KR101687004B1 - Compact marchand balun using metamaterial - Google Patents

Compact marchand balun using metamaterial Download PDF

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KR101687004B1
KR101687004B1 KR1020150050936A KR20150050936A KR101687004B1 KR 101687004 B1 KR101687004 B1 KR 101687004B1 KR 1020150050936 A KR1020150050936 A KR 1020150050936A KR 20150050936 A KR20150050936 A KR 20150050936A KR 101687004 B1 KR101687004 B1 KR 101687004B1
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transmission line
crlh
signal
twenty
line
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KR1020150050936A
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KR20160121222A (en
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박정근
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주식회사 한국피엠그룹
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    • HELECTRICITY
    • H01ELECTRIC ELEMENTS
    • H01PWAVEGUIDES; RESONATORS, LINES, OR OTHER DEVICES OF THE WAVEGUIDE TYPE
    • H01P5/00Coupling devices of the waveguide type
    • H01P5/08Coupling devices of the waveguide type for linking dissimilar lines or devices
    • H01P5/10Coupling devices of the waveguide type for linking dissimilar lines or devices for coupling balanced lines or devices with unbalanced lines or devices

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Abstract

It reveals the miniature Machan de Balun using metamaterial. In the present invention, a balun is designed using a CRLH transmission line, which is a metamaterial, to reduce the size of a Mach-Bund de Balun, thereby reducing the length of the designed CRLH transmission line and reducing the length of the CRLH transmission line. And the phase change is compensated by adding a capacitor, so that it can be reduced to a second order of Machan de Balun. Thus greatly reducing the overall size of the Machan de Balun.

Description

[0001] COMPACT MARCHAND BALUN USING METAMATERIAL [0002]

The present invention relates to a Machan de Valen, and more particularly to a micro Mach Bund de Balun using a CRLH transmission line as a meta material.

Balun (Balanced to Unbalan) is a balanced transmission line that can be transmitted through a balanced transmission line (Balanced transmission line) Unbalance transmission line circuit (Unbalance transmission line) can be converted to an unbalanced signal, Signal to the RF passive element. That is, an interface between the balanced transmission circuit and the unbalanced transmission circuit, and in some cases, may be designed to perform an impedance conversion function between the two circuits. Currently, baluns are widely used in wireless communication system circuits such as antenna and frequency mixers, high power amplifiers and the like.

The balun was originally released as a way of connecting a balanced two-wire line to a single coaxial cable by Marchand, and then developed into various forms. However, although various baluns have been developed, the Machan de Balun is still being used because of its broadband characteristics and its planar structure.

Figure 1 shows a Machan de Balun as an example of a conventional balun.

Referring to FIG. 1, a Machan de Balun may be implemented using a Planar Transmission Line such as a Microstrip. The Mach-channel de-balun is connected to the first transmission line (T1) and the first transmission line (T1) through which the unbalanced signal is input as a transmission signal and the other end is opened. The pair of balanced signals And second and third transmission lines (T2, T3) for outputting the output signal.

The first and second transmission lines T1 and T2 have a length of 1/2 of the transmission signal wavelength λ and the second and third transmission lines T2 and T3 are 1/2 of the length of the first transmission line T1, Has a length of 1/4 of the transmission signal wavelength (?).

As shown in FIG. 1, the Mach-band de-balun may be implemented as a coupled line. When one unbalanced signal is applied to the first transmission line T1, the second and third transmission lines T2, and T3 output two balanced signals having the same power and 180 degree phase difference by coupling.

However, since the first transmission line T1 has a half wavelength (lambda / 2) length of the transmission signal, the Mach-bin de-balun basically needs a size larger than half a wavelength (lambda / 2) of the transmission signal. Therefore, Machong de Baloon has a limitation that it is not easy to apply to the current mobile communication system which is becoming smaller.

Korean Registered Patent No. 10-1451360 (Registered on October 10, 2014)

It is an object of the present invention to provide an ultra small Mach number de balun which uses a meta material and greatly reduces its size.

