適用於Bluetooth /Zigbee / Wi-Fi頻帶之共平面帶線柴氏帶通濾波器

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Coplanar Stripline Bandpass Filter with Tchebyshev

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Dr. Chi-Yang Chang

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A Thesis

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for the Degree of

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Industrial Technology R and D Master Program on

Communication Engineering

June 2008

HsinChu, Taiwan, Republic of China

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Coplanar Stripline Bandpass Filter with Tchebyshev Response for

Bluetooth / Zigbee / Wi-Fi Applications

Student: Yi-Ming Shih

Advisor: Dr. Chi-Yang Chang

Industrial Technology R and D Master Program of

Electrical and Computer Engineering College

National Chiao Tung University

Abstract

Filter design procedure is using the equivalent J and K inverter model in co-operation with λ/2 and λ/4 resonators to achieve Tchebyshev response, and using the CPS to implement circuit with differential I/O. The proposed circuit has the benefits of no need via holes or air-bridges, insensitive to the variation of substrate thickness, and relatively higher characteristic impedances. The proposed filters are very suitable for differential wireless communication system and radio-frequency integrated circuits.

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Acknowledgement

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List of Tables

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List of Figures

1.1 Architecture of transceiver system . . . 2

1.2 Cross section of coplanar stripline . . . 4

1.3 Simplified architecture of balanced transceiver system . . . 5

2.1 Three dimmensional view of CPS for analyzing of 4-port Z-parameters 8 2.2 Analysis Z-parameters of coplanar stripline for top view(a)even-even(b)even-odd(c)odd-even(d)odd-odd . . . 9

2.3 Tchebyshev lowpass response . . . 11

2.4 Admittance inverter (J inverter)(a) lumped element (b) transmission line . . . 13

2.5 Equivalent model for J inverter . . . 14

2.6 Impedance inverter (K inverter)(a) lumped element (b) transmission line . . . 15

2.7 Equivalent Model for K inverter . . . 15

2.8 Diagram of J inverter filter . . . 16

2.9 Diagram of K inverter filter . . . 17

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2.10 Proposed J and K inverter for CPS (a)J inverter (b)J inverter (c)K

inverter . . . 19

2.11 Capacitance versus physical dimmension in(a)Gap(b)Lengh . . . 20

2.12 Inductance versus physical dimmension in (a)size-I (b)size-II . . . . 21

2.13 Diagram of design procedure flow . . . 23

3.1 (a)Diagram of single-ended 4-port DUT (b)Diagram of differential 2-port DUT . . . 24

3.2 (a)Mixed-mode S-parameters (b)Differential S-parameters . . . 30

3.3 Circuit photo of type-I . . . 31

3.4 Narrow band differential mode simulation result . . . 32

3.5 broad band differential mode measurement result . . . 32

3.6 Broad band common mode measurement result . . . 33

3.7 Circuit photo of type-II . . . 33

3.9 Broad band differential mode measurement result . . . 34

3.10 Broad band common mode measurement result . . . 35

3.11 Circuit photo of type-III . . . 35

3.13 Broad band differential mode measurment result . . . 36

3.14 Broad band common mode measurment result . . . 37

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4.2 Narrow band ideal response of second order band-pass filter . . . . 39

4.3 Equivalent circuit of second order band-pass filter . . . 39

4.5 Photo of the second order band-pass filter . . . 41

4.8 Half circuit model of a third order band-pass filter . . . 42

4.9 Narrow band ideal response of third order band-pass filter . . . 43

4.10 Equivalent circuit of third order band-pass filter . . . 43

4.12 Photo of the third order band-pass filter . . . 44

4.15 Half circuit model of a fourth order band-pass filter of architecture-I 46 4.16 Narrow band ideal response of fourth order band-pass filter of architecture-I . . . 46

4.17 Equivalent circuit of fourth order band-pass filter of architecture-I . 46 4.18 Narrow band differential mode simulation result of architecture-I . . 47

4.19 Photo of the fourth order band-pass filter I . . . 47

4.21 Broad band common mode measurment result . . . 48 4.22 Half circuit model of a fourth order band-pass filter architecture-II . 49

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4.23 Narrow band ideal response of fourth order band-pass filter of architecture-II . . . 49 4.24 Equivalent circuit of fourth order band-pass filter of architecture-II 50 4.25 Narrow band differential mode simulation result of architecture-II . 50 4.26 Photo of the fourth order band-pass filter II . . . 50 4.27 Broad band differential mode measurment result . . . 51 4.28 Broad band common mode measurment result . . . 51

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Chapter 1 Introduction

In this chapter , we are going to introduce the importance of microwave / RF filters in modern wireless communication system. Three commercial wireless com-munication systems, namely, Bluetooth, Zigbee, and Wi-Fi. Moreovr, the basics of coplanar stripline (CPS) will also be introduced.

1.1 The Importance of Microwave- / RF Filters

in Modern Wireless Communication System

Recently, communication industry is rising in the global range. Each communi-cation system equips with more and more functions at the same time. Generally, modern wireless communication systems include mobile phone, personal communi-cation system, satellite communicommuni-cation, and wireless area network,..., etc.

Microwave / radio frequency (RF) passive component (such as resistor, capac-itor, inductor, filter, and coupler) still takes the most important position in the wireless communication modules. Filter is an important component, and its func-tions are passing the desired signals and rejecting the undesired one.

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According to Fig. 1.1, filter locats in front of the low noise amplifier (LNA) and after the antenna. Passive components take almost 65 percent area of the front-ended circuit in the wireless communication systems, especially antenna and filters. Antenna and filters can not convert to silicon substrate, due to their fre-quency response characteristic will affect accuracy and quality of whole circuit when processing signals.

Figure 2.1 Analysis s-parameter of coplanar strip 3D view 1 3 2 4 (a) 1 3 2 4 even even (c) 1 3 2 4 odd even (b) 1 3 2 4 even odd (d) 1 3 2 4 odd odd +V +V +V +V +V -V +V -V -V +V +V -V -V -V +V -V

Figure 1.1 Architecture of transceiver system LNA Antenna RF BPF Band-select filter RF BPF Image-reject filter Mixer 1 PLL VCO 1 LO 1 Frequency synthesizer IF BPF Chennel-select filter PLL controller Mixer 2 Mixer 2 PLL VCO 2 LO 2 Frequency synthesizer 90 degree shifter IF LPF LPF I Q I Q AGC AGC

Figure 1.1: Architecture of transceiver system

1.2 Comparison with Bluetooth/ Zigbee/ Wi-Fi

In this section, we introduce three commercial wireless communication systems.

standard frequency bandwidth data rate outdoor distance Bluetooth 2.4-2.483 (GHz) 1 (MHz) 1 (Mbps) 1-100 (m)

Zigbee 2.4-2.483 (GHz) 5 (MHz) 256 (Kbps) 10-75 (m) Wi-Fi 2.4-2.483 (GHz) 20(MHz) 11/54 (Mbps) 32-95 (m) Table 1.1: Table of comparison between Bluetooth/ Zigbee/ Wi-Fi

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Bluetooth is a wireless protocol with short-range communications technology. It utilizes data transmissions over short distances from fixed and/or mobile devices, and causes wireless personal area networks (PANs). It also provides a way to con-nect and exchange information between devices such as mobile phones, personal computers, printers, GPS receivers, and video game consoles over a secure, glob-ally unlicensed Industrial, Scientific, and Medical (ISM) 2.4 GHz short-range radio frequency bandwidth.

