Advances in Materials Science and Engineering

Volume 2015, Article ID 645638, 7 pages

http://dx.doi.org/10.1155/2015/645638

## Design of Tunable Equalizers Using Multilayered Half Mode Substrate Integrated Waveguide Structures Added Absorbing Pillars

^{1}Department of Electromagnetic Wave and Antenna Propagation, Institute of Information Science and Technology of Zhengzhou, Zhengzhou, Henan 450001, China^{2}Microwave Tech and Antenna, Department of Electronic Engineering, Tsinghua University, Beijing 100084, China

Received 7 June 2015; Revised 17 September 2015; Accepted 28 September 2015

Academic Editor: Giovanni Berselli

Copyright © 2015 Shuxing Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

An equalizer based on multilayered half mode substrate integrated waveguide (HMSIW) structures with high -factor, low loss, and compact size is proposed for the first time. Resonant cavities distributing in the upper substrate and the bottom substrate, with the middle substrate layer which works as the transmission line together, constitute a multilayer structure. The design method and theoretical analysis are summarized first. The mode analysis, simulated results, and measured results are all provided. The measured results show a good performance and are in agreement with the simulated results, and the maximum attenuation slope reaches −16 dB over 12.5 GHz~14.5 GHz. With the use of absorbing pillars, the attenuation and value can be tuned more easily than the other planar equalizers. Compared with the SIW equalizer, the size of this structure reduces by 50%. Furthermore, this structure is suitable for the miniaturization development of equalizers.

#### 1. Introduction

The equalizers are used to compensate the output gain slope fluctuation of traveling wave tube amplifiers (TWTAs) in the radar systems [1]. The equalizers are placed mostly between the preamplifier and the postequipped TWTA rather than the back-end of TWTA due to the high output power of TWTA. The preamplifier provides the same exciting power at each frequency point for the post-TWTA. In this way, the output gain of TWTA has a large fluctuation, whereas the output power of TWTA we need is the same at each frequency point. The equalizer, whose attenuation frequency characteristics are complementary with the output power characteristics of TWTA in form, is designed to transform the original exciting power into the optimal exciting power required by TWTA to get the best output power. Equalizers play an important role in improving the detection distance of radars. value is the ratio of the energy stored in the resonant cavity to the energy loss of each cycle and it is an important parameter in resonant circuits. The bigger the value is, the more energy the resonant cavity stores. The equalizers with high value can be used in high power amplifier system.

Nowadays, equalizers in rectangular waveguide type loaded coaxial cavity (narrow bandwidth) and planar type loaded open resonant stub (relatively wide bandwidth) have been applied in lots of microwave and millimeter systems [2–6]. On the other hand, the integrated level of RF, microwave, and millimeter wave circuits is getting higher and the size of components is getting smaller due to the rapid development of new materials and new technology. The miniaturization has become the development trend of passive microwave components, including equalizers [7]. The demand for equalizers with small size, low loss, and high value grows gradually. The traditional equalizers, such as coaxial cavity equalizers with large size and microstrip equalizers with high insertion loss and low value, cannot meet the need of TWTAs.

Substrate integrated waveguide (SIW) is a new planar electromagnetic guide wave structure and is better than the traditional microstrip and waveguide type for the superiority of the small size, high value, and low insertion loss. Nowadays, this structure is being widely used in the design of microwave and millimeter wave devices [8–14]. In [12] a single layer SIW equalizer with large size is proposed whose attenuation cannot be tuned. In [13] an equalizer is fabricated using complex LTCC technology, and it has a large insertion loss because of the substrate’s uneven surface. In [14] a dual layer equalizer is designed which cannot tune the attenuation and value, and the probe excitation plays a poor role in coupling energy into cavities. What is worse, the size of SIW structure is still difficult to meet the requirement of the equalizer’s miniaturization.

Compared with SIW, Half mode substrate integrated waveguide (HMSIW) has a smaller size but with the same performance, and the integrated degree of the substrate integrated waveguide type device is improved [15]. This structure has been widely used in microwave and millimeter wave devices [16, 17] except equalizers.

Based on [14] written by authors, for the first time, an equalizer based on multilayered HMSIW structures is designed and fabricated. It has six cascaded HMSIW resonators. Each of them serves as an independent attenuation tune substructure unit.

#### 2. Design Procedure and Analysis

A linear array of metallized via holes in substrate, with the upper metallic surface and bottom metallic surface, constitutes the HMSIW structure. A substrate with dielectric constant 11.9 is selected in this paper to simulate and fabricate the equalizer. The thickness of substrate is 0.6 mm.

##### 2.1. The Design of HMSIW Transmission Line

To design the HMSIW equalizer, the HMSIW transmission line should be discussed first. It locates in the middle layer. This structure is used to transmit energy and to excite HMSIW cavities distributing in the upper and bottom layer. To only transit the dominant mode, TE_{10} mode, and to inhibit the high-order modes, the dimension of HMSIW should be calculated precisely.

HMSIW can be equivalent with the conventional rectangle waveguide; transformation equations are given as follows [18]:where and are the length and width of HMSIW, respectively, and and are the width and length of rectangle waveguide, respectively. is the diameter of via hole and is the distance between via holes. When and , the rectangle waveguide resonant cavity theory can be applied to the design of HMSIW resonant cavity.

##### 2.2. The Design of Transition between Microstrip and HMSIW

As the HMSIW transmission line is excited by a microstrip line, the microstrip-to-HMSIW transition is designed to guarantee the impendence matching. It is the characteristic impedance rather than the wave impedance that should be focused. The equivalent characteristic impedance of HMSIW derived from the characteristic impedance of conventional rectangular waveguide [19] is given in (4).

The equation of characteristic impedance of conventional rectangular waveguide is as follows: where and are the width and height of conventional rectangular waveguide, respectively, is magnetic permeability, is dielectric constant, and is working wavelength.

We replace and with the height and the equivalent width of HMSIW, respectively. Using the equation, where is the wave impedance, we get where is the wave impedance of TEM mode in the air, is the height of the dielectric substrate, and is relative permittivity.

The microstrip line is well suited to excite the waveguide because the electric fields of the two dissimilar structures are approximately oriented in the same direction and also they share the same profile.

Multiple microstrip lines with different widths and lengths are adopted in this paper to design the transition. The main idea is (1) getting the impedance of HMSIW by (4) and then making it equal to the impedance of microstrip; (2) using the microstrip transmission line impedance equation to calculate the width of a single tapered transmission line; and (3) giving the length of this line segment and calculating the input impedance and repeating the steps above, until the input impedance nearly reaches .

Figure 1 shows the measured and the simulated result of the proposed transition made up of five microstrip segments. The maximum measured insertion loss is nearly 0.15 dB in the entire band, better than 0.7 dB in [19].