Brief History

The exact beginnings of directional couplers using parallel wires are not clear.

Such couplers were used for various applications before any of the modern theories or design data were available. The first directional coupler using a quarter-wave-long two-wire configuration, U.S. Patent 1,615,896, entitled “High Frequency Signaling System” [1] was filed in 1922 and granted in 1927 to Herman A. Affel, and assigned

to American Telephone and Telegraph Company. Affel refers to a ”loop antenna”, which is shown in Figure 1.1 consists of a two-wire transmission line quarter-wavelength long, with a resistive termination at one end and a detector at the other end. This quarter-wavelength line which was called loop antenna is parallel to another longer two-wire transmission line, and could work like a directional coupler at midband of properly design. However, it is not explicitly referred to as a directional coupler.

A clear description with formulas of a TEM-mode quarter-wavelength parallel-line backward coupler was filed in U.S. Patent 2,606,974, entitled

“Directional Coupler” [2] in 1946, and granted in 1952 to Harold A. Wheeler, being assigned to Hazeltine Research, Inc. The cover is reproduced here as Figure 1.2.

Wheeler states that it was used in 1944 at the Hazeltine laboratory.

Directional couplers using planar TEM lines such as coupled striplines were developed in the mid-1950s. Numerous papers were published in the 1950s and 1960s describing the theory, design, fabrication, and measured data for the TEM-line edge-coupled directional couplers and significant contributions were made in the development of planar couplers. These couplers can provide coupling in the 8- to 40-dB range. Early works on these homogeneous couplers can be found in [3]-[4].

These couplers are also known as backward couplers because the coupled wave on the secondary line travels in the opposite direction compared with the incident wave on the primary line when excited with a microwave signal.

Figure 1.1 The first directional coupler using a quarter-wave-long two-wire configuration.

Figure 1.2 The first TEM-mode quarter-wavelength parallel-line backward coupler with clear description with formulas.

1.2 Research Motivations

Microstrip coupling structure has become very popular due to insensitivity to fabrication tolerance and simple synthesis procedures. Its planar structure allows laying solid-state devices and lumped elements on its surface. Microstrip coupling structure can be used to design many various microwave circuits, such as directional coupler, edge-coupled line filter, balun, delay line, dc block, interdigital capacitor, spiral inductor, coupled-line impedance transformer, and spiral transformer. And it also frequently appears in high-speed digital signal printed circuit board and in many microwave measurement systems.

However, based on its semi-open structure, the electromagnetic field distributes in both air and dielectric region, and the propagation mode is quasi TEM. Due to the inhomogeneous material that results the odd-mode phase velocity commonly faster than the even-mode value, in another word, that causes the odd-mode transmission phase smaller than the even-mode value. The inequality of modal phase velocities (and transmission phases) will degrade the isolation or directivity performance of the microstrip coupled-line structure. The performances of many of the microwave circuits mentioned above degrade because of poor directivity. For a backward-wave directional coupler, the coupling value might change, as the coupler isolation is not very good and in the mean time the coupler is not well terminated. For a Machand type balun, the balance of amplitude and/or phase degrade due to poor directivity. For a coupled-line bandpass filter, extra spurious passband appears and it might make the upper stopband performance get worse. For some of other circuits, the parasitic effects might cause undesirable performances. Therefore, a microstrip coupled-line structure with good isolation is important for various microwave circuits design.

The second problem encountered in the microstrip coupled-line coupler is that as the coupling gets loose, two lines of convention coupler becomes wider spaced. That makes the coupler not only occupies more circuit area but also has very poor directivity. Because of the large line spacing, the capacitor compensation of phase velocity becomes very difficult. In addition, in order to get a near-constant coupling over a wider frequency bandwidth, a multisection coupler that consists of a number of single-section couplers with tight and loose coupling is commonly used. However, the different coupling has different spacing between the two coupled lines for each section of coupler. This means that the discontinuities certainly exist in the junctions of different single-section couplers, even if the small lengths of tapered transmission lines are used. In higher frequency, these discontinuities will produce extra reactance and lengths and then degrade the input matching and directivity. Therefore, a loose coupler with narrower coupled-line spacing is needed for reducing the discontinuities.

Besides, the directivity of a single-section coupler is more important in multisection coupler application. The unequal phase velocities will get poor directivity and make the coupling to be inaccurate especially when the whole coupled line length get longer.

