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Double-Y baluns for MMICs and wireless applications.

Balun circuits find wide application in a variety of important microwave components such as balanced mixers, push-pull amplifiers, multipliers, antennas and other applications requiring conversion between an unbalanced transmission line, such as coaxial line, microstrip, CPW or [CPW.sub.FGP], and a balanced line, such as two-wire transmission line, slotline, CPS or parallel microstrip. In recent years, the wideband MMIC balun has been a hot topic because it is a crucial element in high performance transceivers. The performance of the balun often predominantly determines the performance of the overall circuit. In the design of wideband baluns, difficulties are encountered because the baluns' physical dimensions are too large to fit into the MMIC chip. A similar problem occurs in new wireless systems operating in the 1 to 2 GHz range, where the physical dimensions of the baluns are too large due to the low frequency range. A multi-dielectric-layer Marchand balun(1) requires special processes, although the results generally are good. Coplanar waveguides, slotlines and coplanar strips have been combined to realize a balun in a single-planar configuration, but the geometry was still too large.(2)

Double-Y baluns offer a completely different solution for wideband and small-size baluns compared to various versions of Marchand baluns modified to fit into the MMIC chip. Double-Y baluns are based on a six-port double-Y junction that consists of three balanced and three unbalanced transmission lines placed alternately around the center of the junction. To create a structure that operates as a balun with perfect transmission between opposite balanced and unbalanced ports, an opposed pair of transmission lines must possess reflection coefficients with opposite phases, that is, one pair of lines should be short circuited and the other pair should be open circuited. The electrical length of the lines from the junction to the short or open circuits should be equal. Double-Y baluns approach the upper edge of their bandwidth limitation when the electrical length of that distance becomes [Lambda]/8.

Four different realizations of double-Y baluns are shown in Figure 1: microstrip-to-slotline,(3) CPW-to-slotline,(4) [CPW.sub.FGP]-to-CPS(5) and [CPW.sub.FGP]-to-parallel microstrip baluns.(6) According to the equivalent circuit,(5) double-Y baluns are symmetrical lattice networks with equal characteristic impedances of the balanced and unbalanced lines. The baluns belong to a special class of lattice networks known as constant-resistance networks due to the reciprocal normalized impedances of the open- and short-circuited lines. Constant-resistance networks exhibit a constant input impedance over their entire frequency range.

In contrast to theory, practical realizations of micro-strip-to-slotline and CPW-to-slotline baluns do not demonstrate characteristics of an all-pass network. The main reason for the limited frequency bandwidth of these baluns is the circular slotline, which is a good open circuit only over two to three octaves. As a result of the almost ideal open- and short-circuited stubs realized by low dispersion [CPW.sub.FGP] and CPS lines, [CPW.sub.FGP]-to-CPS and [CPW.sub.FGP]-to-parallel microstrip baluns have an impressive bandwidth of a few decades.

Double-Y baluns are simple to design, and good first-pass results can be obtained following a few instructions. In this article, the physical dimensions of all realized baluns are provided, as well as the measured transmission loss and SWR for a structure consisting of two back-to-back baluns. Losses are calculated using measured [S.sub.11] and [S.sub.21] parameters as 1 - [absolute value of [S.sub.11]] - [absolute value of [S.sub.21]] .The realized double-Y baluns are compared with respect to bandwidth, losses and parasitic resonances. In addition, a theoretical analysis based on circuit theory, which includes the different characteristic impedances of the balanced and unbalanced transmission lines and their influence on the overall characteristics of the baluns, is discussed. Note that all the presented baluns provide a transition from 50 [ohms] unbalanced to 50 [ohms] balanced lines, unlike Marchand baluns, which operate both as baluns and impedance transformers.

This article demonstrates the simple design of a uniplanar double-balanced mixer in a ring configuration and two star mixers in which [CPW.sub.FGP]-to-CPS and [CPW.sub.FGP]-to-parallel microstrip baluns are applied. All the realized mixers show good conversion loss and isolation in the predicted frequency range without any complicated calculations and additional trimming.