ZigBee is the name of a specification for a suite of high level communication protocols using small, low-power digital radios based on the IEEE 802.15.4 standard for wireless personal area networks (WPANs). The technology is intended to be simpler and cheaper than other WPANs, such as Bluetooth. ZigBee is targeted at radio frequency applications that require a low data rate, long battery life, and secure networking.

Wi-Fi is the trade name for a popular wireless technology used in home networks, mobile phones, video games and more. Wi-Fi is supported by nearly every modern personal computer operating system and most advanced game consoles [1]-[3].

1.3 Basic Concepts of Coplanar Stripline

The coplanar stripline (CPS) was introduced in the mid-1970’s [4]-[6] as a transmis-sion medium with the capability to provide uniplanar designs. Its cross sectional is shown in Fig. 1.2 [7], [8]. There are top metal , middle dielectric, and no bot-tom metal layer. That is the most different portion between CPS and coupled

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microstripline. Cg Cp Cp Ls Lp Ls

Figure 1.2 Simplified architecture of balanced transceiver system

ЄоЄr X Y Z Dielectric substrate Electric field lines Metal strip D

Figure 1.3 Cross section of coplanar stripline

W W S Balun Balun ∆ ∆ 4-port network [ S ]4 X 4 (a) ∆ Balun Balun (b)

Figure 3.1 (a) balanced s-parameter (b) only differential s-parameter

4-port network [ S ]4 X 4 ∆ ∑ ∑ Balun Balun (a) Differential (Odd) Common (Even) Differential (Odd) Common (Even) Balun Balun Differential

(Odd) Differential_(Odd)

(b)

Figure 3.1(a) balanced s-parameter (b) only differential s-parameter

4-port network [ S ]4 X 4

Figure 2.3.2 Impedance inverter (K-inverter) (a) lumped element (b) transmission line element - L L - L - C C - C (a) K=WL K=1/WC (b) X =WL Φ/2 Φ/2 Z0 Z0 X = - 1/WC Φ/2 Φ/2 Z0 Z0 Φ/2 <0 X> 0 Φ/2 > 0 X< 0 L -L -L

Figure 2.3.1 Admittance inverter (J-inverter) (a) lumped element (b) transmission line element

(a) B < 0 Φ/2 Φ/2 Y0 Y0 Φ/2 > 0 B > 0 Φ/2 Φ/2 Y0 Y0 Φ/2 < 0 B= -1/WL B=WC J=1/WL _J=WC C - C - C (b) Dipole-antenna Balanced Mixer LNA RF IF Baseband LO Balanced Oscillator Balanced Pre-select Filter Balanced Image-reject Filter Mixed signal circuit

Figure 1.2: Cross section of coplanar stripline

According to the Fig. 1.2. The electromagnetic wave is only propagating on the top metal, which is odd mode excitation. It cause differential input and output, which is better to reject the noise.

It could be regarded as virtual ground in the middle of two stripline of top metal layer, which also considered that electrical-wall or perfect conductor (PEC) there. Furthermore, a CPS can achieve higher characteristic impedances (Z0 over

150 ohm) than a coplanar waveguide (CPW) and a microstripline by increasing the distance between the two striplines. It only need to analysis half circuit for design whole circuit. CPS has gained a significant momentum in the design and applications of high-density radio-frequency integrated circuits (RFICs) [9].

Besides, many RF components are designed with differential I/O, such as am-plifiers, mixers and some of the antennas with symmetric structures. The uniform design of RF components with balanced structure can remove the requirement of unbalance-balance transformation which may cause loss to the system. CPS has the

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capability to provide excellent propagation characteristics, such as small dispersion and less sensitivity to substrate thickness when appropriately designed. Moreover , this kind of structure is able to provide integration in a high level, efficient in use of wafer area and has great flexibility in design of uniplanar circuits while the via hole or air-bridge is not needed.

Another advantage of this kind of CPS resonator is that the series connection of the stubs are capable of providing high impedance level and increased Q-value which is desirable in certain case of filter design [10]-[12]. The whole system has been reported [13]-[15] with the co-design of filter and antenna, as shown in Fig. 1.3. Furthermore, it has been widely used as interconnects in high-speed digital circuits and integrated electrooptic components.

Cg

Cp Cp

Ls

Lp Ls

Dipole-antenna Balanced Mixer LNA RF IF Baseband LO Balanced Oscillator Balanced Pre-select Filter Balanced Image-reject Filter Mixed signal circuit ЄоЄr X Y Z Dielectric substrate Electric field lines Metal strip D

(b)

(a) B < 0 Φ/2 Φ/2 Y0 Y0 Φ/2 > 0 B > 0 Φ/2 Φ/2 Y0 Y0 Φ/2 < 0 B= -1/WL B=WC J=1/WL _J=WC C - C - C (b)

Figure 1.3: Simplified architecture of balanced transceiver system

1.4 Summary

Chapter 1 introduced basic concepts about microwave- / RF filter, commercial wireless communication systems and coplanar striplines. Next chapter will discuss

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band-pass filter design theory. Chapter 3 introduces the measurement theory about mixed-mode S-parameters and taper transition circuit. Then, chapter 4 shows de-sign examples and its measurement data. The last chapter is conclusion.

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Chapter 2 Band-Pass Filter Design Theory

This chapter, we will discuss 4-port scattering parameters of CPS, formulas for band-pass filters with Tchebyshev response, and the analytical design method for band-pass filter. The analytical design procedure includes basic concepts of ad-mittance inverter and impedance inverter, and design procedure flow of a CPS band-pass filter.

