微波集成电路中的非对称无源器件深度解析

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《微波电路中的非对称无源器件》是一本由韩国作者Hye-Ran Ahn编著的经典著作，专为研究射频无源元件的专业人士设计。这本书深入探讨了在微波集成电路（MIC）中至关重要的非对称被动组件。非对称无源器件在现代通信、雷达、无线通信系统以及信号处理等领域扮演着关键角色，它们通常包括但不限于滤波器、功率分配器、衰减器、相移器等，这些器件的设计必须考虑到性能的不对称性，以适应不同频率范围、带宽和线性度的要求。书中详细介绍了非对称性如何影响器件的性能特性，如增益、隔离度、插入损耗和群延迟特性等。作者阐述了非对称设计的基本原理，涵盖了材料选择、电路结构优化以及制造工艺等方面，这些都是实现高效、稳定且具有低噪声特性的微波电路的关键要素。通过实例分析和理论推导，读者可以学习到如何在实际设计中权衡各种参数，以达到最佳的系统性能。此外，书中还涵盖了非对称无源器件的噪声分析，这对于噪声性能敏感的应用至关重要。同时，针对新兴技术如毫米波和太赫兹通信，书中可能还会介绍相应的非对称器件设计挑战与解决方案。书中的每章通常会提供实用的设计方法和计算工具，帮助读者提升在微波集成电路设计中的实践能力。由于版权原因，本书可能受限于复制、存储或传播的规定，只有在符合美国1976年版权法的第107或108条款的情况下，未经出版商John Wiley & Sons, Inc.事先许可或支付适当的复制费用，才能进行相关操作。对于寻求授权的读者，应直接联系出版社的许可部门获取许可。《微波电路中的非对称无源器件》是一本权威且实用的参考资料，对于那些希望在高速电子和无线通信领域深入研究非对称无源器件及其在微波集成电路中的应用的专业人员来说，是不可或缺的读物。通过阅读这本书，读者将能掌握这一领域的核心技术，提升其设计和优化微波电路的技能。

CHAPTER ONE

Introduction

1.1 ASYMMETRIC PASSIVE COMPONENTS

In microwave integrated circuits, there are three classes of components: one

passive, the others active and nonreciprocal ferrite components. Power dividers,

phase shifters, impedance transformers, and ﬁlters are typical passive compo-

nents, and their conventional structures have been symmetric. However, asym-

metric structures, with arbitrary termination impedances, are strongly preferable

since they allow elimination of the matching networks needed to obtain the out-

put performances desired when symmetric components are integrated with other

elements.

The study of asymmetric passive components started with asymmetric ring

hybrids in 1991 [1–5], and the design equations of asymmetric 3-dB ring hybrids

were derived in 1994 by Ahn et al. [6]. Shortly after, those of asymmetric ring

hybrids with arbitrary power divisions were synthesized assuming conditions of

perfect isolation [7,8]. In 2000, a new concept [9], which stated that ring hybrids

are not different from branch-line hybrids [10–13], allowed two types of asym-

metric branch-line hybrids to be investigated and their design equations derived.

In this book, asymmetric ring hybrids and branch-line hybrids are discussed in

Chapters3to5.

For asymmetric three-port power dividers, Ahn and Wolff [14,15] derived

a perfect isolation condition that had never been analyzed for these types of

conventional three-port power dividers. Using perfect isolation conditions 3-dB

three-port power dividers terminating in different impedances could be con-

structed and their design equations derived. However, the design equations were

available only for three-port power dividers with equal power division. In 2000,

general design equations were derived for three-port power dividers with both

arbitrary termination impedances and arbitrary power divisions [16,17]. In this

Asymmetric Passive Components in Microwave Integrated Circuits,byHee-RanAhn

 2006 John Wiley & Sons, Inc.

2 INTRODUCTION

book, the design of asymmetric three-port power dividers with arbitrary power

divisions is treated in Chapters 7 and 8.

