CN103022619B - Microwave phase inverter based one-to-three power divider and power dividing method thereof - Google Patents

Abstract

The invention discloses a microwave phase inverter based one-to-three power divider. The one-to-three power divider comprises a transmission coil formed by end-to-end connection of six 90-degree transmission lines with characteristic impedance of Z2, three 90-degree transmission lines with characteristic impedance of Z1 are arranged in the transmission coil, one ends of the three transmission lines are converged to a circle center of the transmission coil, an input end P1 is arranged at the position of the circle center, the other ends of the three transmission lines are respectively intersected with the transmission coil and trisect the same, output ends P2, P3 and P4 are arranged at the other ends of the three transmission lines respectively, a phase inverter is arranged on the circumferential center included by each two adjacent 90-degree transmission lines with the characteristic impedance of Z1, and two ends of each phase inverter are connected with isolation resistors R. The invention further discloses a power dividing method of the power divider. The method includes: inputting power from the input port P1, obtaining matching conditions of the P1 end by the aid of an even-even mode equivalent circuit, then obtaining voltage of the P1 end, and obtaining the characteristic impedance Z2 and the resistors R according to an odd-even circuit so that power dividing is completed. The microwave phase inverter based one-to-three power divider is small in size, good in amplitude and phase consistency and high in isolation degree.

Description

Based on one point of three power divider and the power distribution method thereof of microwave phase inverter

Technical field

The invention belongs to power distribution apparatus technical field, relate to a kind of power divider, be specifically related to a kind of one point of three power divider based on microwave phase inverter, the invention still further relates to the power distribution method of above-mentioned one point of three power divider.

Background technology

Power divider can be widely used in microwave, communication and radio system.The number of classical power divider circuits signal output port is mostly even number.Nineteen sixty, Ernest J.Wilkinson proposes the power divider circuits structure that classical constant amplitude homophase exports, and this circuit structure is widely used in the design of various microwave circuit; Up to now, also been proposed many power divider circuits structures that any merit proportion by subtraction can be provided newly.But these electric power distributor circuit structures are only applicable to the situation that signal output port number is even number, be difficult to be applicable to the situation that signal output port number is odd number.

Existing one point of three power divider circuits is dissymmetrical structure, and such structure exists three output port amplitude-phase consistencies and is difficult to ensure, isolation is also not high enough, the defect that bandwidth is not easily widened.The way that existing one point of three power divider generally adopts two-stage merit to divide, the first order adopts not decile one-to-two, and wherein road one-to-two is again incited somebody to action in the second level, and the symmetry of whole circuit is poor.

Summary of the invention

The object of the present invention is to provide a kind of one point of three power divider based on microwave phase inverter, there is compact size, structure is simple, amplitude-phase consistency good and isolation is high feature.

The first technical scheme of the present invention is, based on one point of three power divider of microwave phase inverter, the characteristic impedance including six length equal is Z ₂90 ° of transmission lines, every bar characteristic impedance is Z ₂90 ° of transmission lines join end to end successively and form circular transmission coil, the characteristic impedance including three length in circular transmission coil equal is Z ₁90 ° of transmission lines, three characteristic impedances are Z ₁one end of 90 ° of transmission lines be intersected in the center of circle of circular transmission coil, the circle centre position of circular transmission coil is provided with input port P ₁, three characteristic impedances are Z ₁the other end of 90 ° of transmission lines crossing with circular transmission coil respectively, three intersection points are by circular transmission coil trisection, and three characteristic impedances are Z ₁the other end of 90 ° of transmission lines be respectively arranged with output port P ₂, output port P ₃, output port P ₄, every two adjacent characteristic impedances are Z ₁the circular transmission coil central authorities folded by 90 ° of transmission lines be provided with microwave phase inverter, the two ends of each microwave phase inverter are connected to an isolation resistance R.

The feature of the first technical scheme of the present invention is also,

Microwave phase inverter is the one in two-sided parallel strips phase inverter or micro-band phase inverter.

Two-sided parallel band line style phase inverter is two-sided parallel strips and metallization via structure.

