**International Journal of Emerging Technology and Advanced Engineering **

**Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 1, January 2012)**

### 92

## Review of Impedance Matching Networks for Bandwidth

## Enhancement

### Rashmi Khare

1### , Prof. Rajesh Nema

2*1*

*M.Tech Scholar, Department of Electronics And Communication, NIIST, Bhopal, M.P. India *

2

Department of Electronics And Communication, NIIST, Bhopal, M.P. India

1_{rashmi.khare17@gmail.com }

2_{rajeshnema2010@rediffmail.com }

**Abstract—****A number of techniques can be used to eliminate **
**reflections when the characteristic impedance of the line and **
**the load impedance are mismatched. Impedance matching **
**techniques can be designed to be effective for a specific **
**frequency of operation (narrow band techniques) or for a **
**given frequency spectrum (broadband techniques). The **
**purpose of this paper is to make a comparative study on **
**bandwidth enhancement techniques of impedance matching **
**networks that help to overcome the bandwidth constraint of **
**transmission line. In this paper work narrowband impedance **
**matching networks like lumped element, single stub, double **
**stub, quarter-wave transformer and broadband impedance **
**matching techniques like binomial, and chebyshev are studied**.** **

* Keywords*—

**Bandwidth, Narrowband matching,**

**Character-istic impedance, Broadband matching, Reflection coefficient**

I. INTRODUCTION

In many cases, loads and termination for transmission lines in practical will not have impedance equal to the characteristic impedance of the transmission line. This result in high reflections of wave transverse in the transmission line and correspondingly a high VSWR due to standing wave formations, one method to overcome this is to introduce an arrangement of transmission line section or lumped elements between the mismatched transmission line and its termination/loads to eliminate standing wave reflection. This is called as impedance matching. Matching the source and load to the transmission line or waveguide in a general microwave network is necessary to deliver maximum power from the source to the load. In many cases, it is not possible to choose all impedances such that overall matched conditions result. These situations require that matching networks be used to eliminate reflections.

Depending on the application, matching may be required over a band of frequencies such that the bandwidth of the matching network is an important design parameter. If the load impedance varies over a given range, a matching network which can be adjusted or tuned as necessary. In general, matching networks are constructed with reactive components only so that no loss is added to the overall network.

T-line or waveguide to termination matching network

T-line or waveguide to T-line or waveguide matching network

**International Journal of Emerging Technology and Advanced Engineering **

**Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 1, January 2012)**

### 93

Impedance matching networks at a single frequency can be designed without much difficulty to provide a reflection coefficient of zero at the desired frequency. However, in many applications it is desirable to match impedances over a range of frequencies. One method of improving control over the bandwidth of the matching network is by adding one more element to the simple L-section lumped-element (lumped-elements are feasible for frequencies up to about 1 GHz.) matching circuit thereby creating a T-section. However, with the use of an iterative optimization routine, L-sections can simply be added to provide the required impedance matching over a given bandwidth. It should be noted that an iterative procedure is not necessary for fixed known loads. However, it is very useful for loads that varywith frequency and parasitic effects

### .

### One way of designing broadband matching networks is to use multiple sections of transmission line rather than just one section as in the case of the quarter wave transformer. In order to simplify the analysis of these multiple section matching networks, the theory of small reflections is utilized.

II. LITERATURE SURVEY

A paper by Unlu Mehmet was published in 2003 that describes how to design, model, and fabricate an RF MEMS adjustable impedance matching network. The device employs the basic triple stub matching technique for impedance matching. It has three adjustable length stubs which are implemented using capacitive loaded coplanar waveguides. The capacitive loading of the stubs are realized using the MEMS switches which are evenly distributed over the stubs. There are 40 MEMS bridges on each stub which are separated with λ/40 spacing making a total of 120 MEMS switches in the structure. The variability of the stub length is accomplished by closing the MEMS switch nearest to the required stub length, and making a virtual short circuit to ground. The device is theoretically capable of doing matching to every point on the Smith chart.

