LOW PASS FILTER DESIGN COMPARISON USING AGILENT GENESYS

LOW PASS FILTER DESIGN COMPARISON USING AGILENT GENESYS

ABSTRACT

Wireless communication is becoming more and more popular. In this paper, a maximally flat low-pass filter and a equal-ripple low-pass filter have been designed for Ultra High Frequency (UHF) band ie I.T.U. band 9 (Frequency 300Mhz – 3000Mhz; Wavelength 1m – 100mm).Application of UHF band includes television, microwave ovens, mobile phones, wireless LAN, Bluetooth, etc. The filters are designed from the method of „Impedance and Frequency Scaling‟. The design parameters and return loss are discussed. Also the amplitude (attenuation in dB) vs frequency graph is obtained for both the filters and their results are compared and suitable conclusions are drawn. The filters are designed using Agilent Genesys 2010.05

Keywords: Agilent Genesys Simulator; Low Pass Filter; Equal-ripple filter; Smith chart; Polar Chart; Maximally flat filter; Wireless communication; UHF Band Spectrum; S Parameters.

INTRODUCTION

Various mobile cellular systems need a miniaturized size filter which should ideally have a sharp cut-off. Also, various radio frequency communication filters are gaining popularity. Low pass filters are widely preferred today. The need to filter out the transmitted and received signals with a specific bandwidth has been the task for many engineers today. Filter designs beyond 500MHz are difficult to realize with discrete components because the wavelength becomes comparable with the physical filter element dimensions, resulting in various losses severely degrading the circuit performance. Thus to arrive at practical filters, Impedance and Frequency Scaling is done and the lumped elements are directly simulated using RF simulator Agilent Genesys 2010.05.

In this paper, a maximally flat low-pass filter and an equal ripple low-pass filter have been designed for Ultra High Frequency (UHF) band with a cutoff frequency of 700 Mhz and order 7. A lumped L-C network is modeled with the „minimum inductor‟ and „minimum capacitor‟ configurations after Impedance and Frequency Scaling. Then, the amplitude (attenuation in dB) vs frequency plot is compared between the two filters. RF synthesis software „Agilent Genesys 2010.05‟ is used for the purpose.

Agilent Genesys 2010.05 is an affordable, accurate, easy-to-use RF and microwave simulation software created for the circuit board and subsystem designer. It’s key features includes RF system analysis and frequency planning with interactive root cause problem identification and linear and nonlinear RF circuit simulators with optimization and statistical analysis for high-performance and high-yield designs.

RELATED WORK

In this paper, a maximally flat low-pass filter and an equal ripple low-pass filter have been designed for Ultra High Frequency (UHF) band with a cutoff frequency of 700 Mhz and order 7. The filters have input and output resistances of 50 ohms. The filters are designed from the method of „Impedance and Frequency Scaling‟. The design parameters and return loss are discussed. Also the amplitude (attenuation in dB) vs frequency graph is obtained for both the filters and their results are compared and suitable conclusions are drawn. The filters are designed using Agilent Genesys 2010.05

THEORY

For a normalized low-pass design, where the source impedance is 1 Ω and the cutoff frequency is ωc = 1 rad/sec, the element values for the ladder-type circuits in the below figures can be tabulated by using the standards tables.

 

Fig.1. Ladder circuits for low-pass filter prototypes – Prototype beginning with a shunt element.

 

Fig.2. Ladder circuits for low-pass filter prototypes – Prototype beginning with a series element.

IMPEDANCE SCALING

In the prototype design, the source and load resistances are unity. A source resistance of R0 can be obtained by multiplying all the impedances of the prototype design by R0. Thus, if we let primes denote impedance scaled quantities, the new filter component values are given by

𝐿′ = 𝑅0𝐿;

𝐶′ = 𝐶

𝑅0;

𝑅′𝑆 = 𝑅0;

𝑅′𝐿 = 𝑅0𝑅𝐿;

Where L, C, and RL are the component values for the original prototype.

FREQUENCY SCALING

To change the cutoff frequency of a low-pass prototype from unity to 𝜔𝑐 requires that we scale the frequency dependence of the filter by the factor 1/𝜔c,which is accomplished by replacing 𝜔 by

Then the new power loss ratio will be

where ωc is the new cutoff frequency; cutoff occurs when 𝜔/𝜔c =1, or ω = ωc. This transformation can be viewed as a stretching, or expansion, of the original passband. The new element values are determined by applying the substitution of 𝜔 ←𝜔/𝜔𝑐 to the series reactances, 𝑗𝜔𝐿 , and shunt susceptances, 𝑗𝜔𝐶𝑘 , of the prototype filter.