According to an aspect of the present invention, there is provided a first CRLH transmission line for receiving an unbalanced signal and outputting a first balanced signal corresponding to the unbalanced signal. And a second CRLH transmission line receiving the unbalanced signal applied through the first CRLH transmission line and outputting a second balanced signal having a phase inverted from the first balanced signal; Wherein the first and second CRLH transmission lines each include two transmission lines and an impedance compensation capacitor connected in parallel with one transmission line of the two transmission lines so as to include an inductance and a capacitance connected in series with each other And a parallel line connected in parallel with the series line. The parallel line includes an inductance and a capacitance connected in parallel to each other.

The impedance compensation capacitor has a capacitance corresponding to a change in impedance caused by a decrease in length of the two transmission lines designed in advance to a pattern capable of implementing the equivalent circuit using a pattern of a CRLH transmission line as a meta material do.

And the lengths of the two transmission lines are shortened by a length corresponding to a changeable impedance change by adjusting a capacitance of the impedance compensation capacitor in the designed pattern.

An eleventh transmission line receiving the unbalance signal as one end of the first CRLH transmission line; A twelfth transmission line forming a CRLH transmission line together with the eleventh transmission line, one end of the twelfth transmission line being connected to a ground power source and outputting the first balance signal to the other end; A first impedance compensation capacitor connected in parallel to the other end of the twelfth transmission line for compensating impedance so that the first balance signal has a power and a phase corresponding to the unbalanced signal; And a control unit.

A twenty-first transmission line receiving the unbalanced signal output from the other end of the eleventh transmission line as one end; A twenty-second transmission line forming a CRLH transmission line together with the twenty-first transmission line, one end of the twenty-second transmission line being connected to the ground power source, and outputting the second balance signal to the other end; And a second impedance compensation capacitor connected in parallel to the other end of the twenty second transmission line for compensating impedance so that the second balanced signal has a power and a phase corresponding to the unbalanced signal. And a control unit.

The second CRLH transmission line is serially connected between the other terminal of the twenty-first transmission line and the grounding power supply, and compensates the second balanced signal to have a phase difference of 180 degrees with the first balanced signal; And further comprising:

The eleventh, twelfth, twenty first, twenty-second, and twenty-second transmission lines are microstrip lines formed in a predetermined pattern on one surface of a substrate.

The ground power source is formed on the other surface of the substrate, and the first and second CRLH transmission lines are connected to the ground power source via vias.

Therefore, it is possible to design a balun by using a CRLH transmission line as a meta material and to reduce the size of the Mach-Bund de Balun, to reduce the length of the designed CRLH transmission line, The impedance change caused by the reduction of the length of the capacitor is compensated by adding a capacitor, thereby greatly reducing the size of the Machan de Balun. Therefore, micro-sized wireless devices such as mobile communication terminals can be easily applied by the Machan de Balun.

Figure 1 shows a Machan de Balun as an example of a conventional balun.
2 shows an example of a conventional CRLH transmission line.
FIG. 3 shows a micro-Mach number de balun using CRLH according to an embodiment of the present invention.
Fig. 4 shows an actual design circuit for the Machan de Balun of the present invention shown in Fig.
Figures 5 and 6 show S-parameter simulation results for the design circuit of Figure 4, respectively.

In order to fully understand the present invention, operational advantages of the present invention, and objects achieved by the practice of the present invention, reference should be made to the accompanying drawings and the accompanying drawings which illustrate preferred embodiments of the present invention.

Hereinafter, the present invention will be described in detail with reference to the preferred embodiments of the present invention with reference to the accompanying drawings. However, the present invention can be implemented in various different forms, and is not limited to the embodiments described. In order to clearly describe the present invention, parts that are not related to the description are omitted, and the same reference numerals in the drawings denote the same members.

Throughout the specification, when an element is referred to as "including" an element, it does not exclude other elements unless specifically stated to the contrary. The terms "part", "unit", "module", "block", and the like described in the specification mean units for processing at least one function or operation, And a combination of software.

2 shows an example of a conventional CRLH transmission line.

Fig. 2 (a) shows an equivalent circuit to a CRLH transmission line, and Fig. 2 (b) shows an actual implementation pattern example of a CRLH designed in a pattern.

Recently, studies on a meta-material having a negative dielectric constant and a negative conductivity have been actively conducted, and microwave devices using the same have been developed.

Metals or LHM (Left-Handed Material) began to be studied by Russian physicist Velselago in 1967. Since the permittivity and permeability are negative, the phase and group velocity are opposite to each other, And exhibits peculiar electromagnetic characteristics such as transmission direction and negative transmission coefficient.

