of the halving power divider in the second embodiment is shown in fig. 12. From the foregoing analysis, the odd-mode equivalent circuit of the halving power divider in fig. 12 is shown in fig. 13. Its odd-mode input admittance Y_oIs composed of

Admittance Y by odd mode input_oThe odd mode reflection coefficient gamma can be derived_oI.e. by

Thus, the

Therefore, in order to ensure that the return loss of the port 1 (or the port 2) and the isolation between the port 1 and the port 2 satisfy the requirements, the appropriate resistor R may be selected_mLet the odd-mode reflection coefficient Γ_oApproximation of even mode reflection coefficient gamma_e. For example, the even mode reflection coefficient Γ_eThe molecular polynomial in the expression of (1) lacks odd-order terms, so that the odd-mode reflection coefficient Γ can be made_oIn the expressionThereby obtaining R_m100 Ω. Finally, the frequency simulation result of the halving power divider in the second embodiment is shown in fig. 14. As can be seen, | S₂₁The maximum value of | is-3.01 dB, and the fluctuation range is limited to a prescribed 0.0436dB, which shows that when a signal is input from port 1, signals after being equally divided are output from port 1 and port 2, respectively. Return loss | S of port 0₁₁L is greater than 20dB over the passband frequency range. Return loss | S of Port 1 (and Port 2)₁₁L is greater than 13dB over the passband frequency range. The isolation between port 1 and port 2 is greater than 14dB over the passband frequency range.

Since various matching networks MN can be selected₁、MN₂、…、MN_mAccess is to improve the return loss of port 1 (or port 2) and the isolation between port 1 and port 2. And in the second embodimentThe halving power divider selects a resistor R_mSlightly different from the matching network, the halving power divider in the third embodiment selects a resistor R_mAn inductor L_mAnd a capacitor C_mTo improve the return loss of port 1 (or port 2) and the isolation between port 1 and port 2. The selection of multiple components will provide greater flexibility, possibly with odd mode reflection coefficient Γ_oBetter approximation to the even mode reflection coefficient gamma_eThereby improving the return loss of port 1 (or port 2) and the isolation between port 1 and port 2. An implementation network of the halving power divider in the third embodiment is shown in fig. 15. The even-mode equivalent network of the power divider is the same as that of the halving power divider in the first embodiment. Its odd-mode equivalent network is shown in fig. 16, from which the odd-mode input admittance Y can be derived_oIs composed of

Similar to example two, admittance Y is input by odd mode_oThe odd mode reflection coefficient gamma can be derived_o。

The appropriate resistance R can be selected_mInductor L_mAnd a capacitor C_mLet the odd mode reflection coefficient gamma_oApproximation of even mode reflection coefficient gamma_eThereby improving the return loss of port 1 (or port 2) and the isolation between port 1 and port 2. For example, R is selected_m＝80Ω，L_m＝45.2560nH，C_mThe frequency simulation result of the corresponding power divider is shown in fig. 17, which is 0.5993 pF. As can be seen, | S₂₁The maximum value of | is-3.01 dB, and the fluctuation range is limited to a prescribed 0.0436dB, which shows that when a signal is input from port 0, signals after being equally divided are output from port 1 and port 2, respectively. Return loss | S of port 0₁₁In passband frequency rangeGreater than 20 dB. The return loss of port 1 (and port 2) is greater than 15dB over the passband frequency range. The isolation between port 1 and port 2 is greater than 23dB over the passband frequency range. It can be seen that the performance of the halving power divider in the second embodiment is improved to some extent compared to the performance of the halving power divider in the first embodiment.

In fact, as previously mentioned, by the same scattering matrix S]_TNVarious TN meeting the requirements can be comprehensively obtained. In the fourth embodiment, a transmission network TN as shown in fig. 18 may also be selected to meet the requirement of the transmission characteristic between the port 0 and the port 1 (or the port 2), and the element values are: r₀＝R₁＝50Ω，L₁＝43.8645nH，C₁＝0.4793pF，L₂＝12.7213nH，L₃＝15.5655nH，C₃0.9589 pF. Its frequency response is shown in fig. 9. As with the second and third embodiments, a halved power divider network as shown in fig. 19 may be constructed. In which a resistor R is introduced_mAs a matching network MN₁Access is to improve the return loss of port 1 (or port 2) and the isolation between port 1 and port 2. Its odd-mode equivalent circuit can be derived from a halving power divider network as shown in fig. 19, as shown in fig. 20. Thus, the odd-mode input admittance Y_oIs composed of

Input admittance Y from odd mode_oThe odd mode reflection coefficient gamma can be derived_oI.e. by

The appropriate resistance R can be selected_mLet the odd mode reflection coefficient gamma_oApproximation of even mode reflection coefficient gamma_eThereby improving the return loss of port 1 (or port 2) and the isolation between port 1 and port 2. For example, R is selected_m1510 Ω, the frequency simulation result of the corresponding power divider is shown in fig. 21. As can be seen, | S₂₁The maximum value of | is-3.01 dB, and the fluctuation range is limited to a prescribed 0.0436dB, which shows that when a signal is input from port 0, signals after being equally divided are output from port 1 and port 2, respectively. Return loss | S of port 0₁₁L is greater than 20dB over the passband frequency range. The return loss of port 1 (and port 2) is greater than 16dB over the passband frequency range. The isolation between port 1 and port 2 is greater than 20dB over the passband frequency range.

