KR102046408B1 - A power divider with enhanced selectivity performance - Google Patents

Abstract

Disclosed is a high output power divider (PD) with the improved selectivity performance. The high output PD comprises: a substrate; an input port; an output port; a transmission line (Z_1); and a power dividing unit. The PD uses only one via hole without additional lumped elements. In addition, the good selectivity performance is improved for RF/Microwave system.

Description

A power divider with enhanced selectivity performance}

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a power divider with improved selectivity performance. More particularly, high power with improved selectivity characteristics has port 2 and port 4 having open-circuited coupled lines. Relates to a power divider.

This research was funded by the Korea Research Foundation (NRF-2016R1D1A1B03935640) and Kwangwoon University in 2017.

As prior art 1 related to a power divider (PD), Patent Registration No. 10-1070009 discloses "1: 2 ultra-wideband power divider / combiner with improved isolation", which is combined with transmission lines and capacitively. The short-circuit line can be used to adjust the bandwidth of the input or output signal to the ultra-wide band, and isolate the output transmission lines from each other to provide an ultra-wideband power divider / combiner with improved stability.

The ultra-wideband power divider can accurately set the bandwidth of the input / output signal to the desired ultra-wideband by adjusting the size of the capacitive coupling between the transmission line and the shorting line. In addition, the ultra-wideband power divider improves isolation between transmission lines through which signals are output by inserting isolation resistors between transmission lines through which signals are output.

As a related art 2, Patent Registration No. 10-1070035 discloses an "ultra wideband power divider / combiner", and capacitively couples two T-shaped transmission line portions having a transmission line of λ / 4 length to each other, Ultra wide band for distributing the size of the output signal or combining the input signal by using λ / 2-length short-circuit line which is capacitively coupled to the transmission line to adjust the bandwidth and attenuation pole in each transmission line. Provide a power divider / combiner.

Accordingly, the ultra-wideband power divider can accurately set the bandwidth of the input / output signal to the desired ultra-wideband by adjusting the size of the capacitive coupling between the transmission line and the short-line. In addition, the ultra-wideband power divider capacitively combines the two T-shaped transmission line portions with capacitive coupling of the transmission lines and the short-circuit lines of each T-shaped transmission line portion, thereby providing the size or the capacitive coupling of the T-shaped transmission line portions. By adjusting the size of the capacitive coupling of the transmission line and the short-circuit line of each T-shaped transmission line part, it is possible to adjust the size of the output signal equally or differentially.

In this article, a new structure of the power divider (PD) was introduced. This design shows high power handling. The power divider PD converts the input signal into two or more identical output signals. In particular, Wilkinson PD and Gysel PD are the most widely used PD types of RF / Microwave systems, such as two radar systems and power amplifiers.

Compared to Wilkinson PD, Gysel PD has high power handling by the configuration where isolation resistors are used on two ports. In Wilkinson PD, the insulation resistance is inherent in the network, and the parasitic phase response of the isolation resistor should be nearly zero. The very short wavelength limits the applications for Wilkinson PD in high frequency systems because of the parasitic phase response of the insulated resistance, which cannot be ignored at high frequencies.

However, Gysel PD has a reasonable phase response without being affected by insulation resistance, where some disadvantages still exist, such as bulk size, poor selectivity performance, and narrow bandwidth. has a response.

Recently, many researchers have been working on the redesign of Gysel PD [1-9].

Additional transmission line type resonators or right- and left-handed transmission lines are used to achieve dual-band designs.

In references [7, 8], the authors should be careful to replace the original transmission lines with lumped elements to make the power divider PD smaller and smaller.

In Ref. [9], a structure combined with Gysel PD and Balun has been proposed for wideband applications. However, all of these designs cannot reject out-of-band signals, which means low selectivity.

Ref. [10,11] proposed Gysel PDs with bandpass or enhanced selectivity performance.