The electromagnetic characteristics of the LHM can be realized through artificial structural design and generally consist of a unit cell type structure. The unit cell of the LHM must have an electrical size of 1/4 or less of the transmission signal wavelength (λ), and the application of the microwave device of the LHM is a combination of a series capacitance and a parallel inductance when the transmission line is equivalent to a lossless transmission line model .

However, since the ideal LHM transmission line can not exist due to the current and voltage induced by electromagnetic wave propagation, the RH characteristics can be equated to a combined CRLH transmission line (Composite Right / Left Handed Transmission Line). When such a CRLH transmission line is applied to a microwave device, it can be applied to the design of a wide band, a miniaturization, and a dual band.

a left-handed (LH) transmission line having a high-pass characteristic and a serial inductor L R are formed by forming a series capacitor C L and a parallel inductor L L as a CRLH transmission line, And a right-handed (RH) transmission line having a low-pass characteristic by forming a parallel capacitor (C R ). Here, the LH transmission line generates a phase lead of the signal, and the RH transmission line generates a phase delay of the signal.

Therefore, when the resonant frequency to the RH transmission line and the resonant frequency to the LH transmission line satisfy the balanced condition, the 0th order resonance occurs in which the frequency exists but the phase and the propagation constant become 0, Zeroth Order Resonance (ZOR) phenomenon occurs

In this case, since the resonance condition is made independently of the transmission line length, the length of the CRLH transmission line is less than 1/4 of the transmission signal wavelength (?). That is, the length of the transmission line for inducing resonance can be greatly reduced. Therefore, when a Mach-Zehnder balun is implemented using a CRLH transmission line, the size of the Mach-val dehalon can be reduced to less than half of the Machan de balun shown in Fig. 1 having a half length of the transmission signal wavelength ([lambda]).

(b) shows an example of a CRLH transmission line in which the equivalent circuit of (a) is embodied as a microstrip line on a substrate. The pattern form of the CRLH transmission line is not limited to FIG. 2 (b) Research is underway.

FIG. 3 shows a micro-Mach number de balun using CRLH according to an embodiment of the present invention.

3 has a first CRLH transmission line CRLH1 and a second CRLH transmission line CRLH2, which are implemented in a meta-material structure other than the conventional transmission line, unlike the Machong de Balun of FIG.

The first CRLH transmission line CRLH1 includes an eleventh transmission line TL11 and a twelfth transmission line TL12 and a twelfth transmission line TL12 in which the pattern is designed to correspond to the CRLH equivalent circuit shown in FIG. And a first impedance compensation capacitor (CC1) connected in parallel with the first impedance compensation capacitor (TL2).

An unbalanced signal IN, which is a transmission signal, is input to one end of the eleventh transmission line TL11. One end of the twelfth transmission line TL12 is connected to the ground power supply, and the other end of the twelfth transmission line TL12 outputs the first balanced signal OUT1 having a phase and power corresponding to the unbalanced signal IN. The first impedance compensation capacitor CC1 has one end connected to the other end of the twelfth transmission line TL12 and the other end connected to the ground power source.

The second CRLH transmission line CRLH2 includes a twenty-first transmission line TL21 and a twenty-second transmission line TL22 in which the pattern is designed to correspond to a CRLH equivalent circuit as in the first CRLH transmission line CRLH1, And a second impedance compensation capacitor CC2 connected in parallel with the second transistor TL22.

One end of the twenty first transmission line TL21 is electrically connected to the other end of the eleventh transmission line TL11 and the unbalanced signal IN transmitted from the eleventh transmission line TL11 is input. One end of the twenty second transmission line TL22 is connected to the ground power supply, and the other end of the twenty second transmission line TL22 outputs the second balance signal OUT2. At this time, the second balance signal OUT2 has the same power as the first balance signal OUT1 and is output as a signal having a phase difference of 180 degrees. The second impedance compensation capacitor CC2 has one end connected to the other end of the twenty second transmission line TL22 and the other end connected to the ground power source.

However, unlike the first CRLH transmission line CRLH1, the second CRLH transmission line CRLH2 has a phase compensation capacitor CP connected at one end to the other end of the twenty-first transmission line TL21 and at the other end to a ground power source Respectively.