THE EQUIVALENT CIRCUIT

The equivalent circuit of a double-Y balun neglecting the junction effects is shown in Figure 2. In general, this circuit is identical for all the double-Y baluns shown previously. The air bridge positions are denoted as a-a, c-c and d-d. Impedances [Z.sub.bal] and [Z.sub.unbal] are the characteristic impedances of the balanced and unbalanced lines forming the balun, respectively. Electrical lengths [Theta] of the open- and short-circuited stubs are supposed to be equal. Since the main goal in designing double-Y baluns is to provide a transition between balanced and unbalanced transmission lines without an impedance transformation, the first case analyzed is when [Z.sub.bal] = [Z.sub.unbal] = [Z.sub.0], that is, when the equivalent circuit of the double-Y baluns is a symmetrical lattice network with Z-parameters

[Z.sub.11] = [Z.sub.22]

= 1/2([Z.sub.a] + [Z.sub.b])

[Z.sub.12] = 1/2([Z.sub.b] - [Z.sub.a])

[Z.sub.a] = j[Z.sub.0] tan [Theta]

[Z.sub.b] = - j[Z.sub.0] cot [Theta] (1)

Due to the reciprocal normalized impedances [Z.sub.a]/[Z.sub.0] and [Z.sub.b]/[Z.sub.0] (-jcot[Theta] * jtan[Theta] = 1), this type of symmetrical lattice network is known as a constant-resistance network.(7) When terminated with a characteristic impedance [Z.sub.0], this lattice has an input impedance that is a pure resistance equal to [Z.sub.0].

Using Bartlett's bisection theorem, which provides the equivalence relations between the impedances of a symmetrical lattice and any other form of physically and electrically symmetrical structures into which the lattice may be transformed, the conversion of the lattice to symmetrical T and [Pi] networks is shown in Figure 3. Both transformations are helpful when commercial software packages are used. For the T network,

[Z.sub.1] = [Z.sub.a]

= j[Z.sub.0]tan [Theta]

[Z.sub.2] = 1/2([Z.sub.b] - [Z.sub.z]) = -j[Z.sub.0]/sin2[Theta] (2)

Analogously (on an admittance basis), the transformation for the [Pi] network is expressed as

[Y.sub.2] = [Y.sub.b]

= j[Y.sub.0] tan [Theta]

[Y.sub.1] = 1/2([Y.sub.a] - [Y.sub.b])

= - j[Y.sub.0]/sin 2[Theta] (3)

Bartlett's bisection theorem also is applied to the structure of two back-to-back baluns, as shown in Figure 4. The structure is analyzed as a symmetrical lattice network with serial impedance [[Z.sup.*].sub.a] and parallel impedance [[Z.sup.*].sub.b] as

[[Z.sup.*].sub.a] = j[Z.sub.0] cot 2[Theta] + j[Z.sub.0] cos [Phi]/sin 2[Theta] cos (2[Theta] + [Phi]) (4)

[[Z.sup.*].sub.b] = -j[Z.sub.0] cot 2[Theta] + j[Z.sub.0] sin [Phi]/sin 2[Theta] sin (2[Theta] + [Phi]) (5)

where

2[Phi] = electrical length of the distance between the centers of the two baluns

This structure also is a constant-resistance network.