One structure is formed by replacing two impedance transformers with coupling structure 10 between the input port and the output port, and the other structure is an expanded coupled-resonator circuit model. model.11). However, the bandwidth of both designs is a design with a narrow bandwidth of less than 12%.

Patent Registration No. 10-10700090000 (Registration date September 27, 2011), "1: 2 ultra-wideband power divider / combiner improves isolation", Kyung Hee University Patent Registration No. 10-10700350000 (Registration date September 27, 2011), "1: 3 Ultra-wideband Power Divider / Combiner", Kyung Hee University

 Hayati M, Malakooti SA, Abdipour A. A novel design of tripleband Gysel power divider. IEEE Trans Microw Theory Tech. 2013; 61 (10): 3558-3567.  Sun Z, Zhang L, Liu Y, Tong X. Modified Gysel power divider for dual-band applications. IEEE Microw Wirel Compon Lett. 2011; 21 (1): 16-18.  Shahi Gharehaghaji H, Shamsi H. Design of unequal dual band Gysel power divider with isolation bandwidth improvement. IEEE Microw Wirel Compons Lett. 2017; 27 (2): 138-140.  Ren X, Song K, Fan M, Zhu Y, Hu B. Compact dual-band Gysel power divider based on composite right- and left-handed transmission lines. IEEE Microw Wirel Compon Lett. 2015; 25 (2): 82-84.  Park MJ. Coupled line Gysel power divider for dual-band operation. Electron Lett. 2011; 47 (10): 599-601.  Park MJ, Lee B. A dual-band Gysel power divider with the even-mode input extension / stub lines. Microw Opt Technol Lett. 2011; 53 (6): 1213-1216.  Ren X, Song K, Zhang F, Hu B. Miniaturized Gysel power divider based on composite right / left-handed transmission lines. IEEE Microw Wirel Compon Lett. 2015; 25 (1): 22-24.  Tang B, Hayashi H, Ueda R. Reduced-size Gysel power dividers using lumped-element components. Microw Opt Technol Lett. 2016; 58 (10): 2341-2344.  Abbasi Arand B, Amrollahzadeh M, Kamalzadeh S. A wideband Gysel power divider / combiner based on a modified marchand balun. Microw Opt Technol Lett. 2017; 59 (10): 2704-2955.  Wang KX, Zhang XY, Hu BJ. Gysel power divider with arbitrary power ratios and filtering responses using coupling structure. IEEE Trans Microw Theory Tech. 2014; 62 (3): 431-440.  Wu LS, Guo YX, Mao JF. Balanced-to-balanced Gysel power divider with bandpass filtering response. IEEE Trans Microw Theory Tech. 2013; 61 (12): 4052-4062.  Pozar DM. Micowave Engineering. 4th ed. New York: Wiley; 2012.

SUMMARY OF THE INVENTION An object of the present invention to solve the above problems is to provide a high power power divider having improved selectivity, having open-circuited coupled lines in which port 2 and port 4 are open. The new structure of Gysel PD has improved enhanced selectivity performance.

In order to achieve the object of the present invention, a power divider having improved selectivity characteristics may include a substrate; And an input port having an input port 1 for receiving power; an output port having port 2 and port 3; Port 2 and port 4 are open and connected to each of ports 1, 2 and 3, and as an open-circuited coupled line having a gap between the first transmission line and the second transmission line in parallel. A coupled transmission line, Z ₁ , configured and matched in input / output impedance; And Z ₂ and Z _{3, each} of which is connected to the coupled transmission line (Z ₁ ), and converts 1 power applied to the input port 1 into 1/2 power of the output port port 2 and port 3. And a power divider (PD) that includes;
It further comprises an isolation resistor (R) between the output port port 2, port 3, respectively,

The power divider uses only one via hole between each isolation resistor R without additional lumped elements.

delete

The first transmission line and the second transmission line use a coupled microstrip line.

The power divider (PD) is provided with a transmission line (coupled-line) and an output port (port 2,3) coupled with the input port (port 1), the combined line based circuit is a terminal with a load impedance Z _L Have port 3 on it

The substrate uses a Teflon substrate.