Thus,

which shows that the new element values are given by

When both impedance and frequency scaling are required, the results of both Impedance and Frequency Scaling can be combined to give

CALCULATIONS AND DISCUSSION FOR BUTTERWORTH FILTER

First we find the order of the maximally flat filter to satisfy the insertion loss of 30 dB specification at 1200 MHz. We have that by |ω/ωc| − 1 and from attenuation versus normalized frequency for maximum flat filter prototypes, we find the order to be N=7.

Fig.3. Attenuation versus normalized frequency for maximally flat filter prototypes.

Fig.4. Element Values for Maximally Flat LowPass Filter Prototypes.

Now, we get the lowpass prototype values from the standard Butterworth table given above:

Then Impedance and Frequency Scaling method {(1.) and (2.)} can be used to obtain the scaled element values for „minimum inductor‟ type as : (Here : R0 = 50 Ohms ; fc = 700Mhz )

Similarly, the Impedance and Frequency Scaling method {(1.) and (2.)} can be used to obtain the scaled element values for „minimum capacitor‟ type as : (Here : R0 = 50 Ohms ; fc = 700Mhz )

CALCULATIONS AND DISCUSSION FOR EQUIRIPPLE FILTER

Here too, we first find the order of the maximally flat filter to satisfy the insertion loss of 35 dB specification at 1000 MHz and a passband ripple of 0.25dB. We have that by |ω/ωc| − 1 and from attenuation versus normalized frequency for equi-ripple filter prototypes, we find the order to be N=7.

Fig. 5. Example of an attenuation versus normalized frequency for equal ripple filter prototypes with 0.5 dB ripple level ( In this paper 0.25 dB ripple level plot is considered and the order thus calculated is 7).

The order can also be found out by using the equation the standard Chebyshev model

Fig.6. Standard Chebyshev table with pass band ripple of 0.25dB.

Now, we get the low pass prototype values from the standard Chebyshev table given above:

Then Impedance and Frequency Scaling method {(1.) and (2.)} can be used to obtain the scaled element values for „minimum inductor‟ type as : (Here : R0 = 50 Ohms ; fc = 700Mhz )

Similarly, the Impedance and Frequency Scaling method {(1.) and (2.)} can be used to obtain the scaled element values for „minimum capacitor‟ type as : (Here : R0 = 50 Ohms ; fc = 700Mhz )

SIMULATION DESIGN, RESULTS AND DISCUSSION FOR BUTTERWORTH FILTER

The design was simulated using Agilent Genesys 2010.05 and a response was generated. The filter is a low pass Butter worth filter with input resistance = 50 ohm, cutoff frequency = 700 MHz and Order = 7.

The Minimum Inductor type 7th order filter layout is shown below.

Fig.7. Minimum Inductor type 7th order filter layout.

The result is generated, with parameter values which meet the requirements. A plot of S21 and S11 are produced.

Fig. 8. The amplitude (attenuation in dB) vs frequency results for the 7^th order minimum Inductor type filter.

Fig.9. Gain and return loss on a smith chart of the filter.

Fig.10. Gain and return loss on a polar chart of the filter.

The Minimum Capacitor type 7th order filter layout is shown below.

Fig.11. Minimum Capacitor type 7th order filter layout.

The required results were obtained for the minimum capacitor type filter. A plot of S21 and S11 are produced.

Fig.12. The amplitude (attenuation in dB) vs frequency results for the 7^th order minimum Capacitor type filter.

Fig.13. Gain and return loss on a smith chart of the filter.

Fig.14. Gain and return loss on a polar chart of the filter.

SIMULATION DESIGN, RESULTS AND DISCUSSION FOR CHEBYSHEV FILTER

The design was simulated using Agilent Genesys 2010.05 and a response was generated. The filter is a low pass Chebyshev filter with input resistance = 50 ohm, cutoff frequency = 700 MHz and Order = 7.

The Minimum Inductor type 7th order filter layout is shown below.

Fig.15. Minimum Inductor type 7th order filter layout.

The result is generated, with parameter values which meet the requirements. A plot of S21 and S11 are produced.

Fig.16. The amplitude (attenuation in dB) vs frequency results for the 7^th order minimum Inductor type filter.

Fig.17. Gain and return loss on a polar chart of the filter.

Fig.18. Gain and return loss on a Smith chart of the filter.

The Minimum Capacitor type 7th order filter layout is shown below.

Fig.19. Minimum Capacitor type 7th order filter layout.

The result is generated, with parameter values which meet the requirements. A plot of S21 and S11 are produced.

Fig. 20. The amplitude (attenuation in dB) vs frequency results for the 7^th order minimum Capacitor type filter.

Fig.21. Gain and return loss on a Smith chart of the filter.