2.1 4-port Z-Parameter Analysis of the CPS

Cir-cuit

According to the section 1.3, we could analysis a CPS by even mode and odd mode to find its scattering parameters (S-parameters), as shown in Fig. 2.1 and Fig. 2.2. It is a lossless, matched,reciprocal network. θ is electrical length, θeis the even mode

electrical length, and θois the odd mode electrical length. The input impedances are

Zshort−circuit = jZ0tanθ (2.1)

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Figure 2.1 Analysis s-parameter of coplanar strip 3D view

Figure 2.2 Analysis s-parameters of coplanar strip for top view (a) even-even(b) even-odd (c)odd-even (d) odd-odd 1 3 2 4 (a) (b) 1 3 2 4 even odd +V -V +V -V -V +V +V -V (d) 1 3 2 4 odd odd -V (c) 1 3 2 4 odd even -V +V +V 1 3 2 4 even even +V +V +V +V

Figure 2.1: Three dimmensional view of CPS for analyzing of 4-port Z-parameters

Zopen−circuit = −jZ0cotθ (2.2)

In Fig. 2.2 (a) to (d), a PMC in the middle of two stripline in even mode exci-tation and a PEC located between them in odd mode exciexci-tation :

Zee = −jZecot(θe/2),

Zeo = −jZocot(θo/2),

Zoe = jZetan(θe/2),

Zoo = jZotan(θo/2),

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Figure 2.1 Analysis s-parameter of coplanar strip 3D view

Figure 2.2 Analysis s-parameters of coplanar strip for top view (a) even-even(b) even-odd (c)odd-even (d) odd-odd 1 3 2 4 (a) -V (c) 1 3 2 4 odd even -V +V +V 1 3 2 4 even even +V +V +V +V (b) 1 3 2 4 even odd +V -V +V -V -V +V +V -V (d) 1 3 2 4 odd odd

Figure 2.2: Analysis Z-parameters of coplanar stripline for top view(a)even-even(b)even-odd(c)odd-even(d)odd-odd Z11 = −j 2 (Zecotθe+ Zocotθo) Z21 = −j 2 (Zecscθe+ Zocscθo) Z31 = −j 2 (Zecotθe− Zocotθo) Z41 = −j 2 (Zecscθe− Zocscθo) (2.4) as we known: 9

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Z11 = Z22 = Z33 = Z44

Z12 = Z21 = Z34 = Z43

Z13 = Z31 = Z24 = Z42

Z14 = Z41 = Z23 = Z32

Finally, we can obtain the 4-port Z-parameters:

Z =            Z11 Z12 Z13 Z14 Z21 Z22 Z23 Z24 Z31 Z32 Z33 Z34 Z41 Z42 Z43 Z44           

2.2 Tchebyshev Response and Formula

The transfer function of a filter network is a mathematical description of network response characteristics, namely, a mathematical expression of S21. On many

occa-sions,an amplitude-squared transfer function for a lossless passive filter network is defined as

|S21(jΩ)|2 =

1

1 + 2_{F n}2_(Ω) (2.5)

where is a ripple constant, Fn() represents a filtering or characteristic function, and Ω is a frequency variable. For our discussion here, it is convenient to let Ω

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represent a radian frequency variable of a low-pass prototype filter that has a cutoff frequency at Ω = Ωc. For a given transfer function of (2.5), the insertion loss

response of the filter, following, can be computed by LA(Ω) = 10log

1 1 + |S21(jΩ)|2

(2.6) Since |S11|2 + |S21|2 = 1 for a lossless, passive 2-port network,the return loss

re-sponse of the filter can be found

LR(Ω) = 10log[1 − |S21(jΩ)|2](dB) (2.7)

The Tchebyshev response exhibits the equal-ripple pass band and maximally flat stop band, as shown in Fig. 2.3.

Figure 2.3: Tchebyshev lowpass response

The amplitude-squared transfer function that describes this type of response is |S21(jΩ)|2 =

1

1 + 2_{T n}2_(Ω) (2.8)

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where the ripple constant is related to a given pass band ripple LAr in dB by

= q

10LAr10 − 1 (2.9)

Tn(Ω) is a Tchebyshev function of the first kind of order n, which is defined as

T n(Ω) =          cos(ncos−1(Ω)) if |Ω| ≤ 1 cosh(ncosh−1(Ω)) if |Ω| ≥ 1 (2.10)

Hence, the filters realized from (2.8) are commonly known as Tchebyshev filters. For Tchebyshev low-pass prototype filters have a transfer function given in (2.8) with a pass band ripple LAr dB and the cutoff frequency Ωc = 1,the element values

for the 2-port networks may be computed by the following formulas: g0 = 1 ai = sin[ (2i − 1)π 2N ] bk= γ2+ sin2( iπ N) g1 = a1 γ gi = 4ai−1ai bi−1gi−1 i = 1, 2, 3, ..., N (2.11) and gN +1=          coth2₍β 4) if N ∈ even 1 if N ∈ odd (2.12)

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where

β = ln(cothLAr

17.37)

γ = sinh(_2Nβ ) N is order number

In (2.11) and (2.12), we could find any Tchebyshev low-pass prototype element values for any ripple value [16], [17].

2.3 Analytical Method

2.3.1 Basic Concepts of Admittance Inverter and Impedance

Inverter

In this section, we consider the basic admittance-inverter and impedance-inverter model for filter synthesizing [16], [17].

Cg

Cp Cp

Ls

Lp Ls

(b)

L -L -L (a) B < 0 Φ/2 Φ/2 Y0 Y0 Φ/2 > 0 B > 0 Φ/2 Φ/2 Y0 Y0 Φ/2 < 0 B= -1/WL B=WC J=1/WL _J=WC C - C - C (b)

Figure 2.3.2 Impedance inverter (K-inverter) (a) lumped element (b) transmission line element - L L - L - C C - C (a) K=WL K=1/WC (b) X =WL Φ/2 Φ/2 Z0 Z0 X = - 1/WC Φ/2 Φ/2 Z0 Z0 Φ/2 <0 X> 0 Φ/2 > 0 X< 0

Figure 2.4: Admittance inverter (J inverter)(a) lumped element (b) transmission line

First, there are two different types of the admittance inverter (J inverter) model 13

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at Fig.2.4 (a) and (b). One is suited for lumped element and the other is suited for transmission line. The formulas for Fig. 2.4(b) are given as:

J = Y0tan| Φ 2|, Φ = −tan−1(2B Y0 ), |B Y0 | = ( J Y0) 1 − (_YJ 0) 2, (2.13)

Their equivalent model for admittance inverter (J inverter) is at Fig. 2.5.

Cg

Cp Cp

Ls

Lp Ls

Balun Balun ∆ ∆ 4-port network [ S ]4 X 4 (a) ∆ Balun Balun (b)

∆

∑ ∑

Impedance inverter (K-inverter)

(a) lumped element (b) transmission line element - L L - L - C C - C (a) K=WL K=1/WC (b) X =WL Φ/2 Φ/2 Z0 Z0 X = - 1/WC Φ/2 Φ/2 Z0 Z0 Φ/2 <0 X> 0 Φ/2 > 0 X< 0 Dipole-antenna Balanced Mixer LNA RF IF Baseband LO Balanced Oscillator Balanced Pre-select Filter Balanced Image-reject Filter Mixed signal circuit ЄоЄr X Y Z Dielectric substrate Electric field lines Metal strip D W W S Balun Balun (a) Differential (Odd) Common (Even) Differential (Odd) Common (Even) Balun Balun Differential

(b) 4-port network

[ S ]4 X 4

Admittance inverter (J-inverter)

(a) lumped element (b) transmission line element L -L -L (a) B < 0 Φ/2 Φ/2 Y0 Y0 Φ/2 > 0 B > 0 Φ/2 Φ/2 Y0 Y0 Φ/2 < 0 B= -1/WL B=WC J=1/WL _J=WC C - C - C (b)

J

K

Figure 2.5: Equivalent model for J inverter

By duality, there also have two different types of the Impedance inverter (K inverter) model at Fig.2.5 (a) and (b). One is for lumped element, and the other is for transmission line, too. Fig. 2.7 is their equivalent circuit for Impedance inverter (K inverter). The design formular are shown below in (2.14).