In the practical realization of double-Y baluns, it is difficult to achieve equal characteristic impedances of the balanced and unbalanced lines by maintaining equal cross sections of the lines to provide the symmetry of a double-Y junction. Using the equivalent circuit of two back-to-back baluns, a slight difference that occurs between impedances [Z.sub.bal] and [Z.sub.unbal] (k = [Z.sub.bal]/[Z.sub.unbal]) has been analyzed. In addition, the influence of different lengths of open- and short-circuited stubs [L.sub.s] on the characteristics of the network has been analyzed. The calculated transfer characteristics [S.sub.21] (dB) and SWR are shown in Figure 5 for three different stub lengths ([L.sub.s] = 2.4, 4.6 and 6.2 mm), where k = 1.1 and L = 13.6 mm (distance between the baluns). In both characteristics, sharp peaks appear at 15.6, 8.2 and 6, and 18 GHz, respectively, when [L.sub.s] becomes an odd multiple of [Lambda]/8. These peaks are inherent to the structure of the double-Y balun and determine the upper edge of its bandwidth. The peaks can be shifted toward higher frequencies by reducing the lengths of the stubs, as shown previously.

If impedances [Z.sub.bal] and [Z.sub.unbal] differ from each other considerably, in addition to sharp peaks in the baluns' transfer characteristics, some shallow peaks appear at certain frequencies depending on the distance L. The calculated [S.sub.21] (dB) and SWR are shown in Figure 6 for k = 2.0, 1.4 and 0.4; [L.sub.s] = 4.6 mm; and L = 13.6 mm. The results suggest that, for a good balun, impedances [Z.sub.bal] and [Z.sub.unbal] should be kept within the range of k = 0.8 to 1.2 to prevent additional peaks.

DOUBLE-Y BALUN CHARACTERISTICS

The measured characteristics of double-Y baluns are presented and compared as well as the physical dimensions of all realized circuits. The test devices consist of two baluns connected back to back and two input coaxial connectors. The insertion loss of a single balun is determined as half of the measured value in decibels and the single-balun SWR is considered to be the square root of the measured SWR.

The Microstrip-to-slotline Balun

The microstrip-to-slotline balun is the first in the family of double-Y baluns, and was published in 1976. Surprisingly, this balun, shown in Figure 7, did not find wide usage in MICs although it demonstrated good electrical characteristics. The balun's measured back-to-back characteristics are shown in Figure 8. The balun is realized as a double-sided structure on an Epsilam 10 substrate with a thickness of 0.635 mm and [[Epsilon].sub.r] = 10.2. The short circuit on the microstrip side is provided by a plated-through hole and the open circuit on the slot side is realized using a circular slotline.

Insertion loss for the single balun is less than 0.5 dB in the 2.5 to 9.5 GHz range. Insertion loss increases considerably above 10 GHz due to the electrical length of [L.sub.s], which becomes [Lambda]/8 at that frequency. In addition, the circular slotline is a good open circuit over two to three octaves and, with a diameter of 6 mm, has an upper frequency limit of approximately 10 GHz.

The CPW-to-slotline Balun

The CPW-to-slotline double-Y balun is proposed as a uniplanar equivalent of a microstrip-to-slotline balun and, therefore, is easier to realize. The microstrip line is replaced by a CPW line and placed on the slot side of the substrate. Three air bridges, which are essential for balun operation, are connected with three CPW lines near the double-Y junction. To minimize transverse dimensions of the junction, the CPW's physical dimensions are changed (strip width of 0.25 mm and gap width of 0.1 mm) through the linear transition without changing the characteristic impedance. The magnitude of ripples in the balun's transfer characteristic depends on the length of the linear CPW taper.(4) Lower ripples were obtained with a longer taper.

The construction and measured back-to-back characteristics of two different baluns are shown in Figures 9 and 10, respectively. The baluns differ from each other in length [L.sub.s] and diameter D of the circular slotline and are realized on substrates with a 0.635 thickness and [[Epsilon].sub.r] = 9.8. Reducing the diameter D causes the upper edge of the bandwidth to increase, but the lower edge also increases. Generally, this balun has greater insertion loss and almost the same bandwidth as the microstrip-to-slotline balun. However, this condition exists only if baluns having the same circular slotline diameter are compared.