Micro strip line type phase inverter adopts ground plate opened round vallecular cavity, microstrip line interdigital metallization via hole ground structure.

Characteristic impedance is Z ₁the length of 90 ° of transmission lines be greater than the radius of circular transmission coil and characteristic impedance is Z ₁the length of 90 ° of transmission lines be 1/4th λ wavelength.

The second technical scheme of the present invention is, based on the power distribution method of one point of three power divider of microwave phase inverter, specifically implements according to following steps:

Step 1, by power by input port P ₁input, adopts even mould equivalent electric circuit to obtain and meets input port P ₁matching condition;

Step 2, according to output port P ₂, output port P ₃, output port P ₄excitation value, the matching condition that obtains in three output ports isolation conditions and step 1, obtain input port P ₁voltage, circuit structure is equivalent to odd even equivalent electric circuit, namely acquired character impedance is Z ₂the characteristic impedance Z of 90 ° of transmission lines ₂with the value of isolation resistance R;

Step 3, through step 2, by fan-in mouth P ₁power averaging be dispensed to three outputs, namely mean allocation is to output port P ₂, output port P ₃, output port P ₄.

The feature of the second technical scheme of the present invention is also,

Step 1 is concrete to be implemented in accordance with the following methods:

By power by input port P ₁input, by input port P ₁be Z with three characteristic impedances ₁90 ° of transmission lines respectively by power delivery to output port P ₂, output port P ₃, output port P ₄, the isolation resistance R short circuit that microwave phase inverter two ends connect, whole circuit equivalent is even mould equivalent electric circuit, and at center frequency point place, characteristic impedance is Z ₁90 ° of transmission lines be short-circuit line, the impedance of input is infinitely great, namely obtains and meets input port P ₁matching condition be:

$Z_1=\sqrt{3}{Z}_0.$

Step 2 is specifically implemented according to following steps:

Step 2.1, output port P ₂, output port P ₃, output port P ₄excitation value be respectively 2E _s,-2E _s, 0, according to the matching condition obtained in three output ports isolation conditions and step 1, obtain input port P according to following algorithm ₁voltage:

V _1o＝S ₂₁E _s+S ₃₁(-E _s)+S ₄₁*0＝0；

Step 2.2, the input port P obtained through step 2.1 ₁magnitude of voltage be 0, be odd even equivalent electric circuit by the circuit equivalent of power divider of the present invention, the characteristic impedance obtaining transmission line is respectively Z ₂with the value of isolation resistance R, specifically implement according to following algorithm:

E _s＝A·(-E _s)+B·I _3o（1）

I _2o＝C·(-E _s)+D·I _3o（2）

I _2o＝E _s/Z ₀（3）

I _3o＝E _s/Z ₀（4）

Cascade circuit transfer matrix is

$\left[A_2\right]=\left[\begin{array}{cc}0& {\mathrm{jZ}}_2\\ j/Z_2& 0\end{array}\right]\left[\begin{array}{cc}1& 0\\ 1/R& 1\end{array}\right]\left[\begin{array}{cc}-1& 0\\ 0& -1\end{array}\right]\left[\begin{array}{cc}1& 0\\ 1/R& 1\end{array}\right]\left[\begin{array}{cc}0& {\mathrm{jZ}}_2\\ j/Z_2& 0\end{array}\right]=\left[\begin{array}{cc}1& {2Z}_2^2/R\\ 0& 1\end{array}\right]$

$\left[A_1\right]=\left[A_3\right]=\left[\begin{array}{cc}1& 0\\ R/\left(2Z_2^2\right)& 1\end{array}\right]$

$\left[A\right]=\left[\begin{array}{cc}A& B\\ C& D\end{array}\right]=\left[A_1\right]\left[A_2\right]\left[A_3\right]=\left[\begin{array}{cc}1& 0\\ R/\left({2Z}_2^2\right)& 1\end{array}\right]\left[\begin{array}{cc}1& {2Z}_2^2/R\\ 0& 1\end{array}\right]\left[\begin{array}{cc}1& 0\\ R/\left({2Z}_2^2\right)& 1\end{array}\right]$ (5)