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Cg

Cp Cp

Ls

Lp Ls

(b)

L -L -L (a) B < 0 Φ/2 Φ/2 Y0 Y0 Φ/2 > 0 B > 0 Φ/2 Φ/2 Y0 Y0 Φ/2 < 0 B= -1/WL B=WC J=1/WL _J=WC C - C - C (b)

Figure 2.3.2 Impedance inverter (K-inverter) (a) lumped element (b) transmission line element - L L - L - C C - C (a) K=WL K=1/WC (b) X =WL Φ/2 Φ/2 Z0 Z0 X = - 1/WC Φ/2 Φ/2 Z0 Z0 Φ/2 <0 X> 0 Φ/2 > 0 X< 0

Figure 2.6: Impedance inverter (K inverter)(a) lumped element (b) transmission line K = Z0tan| Φ 2|, Φ = −tan−1(2X Z0 ), |X Z0 | = ( K Z0) 1 − (_ZK 0) 2, (2.14) Cg Cp Cp Ls Lp Ls

Balun Balun ∆ ∆ 4-port network [ S ]4 X 4 (a) ∆ Balun Balun (b)

∆

∑ ∑

Impedance inverter (K-inverter)

(a) lumped element (b) transmission line element - L L - L - C C - C (a) K=WL K=1/WC (b) X =WL Φ/2 Φ/2 Z0 Z0 X = - 1/WC Φ/2 Φ/2 Z0 Z0 Φ/2 <0 X> 0 Φ/2 > 0 X< 0 Dipole-antenna Balanced Mixer LNA RF IF Baseband LO Balanced Oscillator Balanced Pre-select Filter Balanced Image-reject Filter Mixed signal circuit ЄоЄr X Y Z Dielectric substrate Electric field lines Metal strip D W W S Balun Balun (a) Differential (Odd) Common (Even) Differential (Odd) Common (Even) Balun Balun Differential (Odd) Differential (Odd) (b) 4-port network [ S ]4 X 4 4-port network [ S ]4 X 4

Admittance inverter (J-inverter)

(a) lumped element (b) transmission line element L -L -L (a) B < 0 Φ/2 Φ/2 Y0 Y0 Φ/2 > 0 B > 0 Φ/2 Φ/2 Y0 Y0 Φ/2 < 0 B= -1/WL B=WC J=1/WL _J=WC C - C - C (b)

J

K

Figure 2.7: Equivalent Model for K inverter 15

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All of them can be proved by Y matrix and Z matrix [18]. Y =     Y11 Y12 Y21 Y22     Z =     Z11 Z12 Z21 Z22     (2.15)

They are useful for filter design which Φ₂ can be absorbed into resonator’ s electrical length in (2.13) and (2.14). Examples electrical length are shown in Fig. 2.8 and Fig. 2.9, where 180o _{means λ/2 resonator.}

DUT

Port 1

Port 3

Port 2

Port 4

DUT

Port 1

Port 2

(a)

(b)

dB(4,3)

dB(3,3)

Figure 2.8: Diagram of J inverter filter

The formulas for J inverter filter as shown in Fig. 2.8 are depicted below.

J01= s GSb1r∆ g0g1 Jjj+1= ∆ s bjrbj+1r gjgj+1 Jnn+1= s GLbnr∆ gngn+1 GS = 1 Z0 = GL (2.16)

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DUT

Port 1

Port 3

Port 2

Port 4

DUT

Port 1

Port 2

(a)

(b)

dB(4,3)

dB(3,3)

Figure 2.9: Diagram of K inverter filter

The design formulas for a filter with K inverters are shown in the following.

K01= s RSx1r∆ g0g1 Kjj+1= ∆ r_x jrxj+1r gjgj+1 Knn+1= s RLxnr∆ gngn+1 RS = RL = Z0 (2.17)

In (2.16) and (2.17), the bjr is susceptance slope parameter of the j-th shunt

resonance, ∆ is fractional bandwidth, use lower case latter. Xjr is reactance slope

parameter of the j-th series resonance, and gj is the Tchebyshev low-pass prototype

element values, which could be obtained in (2.11). By their definition:

bj = ω0 2 dBj(ω) dω |ω=ω0 xj = ω0 2 dXj(ω) dω |ω=ω0 17

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We could obtain: bj =          π 2Yo , λ 2 − resonator π 4Yo , λ 4 − resonator xj =          π 2Zo , λ 2 − resonator π 4Zo , λ 4 − resonator (2.18)

2.3.2 Novel J and K Inverter for CPS

As section 2.1, we already known that CPS could be analyzed by half circuit analy-sis [19]-[22]. In this section, we inductre J and K inverter equivalent model for filter as shown in Fig. 2.10. The half-circuit of the CPS J and K inverter are also shown in the figure.

From Fig. 2.10 (a) to (c), they can be modeling as the equivalent model of CPS’ half-circuit, which also could be proved by (2.15).

The capacitance Cg and Cp that appear in the equivalent π-network as shown in Fig. 2.10(a)and (b) may be determined as Fig. 2.11(a) and (b) by using the EM-simulator, and also the inductance Ls and Lp that appear in the equivalent T -network in Fig. 2.10(c) as Fig. 2.12(a) and (b). In Fig. 2.12, (a) is size-I and (b)is size-II, which W1 of (a) is smaller than (b), and length of (a) is bigger than (b).