The device is built on coplanar waveguide transmission lines. It has a center operating frequency of 10GHz, but because of its adjustability property it is expected to work in 1-40GHz range. It has dimensions of 8950 × 5720μm2.

This work is the continuation of the first national work on fabrication of RF MEMS devices. The device in this work is fabricated using the surface micromachining technology in the microelectronic facilities of Middle East Technical University.

A paper by Alfred R. Lopez was published in 2004 which states many antennas can be characterized by their radiation Q (The ratio of reactance to radiation resistance. A classic problem is determining the maximum possible bandwidth.

Constrained by the maximum permissible reflection
magnitude R, and the no. of tuned circuit n in the
impedance matching circuit.This paper presents the fano’s
relationship among *Bn, Q, R , for any number of tuned *
circuits and these fano’s equations are solved by using
MATHCAD software. This paper presents a multiple
tuning impedance-matching networkit is clear that increase
in bandwidth occurs when impedance matching circuit
increase by one tuning level.

A paper by Bo-Yang Chang was published in 2005 that describes a low-voltage; low-power ultra-wideband (UWB) low-noise amplifier (LNA) for IEEE 802.15.3a. A simplified Chebyshev filter is used to achieve the input broadband matching. This input network has lower complexity and good reflected coefficient from 3.1GHz to 10.6GHz. An output-matching buffer is designed specially to match for maintaining high gain at upper frequency. Therefore, it can both achieve flat gain over the whole bandwidth and generate more output current. The LNA is simulated based on TSMC 0.18μm mixed signal/RF process. With only 1V bias voltage, the LNA can achieve power flat gain of 10dB with input matching of -9.76dB; the minimum noise figure 3.7dB; and input third-order-intercept point (IIP3) of -1dB. The power dissipation is only 7.2mW.

**International Journal of Emerging Technology and Advanced Engineering **

**Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 1, January 2012)**

### 94

It is found that employing an impedance-matching network directly to HTS micro-strip antennas to broaden their bandwidth is of little significance.A paper by G. Castaldi was published in 2008 that describes an exact synthesis method which allows the design of dual-band transformers with an arbitrary even number of uniform sections giving equi-ripple impedance matching in two separate bands centered at two arbitrary frequencies. This method is a generalization of the exact Collin-Riblet synthesis of Chebyshev single-band transformers. As compared to a single-band Collin-Riblet transformer encompassing both required pass-bands, the proposed design yields significantly better performance in terms of pass-band tolerance and width. Reflection coefficient equation for chebyshev

A paper by Y. Wu, Y. Liu and S. Li was published in 2008 that describes a compact pi-structure transformer operating at arbitrary dual band is proposed in this paper. To achieve the ideal impedance matching, the exact design formulas with no restrictions are obtained. In addition, it is found that there are infinite solutions for this novel transformer considering the fact that three independent variables exist in two equations. Furthermore, to verify the design formulas, the reflection characteristics in different cases are shown by numerical simulations. The horizontal length of this transformer is half of the Monzon’s dual band transformer. The proposed dual band transformer can be used in many compact dual band components such as antennas, couplers and power dividers.

A paper by Vicente Gonzalez-Posadas was published in 2008 that describes a semi-lumped balun transformer for UHF and ultra wideband (UWB) dipole antennas. The proposed structure is based on two asymmetric filters that also transform the variable antenna impedance into the desired source impedance. These asymmetric filters make use of a binomial impedance transformer in each filter section. The asymmetric filters (one low pass filter, LPF, and other high pass filter, HPF) allow the balun bandwidth to be increased while the binomial transformer matches the variable balanced dipole impedance.

In this way the ripple in the balun response due to the variation of the UWB dipole impedance is reduced. A balun for a UHF and UWB dipole antenna working from 220 to 820 MHz (bandwidth of 4:1) has been achieved with losses lower than 1 dB. These types of baluns are particularly useful in the low microwave frequency band.

