International Journal of Electronics, Communication & Instrumentation Engineering Research and Development (IJECIERD) ISSN 2249-684X Vol. 3, Issue 2, Jun 2013, 101-108 © TJPRC Pvt. Ltd.

DESIGN OF S PARAMETERS FOR VARIOUS FILTERS

P. CHANDRA SEKHAR1, Y. RAJ GOPAL2 & T. NAGA VENKATA CHANDRA SEKHARA RAO3 1Member, IEEE & Assistant Professor in Department of ECE, Gitam Institute of Technology, GITAM University, Visakhapatnam, Andhra Pradesh, India 2,3Student Member, IEEE & B.Tech, Department of ECE, GITAM University, Visakhapatnam, Andhra Pradesh, India

ABSTRACT

The response of scattering parameters for various filters at microwave frequency range is presented in this paper. Although applicable at any frequency, S-parameters are mostly used for networks operating at radio frequencies (RF) where signal power and energy considerations are more easily quantified than currents and voltages. The basic idea consists of considering the filter as a two port network, then the open circuit and closed circuit responses of the filter can be derived by using the Impedance parameters. The scattering parameters are obtained by using the Impedance parameters.Insertion loss, return loss, voltage standing wave ratio (VSWR) for different filters in terms of S-parameters have been plotted at X-band frequency.Return loss is a measure of how well devices or lines are matched. A match is good if the return loss is high. A high return loss is desirable and results in a lower insertion loss. This paper which in turns provides most efficient filters used at radar receivers.

KEYWORDS: S-Parameters, Insertion Loss, Return Loss, Voltage Standing Wave Ratio etc

INTRODUCTION

In many applications of electric networks a pair of terminals are designated as the input terminals and another pair of terminals as the output terminals. If we consider an audio amplifier, we can designate the microphone end and the speaker end as the input and output terminals, respectively.

The nodes internal to the amplifier itself are of secondary importance. In this case/ the amplifier is considered as a block. Of course, we can think of systems which are made up of a number of such blocks. Each block is characterized by relationships between its terminal currents and voltages. A pair of terminals, such that the current entering one of the terminals is the same as the current leaving the other, is designated as a "port”[2].

A two port network or junction is formed when there is a discontinuity between the input and output ports of a transmission line. Many configurations of such junctions practically exist.

During propagation of microwaves through the junction from one port to other ,evanescent modes are excited at each discontinuity which contain reactive energy. Evanescent Modes decay very fast away from the junction and become negligible after a distance of order one wavelength.

The terminal reference planes 1 and 2 are chosen beyond this distance so that the equivalent voltage and currents at these positions are proportional to the total transverse electric and magnetic fields, respectively, for the propagating mode only. These circuits are analysed using S-matrix formulation[5][4].

The following figures show a general two-port and the standard convention adopted in designating the terminal voltages and currents. 102 P. Chandra Sekhar, Y. Raj Gopal & T. Naga Venkata Chandra Sekhara Rao

Figure 1: Low Pass Filter

Figure 2: High Pass Filter

Figure 3: Band Pass Filter

Figure 4: Band Stop Filter

Z-PARAMETERS

The z-parameters are also known as open-circuit impedance parameters. In z-parameters the input and output voltages for a two-port network i.e and are expressed in terms of the input and output currents[8]. Design of S Parameters for Various Filters 103

While the lower frequency network parameters (such as Z- or Y- matrices, etc.) are defined in terms of net voltage and currents at the ports, these concepts are not practical at high RF/Microwave frequencies where it is found that any set of parameters to be meaningful, must be defined in terms of a combination of traveling waves[1].

S- PARAMETERS

The network representation of a two-port network at high RF/microwave frequencies is called “scattering parameters”[1] (or “S-parameters” for short).The high frequency S-parameters are used to characterize high RF/Microwave two-port networks. These parameters are based on the concept of travelling waves and provide a complete characterization of any two-port network under analysis or test at RF/Microwave frequencies[1].In view of the linearity of the electromagnetic field equations and the linearity displayed by most microwave components and networks, the “scattered waves” (i.e. the reflected and transmitted wave amplitudes ) are linearly related to the incident wave amplitude. The matrix describing this linear relationship is called the “scattering matrix” or [S] [1].

S-parameters as defined above, have many advantages at high RF/Microwave frequencies which can be briefly stated as :

 S-parameters provide a complete characterization of a network, as seen at its ports.

 S-parameters make the use of short or open (as prescribed at lower frequencies) completely unnecessary at higher frequencies. It is a known fact that the impedance of a short or an open varies with frequency which is one reason why they are not useful for device characterization at high RF/Microwave frequencies. Furthermore, the presence of a short or open in a circuit in a circuit can cause strong reflections which usually lead to oscillations or damages to the transistor circuitry.