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Gap Gap Gap (a) Cg Cp Cp PEC Legth (b) PEC Legth Legth Cg Cp Cp (C) W1 length 2W 2W length W1 Ls Lp Ls PEC

Figure 2.10: Proposed J and K inverter for CPS (a)J inverter (b)J inverter (c)K inverter Cg = − Im(Y21) ω0 Cp = Im(Y11+ Y21) ω0 19

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Ls= Im(Z21) ω0 Lp = Im(Z11− Z21) ω0 (a) (b) 0 0.05 0.1 0.15 0.2 0 10 20 30 40 50 60 70 80 90 100 Gap (mil) Capacitance (pF ) Cg Cp 0 0.1 0.2 0.3 0.4 0.5 0.6 0 100 200 300 400 500 600 Length (mil) Capacitance (pF) Cg Cp

Figure 2.11: Capacitance versus physical dimmension in(a)Gap(b)Lengh According to Fig. 2.11 and 2.12 , we could find the values for filter design, which we need. And then, use (2.19) and (2.20) to calculate the initial guess. We will use

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0 0.5 1 1.5 2 2.5 3 0 10 20 30 40 50 60 70 80 90 100 Width(mil) In duc tanc e(n H ) Ls Lp 0 0.5 1 1.5 0 10 20 30 40 50 60 70 80 90 100 Width (mil) Inducta nce (nH) Ls Lp (a) (b)

Figure 2.12: Inductance versus physical dimmension in (a)size-I (b)size-II them in chapter 4. θj = π − 1 2[tan −1 (2Bj−1j Y0 ) + tan−1(2Bjj+1 Y0 )](radians) C_gjj+1 = Bjj+1 ω0 lj = λg0 2πθj− ∆ e1 j − ∆ e2 j ∆e1_j = ω0C j−1j p Y0 λg0 2π ∆e2_j = ω0C jj+1 p Y0 λg0 2π (2.19)

By duality, there also have:

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θj = π − 1 2[tan −1 (2Xj−1j Z0 ) + tan−1(2Xjj+1 Z0 )](radians) Ljj+1_p = Xjj+1 ω0 lj = λg0 2πθj− ∆ e1 j − ∆ e2 j ∆e1_j = ω0L j−1j s Y0 λg0 2π ∆e2_j = ω0L jj+1 s Y0 λg0 2π (2.20)

where ω0 = 2πf0, and f0 is center frequency. If changes the π to π/2 in

(2.19)-(2.20), we can obtained the formulas for λ/4 resonators cases.

2.3.3 Design Procedure Flow Chart

After knowing the filter parameters for Tchebyshev response and formulas for J / K inverters, we follow the design flow shown in Fig. 2.13 to complete the filter design. First, we have to define band-pass filter’ s center frequency, fractional bandwidth, order, and ripple level. Second, calculate its low-pass prototype element values to obtain J inverter or K inverter values. Third, use analytical method to get the initial design of the filter and fine tune it on EM-simulator. Finally, implement circuit and measure it.

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dB(4,3)

dB(3,3)

band-pass filter design

filter specifications

(fo , FBW, N, response,...)

low-pass prototype element values

( g

0

~ g

n

)

applying J / K inverter model

EM Simulation

choose transmission line type

(µ-stripline , cpw , ...)

Substrate (Є

r

)

implement

measurment

finish

ok no

Figure 2.13: Diagram of design procedure flow

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Chapter 3 Measurement Theory and Taper

Transition Circuit

In this chapter, we will disscuss the measurement of mixed-mode S-parameters. And then compare three types of taper transition circuits for measurement.

3.1 Mixed-mode S-Parameters

DUT Port 1 Port 3 Port 2 Port 4 DUT Port 1 Port 2 (a) (b)

Figure 3.1: (a)Diagram of single-ended 4-port DUT (b)Diagram of differential 2-port DUT

An S-parameter is defined as the ratio of two normalized power waves, that is the response divided by the stimulus. A full S-matrix (3.1) describes every possible

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combination of a response divided by a stimulus. The matrix is arranged in such a way that each column represents a particular stimulus condition, and each row rep-resents a particular response condition. The standard 4-port S-parameters matrix is given below.            b1 b2 b3 b4            =            S11 S12 S13 S14 S21 S22 S23 S24 S31 S32 S33 S34 S41 S42 S43 S44                       a1 a2 a3 a4            (3.1)

Or Bstd = SstdAstd, where Bstd, and Astd are column vectors correspondes incident

outgoing waves respectivly. And Sstd is the standard 4-port S-parameters matrix.

They are shown in (3.2) and (3.3) respectivly .

Bstd =            b1 b2 b3 b4            ; Astd =            a1 a2 a3 a4            (3.2) Sstd=            S11 S12 S13 S14 S21 S22 S23 S24 S31 S32 S33 S34 S41 S42 S43 S44            (3.3) 25

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For a balanced device, differential and common mode voltages and currents can be defined on each balanced port. Differential and common mode impedances can also be defined. A block diagram of a 2-port differential device-under-test (DUT) is shown in Fig. 3.1(b). A mixed-mode S matrix in (3.4) can be organized in a way similar to the single-ended S-matrix, where each column (row) represents a different stimulus (response) condition. The mode information as well as port information must be included in the mixed-mode S matrix.

           bd1 bd2 bc1 bc2            =            Sd1d1 Sd1d2 Sd1c1 Sd1c2 Sd2d1 Sd2d2 Sd2c1 Sd2c2 Sc1d1 Sc1d2 Sc1c1 Sc1c2 Sc2d1 Sc2d2 Sc2c1 Sc2c2                       ad1 ad2 ac1 ac2            (3.4)

Sdidjand Scicj (i, j=1, 2) are the differential mode and common mode S-parameters

respectively. Sdicj and Scicj (i, j=l, 2) are the mode-conversion/ cross mode

S-parameters. The parameters Sdidj (i, j=1, 2) in the upper-left corner of the

mixed-mode S-matrix (3.4) describe the performance with a differential stimulus and dif-ferential response. Sdicj (Scidj) (i, j=1, 2) describes the conversion of common mode

(differential mode) waves to differential mode (common mode) waves.

The mixed-mode parameters in (3.4) can be transformed to standard 4-port S-parameters (3.3). Consider nodes 1 and 2 in Fig. 3.1(a) as a single differential port, and nodes 3 and 4 as another differential port . The relations between the

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response and stimulus of standard-mode and mixed-mode are shown in (3.5) and (3.6). Where ai and bi (i=l to 4) are the waves measured at ports 1-4 in Fig. 3.1(a).

ad1 = √1₂(a1− a3) ac1= √1₂(a1+ a3) bd1 = √1₂(b1− b3) bc1= √1₂(b1+ b3) (3.5) ad2 = √1₂(a2− a4) ac2= √1₂(a2+ a4) bd2 = √1₂(b2− b4) bc2= √1₂(b2+ b4) (3.6)

(3.7)-(3.12) gives the transformation between standard and mixed-mode S-matrices.

Amm = M Astd =            ad1 ad2 ac1 ac2            = √1 2            1 0 −1 0 0 1 0 −1 1 0 1 0 0 1 0 1                       a1 a2 a3 a4            (3.7) Bmm = M Bstd=            bd1 bd2 bc1 bc2            = √1 2            1 0 −1 0 0 1 0 −1 1 0 1 0 0 1 0 1                       b1 b2 b3 b4            (3.8) 27

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M = √1 2            1 0 −1 0 0 1 0 −1 1 0 1 0 0 1 0 1            (3.9) M−1 = M ? |M | = 1 √ 2            1 0 −1 0 0 1 0 −1 1 0 1 0 0 1 0 1            = MT (3.10)

where M is the conversion matrix.