A single balun with a larger circular slot (D = 6 mm) has an insertion loss of less than 1 dB and SWR less than 1.6 in the 1.45 to 8.7 GHz frequency range, while a balun with a smaller circular slot (D = 3 mm) has a 2.3 to 12.8 GHz frequency range. This balun was realized successfully on a silicon substrate of h = 0.33 mm with a 0.85 mm diameter circular slotline open for the 7.5 to 40 GHz frequency range.[8]

The [CPW.sub.FGP]-to-CPS Balun

A [CPW.sub.FGP]-to-CPS balun is realized to avoid drawbacks caused by the circular slotline open, which was used in the CPW-to-slotline balun. The new balun is realized with CPS lines instead of slotlines, a solution that requires the use of CPW lines with a finite ground plane instead of the CPW lines used in the CPW-to-slotline balun. This modification provides almost ideal open and short circuits, and considerably wider frequency bandwidth is obtained compared to both the microstrip-to-slotline and CPW-to-slotline baluns. Furthermore, due to their low dispersion, CPS and [CPW.sub.FGP] lines enable the balun to operate at low frequencies. The lower edge of the frequency bandwidth is practically DC. Among double-Y baluns, the [CPW.sub.FGP]-to-CPS balun was the first to prove the theoretical prediction of an extremely wide frequency range inherent to the structure of double-Y baluns.

The construction and measured back-to-back response for two versions of the [CPW.sub.FGP]-to-CPS balun are shown in Figures 11 and 12, respectively. Both baluns are realized on an alumina substrate of h = 0.635 mm, [[Epsilon].sub.r] = 9.8 with different line cross sections and, consequently, different open- and short-circuited stub lengths. The first balun has a cross section old = 1 mm and [L.sub.s] = 2 mm, and approaches the upper edge of its frequency bandwidth at 8.2 GHz when the electrical length of [L.sub.s] equals [Lambda]/8. The cross section and [L.sub.s] of the second balun are twice as small as those of the first balun (d = 0.5 mm and [L.sub.s] = 1 mm). The transfer characteristic of this balun shows there is no distinctive peak at 15.6 GHz as predicted by the equivalent circuit but there is a peak at that frequency in the SWR curve.

Both baluns have sharp peaks at 4.4 and 4.9 GHz in their transfer characteristics due to the parasitic antenna mode. The mode's resonances appear at the frequencies in which the length of the structure ([L.sub.0] = 25.4 mm) is equal to an odd multiple of [Lambda]/2. The second balun exhibits this resonance at a higher frequency because of the metallic frame printed on the substrate, which, to a certain degree, reduces the circuit's overall length and shifts the resonance to 4.9 GHz. The parasitic antenna mode can be suppressed with suitable shielding.

According to the calculated losses of the baluns, both baluns have approximately the same losses up to 11.5 GHz if peaks are neglected. This result means that the length [L.sub.s] of the first balun was not chosen properly and the first balun could operate correctly above 8 GHz if length [L.sub.s] is shortened.

Generally, [CPW.sub.FGP]-to-CPS baluns can be realized with a two- to three-times higher upper edge of the frequency band without changing the lower edge limit if the gap width is reduced three to five times. After reducing the cross section of the lines, the length [L.sub.s] can be shortened by the same proportion to increase the upper edge of the bandwidth. The length [L.sub.s] (distance between the center of the junction and the open/short circuit) should be twice as long as the cross section of the lines to minimize junction parasitic effects.

The [CPW.sub.FGP]-to-parallel Microstrip or Hybrid Double-Y Balun

Instead of the long microstrip taper balun[8] that has been used widely, hybrid double-Y baluns offer both an impressive frequency bandwidth and small physical dimensions. The hybrid double-Y balun is realized as a double-sided version of the [CPW.sub.FGP]-to-CPS balun. The CPS lines are replaced partly with balanced microstrip lines. The balun's top and bottom sides are connected via plated-through holes placed in the center of the double-Y junction. The canonical form of the double-Y junction comprises two symmetrical Y junctions. One of the Y junctions is realized with balanced transmission lines, and the other is realized with unbalanced transmission lines. The [CPW.sub.FGP]-to-parallel microstrip balun is referred to as a hybrid balun because it consists of three different transmission lines that form two asymmetrical Y junctions. The unbalanced Y junction is asymmetrical because it comprises three identical lines that are placed on different sides of the substrate. The balanced Y junction is asymmetrical because it comprises two different balanced lines placed on different sides of the substrate.