 S-parameters require the use of matched loads for termination and since the loads absorb all the incident energy, the possibility of serious reflections back to the device or source is eliminated[1].

This paper describes the normalized S-parameters at x-band frequency for various filters (i.e for Fig.1,Fig.2,Fig.3,Fig.4) that are calculated from the Z-parameters using the formulas given in [3].

The values of resistors, capacitors, inductors and characteristic impedance used for plotting graphs between S parameters and frequency are given below: R = 50 Ω,C = 10 µF ,L = 0.5 H and = 50 Ω.

Figure 5: Scattering Parameters of Low Pass Filter 104 P. Chandra Sekhar, Y. Raj Gopal & T. Naga Venkata Chandra Sekhara Rao

Figure 6: Scattering Parameters of High Pass Filter

Figure 7: Scattering Parameters of Band Pass Filter

Figure 8: Scattering Parameters of Band Stop Filter

Figure 9: Parameters for Various Filters Design of S Parameters for Various Filters 105

Figure 10: Parameters for Various Filters

INSERTION LOSS, RETURN LOSS AND VSWR

When dealing with the broad field of telecommunication engineering, we will often encounter the terms Insertion loss, Return loss and VSWR .These terms give us important information about a two port network in place in a circuit. Two port just means that we have an input(port) and output(port)[7].Insertion loss is defined as the ratio of power available from the source to the power delivered to the load[6]. Return loss is defined as the ratio of power available from the source to the power reflected from the filter[6]. Return loss is an important concept that sometimes confuses the student, particularly when dealing with the telephone network. We must remember that we achieve a maximum power transfer in an electronic circuit when the output impedance of a device (network) is exactly equal to the impedence of the device or transmission line connected to the output port. Return loss tells us how well these impedances match ; how close they are to being equal in value (ohms) to each other[7].

When EM Waves propagate in two directions inside a transmission line, a “standing-wave” pattern is formed. Voltage standing wave ratio (VSWR) is by definition the ratio of the maximum to the minimum voltages in the line. During measurements, the probe was slid along the line through a distance of at least a quarter-wavelength to record the maximum and minimum voltages of the standing wave pattern[9].

The values of resistors, capacitors, inductors and characteristic impedance used for plotting the following graphs are given below:

R = 50 Ω,C = 10 µF ,L = 0.5 H and = 50 Ω.

Figure 11: Insertion Loss for Various Filters at Different Frequencies

106 P. Chandra Sekhar, Y. Raj Gopal & T. Naga Venkata Chandra Sekhara Rao

Figure 12: Return Loss for Various Filters at Different Frequencies

Figure 13: VSWR for Various Filters at Different Frequencies

CONCLUSIONS

Scattering parameters are mostly used for networks operating at micro wave frequencies.This paper describes the design of S-parameters for various filters. Insertion loss, return loss and voltage standing wave ratio (VSWR) are obtained and have been plotted at X-band frequency(microwave frequencies). This paper which in turn provides most efficient filters used at radar receivers.

REFERENCES

1. Matthew M.Radmanesh. “Advanced Rf &Microwave Circuit Design: The Ultimate Guide to Superior Design”, AuthorHouse,2009. 2. vasudev k Aatre. , “Network theory and filter design”, New age international publishers,Second edition, 1980. 3. Ian A.Glover,Steve Pennock, Peter Shepherd ,“Microwave, Devices, Circuits and subsystems for communications”, John Wileyand sons, 2005 4. Ian Hunter, “Theory and design of microwave filters”, The, institution of Electrical Engineers, 2001. 5. Annapurna Das,Sisir K.Das, “Microwave Engineering” , tatamcgraw hills, 2000 6. V.S.bagad , “Microwave engineering” , Technical, communications,Jan 2009 7. Roger L. Freeman , “Fundamentals of telecommunications”, John Wiley and sons, second edition. 8. Smarajit Ghosh, “Network Theory:Analysis And Synthesis”, Prentice Hall of India Limited,2005 9. Les Besser,Rowan Gilmore,“Pratical RF Circuit Design for Modern Wireless Systems,VolumeI”,Artech House,INC.2003 Design of S Parameters for Various Filters 107

AUTHOR’S DETAIL

Mr.P.Chandrasekhar, Member of IEEE& Antenna Propagation Society has completed B.Tech in Electronics and Communication Engineering from Andhra University. He completed M.Tech from AndhraUniversity with a specialization in Radar and Microwave Engineering. Presently he is working as an Assistant Professor in Department of ECE, Gitam Institute of Technology, GITAM University, Visakhapatnam.

Mr.Y.Raj Gopal, Student member of IEEE is currently pursuing his B.Tech degree in Electronics and communication Engineering from GITAM University

Mr. T. Naga venkata Chandra sekhara rao, Student member of IEEE is currently pursuing his B.Tech degree in Electronics and communication Engineering from GITAM University