Bmm = SmmAmm =            bd1 bd2 bc1 bc2            =            Sd1d1 Sd1d2 Sd1c1 Sd1c2 Sd2d1 Sd2d2 Sd2c1 Sd2c2 Sc1d1 Sc1d2 Sc1c1 Sc1c2 Sc2d1 Sc2d2 Sc2c1 Sc2c2                       ad1 ad2 ac1 ac2            (3.11)

Use (3.8), (3.7) to substitute (3.11) which can be obtained: M Bstd= SmmAmm

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By multipling A−1_std which can be obtained:

M SstdAstd = SmmM Astd

M SstdAstdA−1std = SmmM AstdA−1std

Here, I=AstdA−1_std and do it against with M matrix which can be written:

M Sstd = SmmM M SstdM−1 = SmmM M−1 At last: Smm = M SstdM−1 =     Sdd Sdc Scd Scc     where Sdd = 1 2     S11− S13− S31+ S33 S12− S14− S32+ S34 S21− S23− S41+ S43 S22− S24− S42+ S44     Sdc = 1 2     S11+ S13− S31− S33 S12+ S14− S32− S34 S21+ S23− S41− S43 S22+ S24− S42− S44     Scd = 1 2     S11− S13+ S31− S33 S12− S14+ S32− S34 S21− S23+ S41− S43 S22− S24+ S42− S44     Scc = 1 2     S11+ S13+ S31+ S33 S12+ S14+ S32+ S34 S21+ S23+ S41+ S43 S22+ S24+ S42+ S44     (3.12) 29

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Cg Ls Ls

Balun Balun (a) Differential (Odd) Common (Even) Differential (Odd) Common (Even) Balun Balun Differential

(b)

(a) B < 0 Φ/2 Φ/2 Y0 Y0 Φ/2 > 0 B > 0 Φ/2 Φ/2 Y0 Y0 Φ/2 < 0 B= -1/WL B=WC J=1/WL _J=WC C - C - C (b) Dipole-antenna Balanced Mixer LNA RF IF Baseband LO Balanced Oscillator Balanced Pre-select Filter Balanced Image-reject Filter Mixed signal circuit ЄоЄr X Y Z Dielectric substrate Electric field lines Metal strip D

W W S Balun Balun ∆ ∆ 4-port network [ S ]4 X 4 (a) ∆ Balun Balun (b) 4-port network [ S ]4 X 4 ∆ ∑ ∑

Figure 3.2: (a)Mixed-mode S-parameters (b)Differential S-parameters As obtained 4-port Z-parameters of CPS in (2.5), and then to extract the mixed-mode S-parameters by (3.12). Actually, the method to find mixed-mixed-mode S-parameters by using a balun in Fig. 3.2(a) is identical to make basis transformation mathe-matically [23]-[25]. In Fig. 3.2(b), it is a test set-up to measure differential mode S-matrix of a DUT.

3.2 Taper Transition Circuits

In this section, three types of transition circuit are introduced and compared for measurement of a CPS line. All circuit are designed with RT/Duroid 4003 substrate with dielectric constant of 3.58 and thickness of 20 mil.

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3.2.1 Type-I Transition Circuit

Type-I, which is shown in Fig. 3.3, considers only couple line effect. The simulation results about Sd1d1 Sd2d1 are shown in Fig. 3.4.

dB(4,3)

dB(3,3)

Figure 3.3: Circuit photo of type-I

In addition, its common to common response is shown in Fig. 3.6.

(4,

3))

Figure 3.6: Broad band common mode measurement result

dB(4,3)

dB(3,3)

Figure 3.7: Circuit photo of type-II

3.2.3 Type-III Transition Circuit

Type-III transition circuit is shown in Fig. 3.11. Not only a taper line portion is added, but also the decreasing of the coupling effect is taken into account. And it is

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dB(4,3) dB(3,3) 1.5 2.0 2.5 3.0 3.5 1.0 4.0 -60 -40 -20 -80 0

freq, GHz

dB

(S

(1,

1))

dB

(S

(2,

1))

dB(4,3) dB(3,3) 2 3 4 5 6 7 1 8 -60 -40 -20 -80 0

freq, GHz

dB

(S

(1,

1))

dB

(S

(2,

1))

Figure 3.9: Broad band differential mode measurement result

the best of all three types of transition circuit. The type-III transition will be used in chapter 4 for measuring of proposed CPS filters. The simulated and measured

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dB(4,3) dB(3,3) 2 3 4 5 6 7 1 8 -60 -40 -20 -80 0

freq, GHz

dB

(S

(3,

3))

dB

(S

(4,

3))

Figure 3.10: Broad band common mode measurement result performances are depicted in Fig. 3.12-3.14.

dB(4,3)

dB(3,3)

Figure 3.11: Circuit photo of type-III

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dB(4,3) dB(3,3) 1.5 2.0 2.5 3.0 3.5 1.0 4.0 -60 -40 -20 -80 0

freq, GHz

dB

(S

(1,

1))

dB

(S

(2,

1))

dB(4,3) dB(3,3) 2 3 4 5 6 7 1 8 -60 -40 -20 -80 0

freq, GHz

dB

(S

(1,

1))

dB

(S

(2,

1))

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dB(4,3) dB(3,3) 2 3 4 5 6 7 1 8 -60 -40 -20 -80 0

freq, GHz

dB

(S

(3,

3))

dB

(S

(4,

3))

Figure 3.14: Broad band common mode measurment result

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Chapter 4 Design Example and

Measurement Data

In the previous chapters we have already known the design formulas and proce-dures for designing a CPS filter, and the measurement techniques have also been discussed in detail in chapter 3. In this chapter, we show a few design examples and their simulated and measured data. All circuit are designed with RT/Duroid 4003 substrate with dielectric constant of 3.58 and thickness of 20 mil.