$=\left[\begin{array}{cc}2& {2Z}_2^2/R\\ 3R/\left({2Z}_2^2\right)& 2\end{array}\right]$

(5) (3) are substituted into (1):

Namely obtain $Z_2=\sqrt{1.5Z_{0}R}$ Or $R=\frac{{2Z}_2^2}{{3Z}_0}.$

Beneficial effect of the present invention is,

(1) simple, the engineering of one point of three power divider compact based on microwave phase inverter of the present invention, structure easily realizes;

(2) one point of three power divider based on microwave phase inverter of the present invention adopts and is symmetrical arranged, and ensure that the amplitude-phase consistency of three output ports;

(3) one point of three power divider isolation based on microwave phase inverter of the present invention is high;

(4) one point of three power divider based on microwave phase inverter of the present invention is applicable to some large-power occasions such as various microwave circuit, antenna array feed system, has wide range of applications.

Accompanying drawing explanation

Fig. 1 is the structure chart of one point of three power divider based on microwave phase inverter of the present invention;

Fig. 2 is the even mould equivalent circuit diagram of idol of one point of three power divider based on microwave phase inverter of the present invention;

Fig. 3 is the circuit diagram after the even mould equivalent circuit diagram of idol of one point of three power divider based on microwave phase inverter of the present invention simplifies;

Fig. 4 is the parity mode equivalent circuit diagram of one point of three power divider based on microwave phase inverter of the present invention;

Fig. 5 is the circuit diagram after the parity mode equivalent circuit diagram of one point of three power divider based on microwave phase inverter of the present invention simplifies;

Fig. 6 is the structure chart based on the two-sided parallel band line style phase inverter in one point of three power divider of microwave phase inverter of the present invention;

Fig. 7 is the circuit structure of the two-sided parallel band line style power divider of one point of three power divider based on microwave phase inverter of the present invention;

Fig. 8 be of the present invention based in one point of three power divider of microwave phase inverter based on the return loss simulation result figure of two-sided parallel band line style phase inverter power divider;

Fig. 9 be of the present invention based in one point of three power divider of microwave phase inverter based on the insertion loss simulation result figure of two-sided parallel band line style phase inverter power divider;

Figure 10 be of the present invention based in one point of three power divider of microwave phase inverter based on the isolation simulation result figure of two-sided parallel band line style phase inverter power divider;

Figure 11 is the circuit planes structure of the micro strip line type allotter circuit of one point of three power divider based on microwave phase inverter of the present invention;

Figure 12 is the structure chart of the micro-band phase inverter in the circuit planes structure of the micro strip line type allotter circuit of one point of three power divider based on microwave phase inverter of the present invention;

Figure 13 is the return loss simulation result figure of the micro strip line type allotter circuit of one point of three power divider based on microwave phase inverter of the present invention;

Figure 14 is the insertion loss simulation result figure of the micro strip line type allotter circuit of one point of three power divider based on microwave phase inverter of the present invention;

Figure 15 is the isolation simulation result figure of the micro strip line type allotter circuit of one point of three power divider based on microwave phase inverter of the present invention;

Figure 16 is the return loss analogous diagram of the schematic circuit of one point of three power divider based on microwave phase inverter of the present invention;

Figure 17 is the insertion loss analogous diagram of the schematic circuit of one point of three power divider based on microwave phase inverter of the present invention;

Figure 18 is the isolation analogous diagram of the schematic circuit of one point of three power divider based on microwave phase inverter of the present invention.

In figure, 1. characteristic impedance is Z ₁90 ° of transmission lines, 2. characteristic impedance is Z ₂90 ° of transmission lines, 3. microwave phase inverter, 4. isolation resistance R, 5. conductor pin, the 6. line of rabbet joint.

Embodiment

Below in conjunction with the drawings and specific embodiments, the present invention is described in detail.