Two hybrid baluns (hybal 1 and hybal 2), shown in Figure 13, are realized on Epsilam 10 ([[Epsilon].sub.r] = 10.2, h = 0.635 mm) and TMM 10 ([[Epsilon].sub.r] = 9.2, h = 0.381 mm) soft substrates, respectively, for easier realization of via holes. The anisotropy of the dielectric constant ([[Epsilon].sub.xy]/[[Epsilon].sub.z]) of Epsilam 10 is high and should be taken into account to determine the characteristic impedance and electrical lengths of the transmission lines correctly. Anisotropy is neglected for the TMM material due to its low dielectric constant ([[Epsilon].sub.xy]/[[Epsilon].sub.z] = 1.1). The measured back-to-back responses of hybrid baluns are shown in Figure 14.

The first peak at 3.4 GHz in the hybal 1 transfer characteristics is due to a parasitic antenna mode. In the hybal 2 transfer characteristics, this peak is shifted to 4.4 GHz. However, there is a shallow dip at the same frequency in the hybal 1 response. In addition, the hybal 1 characteristics exhibit several shallow dips below the antenna resonance that are not found in hybal 2. The peak at 7.7 GHz was not expected based on a comparison with the [CPW.sub.FGP]-to-CPS balun that has the same length [L.sub.s]. More parasitic resonances are observed using hybal 1 due to the different layout compared to other test circuits. All other baluns are realized in an even back-to-back configuration that possesses single-plane symmetry between the two baluns. The hybal 1 test circuit is realized in an odd back-to-back configuration, that is, symmetry exists about the z-axis perpendicular to the substrate at the center of the circuit, as shown in Figure 15. If these two configurations are analyzed using an equivalent circuit that does not include parasitic effects, a 180 [degrees] phase difference is noticed between Arg([S.sub.21even]) and Arg([S.sub.21odd]).

Other peaks at 6 and 10.7 GHz in the hybal 1 and 2 characteristics, respectively, are close to the frequencies where the electrical length [L.sub.s] approaches [Lambda]/8. Hybal 1 has a greater loss (1 - [[absolute value of [S.sub.11]].sup.2] - [[absolute value of [S.sub.12]].sup.2]) than hybal 2 because hybal 1 has a wider cross section of the lines forming the junction ([d.sub.1] [congruent] 0.9 mm and [d.sub.2] [congruent] 0.6 mm).

The physical dimensions and electrical characteristics of hybal 2 and the corresponding [CPW.sub.FGP]-to-CPS balun that have almost equal losses are shown in Figures 16 and 17, respectively. The baluns are realized on different substrates (TMM 10 and alumina), but the value of tan[Delta] is similar for both. Although hybal 2 has a smaller cross section of lines (d [congruent] 0.6 mm compared to the [CPW.sub.FGP]-to-CPS balun on a 0.635-mm-thick substrate of [[Epsilon].sub.r] = 9.8 with d [congruent] 1 mm), their losses are approximately equal. The hybrid double-Y junction has greater parasitic effects due to its asymmetrical geometry and the via hole placed at the junction's hot line. For the same losses, the radius of the hybrid double-Y junction should be approximately twice as small as at the [CPW.sub.FGP]-to-CPS junction.