4.1 Second Order Band-Pass Filter

The ideal half circuit model is shown in Fig. 4.1. We can find the ideal response as shown in Fig. 4.2 by (2.11)-(2.14), and also can obtain the equivalent circuit as shown in Fig. 4.3. Its center frequency f0 is 2.45GHz, and fractional bandwidth ∆

0

Z

0

Figure 4.1: Half circuit model of a second order band-pass filter

1.5 2.0 2.5 3.0 3.5 1.0 4.0 -60 -40 -20 -80 0

freq, GHz

dB

(S

(4,

3))

dB

(S

(3,

3))

Figure 4.2: Narrow band ideal response of second order band-pass filter

dB(4,3) dB(3,3) L L6 R= L=L01 H TLIN TL195 F=2.45 GHz E=E01 Z=50.0 Ohm TLIN TL194 F=2.45 GHz E=90 Z=50.0 Ohm Term Term7 Z=50 Ohm Num=7 TLIN TL196 F=2.45 GHz E=E01 Z=50.0 Ohm C C2 C=C12 F TLIN TL219 F=2.45 GHz E=E12 Z=50.0 Ohm TLIN TL199 F=2.45 GHz E=90 Z=50.0 Ohm TLIN TL197 F=2.45 GHz E=E23 Z=50.0 Ohm Term Term8 Z=50 Ohm Num=8 TLIN TL193 F=2.45 GHz E=90 Z=50.0 Ohm TLIN TL201 F=2.45 GHz E=90 Z=50.0 Ohm TLIN TL198 F=2.45 GHz E=E23 Z=50.0 Ohm L L7 R= L=L23 H TLIN TL200 F=2.45 GHz E=90 Z=50.0 Ohm TLIN TL220 F=2.45 GHz E=E12 Z=50.0 Ohm

Figure 4.3: Equivalent circuit of second order band-pass filter

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frequency f0 is 2.45GHz, and fractional bandwidth ∆ is 7 percent. dB(4,3) dB(3,3) 1.5 2.0 2.5 3.0 3.5 1.0 4.0 -60 -40 -20 -80 0

freq, GHz

dB

(S

(1,

1))

dB

(S

(2,

1))

Circuit photo is shown in Fig. 4.5. The measured results are shown in Fig. 4.6 and 4.7. Fig. 4.5 shown center frequency f0 is 2.4GHz, and fractional bandwidth

∆ is 8 percent. Fig. 4.7 is shown broad band common mode response.

4.2 Third Order Band-Pass Filter

Repeat all steps as second order band-pass filter to design a third order filter. Its ideal circuit model is shown in Fig. 4.8, and its ideal circuit model simulated results are shown in Fig. 4.9. Fig. 4.9 shown center frequency f0 is 2.45GHz, and fractional

bandwidth ∆ is 10 percent.

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dB(4,3)

dB(3,3)

Figure 4.5: Photo of the second order band-pass filter

dB(4,3) dB(3,3) 1 2 3 4 5 6 7 0 8 -60 -40 -20 -80 0

freq, GHz

dB

(S

(1,

1))

dB

(S

(2,

1))

Figure 4.6: Broad band differential mode measurment result

be obtained in Fig. 4.10. After fine tuning, the EM simulated results are depicted in Fig. 4.11, which shown center frequency f0 is 2.45GHz, and fractional bandwidth

∆ is 8 percent.

Circuit photo is shown in Fig. 4.12. The measured results are shown in Fig. 4.13

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dB(4,3) dB(3,3) 1 2 3 4 5 6 7 0 8 -60 -40 -20 -80 0

freq, GHz

dB

(S

(3,

3))

dB

(S

(4,

3))

Figure 4.8: Half circuit model of a third order band-pass filter

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1.5 2.0 2.5 3.0 3.5 1.0 4.0 -120 -100 -80 -60 -40 -20 -140 0 freq, GHz d B (S(3 ,3 )) d B (S(4 ,3 ))

Figure 4.9: Narrow band ideal response of third order band-pass filter

dB(4,3) dB(3,3) TLIN TL193 F=2.45 GHz E=90 Z=50.0 Ohm Term Term8 Z=50 Ohm Num=8 TLIN TL198 F=2.45 GHz E=E34 Z=50.0 Ohm L L7 R= L=L34 H TLIN TL325 F=2.45 GHz E=90 Z=50.0 Ohm TLIN TL197 F=2.45 GHz E=E34 Z=50.0 Ohm TLIN TL221 F=2.45 GHz E=E23 Z=50.0 Ohm C C3 C=C23 F TLIN TL222 F=2.45 GHz E=E23 Z=50.0 Ohm TLIN TL199 F=2.45 GHz E=180 Z=50.0 Ohm Term Term7 Z=50 Ohm Num=7 TLIN TL219 F=2.45 GHz E=E12 Z=50.0 Ohm C C2 C=C12 F TLIN TL194 F=2.45 GHz E=90 Z=50.0 Ohm TLIN TL195 F=2.45 GHz E=E01 Z=50.0 Ohm TLIN TL196 F=2.45 GHz E=E01 Z=50.0 Ohm L L6 R= L=L01 H TLIN TL200 F=2.45 GHz E=90 Z=50.0 Ohm TLIN TL220 F=2.45 GHz E=E12 Z=50.0 Ohm

Figure 4.10: Equivalent circuit of third order band-pass filter

4.3 Fourth Order Band-Pass Filter

We try against to design fourth order band-pass filter for two kinds architecture.

4.3.1 Architecture-I

Its ideal model, ideal response, equivalent circuit, and EM-simulation are shown in Fig. 4.15-4.18, respectively.

Fig. 4.16 shown center frequency f0 is 2.45GHz, and fractional bandwidth ∆ is 15

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dB(4,3) dB(3,3) 1.5 2.0 2.5 3.0 3.5 1.0 4.0 -60 -40 -20 -80 0

freq, GHz

dB

(S

(1,

1))

dB

(S

(2,

1))

dB(4,3)

dB(3,3)

Figure 4.12: Photo of the third order band-pass filter

percent. Fig. 4.18 shown center frequency f0 is 2.45GHz, and fractional bandwidth

∆ is 15 percent.

Circuit photo is shown in Fig. 4.19. The measured results are shown in Fig. 4.20 and 4.21. Fig. 4.20 shown center frequency f0 is 2.34GHz, and fractional bandwidth

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1 2 3 4 5 6 7 0 8 -60 -40 -20 -80 0

freq, GHz

dB

(S

(1,

1))

dB

(S

(2,

1))

1 2 3 4 5 6 7 0 8 -60 -40 -20 -80 0

freq, GHz

dB

(S

(3,

3))

dB

(S

(4,

3))

dB(4,3) dB(3,3)

Figure 4.14: Broad band common mode measurment result ∆ is 15 percent. Fig. 4.21 is shown broad band common mode response.