III. PROBLEM ANALYSIS

For frequencies up to approximately 1 GHz, matching networks containing lumped elements (L-networks) may be used. The circuit elements (capacitors and inductors) must be small enough relative to wavelength so that the normal circuit equations for voltage and current are valid. This is

used for narrowband frequency impedance matching

### .

We can obtain any value of reactance or susceptance with the proper length of short-circuited or open-circuited transmission line, we may use these transmission line stubs as matching networks. A single stub network suffers from the disadvantage of requiring a variable length of t line between the load and the stub. This may not be a problem for fixed transformation network, but would pose some difficulty if an adjustable tuning network is desired.Short-circuited or open-circuited transmission line, we may use these transmission line stubs as matching networks. A single stub network suffers from the disadvantage of requiring a variable length of t line between the load and the stub. This may not be a problem for fixed transformation network, but would pose some difficulty if an adjustable tuning network is desired.

A quarter-wave transformer (QWT) is a simple and useful circuit for matching real load impedance to a transmission line. An additional feature is that it can be extended to multi-section design for broader bandwidth. Although quarter-wave transformer can in theory used to match complex Impedance, it is more common to use it to match real impedance. At the operating frequency fo, the

electrical length of the matching section is o/4. But at

**International Journal of Emerging Technology and Advanced Engineering **

**Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 1, January 2012)**

### 95

For applications requiring more bandwidth than a single quarter wave section can provide, multi-section transformers can be used.BINOMIAL TRANSFORMER

•Impedance of consecutive 1/4 wave lines are proportional to binomial coefficients.

•Gives maximally flat pass-band characteristic.

A Binomial Multi-section matching network will have a perfect match at the frequency where the section lengths are a quarter wavelengths!

CHEBYSHEV TRANSFORMER

•Wider bandwidth than Binomial Transformer for the same number of ¼ wave sections.

• Ripple over pass-band.

A Chebyshev multi-section matching transformer can provide even larger bandwidths than a binomial multi-section matching transformer for a given number of transmission line sections. The increased bandwidth of the Chebyshev transformer comes at the cost of increased ripple over the pass-band of the matching network. However, we may still designate some maximum allowable reflection coefficient for the design of the Chebyshev transformer. The Chebyshev transformer exploits the characteristics of the Chebyshev polynomials

IV. METHODOLOGY

Ideal lumped element and single stub matching networks provide perfect matching (Ã=0) at only one frequency. However, the component configuration in a lumped element matching network and the stub position in a stub matching network will affect the frequency response of the network away from the design frequency. We may plot the frequency response of the reflection coefficient to illustrate the different responses. Given either type of matching network, the reflection coefficient looking into the matching network may be written as

In order to determine the variation of Z*in with respect to *
frequency, we need to know the variation of the load
impedance with respect to frequency. According to the
design equations, we will find out the input impedances for
the two networks looking into the matching network input
ports are

For the case of the shunt stub networks, the input admittance looking into the matching network is

We find Zin, l by inserting (l1,d1) and find Zin, 2 by inserting

*(l2, d2). *

Compare the frequency responses of the lumped element matching networks and the stub tuners.

In case of **binomial multisection matching transformer**

the general form of the reflection coefficient approximation
for the *N *section matching transformer can easily be
written in terms of a binomial series according
to

**International Journal of Emerging Technology and Advanced Engineering **

**Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 1, January 2012)**

### 96

The percentage bandwidth of the transformer may be written asIn case of chebyshev multi-section matching transformer we will find out the equation for the reflection coefficient reflection coefficient of an N section multi-section matching transformer may be written as

Now we will find out the angle theta m and nth order chebyshev polynomial is found by

Inserting these values in reflection coefficient formula and equating the coefficient associated with the cosine terms and the remaining local reflection coefficients are found by symmetry and then we will find out the resulting characteristics impedances.

V. CONCLUSION

This study provided an insight in determining the performance of impedance matching networks for bandwidth enhancement. As in our study we see that broad-band impedance matching networks like binomial multi-section matching transformer and chebyshev multi-multi-section matching transformer provide more enhanced bandwidth than narrow-band impedance matching networks.

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