The prototype of the power divider (PD) is made of Z ₁ = 70.7Ω, Z ₂ = 50Ω, Z = 35.3Ω, Z _E = 72Ω, Z _O = 172Ω, isolation resistance (R) = 50Ω, It is prepared on a Teflon substrate having a relative permittivity epsilon r = 2.54, a 0.002 dielectric loss tangent value, a thickness of T = 0.54 mm, and a conductor height of h = 0.018 mm.

The ABCD matrix is used to derive the impedance matrix of the open circuit coupling line, the ABCD matrix of the equivalent circuit is obtained by equation (1),

식(1)

Formula (1)

Where Z is the characteristic impedance, and Z _E and Z _O are the even-mode impedance and the odd-mode impedance of the open-circuited coupled line, respectively. impedance, and two series transmission lines have an electrical length of θ,

In the ABCD matrix, the admittance inverter J can be replaced by equations (2) and (3),

, 식(2)

, Equation (2)

, 식(3)

, Equation (3)

Substituting Equation 2 and Equation 3 into Equation 1 and using the conversion relation between the impedance matrix and the ABCD matrix, the impedance matrix of the open circuit coupling line is derived as in Equation (4),

, 식(4)

, Equation (4)

In the structure having port 3 terminated with the load impedance Z _L of the open circuit coupling line, according to the relationship of voltage and current at port 1, the input impedance Z _IN looking at the load impedance Z _L of the coupling line based circuit is Calculated as

, 식(5)

, Equation (5)

When θ = 90 °, the input impedance Z _IN of the combined line based circuit is

, 식(6)과 같이 계산된다.

, Is calculated as in equation (6).

All port impedances of the power divider are equivalent impedances seen from a coupled line connecting the input / output port or core portion, and Z _IN, Z ₀ and Z _EQ1 (Z), respectively. _EQ2 ),

In the case of the conventional Gysel PD, all electrical lengths are equal to λ / 4, so θ ₁ , θ ₂ and θ ₃ should be equal to 90 °, and the parameters of the transmission lines and resistors at the core can be obtained as ,

, 식(7)

, Equation (7)

, 식(8)

, Equation (8)

, 식(9)

, Equation (9)

Where Z ₁ , Z ₂ and Z ₃ are the respective characteristic impedances of the transmission lines of a traditional Gysel PD,

과

의 등가 임피던스를 획득하도록 수행되었으며,

, 식(10)The core part of the simulation

and

To obtain an equivalent impedance of

, Equation (10)

식(11)과 같이 표현된다. Since Z _IN must have the same Z _EQ1 and Z _EQ2 for impedance matching, referring to equations 6 and 8, the impedance matched condition is

It is expressed as Equation (11).

The power divider has a passband of 2.1 to 3.1 GHz at a center frequency of 2.5 GHz and an insertion loss, return loss and isolation of 23.61, 220.2, and 219.3 dB, respectively. It features.

A new structure of a high output power divider (PD) with improved selectivity characteristics is presented, and a new structure of Gysel PD has enhanced selectivity performance. The bandwidth of the proposed power divider (PD) has increased by almost 40%. As with traditional Gysel PDs, the design of the proposed power divider (PD) has high-power handling capability. In addition, the proposed power divider (PD) has good selectivity performance suitable for RF / Microwave system.

The design is based on theoretical analysis using high power processing capability, improved selectivity characteristics and simple structure, and impedance matching. Closed-form design equations Detailed design procedures are given. For verification, a prototype with a center frequency of 2.5 GHz was simulated, and the measurement results matched the simulated ones and showed good results.