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K01 J12 K23 90+(Φ01/2)+(Φ12/2) 90+(Φ12/2)+(Φ23/2) Z0 Z0 K01 90+(Φ01/2)+(Φ12/2) J12 180+(Φ12/2)+(Φ23/2) J23 K34 90+(Φ23/2)+(Φ34/2) Z0 Z0 Z0 J01 90+(Φ01/2)+(Φ12/2) K12 90+(Φ12/2)+(Φ23/2) J23 90+(Φ23/2)+(Φ34/2) K34 90+(Φ34/2)+(Φ45/2) J45 Z0 Z0 Z0 Z0 K01 J12 J34 90+(Φ01/2)+(Φ12/2) K45 90+(Φ12/2)+(Φ23/2) 90+(Φ23/2)+(Φ34/2) K23 90+(Φ34/2)+(Φ45/2) Z0 Z0 Z0 Z0

Figure 4.15: Half circuit model of a fourth order band-pass filter of architecture-I

1.5 2.0 2.5 3.0 3.5 1.0 4.0 -60 -40 -20 -80 0

freq, GHz

dB

(S

(3,

3))

dB

(S

(4,

3))

Figure 4.16: Narrow band ideal response of fourth order band-pass filter of architecture-I dB(4,3) dB(3,3) L L2 R= L=L34 H TLIN TL281 F=2.45 GHz E=E34 Z=50.0 Ohm TLIN TL282 F=2.45 GHz E=E34 Z=50.0 Ohm TLIN TL277 F=2.45 GHz E=90 Z=50.0 Ohm TLIN TL271 F=2.45 GHz E=90 Z=50.0 Ohm C C12 C=C45 F TLIN TL268 F=2.45 GHz E=E45 Z=50.0 Ohm TLIN TL267 F=2.45 GHz E=E45 Z=50.0 Ohm Term Term10 Z=50 Ohm Num=10 TLIN TL280 F=2.45 GHz E=E12 Z=50.0 Ohm L L1 R= L=L12 H TLIN TL279 F=2.45 GHz E=E12 Z=50.0 Ohm TLIN TL278 F=2.45 GHz E=90 Z=50.0 Ohm TLIN TL272 F=2.45 GHz E=90 Z=50.0 Ohm C C13 C=C01 F TLIN TL270 F=2.45 GHz E=E01 Z=50.0 Ohm TLIN TL269 F=2.45 GHz E=E01 Z=50.0 Ohm Term Term9 Z=50 Ohm Num=9 TLINTL276 F=2.45 GHz E=90 Z=50.0 Ohm TLIN TL275 F=2.45 GHz E=90 Z=50.0 Ohm TLIN TL274 F=2.45 GHz E=E23 Z=50.0 Ohm TLIN TL273 F=2.45 GHz E=E23 Z=50.0 Ohm C C14 C=C23 F

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dB(4,3) dB(3,3) 1.5 2.0 2.5 3.0 3.5 1.0 4.0 -60 -40 -20 -80 0

freq, GHz

dB

(S

(1,

1))

dB

(S

(2,

1))

Figure 4.18: Narrow band differential mode simulation result of architecture-I

dB(4,3)

dB(3,3)

Figure 4.19: Photo of the fourth order band-pass filter I

4.3.2 Architecture-II

Its ideal model, ideal response, equivalent circuit, and EM-simulation are shown in Fig. 4.22-4.25, respectively. Circuit photo is shown in Fig. 4.26.

Fig. 4.23 shown center frequency f0 is 2.45GHz, and fractional bandwidth ∆ is 15

percent. Fig. 4.25 shown center frequency f0 is 2.45GHz, and fractional bandwidth

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dB(4,3) dB(3,3) 1 2 3 4 5 6 7 0 8 -100 -80 -60 -40 -20 0 -120 20 freq, GHz d B (S(1 ,1 )) d B (S(2 ,1 ))

dB(4,3) dB(3,3) 1 2 3 4 5 6 7 0 8 -60 -40 -20 -80 0

freq, GHz

dB(4,3) dB(3,3) 1 2 3 4 5 6 7 0 8 -60 -40 -20 -80 0

freq, GHz

dB

(S

(3,

3))

dB

(S

(4,

3))

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Chapter 5 Conclusion

In this thesis, we have proposed J and K inverters which are suitable for designing a CPS band-pass filters with λ/2 and λ/4 resonators. An analytical design procedure has been developed, the related design formulas have also been derived. The design curves to extract the series suceptance value and shunt reactance value for J and K inverters have also been achieved. Three types of transition circuits have been developed to extract the mixed-mode S-parameters of filters.

Several CPS bandpass filters have been designed and realized to demonstrate the feasibility of the proposed design method. The measured performances matched well to the simulated ones.

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[10] Young-Ho Suh, and Kai Chang, ”Coplanar stripline resonators modeling and applications to filters,” IEEE Trans. Microw. Theory Tech., vol. 50, no. 5, pp. 1289-1296, May. 2002.

[11] E. G. Cristal, and L. Young, ”Field-extracted lumped-element models of copla-nar stripline circuits and discontinuities for accurate radio-frequency design and optimization,” IEEE Trans. Microw. Theory Tech., vol. MTT-13, pp. 544-558, Sept. 1965.

[12] N. Yang and Z.N. Chen, ”Serially-connected series-stub resonators for narrow-band coplanar stripline narrow-bandpass filters,” IEEEE Microw. Wireless Compon. Lett., vol 15, no. 12, pp. 835-837, Dec. 2005.

[13] Ning Yang, Christophe Caloz, Ke Wu,and Zhi Ning Chen, ”Broadband and compact coupled coplanar stripline filters with impedance steps,” IEEE Trans. Microw. Theory Tech., vol.55, no. 12, pp. 2874-2886, Dec. 2007.

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[14] Ning Yang, Christophe Caloz, Zhi ning Chen and Ke Wu, ”Broadband and compact double stepped-impedance CPS filters with coupled-resonance en-hanced selectivity,” IEEE MTT-S Int. Microw. Sym. Dig. , in Honolulu, HI, Jun. 2007, pp. 755-758,

[15] Ning Yang, Christophe Caloz, and Ke Wu, ”Co-designed CPS UWB filter-antenna System,” IEEE Int. Antennas Propag. Sym. , pp. 1433-1436, Jun. 2007.

[16] J.-S. Hong and M.J Lancaster, Microstripline Filters for RF Microwave Appli-cations, New York: Wiley, 2001.

[17] G.L Matthaei, L. Young, and E.M.T. Jones, Microwave Filters, Impedance-Matching Network, and Coupling Structures, Boston,MA: Artech House, 1964. [18] D.M. Pozar, Microwave Engeineering,2nd ed., New York: Wiley, 1998.

[19] C.-H. Wu, C.-H. Wang, and C.H. Chen, ”Balanced coupled-resonator band-pass filters using multisection resonators for common-mode suppression and stopband extension,” IEEEE Trans. Microw. Theory Tech., vol. 55, no. 8, pp. 1756-1763, Aug. 2007.

[20] Sergei A. Doberstein, and Vladimir K. Razgoniaev, ”Balanced front-end hybrid SAW modules with impedance conversion,” IEEE Ultrasonics Sym., 2002.

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[21] Chia-Cheng Chuang and Chin-Li Wang, ”Design of three-pole single-to-balanced bandpass filters,” ,in 36th Eur. Microw. Proc., Manchester, UK, Sep. 2006, pp.1193-1196.

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[25] D.E. Bockelman and W.R. Eisenstadt, ”Combined differential and common-mode scattering parameters theory and simulation,” IEEE Trans. Microw. The-ory Tech., vol. 43, no. 7, pp. 1530-1539, July. 1995.

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Abstract

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Contents

List of Tables

List of Figures

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