One point of three power divider based on microwave phase inverter of the present invention, as shown in Figure 1, the characteristic impedance including six length equal is Z to its structure ₂90 ° of transmission lines 2, every bar characteristic impedance is Z ₂90 ° of transmission lines 2 join end to end successively and form circular transmission coil, the characteristic impedance including three length in circular transmission coil equal is Z ₁1, three characteristic impedances of 90 ° of transmission lines be Z ₁one end of 90 ° of transmission lines 1 be intersected in the center of circle of circular transmission coil, the circle centre position of circular transmission coil is provided with input port P ₁, three characteristic impedances are Z ₁the other end of 90 ° of transmission lines 1 crossing with circular transmission coil respectively, three intersection points are by circular transmission coil trisection, and three characteristic impedances are Z ₁the other end of 90 ° of transmission lines 1 be respectively arranged with output port P ₂, output port P ₃, output port P ₄, every two adjacent characteristic impedances are Z ₁the circular transmission coil central authorities folded by 90 ° of transmission lines 1 be provided with microwave phase inverter 3, the two ends of each microwave phase inverter 3 are connected to an isolation resistance R4.

Microwave phase inverter 3 is the one in two-sided parallel strips phase inverter or micro-band phase inverter.

Two-sided parallel band line style phase inverter is two-sided parallel strips and metallization via structure.

Micro strip line type phase inverter adopts ground plate opened round vallecular cavity, microstrip line interdigital metallization via hole ground structure.

Characteristic impedance is Z ₁the length of 90 ° of transmission lines 1 be greater than the radius of circular transmission coil and characteristic impedance is Z ₁the length of 90 ° of transmission lines 1 be 1/4th λ wavelength.

The power distribution method of one point of three power divider based on microwave phase inverter of the present invention, specifically implement according to following steps:

Step 1, by power by input port P ₁input, adopts even mould equivalent electric circuit to obtain and meets input port P ₁matching condition:

By power by input port P ₁input, by input port P ₁be Z with three characteristic impedances ₁90 ° of transmission lines 1 respectively by power delivery to output port P ₂, output port P ₃, output port P ₄, the isolation resistance R4 short circuit that 180 ° of microwave phase inverter 3 two ends connect, whole circuit equivalent is even mould equivalent electric circuit, and at center frequency point place, characteristic impedance is Z ₁90 ° of transmission lines 1 be short-circuit line, the impedance of input is infinitely great, as shown in Figures 2 and 3, can obtain and meet input port P ₁matching condition be:

Step 2, according to output port P ₂, output port P ₃, output port P ₄excitation value, the matching condition that obtains in three output ports isolation conditions and step 1, obtain input port P ₁voltage, circuit structure is equivalent to odd even equivalent electric circuit, namely acquired character impedance is Z ₂the characteristic impedance Z of 90 ° of transmission lines 2 ₂with the value of isolation resistance R4:

Step 2.1, output port P ₂, output port P ₃, output port P ₄excitation value be respectively 2E _s,-2E _s, 0, then according to the matching condition obtained in three output ports isolation conditions and step 1, obtain input port P according to following algorithm ₁voltage:

V _1o＝S ₂₁E _s+S ₃₁(-E _s)+S ₄₁*0＝0；

Step 2.2, the input port P obtained through step 2.1 ₁magnitude of voltage be 0, be odd even equivalent electric circuit by the circuit equivalent of power divider of the present invention, obtaining the characteristic impedance of transmission line 2 is respectively Z ₂with the value of isolation resistance R4, as shown in Figures 4 and 5, specifically implement according to following algorithm:

E _s＝A·(-E _s)+B·I _3o（1）

I _2o＝C·(-E _s)+D·I _3o（2）

I _2o＝E _s/Z ₀（3）

I _3o＝E _s/Z ₀（4）

Cascade circuit transfer matrix is

$\left[A_2\right]=\left[\begin{array}{cc}0& {\mathrm{jZ}}_2\\ j/Z_2& 0\end{array}\right]\left[\begin{array}{cc}1& 0\\ 1/R& 1\end{array}\right]\left[\begin{array}{cc}-1& 0\\ 0& -1\end{array}\right]\left[\begin{array}{cc}1& 0\\ 1/R& 1\end{array}\right]\left[\begin{array}{cc}0& {\mathrm{jZ}}_2\\ {j/Z}_2& 0\end{array}\right]=\left[\begin{array}{cc}1& {2Z}_2^2/R\\ 0& 1\end{array}\right]$