Development of the monolithic microwave integrated circuit (MMIC)

technique has created a strong incentive to reduce circuit size. Three-port power

dividers are key components in microwave integrated circuits, and there have

been many trials to reduce their size. One of them was to adapt lumped-

element circuits to be equivalent to transmission-line sections [1–6,14]. However,

the bandwidths of three-port power dividers with lumped elements were not

sufﬁcient, so wideband impedance transformers were required. For this, two types

of small wideband impedance transformers were introduced: the constant-voltage

standing-wave-ratio transmission-line impedance transformer (CVT) and the

constant-conductance transmission-line impedance transformer (CCT) [17–19].

CVTs and CCTs have arbitrary phase shifts of less than 90

◦

, which differs

considerably from conventional impedance transformers, which have only odd

multiples of 90

◦

phase shifts. Thus, the distinct characteristics of CVTs and CCTs

allow construction of small CVT and CCT 3-dB power dividers (CVT3PD and

CCT3PDs), three-port 45

◦

power dividers, and CVT and CCT ring ﬁlters. One

CCT3PD has the smallest recorded, and three-port 45

◦

power dividers are very

important in getting rid of third harmonics of active devices. The key components

of CVTs and CCTs are treated in Chapter 11 as asymmetric two-port components.

In addition to CVTs and CCTs, asymmetric ring-hybrid phase shifters and

attenuators [20–22] and ring ﬁlters are asymmetric two-port components and are

considered in Chapters 9 and 10. Since asymmetric phase shifters and attenuators

consist of asymmetric ring hybrids, they may be used as impedance transformers

together with their original functions. Conventional 180

◦

phase shifters were used

for building linearizers in high-power systems, but they had narrowband prop-

erties. For this, ring ﬁlters [23] were introduced as wideband 180

◦

transmission

lines. Each ring ﬁlter consists of a ring and two short stubs, and it is possible

to measure an inherent ring resonance frequency by having the two short stubs

differ in length. This measurement technique is treated in Chapter 10.

1.2 CIRCUIT PARAMETERS

The measured quantities of passive components at microwave frequencies are

almost always the scattering parameters. The scattering matrix discussed in

Chapter 2 is admirably suitable for the description of a large class of passive

microwave components and is used as much as possible throughout the book. In

many cases it leads to a complete understanding of a microwave device while

avoiding the need to construct a formal electromagnetic boundary-value problem

for the structure. The entries of the scattering matrix of an n-port junction are a set

of quantities related to incident and reﬂected waves at the ports of the junction that

describe the performance of a network under any termination conditions speciﬁed.

The coefﬁcients along the main diagonal of the scattering matrix are reﬂection

coefﬁcients, whereas those along the off-diagonal are transmission coefﬁcients.

ASYMMETRIC FOUR-PORT HYBRIDS 3

A scattering matrix exists for every linear, passive, and time-invariant network,

and it is possible to deduce important general properties of junctions containing

a number of ports by invoking such junction properties as reciprocity and power

conservation. Since the entries of the scattering matrix S , impedance matrix Y ,

and admittance matrix Z of a symmetric network are linear combinations of the

circuit eigenvalues, their direct evaluation or measurement provides an alternative

formulation of network parameters. Therefore, the relation between the scattering

matrix and other circuit matrices is important and is described in Chapter 2.

1.3 ASYMMETRIC FOUR-PORT HYBRIDS

Many different types of power dividers, with and without isolation between out-

put ports, are used for various applications. They perform a variety of functions,

such as splitting and combining power in mixers (hybrids), sampling power from

sources for level control, separating incident and reﬂected signals in network

analyzers, and dividing power among a number of loads. Certain power dividers,

which provide isolation between their output ports, are branch-line hybrids, ring

hybrids, and parallel-coupled directional couplers, and their two outputs are

in phase or out of phase by 90

◦

or 180

◦

. These power dividers are shown in

Fig. 1.1(a), where the direction of power ﬂow is indicated when power is fed

into port

. As shown, the direction of the ring hybrid is the same as that of

the parallel-coupled directional coupler, but the two output signals of the ring

hybrid are in phase or 180

◦

out of phase, whereas those of the parallel-coupled

directional coupler are 90

◦

out of phase. The branch-line hybrid in Fig. 1.1(b)is

same as that in Fig. 1.1(c), in that the two output signals are out of phase by 90

◦

but the power division directions are different from each other. Thus, the branch-

line coupler (hybrid) is called a forward coupler, whereas the parallel-coupled

directional coupler is called a backward c oupler.