DOUBLE-BALANCED MIXERS

The Ring Mixer

Using [CPW.sub.FGP]-to-CPS baluns at each mixer port and a DMF 3965-000 diode crossover quad, a simple, uniplanar double-balanced mixer is realized.[9] This mixer is distinguished from similar mixer configurations[10] because it does not require any additional circuitry to minimize LO leakage to the RF and IF ports since CPS lines are used instead of slotlines. To couple the diode chip to the LO, RF and IF ports, three identical [CPW.sub.FGP]-to-CPS baluns are used with characteristics similar to those shown previously. RF coplanar strips are connected directly to the diodes while the LO signal is directed to the diodes through the series beam-lead capacitors [C.sub.s]. These capacitors serve three purposes: LO matching, and IF and DC blocking.

The mixer's layout and measured characteristics in the 2 to 15 GHz range are shown in Figure 18. The mixer is realized on an alumina substrate ([[Epsilon].sub.r] = 9.8, h = 0.635 mm). The average conversion loss is 6 dB at midband with a rolloff to 9 dB at band edges for an LO drive of 10 dBm and IF of 200 MHz. Both LO/RF and LO/IF isolations are greater than 20 dB over the entire band.

The Star Mixer

Using compact [CPW.sub.FGP]-to-CPS and [CPW.sub.FGP]-to-parallel microstrip baluns, two star mixers have been realized that offer good electrical characteristics and small size for wireless applications. The first star mixer has high port-to-port isolation because the LO and RF signals propagate along the four-wire line placed between the baluns and the diode's assembly as two mutually orthogonal modes. This high isolation is inherent because there is no cross coupling between the orthogonal modes unless circuit or diode asymmetry is introduced.

This mixer is a significantly improved version of a star mixer described previously.[11] Two small double-Y baluns (a [CPW.sub.FGP]-to-CPS balun and a [CPW.sub.FGP]-to-parallel microstrip balun) are used instead of the long taper balun, which limited the older mixer's bandwidth considerably.[11] The new mixer exhibits two main advantages over the older mixer: broader IF bandwidth and smaller size.[11]

The mixer's layout and measured characteristics are shown in Figure 19. The star mixer is realized on TMM 10 ([[Epsilon].sub.r] = 9.2, h = 0.38 mm) using model DC1567Q beam-lead, low barrier Schottky diodes. The mixer has a minimum conversion loss of 5.5 dB and an IF bandwidth of 1.5 GHz measured at a fixed LO signal of 6 GHz. The LO/RF isolation is greater than 30 dB over the 5 to 10 GHz range and the LO/IF isolation is greater than 25 dB over the same range. The IF bandwidth from DC to 1.5 GHz is achieved as a result of the reduced length of the IF return path.

The second star mixer type is a narrow-bandwidth rat race star mixer that uses two identical [CPW.sub.FGP]-to-parallel microstrip baluns at the RF and LO ports. The mixer's layout and measured characteristics are shown in Figure 20. The LO and RF signals are directed to the four diodes through a rat race coupler realized with parallel microstrip lines. The main function of this coupler is to provide LO/RF isolation in the mixer. This coupler is the only element in the mixer's circuit that limits its bandwidth.

To widen the mixer's bandwidth, an improved broadband rat race coupler[12] is applied. The coupler is designed as a microstrip circuit on a half-thickness substrate using Touchstone[TM] circuit analysis software. This four-port circuit is optimized in the 3.5 to 4.5 GHz range as a two-port circuit with the diodes attached at the rest ports.

The mixer is realized on a RT/Duroid 6010 substrate using type DC1567Q Schottky diodes. The mixer has a minimum conversion loss of 4.3 dB and an IF bandwidth of 1.2 GHz measured at a 3.4 GHz fixed LO signal. The LO/RF isolation is greater than 15 dB over the entire frequency range in which the coupler was optimized and is similar to the [S.sub.21] characteristic of the optimized coupler. The LO/IF isolation is greater than 14 dB.