$\left[A_1\right]=\left[A_3\right]=\left[\begin{array}{cc}1& 0\\ R/\left({2Z}_2^2\right)& 1\end{array}\right]$

$\left[A\right]=\left[\begin{array}{cc}A& B\\ C& D\end{array}\right]=\left[A_1\right]\left[A_2\right]\left[A_3\right]=\left[\begin{array}{cc}1& 0\\ R/\left({2Z}_2^2\right)& 1\end{array}\right]\left[\begin{array}{cc}1& {2Z}_2^2/R\\ 0& 1\end{array}\right]\left[\begin{array}{cc}1& 0\\ R/\left({2Z}_2^2\right)& 1\end{array}\right]$ (5)

$=\left[\begin{array}{cc}2& {2Z}_2^2/R\\ 3R/\left({2Z}_2^2\right)& 2\end{array}\right]$

(5) (3) are substituted into (1):

Namely obtain $Z_2=\sqrt{1.5Z_{0}R}$ Or $R=\frac{{2Z}_2^2}{{3Z}_0};$

Step 3, through step 2, by fan-in mouth P ₁power averaging be dispensed to three outputs, namely mean allocation is to output port P ₂, output port P ₃, output port P ₄.

One point of three power divider based on microwave phase inverter of the present invention includes microwave phase inverter and transmission line composition.Wherein when two-sided parallel band line style phase inverter selected by microwave phase inverter, its structure as shown in FIG. 6 and 7, adopts interdigital two-sided parallel strips and metallization via structure.Wherein in power divider circuits, the girth of circular transmission coil determines the radius of circular transmission coil, and characteristic impedance is Z ₁90 ° of transmission line 1 length be 1/4th λ wavelength, the radius determined compared with girth is slightly long, and adopt stepped impedance line to carry out miniaturization to the two-sided parallel strips of radial direction, choosing dielectric-slab is relative dielectric constant ε _r=2.2, dielectric thickness h=0.8mm, as center frequency points f ₀=4GHz, input port P ₁characteristic impedance Z ₀=50 Ω, radial transmission line characteristic impedance ring property impedance Z ₂during=100 Ω, circuit size parameter is as shown in table 1.

Table 1 two-sided parallel band line style one point of third-class power divider circuits dimensional parameters

Parameter	W 0	W 1	W 2	r 0	W s	l s
							Unit (mm)	3.05	1.55	1.25	12.9	0.2	2

As shown in Fig. 8 ~ Figure 10, result shows, based on one point of third-class power divider of two-sided parallel strips phase inverter in the scope of relative bandwidth 76%, each reflection coefficient of port loss is greater than 11.4dB, and insertion loss is less than 0.5dB, and isolation is greater than 27dB.

Adopt one point of three power divider that micro strip line type phase inverter is formed, as shown in figure 11, micro strip line type phase inverter wherein adopts ground plate opened round vallecular cavity, microstrip line interdigital metallization via hole ground structure, as shown in figure 12, the girth of circular transmission coil determines the radius of circular transmission coil, and characteristic impedance is Z ₁transmission line length be 1/4th λ wavelength, the radius determined compared with girth is slightly long, adopts stepped impedance line to carry out miniaturization to radial microstrip line.

In Figure 12, choosing dielectric-slab is relative dielectric constant ε _r=2.2, dielectric thickness h=0.8mm, as centre frequency f ₀=4GHz, port identity impedance Z ₀=50 Ω, radial transmission line characteristic impedance loop wire characteristic impedance Z ₂during=100 Ω, circuit size parameter is as shown in table 2.