3, all the transmission lines including the first and second CRLH transmission lines CRLH1 and CRLH2 are connected to a single plane transmission line such as a microstrip line or the like on one surface of the dielectric substrate, (Uniplanar Transmission Line), and is connected to a ground power source formed on the other side of the substrate through a via via a high strength coupling structure. The three capacitors CC1, CC2, and CP may be implemented by using a capacitor implemented as a lumped element according to the frequency of a transmission signal, or by a pattern of a single plane transmission line.

The eleventh transmission line TL11 and the twenty-first transmission line TL21 of the first and second CRLH transmission lines CRLH1 and CRLH2 in the Mach-Zon de Balun of the present invention shown in Fig. 1 transmission line T1 and the twelfth transmission line TL12 and the twenty second transmission line TL22 correspond to the second and third transmission lines T2 and T3 of the Mach- .

The pair of transmission lines (TL11, TL12, TL21, TL22) in the first and second CRLH transmission lines CRLH1 and CRLH2 can be designed in various patterns by the existing CRLH study, (TL11, TL12, TL21, TL22) in each of the first and second CRLH transmission lines (CRLH1, CRLH2) in the present invention, ) Are not specified in a specific single pattern.

If the Mach-Zehnder balun is simply implemented using CRLH, the first and second impedance compensation capacitors CC1 and CC2 and the phase compensation capacitor CP may not be provided. It is possible to realize a Machan de Balun with only four transmission lines (TL11, TL12, TL21, TL22) without the first and second impedance compensation capacitors CC1, CC2 and the phase compensation capacitor CP have.

In this case, the length of the Mach-bin de-balun is designed to be not more than 1/4 of the transmission signal wavelength lambda according to the length of each of the four transmission lines (TL11, TL12, TL21, TL22) .

However, in the present invention, three capacitors (CC1, CC2, and CP) are added to realize a miniature Mach-band de-balun that further reduces the size of a Mach-band de-balun.

The patterns of the four transmission lines (TL11, TL12, TL21 and TL22) are designed so as to correspond to the CRLH equivalent circuits and then the transmission lines (TL11, TL12, TL21 and TL22) (B) of the size of the pattern, that is, the transmission lines (TL11, TL12), (TL21, TL22). When the length b of the transmission lines TL11, TL12, TL21 and TL22 is reduced, the inductance of each of the transmission lines TL11, TL12, TL21 and TL22 and the transmission line (TL11, TL12), (TL21, TL22)) are variable. That is, the impedances of the first and second CRLH transmission lines CRLH1 and CRLH2 are varied.

When the impedances of the first and second CRLH transmission lines CRLH1 and CRLH2 are changed, a change occurs in the phases of the unbalanced signal IN as a transmission signal and the first and second balanced signals OUT1 and OUT2 as output signals So that the balun can not output the two balance signals OUT1 and OUT2 corresponding to the unbalanced signal IN.

It is necessary to compensate the impedances of the first and second CRLH transmission lines CRLH1 and CRLH2 whose lengths b of the transmission lines TL11, TL12, TL21 and TL22 are reduced. The first and second impedance compensation capacitors CC1 and CC2 are connected in parallel to the output terminals of the twelfth transmission line TL12 and the twenty second transmission line TL22 for outputting the balance signals OUT1 and OUT2, Thereby compensating for the impedance of the changed first and second CRLH transmission lines CRLH1 and CRLH2.

The equivalent circuit shown on the right side in FIG. 3 is an equivalent circuit of each of the first CRLH transmission line CRLH1 and the second CRLH transmission line CRLH2. Assuming that the right equivalent circuit is the equivalent circuit of the first CRLH transmission line CRLH1, the serial capacitance C L in the equivalent circuit represents the capacitance between the eleventh and twelfth transmission lines TL11 and TL12 And the series inductance L R represents the inductance of the eleventh and twelfth transmission lines TL11 and TL12.

And the parallel capacitance C R represents all the capacitances on the transmission line including the capacitance of the first impedance compensation capacitor CC 1 and the parallel inductance L L represents the transmission line between the twelfth transmission line TL 12 and the ground power supply, Indicates inductance by vias.

As a result, even if the length (b) of the eleventh and twelfth transmission lines TL11 and TL12 is shortened in the first CRLH transmission line CRLH1, the impedance of the first impedance compensation capacitor CC1 When the capacitance is adjusted and compensated, the same equivalent circuit as the equivalent circuit of the CRLH transmission line shown in FIG. 2 can be implemented.