CONCLUSION

A review of double-Y baluns that enable the realization of MICs using almost all printed balanced and unbalanced transmission lines has been presented. According to the characteristics, two groups of double-Y baluns exist, including microstrip-to-slotline and CPW-to-slotline baluns with a pass band response due to a slotline open realized by a circular slotline, and [CPW.sub.FGP]-to-CPS and [CPW.sub.FGP]-to-parallel microstrip baluns that have DC as the lower edge of the frequency bandwidth while the maximum upper edge of the bandwidth depends on the cross section of the lines. Both groups of baluns have uniplanar (CPW-to-slotline and [CPW.sub.FGP]-to-CPS baluns) and double-sided (microstrip-to-slotline and [CPW.sub.FGP]-to-parallel microstrip baluns) versions, which can be useful in some active antenna arrays. In order to suppress junction parasitic effects observed especially in [CPW.sub.FGP]-to-CPS and [CPW.sub.FGP]-to-parallel microstrip baluns and to widen the bandwidth simultaneously, the cross section of the lines forming the junction should be as small as possible.

Simple designs, small dimensions and impressive frequency bandwidths have been achieved with standard technology, qualifying these baluns as a serious alternative to other types of printed baluns, especially for wireless applications. Three realized double-balanced mixers in ring and star configurations show that these baluns can be applied successfully in the design of compact MICs, producing attractive new structures with good first-pass characteristics.

ACKNOWLEDGMENT

The TMM 10 material is a product of Rogers Corp., Chandler, AZ. The type DMF 3965-000 diode quad is from Alpha Industries, Woburn, MA. The type DC1567Q diodes are from Marconi Inc.

References

1. A.M. Pavio and A. Kikel, "A Monolithic or Hybrid Broadband Compensated Balun," 1990 IEEE MTF-S Digest, pp. 483-486.

2. J. Eisenberg, J. Panelli and W. Ou, "Double-double Balanced MMIC Mixer," Applied Microwave, Fall 1991, pp. 101-106.

3. B. Schiek and J. Kohler, "An Improved Microstrip-to-microslot Transition," IEEE Transactions, MTT-24, 1976, pp. 231-233.

4. V. Trifunovic and B. Jokanovic, "New Uniplanar Balun," Electronics Letters, Vol. 27, No. 10, 1991, pp. 813-815.

5. V. Trifunovic and B. Jokanovic, "Four-decade Bandwidth Uniplanar Balun," Electronics Letters, Vol. 28, No. 6, 1992, pp. 534-535.

6. V. Trifunovic and B. Jokanovic, "Star Mixer with High Port-to-port Isolation," Electronics Letters, Vol. 28, No. 6, 1996, pp. 534-535.

7. E.A. Guillemin, A Synthesis of Passive Networks: Part I, John Wiley & Sons Inc., 1957, pp. 194-210.

8. W. Grammer and S. Yngvesson, "Coplanar Waveguide Transitions to Slotline: Design and Microprobe Characterization," IEEE Transactions on MTT, Vol. 41, No. 9, September 1993, pp. 1653-1658.

9. V. Trifunovic and B. Jokanovic, "Review of Printed Marchand and Double-Y Baluns: Characteristics and Applications," IEEE Transactions on MTT, Vol. 42, No. 8, August 1994, pp. 1454-1462.

10. D. Cahana, "A New Coplanar Waveguide/Slotline Double-balanced Mixer," IEEE MTTS Digest, 1989, pp. 967-968.

11. B. Jokanovic and V. Trifunovic, "A Planar Balanced Mixer of the Star Configuration," Proceedings of the Conference on Microwaves and Optoelectronics, MIOP'90, Stuttgart, 1990, pp. 122-127.

12. D.I. Kim and Y. Naito, "Broadband Design of Improved Hybrid-ring 3 dB Directional Coupler," IEEE Transactions on MTT, Vol. 30, No. 11, November 1982, pp. 2040-2046.
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Title Annotation:Wireless Report
Author:Jokanovic, Branka; Trifunovic, Velimir
Publication:Microwave Journal
Date:Jan 1, 1998
Words:4590
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