1 is an equivalent circuit of an open-circuited coupled line consisting of an admittance inverter J and a pair of transmission lines.
FIG. 2 shows a transmission line coupled to an input port port 1 and an output port coupled to a port 2,3, wherein the circuit-based coupled transmission line coupled with port 3 has a load impedance Z. FIG. Figure terminated by _L.
3 is a structural diagram of a high output power divider (PD) with improved selectivity performance according to the present invention.
4 shows simulation results of even mode equivalent impedances 1, 2 Z _EQ1 and Z _EQ2 .
5 is a diagram illustrating a design pattern of the proposed power divider PD according to an embodiment of the present invention.
6 shows the manufactured power divider (PD) and simulation results and measurement results, (A) photograph, (B) S ₁₁ (reflection loss of the intensity of the signal transmitted to port 1) and S ₂₁ (port 1 for port 2). Insertion loss), (C) S ₃₁ (port 1 loss for port 3) and S ₃₂ (Isolation-isolation to isolate port 2, port 3 independently), (D) phase and amplitude imbalances Picture.

Hereinafter, with reference to the accompanying drawings, preferred embodiments of the present invention will be described in detail the configuration and operation of the invention.

The new structure of Gysel PD presents enhanced selectivity performance. Among the proposed structures as an important part, the open-circuited coupled line is analyzed in detail in section 2. In Section 3, the structure is proposed first, and the closed form of the design equations is inferred based on the impedance matching method at the same time.

The prototype was then simulated for verification and measured in section 4. The two results showed a good agreement with each other.

The present invention has proposed a new structure of a power divider (PD). This design has high power processing capability, improved selectivity characteristics and simple structure. A theoretical analysis method using impedance matching was performed. Closed-form design equations Detailed design procedures are given. For verification, a prototype with a center frequency of 2.5 GHz was simulated, and the measurement results matched the simulated ones and showed good results.

2. open-circuited coupled line

As an integral part of the proposed power divider structure, open-circuited coupled lines with gaps in which port 2 and port 4 are opened are analyzed in detail.

1 is an equivalent circuit of an open-circuited coupled line consisting of an admittance inverter J and a pair of transmission lines.

Z is the characteristic impedance, and Z _E and Z _O are the even-mode impedance and the odd-mode impedance of the open-circuited coupled line, respectively. Indicates. Two series transmission lines are represented by an electrical length θ.

The ABCD matrix is used to derive the impedance matrix of the open circuit coupling line. Then, the ABCD matrix of the equivalent circuit is obtained by equation (1).

식(1)

Formula (1)

Referring to reference [12], the admittance inverter J in the ABCD matrix can be replaced by the following equations (2) and (3).

, 식(2)

, Equation (2)

, 식(3)

, Equation (3)

Substituting Equation 2 and Equation 3 into Equation 1 and using the conversion relation between the impedance matrix and the ABCD matrix, the impedance matrix of the open circuit coupling line [12] is derived as follows. Can be.

, 식(4)

, Equation (4)

A coupling line based circuit with port 3 terminated with a load impedance Z _L of an open circuit coupling line is shown in FIG. 2.

FIG. 2 shows a transmission line coupled to an input port port 1 and an output port coupled to a port 2,3, wherein the circuit-based coupled transmission line coupled with port 3 has a load impedance Z. FIG. Figure terminated by _L.

According to the relationship between the voltage and the current at the input port port 1, the input impedance Z _IN looking at the load impedance Z _L of the combined line based circuit can be calculated as follows.

, 식(5)

, Equation (5)

When the electrical length θ = 90 °, the input impedance Z _IN of the combined line based circuit can be calculated as follows.

, 식(6)

, Equation (6)

3. Proposed Power Divider

3 shows a structure of a power divider (PD) proposed in the present invention. Compared with the traditional Gysel PD architecture, three open-circuited coupled line type impedance transformers consist of input / output ports and core components (inside the square of the dashed line).

All the port impedances of the power divider are equivalent impedances seen from a coupled line connecting the input / output port or core part, respectively, Z _IN, Z ₀ and Z _EQ1 (Z _EQ2 ) to be.

In the conventional Gysel PD, all electrical lengths are equal to λ / 4, so θ ₁ , θ ₂ and θ ₃ should be equal to 90 °. Then, the parameters of the transmission lines and resistors of the core part can be obtained as follows.