This is also applicable to the second CRLH transmission line (CRLH2). As a result, the size of the Mach-Bund de Balun can be further reduced as compared with the case of simply implementing the CRLH transmission line.

The lengths of the transmission lines (TL11, TL12, TL21, TL22) ((CRL1, CRL2)) are calculated by using the first and second impedance compensation capacitors CC1, CC2 in the first and second CRLH transmission lines the phase difference between the first and second balanced signals OUT1 and OUT2 output from the first and second CRLH transmission lines CRLH1 and CRLH2 is not 180 degrees even though the variation of the impedance caused by the reduction of the first and second CRLH transmission lines CRLH1 and CRLH2 is compensated . If the phase difference between the first and second balance signals OUT1 and OUT2 is not 180 degrees, it means that the function of the balun that receives the unbalance signal IN and outputs the balance signals OUT1 and OUT2 is not normally performed Therefore, the circuit can not operate normally after receiving the balance signals OUT1 and OUT2. Therefore, it is necessary to correct the phase difference between the balanced signals OUT1 and OUT2 to 180 degrees.

In the present invention, the phase compensation capacitor CP performs phase compensation so that the phase difference between the two balanced signals OUT1 and OUT2 is maintained at 180 degrees.

Fig. 4 shows the actual design circuit for the Machan de Balun of the present invention shown in Fig. 3, and Figs. 5 and 6 show S-parameter simulation results for the design circuit of Fig. 4, respectively.

As described above, according to the present invention, a balun is designed using a CRLH transmission line, which is a meta-material, to reduce the size of a Mach-Bund de Balun, to reduce the length of a designed CRLH transmission line, It compensates by adding capacitors to the impedance change and phase change that occur when the length is reduced, so that it can be reduced to the second order of the Machan de Balun. Thus greatly reducing the overall size of the Machan de Balun.

As shown in FIG. 4, the circuit for measuring the S parameter is designed in the Machan de Balun of the present invention, so that the existing Machan de Balun shown in FIG. 1 converts the unbalanced transmission signal of 2.7 GHz to a balanced signal The size of the Machan de Balun is 42.8 mm in length and 2.16 mm in length depending on the length of the first transmission line T 1. On the other hand, the micro-machined de-balun proposed in the present invention has a transmission line (TL 11, TL 12 ), (TL21, TL22)) was reduced to 5.5 mm and the length was designed to be 2.21 mm.

At this time, it is assumed that both the impedance of the input terminal and the impedance of the output terminal are set to 50 ?.

As a result, it has been confirmed that the Mach-bin de-balun of the present invention can be implemented with a 22-degree phase length in comparison with a conventional Mach-bin de-balun having a length of? / 2 of 180 占 phase length, . Also, it can be seen that this is implemented simply as a CRLH transmission line, and is greatly reduced as compared with the case of implementing a size of less than / 4 (90 DEG phase length).

5A shows a result of simulating the S21 parameter (the first balance signal OUT1 characteristic for the unbalanced signal IN) among the S parameters for the circuit of FIG. 4, and FIG. 5B shows the S31 parameter And a second balance signal (OUT2) characteristic with respect to the signal IN).

FIG. 6 is a result of simulating the phase response difference between the S21 parameter and the S31 parameter, and it can be confirmed that the phase difference of 180 degrees is accurately maintained.

As a result, the Mach-Zonal balun of the present invention can be significantly reduced in size compared to the existing Mach-bin de-balun, and can be easily utilized in small-sized wireless communication devices.

The method according to the present invention can be implemented as a computer-readable code on a computer-readable recording medium. A computer-readable recording medium includes all kinds of recording apparatuses in which data that can be read by a computer system is stored. Examples of the recording medium include a ROM, a RAM, a CD-ROM, a magnetic tape, a floppy disk, an optical data storage device, and the like, and a carrier wave (for example, transmission via the Internet). The computer-readable recording medium may also be distributed over a networked computer system so that computer readable code can be stored and executed in a distributed manner.

While the present invention has been particularly shown and described with reference to exemplary embodiments thereof, it is evident that many alternatives, modifications and variations will be apparent to those skilled in the art.

Accordingly, the true scope of the present invention should be determined by the technical idea of the appended claims.