So, a loose coupler with narrower coupled-line spacing and high directivity is necessary for a multisection coupler.

The purpose of this research is to find some methods to solve the above-described problems.

1.3 Literature Survey

For improving the directivity of the microstrip coupled-line coupler, there are many early works are proposed to equalize or compensate of unequal modal phase velocities (and modal transmission phases). Basically, methods to solve this problem can be summarized in three major groups. The first method is shown in Figure 1.3. By adding single or multiple lumped elements at the end or the center of the coupler, the odd-mode phase velocity slows down due to the raise of the odd-mode effective dielectric constant [5]-[9]. On the other hand, the lumped elements are nearly invisible in the even mode. The initial synthesis procedures and the achievable coupling range of this compensated method are the same as conventional coupler.

Moreover, it is effective to get high directivity in a wide bandwidth. However, the value of lumped component should be calculated and length of coupled section should be shortened due to the odd-mode phase velocity slows down. Although [5]-[7]

provide the formulas for calculating the value of lumped element and shortened length, in practice, the available lumped element value usually does not meet the exact value and the lumped component usually shows parasitic effects as the frequency goes high.

Distributed component is, therefore, a good solution to implement the lumped element in high frequency.

W S

L

C

¹

C

²

Figure 1.3 Lumped capacitor compensation of microstrip coupler.

The second method is shown as Figure 1.4. By placing one or more additional dielectric layers with proper thickness and dielectric constant on top of microstrip coupler, the odd-mode phase velocity can be slowed down due to the increase of odd-mode effective dielectric constant, and can be equaled to the even-mode value [10]-[15]. This thought is straight forward and it can shorten the circuit size by show-wave effect. Furthermore, it makes the realization of tight coupling easier with the same lines spacing. However, it’s not a planar structure anymore and adding any additional material needs extra cost and process. Moreover, due to the variation of dielectric environment, the line width and line spacing are different from the initial dimensions of microstrip coupler and need to be recalculated. Unfortunately, there are no mature synthesis formulas for various dielectric environments. To obtain most of the dimensions require some special design charts and need electro-magnetic field analysis to calculate the characteristics of the proposed special structure. This kind of design is more complicated and time-consuming. The most important drawback is that the design results fit case-by-case and common solution is difficult to obtain.

The third method is shown in Figure 1.5 that the inner edges of a pair of microstrip lines are changed to wiggle or serpentining or slot shape [16]-[20]. Since most of the odd-mode current is propagated along the inner edge, the effective propagating length of the odd-mode signal is increased so that the propagating phase of odd-mode can be equaled to that of the even-mode signal. The circuit structure is pure planar and the slow wave-like effect can effectively shorten the physical length of the circuit. However, the design begins with Fourier transform analysis, and the

synthesized structure is optimized using iterative techniques [20]. These steps cannot be implemented in standard simulators, and the whole process is rather time-consuming. Besides, the unsmooth inner edge not only makes the high order propagating mode easily to be excited but also increases the insertion loss. Moreover, the odd-mode inductance per unit length increases, as the variation of inner edge gets more drastic. That means the odd-mode characteristic impedance increases and results in a looser coupling as comparing to the conventional coupled lines with the same line spacing.

For improving the directivity of loosely coupled microstrip lines, few works have been done on this topic. As [21] indicates, it’s not appropriate to add lump capacitor on the two ends of a loose coupler due to the wide coupled line spacing and only very small compensated capacitance is needed. Conventional lump capacitor is hard to get exact and such a low capacitance value. In the contrary, interdigital capacitor is good for this kind of application, because it is easier to fit the wide coupled-line spacing and to get exact and lower capacitance.

There are some previous works for loose coupler design in microstrip structure, most of them are based on broadside coupling with some slots or apertures in the substrate but no one is based on edge coupling scheme.

1

ε

r 2

ε

r

Figure 1.4 Parallel-coupled microstrip with dielectric overlay compensation.

Figure 1.5 Wiggly two-line coupler.

1.4 Contribution

Comparing to the various methods for directivity improvement described in section 1.3, this dissertation proposes the structure of meandered parallel-coupled line.