To further illustrate that the power divider design method of the present invention is suitable for constructing more complex frequency response to meet the user's requirement. In the fifth embodiment, another example of a halving power divider is given, which has a wider relative bandwidth and steeper frequency selectivity, as shown in fig. 22. Where the characteristic impedances at port 0, port 1 and port 2 are all set to 50 ohms. The transmission characteristic between port 0 and port 1 (or port 2) requires the frequency response of a band-pass filter with a passband set to [3.0,5.0 ]]GHz, the return loss at port 0 is greater than 20dB over the passband frequency range. According to the design process of the previous embodiment, the element values in the halving power divider can be obtained as follows: r₀＝R₁＝50Ω，L₁＝7.9323nH，C₁＝0.2930pF，C₁₂＝0.4682pF，L₂＝7.9577nH，C₂＝0.4994pF，C₂₃＝0.6860pF，L₃＝5.6420nH，C₃＝0.3186pF,L₃₄＝2.3157nH，L₄＝5.6420nH，C₄＝0.3186pF，C₄₅＝0.6860pF，L₅＝7.9577nH，C₅＝0.3807pF，C₅₆＝0.6621pF，L₆＝3.9661nH，C₆0.7910 pF. Following the design process of the previous embodiment, the appropriate resistance R is selected_mLet the odd mode reflection coefficient gamma of the power divider_oApproximation of even mode reflection coefficient gamma_eThereby improving the return loss of port 1 (or port 2) and the isolation between port 1 and port 2. For example, R is selected_mThe frequency simulation result of the corresponding power divider is shown in fig. 23 when the frequency is 720 Ω. As can be seen, | S₂₁Maximum of |)The value is-3.01 dB and the fluctuation range is limited to a specified 0.0436dB, which shows that when a signal is input from port 0, signals after being equally divided are output from port 1 and port 2, respectively. Return loss | S of port 0₁₁L is greater than 20dB over the passband frequency range. The return loss of port 1 (and port 2) is greater than 12dB over the passband frequency range. The isolation between port 1 and port 2 is greater than 15dB over the passband frequency range.

In order to show that the method of the present invention is suitable for an N-equal power divider (N is a natural number, and N is greater than or equal to 2), the design of a trisection power divider is described below with reference to the embodiments. A general structural schematic diagram of a trisection power divider is shown in fig. 24. If a trisection power divider with a band-pass filtering function is to be designed, the characteristic impedances at the port 0, the port 1, the port 2 and the port 3 are required to be 50 ohms. The transmission characteristic between port 0 and port 1 (or port 2 or port 3) is the frequency response of a band-pass filter with a passband set to 0.9,1.1]GHz, return loss at port 0 is less than-20 dB, out-of-band rejection at 0.6GHz is at least-20 dB, and out-of-band rejection at 2.0GHz is at least-15 dB. According to the method of the present invention, a transport network TN is synthesized to satisfy the transmission characteristics between port 0 and port k (where k is 1,2, and 3), as shown in fig. 25. The component values in the two-port network TN are: r₀＝R₁＝50Ω，L₁＝7.1934nH，C₁＝1.6937pF，C₂＝2.0768pF，L₃＝2.3973nH，C₃9.2373 pF. Fig. 26 shows a network for implementing the power divider trisected in the sixth embodiment. In order to improve the return loss of port 1 (or port 2 or port 3) and the isolation between these ports, an impedance R is introduced_mAs a matching network MN₁Connected between these ports. Thus, the odd-mode equivalent circuit of the trisection power divider is shown in fig. 27. Following the design process of the previous embodiment, the appropriate resistance R is selected_mLet the odd mode reflection coefficient gamma of the power divider_oApproximation of even mode reflection coefficient gamma_eThereby improving the return loss of port 1 (or port 2 or port 3) and the isolation between these ports. For example, R is selected_m＝150ΩThen, the frequency simulation result of the trisection power divider is shown in fig. 28. As can be seen, | S₂₁The maximum value of | is-4.77 dB, and the fluctuation range is limited to a prescribed 0.0436dB, which shows that when a signal is input from port 0, signals after being equally divided are output from port 1, port 2, and port 3, respectively. Return loss | S of port 0₁₁L is greater than 20dB over the passband frequency range. The return loss of port 1 (and ports 2 and 3) is greater than 10dB over the passband frequency range. The isolation between ports 1 and 2, between ports 1 and 3, and between ports 2 and 3 is greater than 18dB over the passband frequency range.