Claims (8)

A first CRLH transmission line receiving an unbalanced signal and outputting a first balanced signal corresponding to the unbalanced signal; And
A second CRLH transmission line receiving the unbalanced signal applied through the first CRLH transmission line and outputting a second balanced signal having a phase inverted from the first balanced signal; Lt; / RTI >
Wherein the first and second CRLH transmission lines each include two transmission lines and an impedance compensation capacitor connected in parallel with one transmission line of the two transmission lines and including a series line and an inductance and capacitance connected in series, And a parasitic line connected in parallel to the series line, the parasitic line including an inductance and a capacitance connected in parallel to each other.
2. The apparatus of claim 1, wherein the impedance compensation capacitor
And a capacitance corresponding to a change in impedance caused by a decrease in the length of the two transmission lines designed in advance so as to realize the equivalent circuit using a pattern of a CRLH transmission line as a meta material.
The method of claim 2, wherein the lengths of the two transmission lines are
Wherein the capacitance of the impedance compensation capacitor is set to be shorter by a length corresponding to a compensatable impedance change by adjusting a capacitance of the impedance compensation capacitor in the designed pattern.
4. The apparatus of claim 3, wherein the first CRLH transmission line
An eleventh transmission line to receive the unbalanced signal as one end;
A twelfth transmission line forming a CRLH transmission line together with the eleventh transmission line, one end of the twelfth transmission line being connected to a ground power source and outputting the first balance signal to the other end; And
A first impedance compensation capacitor connected in parallel to the other end of the twelfth transmission line to compensate the impedance so that the first balance signal has a power and a phase corresponding to the unbalanced signal; Wherein said at least one of said at least two of said at least one of said at least one of said at least one of said at least two players.
5. The apparatus of claim 4, wherein the second CRLH transmission line
A twenty-first transmission line receiving the unbalance signal output from the other end of the eleventh transmission line;
A twenty-second transmission line forming a CRLH transmission line together with the twenty-first transmission line, one end of the twenty-second transmission line being connected to the ground power source, and outputting the second balance signal to the other end; And
A second impedance compensation capacitor connected in parallel to the other end of the twenty second transmission line to compensate the impedance so that the second balanced signal has a power and a phase corresponding to the unbalanced signal; Wherein said at least one of said at least two of said at least one of said at least one of said at least one of said at least two players.
6. The method of claim 5, wherein the second CRLH transmission line
A phase compensation capacitor connected in series between the other terminal of the twenty-first transmission line and the ground power source and compensating the second balance signal to have a phase difference of 180 degrees from the first balance signal; Further comprising: a machan de balun.
The method of claim 6, wherein the eleventh, twelfth, twenty first, and twenty second transmission lines
Wherein the microstrip line is a microstrip line formed on a surface of the substrate in a predetermined pattern.
8. A method as claimed in claim 7,
Wherein the first and second CRLH transmission lines are connected to the ground power source via vias.
KR1020150050936A 2015-04-10 2015-04-10 Compact marchand balun using metamaterial KR101687004B1 (en)

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Citations (3)

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Publication number Priority date Publication date Assignee Title
KR100770134B1 (en) 2006-06-12 2007-10-24 이종철 A marchand balun use a improved vertical-coupled line to have tight coupling characteristic
JP2011101341A (en) 2009-11-03 2011-05-19 Korea Electronics Telecommun Marchand balun device for forming parallel and vertical capacitance
JP2014204381A (en) 2013-04-09 2014-10-27 日本電信電話株式会社 Merchant balun

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
KR101451360B1 (en) 2013-08-30 2014-10-15 금오공과대학교 산학협력단 Broadband filter of using parallel structure CRLH transmission line

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
KR100770134B1 (en) 2006-06-12 2007-10-24 이종철 A marchand balun use a improved vertical-coupled line to have tight coupling characteristic
JP2011101341A (en) 2009-11-03 2011-05-19 Korea Electronics Telecommun Marchand balun device for forming parallel and vertical capacitance
JP2014204381A (en) 2013-04-09 2014-10-27 日本電信電話株式会社 Merchant balun

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
문병택 외 2인, "CRLH전송선을 이용한 Marchand 발룬의 소형 격리회로 설계", The Journal of Korean Institute of Electromagnetic Engineering and Science, 2012년 9월.

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