The third-class power divider circuits dimensional parameters of table 2 micro strip line type one point

Parameter	W 0	W 1	W 2	W 3	W s	r 0	r s	l 0	l sm	l ss
											Unit (mm)	3.05	1.55	1.25	1.55	0.2	12.9	5.0	2.0	2.4	2.0

As shown in Figure 13 ~ Figure 15, result shows, based on one point of third-class power divider of micro-band phase inverter in the scope of relative bandwidth 63%, each reflection coefficient of port loss is greater than 11.0dB, and insertion loss is less than 0.5dB, and isolation is greater than 20dB.

Simulating, verifying

Emulate one point of three power divider as shown in Figure 1 with the Microwave Office of AWR company, map parameter is set to: centre frequency f ₀=10GHz, input port P ₁characteristic impedance Z ₀=50 Ω, radial transmission line characteristic impedance ring property impedance Z ₂=100 Ω, isolation resistance $R=Z_2^2/{1.5Z}_0=133.3\mathrm{\Ω}.$

As shown in Figure 16 ~ Figure 18, simulation result can be found out, based on one point of third-class power divider of microwave phase inverter in the scope of relative bandwidth 70%, each reflection coefficient of port loss is greater than 11.4dB, and insertion loss is less than 0.3dB, and isolation is greater than 28dB.

The circuit structure of one point of third-class power divider based on microwave phase inverter of the present invention and Theoretical Design formula, in ideal microwave phase inverter situation, one point of third-class power divider is in the scope of relative bandwidth 70%, each reflection coefficient of port loss is greater than 11.4dB, insertion loss is less than 0.3dB, and isolation is greater than 28dB.According to one point of third-class power divider based on two-sided parallel strips phase inverter of Theoretical Design, in the scope of relative bandwidth 76%, each reflection coefficient of port loss is greater than 11.4dB, and insertion loss is less than 0.5dB, and isolation is greater than 27dB.According to one point of third-class power divider based on micro-band phase inverter of Theoretical Design in the scope of relative bandwidth 63%, each reflection coefficient of port loss is greater than 11.0dB, and insertion loss is less than 0.5dB, and isolation is greater than 20dB.Propose one point of third-class power divider have band wide, size is little, structure is simple, engineering easily realizes, amplitude-phase consistency is good, isolation advantages of higher.Propose structure herein, design theory, design result can be widely used in various broadband microwave circuits and antenna array feed system.

Claims (1)

1., based on the power distribution method of one point of three power divider of microwave phase inverter, this power distribution method depends on one point of three power divider based on microwave phase inverter;

Described one point of three power divider based on microwave phase inverter, the characteristic impedance including six length equal is Z ₂90 ° of transmission lines (2), characteristic impedance described in every bar is Z ₂90 ° of transmission lines (2) join end to end successively and form circular transmission coil, the characteristic impedance including three length in described circular transmission coil equal is Z ₁90 ° of transmission lines (1), described three characteristic impedances are Z ₁one end of 90 ° of transmission lines (1) be intersected in the center of circle of circular transmission coil, the circle centre position of described circular transmission coil is provided with input port P ₁, described three characteristic impedances are Z ₁the other end of 90 ° of transmission lines (1) crossing with described circular transmission coil respectively, three intersection points are by described circular transmission coil trisection, and described three characteristic impedances are Z ₁the other end of 90 ° of transmission lines (1) be respectively arranged with output port P ₂, output port P ₃, output port P ₄, every two adjacent described characteristic impedances are Z ₁the circular transmission coil central authorities folded by 90 ° of transmission lines (1) be provided with microwave phase inverter (3), the two ends of each described microwave phase inverter (3) are connected to an isolation resistance R (4);

Described microwave phase inverter (3) is the one in two-sided parallel strips phase inverter or microstrip type phase inverter;

Described two-sided parallel band line style phase inverter is two-sided parallel strips and metallization via structure;

Described microstrip type phase inverter adopts ground plate opened round vallecular cavity, microstrip line interdigital metallization via hole ground structure;

Described characteristic impedance is Z ₁the length of 90 ° of transmission lines (1) equal the radius of circular transmission coil, characteristic impedance is Z ₁the length of 90 ° of transmission lines (1) be 1/4th λ wavelength;