It will be appreciated by those of ordinary skill in the art that the embodiments described herein are intended to assist the reader in understanding the principles of the invention and are to be construed as being without limitation to such specifically recited embodiments and examples. Those skilled in the art can make various other specific changes and combinations based on the teachings of the present invention without departing from the spirit of the invention, and these changes and combinations are within the scope of the invention.

Claims

1. A design method of an N-equal power divider comprises the following two steps: in the first step, let the characteristic impedance at port 0 of the N-equal power divider be R₀Characteristic impedance at port k is R₁(ii) a According to the transmission characteristic requirements of the N equal power dividers, including bandwidth, passband fluctuation, return loss of a port 0, out-of-band rejection, phase or group delay, a transmission network TN is synthesized firstly, and the transmission network TN is composed of a plurality of transmission network TNs₁、TN₂、…、TN_nIs cascaded, wherein n is a natural number greater than 1, so that the requirement between the port 0 and other ports k is satisfiedWherein k is 1,2, …, N; in the transmission network TN, the characteristic impedance at port 0 is N · R₀The characteristic impedance at port k is R₁(ii) a Scattering matrix S of transport network TN]_TNCan be expressed in the following form:

wherein,andthe scattering parameters defined for the two-port network can be expressed as the ratio of two real coefficient polynomials, and the two real coefficient polynomials take a complex angular frequency variable s as an independent variable; second, the left ends of the N transmission networks TN are merged to be used as the port 0 of the N equal division power dividers, the other ports are respectively used as the port k of the N equal division power dividers, and a proper matching network MN is selected₁、MN₂、…、MN_mAccessing to a space between a port k and a port j, wherein m is a natural number greater than 1, k is 1,2, …, N, j is 1,2, …, N, and j is not equal to k; the scattering parameters in the scattering matrix of the N equal power dividers are as follows:

wherein k is 0, 1, …, N;

where j is 0, 1, …, N, k is 0, 1, …, N, and j is not equal to k;

adjusting a matching network MN₁、MN₂、…、MN_mFurther, the odd-mode reflection coefficient gamma corresponding to the odd-mode equivalent circuit of the power divider is changed_oTo make it approach the even mode reflection coefficient gamma corresponding to the even mode equivalent circuit of the power divider_eIdeally, gamma is_o＝Γ_eThereby meeting the return loss requirement of the port k and the isolation requirement between the port k and the port j.

2. The design method of the N-level power divider according to claim 1, wherein a transport network TN is synthesized according to transmission characteristic requirements including bandwidth, passband ripple, port return loss, out-of-band rejection, phase or group delay, and the transport network TN can be composed of a plurality of transport networks TN₁、TN₂、…、TN_nCascade-connected, so that the transmission characteristic between port 0 and port k has a specified signal processing function, wherein k is 1,2, …, N; let the characteristic impedance at port 0 of the N-equal power divider be R₀Characteristic impedance at port k is R₁(ii) a In the transmission network TN, the characteristic impedance at port 0 is N · R₀The characteristic impedance at port k is R₁(ii) a Scattering matrix S of transport network TN]_TNCan be expressed in the following form:

wherein,andscattering parameters defined for the two-port network, and the corresponding superscript e represents the even mode; the return loss of port 0 is completely determined byThe transfer characteristic between port 0 and port k is determined byOrDetermining; the scattering matrix [ S ] is known from the property of a passive lossless reciprocal network]_TNCan be expressed as a ratio of two real coefficient polynomials, i.e.

Wherein, s is a complex angular frequency variable, and represents a conjugate operation; f(s) is called reflection polynomial, p(s) is called transmission polynomial, e(s) is called common polynomial, which are collectively called filter polynomial; when the polarity of the transmission polynomial P(s) is odd, i.e. P^*(s) ═ P(s), η ═ 1, when the polarity of transmission polynomial P(s) is even, i.e. P^*(s) P(s) and η (1), so that in the even-mode equivalent circuit, the even-mode reflection coefficient is Γ_eCan be expressed as

3. The design method of an N-equal power divider according to claim 1, wherein the scattering coefficient corresponding to each port of the N-equal power divider is

Wherein, a_kIs the normalized incident wave of port k, b_kIs the normalized outgoing wave of port k, b_jIs the normalized outgoing wave for port j; the matching network MN can be implemented by selecting a resistor, an inductor or a capacitor or a combination thereof₁、MN₂、…、MN_mFurther change the odd mode reflection coefficient gamma_oTo make it approximate to even mode reflection coefficient gamma_eIdeally, gamma is_o＝Γ_eThereby meeting the return loss requirement of the port k and the requirement between the port k and the port jWherein k is 1,2, …, N, j is 1,2, …, N, and j is not equal to k.