The even-mode phase velocity can be speeded up by meandering the parallel-coupled line. Proper meandering equals the even- and the odd-mode phase velocities and achieves high directivity. By the single section meandered parallel-coupled lines, we can locate high directivity performance at any narrow frequency band that we want.

Furthermore, the frequency band with high directivity can be wider by dividing the coupled line in to multiple sections of cascaded meandered parallel-coupled lines. In addition, the proposed structure, based on the characteristic of meandering, can effectively miniaturize the circuit for all of its applications, especially in higher order filter design. In practical fabrication, no addition component, material, and process are needed, thus, low fabrication cost can be kept.

In another part of this dissertation, a miniaturized high directivity loose microstrip coupler is proposed. We place a grounded strip between the two parallel-coupled lines to block the coupling and place two interdigital capacitors in both ends of the coupler to improve the directivity. The design procedures and consideration will be discussed in detail.

1.5 Chapter outline

In this dissertation, Chapter 1 is the introduction, which describes the original of parallel-coupled lines and the importance of the directivity. A brief description of the proposed methods is provided with comparison of various previous works. Chapter 2 describes the inherent characteristics and disadvantages of microstrip parallel-coupled lines, and derives the scattering parameters to obtain the necessary conditions for high directivity in the basis of Quasi-TEM mode. Chapter 3 describes the motivation of using the meandered parallel-coupled lines and the characteristics of this kind of parallel-coupled line. Moreover, it also describes the procedures to synthesis the proposed meandered parallel-coupled lines by commercial CAD tools in detail. Then, based on the proposed structure, two couplers are designed and demonstrated with narrow-band and wide-band high directivity performance, respectively. Chapter 4 uses the characteristics of the proposed meandered parallel-coupled lines to design a bandpass filter not only eliminating the spurious passband near twice of the center frequency but also drastically shrinking the circuit size. In this chapter, the design procedures and information are described in detail for this kind of filter. Chapter 5

describes the design of the miniaturized loosely coupled parallel-coupled line coupler with high directivity. Chapter 6 gives the conclusion.

Chapter 2

Theory of the microstrip parallel coupled line coupler

Transmission lines used at microwave frequencies can be briefly divided into two categories: TEM (or Quasi-TEM) mode transmission lines and non-TEM transmission lines. When a signal propagates on a microstrip structure, because the electromagnetic fields are distributed in an inhomogeneous material, the propagation mode is Quasi-TEM. For a symmetric TEM or Quasi-TEM coupled transmission lines, the determination of important electrical characteristics (such as modal characteristic impedances and phase velocities) of coupled lines reduces to finding the modal capacitances associated with the structure and excitation mode. This chapter discusses the general characteristics of symmetric microstrip parallel coupled lines and also gives the design equations. In addition, the scattering parameters of microstrip parallel coupled lines based on Quasi-TEM mode are derived without the constrain of equal modal phase velocities and the necessary conditions for high directivity is also discussed. Finally, some practical suggestions are given for designing a high-directivity microstrip coupler.

2.1 The characteristic of microstrip parallel coupled line

When two conductor lines close to each other, the electromagnetic waves

propagating on each line interferes each other. Coupler is an application based on this scheme. The physical structure of a microstrip coupler is shown in Figure 2.1, where h and εr are the thickness and dielectric constant of substrate, respectively, t is the thickness of conductor, W is the coupled line width, S is the spacing between coupled line, and L is coupled line length. Figure 2.2 is the cross sectional view of the microstrip coupled lines. The structure can be analyzed by even- and odd-mode excitation. The even-mode electrical field distribution of one-half of the structure is shown in Figure 2.3(a). In this case, both lines are driven in phase from equal source of equal impedance and voltage, and the impedance from one line to ground in even-mode excitation can be defined as the even-mode characteristic impedance, Z0e. Since the electrical fields between both coupled lines are parallel to the symmetric plane of the circuit, the normal component of the electric field at PP’ plane is zero. It can be imaged a magnetic wall (M-wall) exists on the symmetric plane PP’ and it is effectively an open-circuit on that plane. The even-mode capacitance of either of the coupled lines, which can be represented as shown in Figure 2.3(b), is given by,

e p f fe

C =C +C +C (2.1)

The capacitance that results from the electrical field in the region directly below the strip is known as the parallel-plate capacitance Cp, while that resulting from the fringing fields in the outer edge is known as the fringing capacitance Cf. Cfe means the fringing capacitance in the inner edge of coupled lines, which is different from Cf, because the inner edge has a M-wall near by.