The power distribution method of described one point of three power divider based on microwave phase inverter, is characterized in that, specifically implement according to following steps:

Step 1, by power by input port P ₁input, adopts even mould equivalent electric circuit to obtain and meets input port P ₁matching condition, specifically in accordance with the following methods implement:

By power by input port P ₁input, by input port P ₁be Z with three characteristic impedances ₁90 ° of transmission lines (1) respectively by power delivery to output port P ₂, output port P ₃, output port P ₄, isolation resistance R (4) short circuit that microwave phase inverter (3) two ends connect, whole circuit equivalent is even mould equivalent electric circuit, and at center frequency point place, characteristic impedance is Z ₁90 ° of transmission lines (1) be short-circuit line, the impedance of input is infinitely great, namely obtains and meets input port P ₁matching condition be: $Z_1=\sqrt{3}{Z}_0;$

Step 2, according to output port P ₂, output port P ₃, output port P ₄excitation value, the matching condition that obtains in three output ports isolation conditions and step 1, obtain input port P ₁voltage, circuit structure is equivalent to odd even equivalent electric circuit, namely acquired character impedance is Z ₂the characteristic impedance of 90 ° of transmission lines (2) be Z ₂with the value of isolation resistance R (4), specifically implement according to following steps:

Step 2.1, output port P ₂, output port P ₃, output port P ₄excitation value be respectively 2E _s,-2E _s, 0, then according to the matching condition obtained in three output ports isolation conditions and step 1, obtain input port P according to following algorithm ₁voltage:

V _1o＝S ₂₁E _s+S ₃₁(-E _s)+S ₄₁*0＝0；

Step 2.2, the input port P obtained through step 2.1 ₁magnitude of voltage be 0, be odd even equivalent electric circuit by the circuit equivalent of power divider of the present invention, the characteristic impedance obtaining transmission line (2) is respectively Z ₂with the value of isolation resistance R (4), specifically implement according to following algorithm:

E _s＝A·(-E _s)+B·I _3o(1)

I _2o＝C·(-E _s)+D·I _3o(2)

I _2o＝E _s/Z ₀(3)

I _3o＝E _s/Z ₀(4)

Cascade circuit transfer matrix is

$\left[A_2\right]=\left[\begin{array}{cc}0& j{Z}_2\\ j/Z_2& 0\end{array}\right]\left[\begin{array}{cc}1& 0\\ 1/R& 1\end{array}\right]\left[\begin{array}{cc}-1& 0\\ 0& -1\end{array}\right]\left[\begin{array}{cc}1& 0\\ 1/R& 1\end{array}\right]\left[\begin{array}{cc}0& j{Z}_2\\ j/Z_2& 0\end{array}\right]=\left[\begin{array}{cc}1& 2Z_2^2/R\\ 0& 1\end{array}\right]$

$\left[A_1\right]=\left[A_3\right]=\left[\begin{array}{cc}1& 0\\ R/\left(2Z_2^2\right)& 1\end{array}\right]$

$\begin{array}{c}\left[A\right]=\left[\begin{array}{cc}A& B\\ C& D\end{array}\right]=\left[A_1\right]\left[A_2\right]\left[A_3\right]=\left[\begin{array}{cc}1& 0\\ R/\left(2Z_2^2\right)& 1\end{array}\right]\left[\begin{array}{cc}1& 2Z_2^2/R\\ 0& 1\end{array}\right]\left[\begin{array}{cc}1& 0\\ R/\left(2Z_2^2\right)& 1\end{array}\right]\\ =\left[\begin{array}{cc}2& 2Z_2^2/R\\ 3R/\left(2Z_2^2\right)& 2\end{array}\right]\end{array}---\left(5\right)$

(5) (3) are substituted into (1):

Namely obtain $Z_2=\sqrt{1.5Z_{0}R}$ Or $R=\frac{2Z_2^2}{3Z_0};$

Step 3, through step 2, by fan-in mouth P ₁power averaging be dispensed to three outputs, namely mean allocation is to output port P ₂, output port P ₃, output port P ₄.