, 식(7)

, Equation (7)

, 식(8)

, Equation (8)

, 식(9)

, Equation (9)

Here, Z ₁ , Z ₂ and Z ₃ are the respective characteristic impedances of the transmission lines of the traditional Gysel PD shown in FIG. 3.

Simulation of the core part was performed to obtain equivalent impedances of Z _EQ1 and Z _EQ2 . Results with a center frequency of 2.5 GHz are shown in FIG. 4 and the following equation is valid.

, 식(10)

, Equation (10)

과

가 동일해야 한다. In design, Z _IN is used for impedance matching

and

Should be the same.

Then, referring to Equations 6 and 8, the impedance matched condition is expressed as Equation 11.

, 식(11)

, Equation (11)

Based on the above analysis, the design procedure can be summarized as follows.

1) Define the center frequency of the proposed power divider (PD), which can be used to calculate the electrical length of all transmission lines and coupled lines.

2) Select the port impedance, design the odd-mode impedance of the open-circuited coupled line, and determine the impedance of each part through equations 7-9 and 11 Acquire.

3) Pass this value in physical length using the basic transmission line theory.

3 is a structural diagram of a high output power divider (PD) with improved selectivity performance according to the present invention.

The power divider having improved selectivity characteristics of the present invention

Board; And

An input port having an input port 1 for receiving power; an output port having port 2 and port 3; Port 2 and port 4 are open and connected to each of ports 1, 2 and 3, and as an open-circuited coupled line having a gap between the first transmission line and the second transmission line in parallel. A coupled transmission line Z ₁ having an input / output impedance matched thereto; And Z ₂ and Z _{3, each} of which is connected to the coupled transmission line (Z ₁ ), and converts 1 power applied to the input port 1 into 1/2 power of the output port port 2 and port 3. And a power divider (PD) that includes;
It further comprises an isolation resistor (R) between the output port port 2, port 3, respectively,

The power divider uses only one via hole between each isolation resistor R without additional lumped elements.

An isolation resistor (R) is further included between the output ports port 2 and port 3.

The first transmission line and the second transmission line use a coupled microstrip line.

The power divider PD has a transmission line coupled to an input port port 1 and an output port port 2,3, the coupling line based circuit being terminated with a load impedance Z _L. Has port 3

The power divider (PD) divides power by input port 1 receiving power and two transmission lines of a branched coupling line type, and output port 2 separated by an isolation resistor (R). 1/2 power output from port 3

The impedance of all ports is denoted by Z ₀ , and the value of isolation resistors (R) is 2Z ₀ .

Z _E , Z ₀ , and θ represent the even-mode / odd-mode impedances of the coupled line, and the electrical length, respectively.

Z _IN Is the input impedance looking at the load impedance Z _L of the coupled line based circuit.

Z _L is the load impedance of the open circuit coupling line.

Z _{EQ1 and} Z _EQ2 are the port impedances of the port.

Z _E is the even-mode impedance of the open circuit coupling line.

Z _O is the odd-mode impedance of the open circuit coupling line.

θ is the electrical length of two consecutive transmission lines.

R is an isolation resistor.

4. Experimental Results

In the embodiment of the present invention, a prototype having a center frequency of 2.5 GHz was used and fabricated by simulation to verify the design method of the proposed power divider (PD). The port impedance is 50 Ω. According to the design procedure summarized above, all values of the designed impedances are obtained as listed in Table 1.

TABLE 1

The prototype of the power divider is made of Z ₁ = 70.7Ω, Z ₂ = 50Ω, Z = 35.3Ω, Z _E = 72Ω, Z _O = 172Ω, isolation resistance (R) = 50Ω, and the relative dielectric constant εr = 2.54, 0.002 dielectric loss tangent value, thickness of T = 0.54 mm, and conductor height of h = 0.018 mm.