The electrical field distribution of one-half of the coupled structure is shown in Figure 2.3(c) for odd-mode excitation. In this case, both lines are driven out of phase from equal source of equal impedance and voltage, and the impedance from one line to ground in odd-mode excitation can be defined as the odd-mode characteristic impedance, Z0o. Since the electrical fields between both coupled lines are perpendicular to the symmetric plane of the circuit, it can be imaged an electric wall (E-wall) exists on the symmetric plane PP’ and the voltage on it is zero. Because PP’

is an E-wall the tangential electric field on it should be zero. The odd-mode capacitance of either of the coupled lines is given by

o p f fo

C =C +C +C (2.2)

where Cfo denotes the fringing capacitance from the inner edges of the coupled lines,

which is assumed to consist of two capacitances Cga and Cgd in parallel; that is,

fo ga gd

C =C +C (2.3)

where Cga and Cgd are the capacitances corresponding to the fringing field between the inner edges exist in the air and dielectric regions, respectively.

ε

r

h

W W

S 1

2

3

4

t L

Figure 2.1 The structure of microstrip coupler.

P

P

W

h

Plane of Symmetry S/2

Figure 2.2 Cross section of symmetrical microstrip coupler.

P

P

W

h

Magnetic Wall

(a)

P W

C_p C_f h C_fe

P Magnetic

Wall

(b)

P

P

W

h

Electric Wall

(c)

P W

C_p C_f h

P Electric

Wall C_gd C_ga

(d)

Figure 2.3 (a) The electrical field distribution and (b) capacitance representation of one-half of the structure for even-mode excitation, (c) The electrical field distribution and (d) capacitance representation of one-half of the structure for odd-mode excitation.

The definitions of the even- and the odd-mod effective dielectric constant are odd-mode phase velocity, respectively. In Figure 2.2, the effective dielectric constants take into account the relative distribution of electric field in the various regions of the inhomogeneous medium. Besides, the effective dielectric constants are a function of frequency and strictly speaking should be evaluated using equation (2.4) where the phase velocity is compute by using some rigorous method based on Maxwell’s equations. However, on the quasi-static assumption, the even- and odd-mode effective dielectric constant can be defined as fellows:

_ / 1

e

r eff C Ce e

ε = (2.5a)

ε^o_{r eff_} =C C_o/ _o1 (2.5b)

where Ce1 and Co1 denote the modal capacitances between the same conductor in a homogeneous dielectric medium of unity dielectric constant. In order to get the sense for the even- and odd-mode dielectric constant, let us refer to Figure 2.3 (a) and (c), which show the even- and odd-mode electrical field distributions of a microstrip parallel coupled line. The figures indicate that the relative E-field distributions in air and substrate region are different for the two modes, and the odd-mode electrical field has more relative distributions in the air region. It implies that the ε^or_eff is smaller than ε^er_eff and V^op is faster than V^ep by equation (2.4).

The transmission phases of both modes are

e e

where ω is operation angular frequency, L is the physical length of the parallel

coupled line.

The even- and odd-mode characteristic impedance are given by

0

The detailed analysis formulas for even- and odd-mode characteristic impedance in microstrip coupled lines can refer to [22].

2.2 The necessary conditions of a high directivity coupler

Figure 2.4 is the schematic circuit of microstrip coupler. Because of symmetry, the excitation in Figure 2.4 can be decomposed into even-mode and odd-mode excitations as shown in Figure 2.5(a) and (b), respectively. In order to analysis easily, the schematic circuits on Figure 2.5(a) and (b) can be simplified as shown in Figure 2.6 (a) and (b) which are two-ports circuit with characteristic impedance Z0e and Z0o, transmission phase θe and θo, respectively. Since the even- and odd-mode circuits are two-port network, the ABCD matrix for the even- and odd-mode are given, respectively, by

And then transfer the ABCD matrix to scattering matrix, we obtain

[ ]

^{11 12}

Z

^0e

, Z

^0o

Figure 2.4 The schematic circuit of microstrip coupler.

θ

e

Figure 2.5 The decomposition of coupled line coupler circuit of Figure 2.3 into even-mode and odd-mode excitations. (a) Even mode. (b) Odd mode.

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