1.3.1 Asymmetric Ring Hybrids

The ﬁrst conventional ring hybrid to be treated in Chapter 3 was investigated

by Tyrrel in 1947 [24]. Tyrrel tried to explain ring hybrids using the concept of

waveguide T-junctions, and described two types of hybrid circuits, one involving

a ring or loop transmission line and the other relying on the symmetry properties

of certain four-arm junctions. After he described the fundamental characteris-

tics of distributed circuit hybrids, a number of workers discussed the perfor-

mance of practical wideband realizations constructed in coaxial line [25–27]

and stripline [28]. One of them was that two coupled-line ﬁlters were used for a

wideband ring hybrid in the 1950s. In 1961, Pon [29] derived design equations

for ring hybrids with arbitrary power divisions. In 1968, March [28] developed a

wideband ring hybrid, adapting one coupled-line ﬁlter instead of a three-quarter-

wavelength transmission line, which causes narrowband responses.

In the 1980s, as uniplanar techniques emerged for MMIC applications, there

were several researchers developed small broadband ring hybrids which employed

ASYMMETRIC THREE-PORT POWER DIVIDERS 5

them. One of these two lines is the main or primary line and the other one

is the secondary line. A small fraction of the energy in the main line is trans-

ferred, through the coupling elements, to the secondary line. The mechanisms

of the power transmission and isolation from the primary line to the secondary

line are discussed in Chapter 5. If the coupling elements are branch lines and

hybrid T-junctions are used for the directional couplers, they are called branch-

line hybrids, and one-stage branch-line hybrids are narrowband. So to increase

the bandwidth, multiple branch-line hybrids [34] are needed and the design of

such a directional coupler and the calculation of its frequency response are also

covered in Chapter 5. The branch-line directional coupler is particularly desirable

since the design constants are readily found and its frequency response can be

calculated. Branch-line hybrids may be used for impedance transformers with

one or two sections [35,36]; their design methods are treated in Chapter 5.

Branch-line hybrids have been studied for a long time. However, these studies

have focused on symmetric branch-line hybrids [33–40]. If branch-line hybrids

are terminated in arbitrary impedances, they are no longer symmetric and a new

design method is needed. In the latter part of Chapter 5, the isolation mechanism

of asymmetric four-port hybrids and design equations for asymmetric branch-line

hybrids are treated.

1.4 ASYMMETRIC THREE-PORT POWER DIVIDERS

The history of three-port power dividers began in 1960 with Wilkinson [41], who

described a device that separated one signal into n equiphase–equiamplitude sig-

nals. Theoretically perfect isolation between all output ports is achieved at one

frequency. With n

D 2, his circuit may be reduced to a three-port power divider.

In 1965, Parad and Moynihan [42] presented a hybrid with the output signals in

phase and an arbitrary amplitude difference. The perfect three-port hybrid prop-

erty was again achieved at one frequenc y. In 1968, Cohn [43] presented a class

of equal-power dividers with isolation and impedance matching at any number

of frequencies. In 1971, Ekinge [44] described a three-port hybrid consisting

of n sections in cascade, each section composed of two coupled lossless trans-

mission lines with a certain electrical length and an intermediate resistor. His

design seems to be similar to that of Cohn [43]. However, Cohn treated equal-

power-split three-port hybrids, whereas Ekinge dealt with three-port hybrids with

arbitrary power split.

For the design of three-port power dividers, it is very important to deter-

mine the isolation conditions or the values of isolation resistors. A number of

papers have dealt with how to get isolation between output signals. Parad and

Moynihan [42] suggested one of many isolation conditions, and Cohn, Ekinge,

et al. [43–45] had to use intensive optimizing methods to derive the isolation

resistances. In this book, a perfect isolation condition without optimization is

discussed in Chapter 7.

In addition to the above, an optimization method for 3-dB three-port

power dividers terminated in complex frequency-dependent impedances was

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