When selecting odd-mode impedance of open circuit coupling lines, the difficulty of processing must be taken into account. The smaller the odd-mode impedance, the smaller the even-mode impedance is a characteristic of the coupled line, and the gap of the open-circuited coupled line. ) Is very small, meaning high fabrication difficulty.

4 shows simulation results of even mode equivalent impedances 1, 2 Z _EQ1 and Z _EQ2 . 5 is a view showing a design pattern of the power divider (PD) proposed in the present invention. The proposed power divider PD includes a power divider including a right input port1, a top left output port 2, a bottom left output port 3, a right Z ₁ part, a central rectangular Z ₂ part, and a left oval Z ₃ part. Include.

Z ₁ , Z ₂ , and Z _{3 have} a width of W ₃ > W ₂ > W ₁ .

Based on these values, the pattern shown in FIG. 5 is designed with 0.54 mm thickness, relative permittivity (ε _r ) 2.54, conductor thickness of 0.018 mm, 0.002 dielectric loss tangent value on a Teflon substrate. It became.

In this pattern, additional lines are used to reduce soldering difficulties and to reduce the effects of intersections between two different lines. The structure is simple and only one via hole is used without additional lumped elements. For reference, lumped elements are lumped elements that minimize R, L, and C elements. All resistors are provided based on surface-mounted technology.

Table 2 shows the physical lengths of the designed patterns calculated through basic transmission line theory.

TABLE 2

6 shows the manufactured power divider (PD) and simulation results and measurement results, (A) photograph, (B) S ₁₁ (reflection loss of the intensity of the signal transmitted to port 1) and S ₂₁ (port 1 for port 2). Insertion loss), (C) S ₃₁ (port 1 loss for port 3) and S ₃₂ (Isolation-isolation to isolate port 2, port 3 independently), (D) phase and amplitude imbalances Picture.

As shown in the photograph, the manufactured power divider PD of FIG. 6 (A) has an input port 1 on the left side, an output port 3 on the right side, and port 2 on the Teflon substrate, and each has a 50 impedance matched SMA connector. do.

The S ₂₁ parameter is the insertion loss of port 1 to port 2 of the power divider PD. When the input power drops by 3dB, the output of the power divider is divided by 1/2 power.

Photographs of the manufactured power divider PD are shown in FIGS. 6A-D, which show simulation results and measurement results.

At the 2.5 GHz center frequency, insertion loss, return loss and isolation are 23.61, 220.2, and 219.3 dB, respectively. FIG. 6D shows that magnitude and phase imbalance in the passband (2.1 to 3.1 GHz) is less than 0.1 dB and 98, respectively.

5. Conclusion

A new structure of a power divider (PD) with high power processing capability and enhanced selectivity performance is presented and analyzed. Closed-form design equations have been proposed that can be used directly in future studies. To verify the summarized design procedure, the prototype simulated and fabricated an antenna with a center frequency of 2.5 GHz.

The measured results showed good agreement with theoretical analysis and simulated ones.

Comparing the designs of Refs [10] and [11], the bandwidth of the proposed power divider (PD) increased by almost 40%. As with traditional Gysel PDs, the design of the proposed power divider (PD) has high-power handling capability. In addition, the proposed power divider (PD) has good selectivity performance suitable for RF / Microwave system.

As described above, the present invention has been described with reference to a preferred embodiment of the present invention, but the present invention is within the scope not departing from the spirit and scope of the present invention as set forth in the appended claims by those skilled in the art. It will be understood that various modifications or variations may be made.

PD: Power Divider
port 1: input port
port2,3: output port
Z: characteristic impedance
Z _IN : Input Impedance Looking at Load Impedance Z _L of Coupled Line Based Circuit
Z _L : Load impedance of open circuit coupling line
Z _EQ1, Z _EQ2 Port impedances
Z _E : Even-mode impedance of open circuit coupling line
Z _O : odd-mode impedance of open circuit coupling line
θ: electrical length of two consecutive transmission lines
R: isolation resistor

Claims (9)

Board; And
An input port having an input port 1 for receiving power; an output port having port 2 and port 3; Port 2 and port 4 are open and connected to each of ports 1, 2 and 3, and as an open-circuited coupled line having a gap between the first transmission line and the second transmission line in parallel. A coupled transmission line Z ₁ having an input / output impedance matched thereto; And Z ₂ and Z _{3, each} of which is connected to the coupled transmission line (Z ₁ ), and converts 1 power applied to the input port 1 into 1/2 power of the output port port 2 and port 3. And a power divider (PD) that includes;
It further comprises an isolation resistor (R) between the output port port 2, port 3, respectively,
Wherein the power divider uses only one via hole between each isolation resistor (R) without additional lumped elements. delete The method of claim 1,
Wherein the first transmission line and the second transmission line use a coupled microstrip line. The method of claim 1,
The power divider (PD) is provided with a transmission line (coupled-line) and an output port (port 2,3) coupled with the input port (port 1), the combined line based circuit is a terminal with a load impedance Z _L Power divider with enhanced port 3, improved selectivity. The method of claim 1,
Wherein said substrate uses a Teflon substrate. The method of claim 1,
The prototype of the power divider (PD) is made of Z ₁ = 70.7Ω, Z ₂ = 50Ω, Z = 35.3Ω, Z _E = 72Ω, Z _O = 172Ω, isolation resistance (R) = 50Ω, A power divider having improved selectivity characteristics fabricated on a Teflon substrate having a relative dielectric constant ε r = 2.54, 0.002 dielectric loss tangent value, T = 0.54 mm thickness, and h = 0.018 mm conductor height. The method of claim 1,
The ABCD matrix is used to derive the impedance matrix of the open circuit coupling line, the ABCD matrix of the equivalent circuit is obtained by equation (1),

Formula (1)
Where Z is the characteristic impedance, and Z _E and Z _O are the even-mode impedance and the odd-mode impedance of the open-circuited coupled line, respectively. impedance, and two series transmission lines are represented by electrical length θ,
In the ABCD matrix, the admittance inverter J can be replaced by equations (2) and (3),

, Equation (2)

, Equation (3)
Substituting Equation 2 and Equation 3 into Equation 1 and using the conversion relation between the impedance matrix and the ABCD matrix, the impedance matrix of the open circuit coupling line is derived as Equation (4),

, Equation (4)
In the structure having port 3 terminated with the load impedance Z _L of the open circuit coupling line, according to the relationship of voltage and current at port 1, the input impedance Z _IN looking at the load impedance Z _L of the coupling line based circuit is Calculated as

, Equation (5)
When θ = 90 °, the input impedance Z _IN of the combined line based circuit is

A power divider with improved selectivity, calculated as Equation (6). The method of claim 1,
All port impedances of the power divider are equivalent impedances seen from a coupled line connecting the input / output port or core part, and are Z _IN, Z ₀ and Z _EQ1, Z _EQ2 , respectively.
For the conventional Gysel PD, all electrical lengths are equal to λ / 4, so θ ₁ , θ ₂ and θ ₃ should be equal to 90 °, and the parameters of the transmission lines and resistors in the core part can be obtained as ,

, Equation (7)

, Equation (8)

, Equation (9)
Where Z ₁ , Z ₂ and Z ₃ are the respective characteristic impedances of the transmission lines of a traditional Gysel PD,
Simulation of the core part was performed to obtain the equivalent impedance of Z _EQ1 and Z _EQ2 ,

Formula (10)
Z _IN is for impedance matching

and

Since Equations 6 and 8 must be equal, the impedance matched condition is

A power divider with improved selectivity, expressed as in equation (11). The method of claim 1,
The power divider has a passband of 2.1 to 3.1 GHz at a center frequency of 2.5 GHz and an insertion loss, return loss and isolation of 23.61, 220.2, and 219.3 dB, respectively. A power divider with improved selectivity characteristics.

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