Fig.22. Gain and return loss on a polar chart of the filter

CONCLUSION

This paper deals with the design of a maximally flat low pass filter and an equal-ripple low-pass filter (pass band ripple = 0.25 dB ripple). Both the filters have a cutoff frequency of 700 MHz, input resistance of 50 ohms and an order of 7. The amplitude (attenuation in dB) vs frequency results for these filters are shown in the above figures.

These results clearly show the trade-offs involved with the two types of filters. The equal-ripple response has the sharpest cutoff. The maximally flat response has a flatter attenuation characteristic in the pass band but a slightly lower cutoff rate. The measured 3 dB frequency is 818.99 MHz for butter worth filter and the measured 3 dB frequency for Chebyshev filter is 731.46 Mhz.

REFERENCES

[1] J.C. Rautio, Planar electromagnetic analysis, IEEE Microwave

Magazine, Vol. 4, No. 1,March 2003, pp. 35-41.

[2] J.S. Hong, and M.J. Lancaster, Microstrip Fitlers for RF/Microwave Applications, Wiley,New York, 2001.

[3] D. Ahn, J. S. Park, C.S. kim, J. Kim, Y. Qian, and T. Itoh., “Design of the Low-Pass Filter using the Novel Microstrip Defected Ground Structure”, IEEE Trans. Microwave Theory Tech, Vol. 49, pp. 86- 92. January.

[4] E.H. Fooks and R.A. Jakarevicius, Microwave Engineering using Microstrip Circuits, Prentice Hall of Australia, pp. 167-169,1990.

[5] M. Makimoto, S.Yamoshita,“Microwave Resonators and Filters”, IEEE Trans. Wireless communication Vol. 2, August,1986.

[6] D.M.Pozar,Microwave Engineering, John Wiley, 2000.

[7] R. Levy, R.V.Snyder and G. Matthaei, “Design of Microwave Filters”, IEEE Transactions On Microwave Theory, vol.50, pp.783- 793, March 2002.

[8] Roman Kaszynski and Jacek Piskorowski, “New Concept of Delay– Equalized Low Pass Butterworth Filters,” IEEE Symposium on Industrial Electronics and Application (ISIEA 2009), vol. 1, pp. 171- 175, 9-12 July, 2006.

[9] Srinath, S. "Design and Electromagnetic Modeling of E-Plane Sectoral Horn Antenna For Ultra Wide Band Applications On WR- 137 & WR-62 Waveguides.", International Journal of Engineering and Science Invention ,Vol.3, Issue.7,pp:11-17, July,2014.

[10] Li Zhongshen, “Design and Analysis of Improved Butterworth Low

Pass Filter”, The Eighth International Conference on Electronic Measurement and Instruments, pp. 1729-1732, 2007.

[11] John T. Taylor and Qiuting Huang, CRC Handbook of Electrical Filters, CRC Press, pp. 22-23, 1997.

[12] C. A Balanis, Antenna Theory: Analysis and Design, 3rd edition, Wiley, 2005.

[13] D. H. Werner and S. Ganguly, “Fractal Antenna Engineering Research,” IEEE Trans. Antennas Propagat., Vol. 45, No.1, pp. 38- 57, Feb 2003.

[14] Ting, S. W., K. W. Tam, and R. P. Martins, “Miniaturized microstrip lowpass fillter with wide stopband using double equilateral U-shaped defected ground structure," IEEE Trans.Microw. Wireless Compon. Lett., Vol. 16, No. 5, May 2006.

[15] Xiao, J.-K., Q.-X. Chu, and H.-F. Huang, “New microstrip lowpass filter with transmission zero and wide stopband," 2008 China- Japan Joint Microwave Conference, Sep. 10-12,2008.

[16] Wuren, T., I. Sakagami, M. Fujii, and M. Tahara, “A miniaturized

microstrip ring resonator lowpass fillter with sharp attenuation," 2008 IEEE MTT-S International Microwave Symposium Digest, Jun. 15, 2008.

[17] Srinath, S. "Design of 4 th Order Parallel Coupled Microstrip Bandpass Filter at Dual Frequencies of 1.8 GHz and 2.4 GHz for Wireless Application.", International Journal of Innovative Research in Computer and Communication Engineering, Vol.2 , Issue.6 , June,2014.

[18] S. S. Mohammed, K. Ramasamy, and T. Shanmuganantham, “Wireless power transmission - A next generation power transmission system,” International Journal of Computer Applications, vol. 1, no. 13, pp. 100-103, 2010.

[19] R. Ludwig and P. Bretchko, RF Circuit Design - Theory and Application, New Jersey, USA: Prentice-Hall, Inc., 2000.

[20] P. K. Sharma, V. S. Jadun, D. K. Mahor, and A. Verma, “Designing

micrsotrip low pass filter in ISM band for rectenna system,” International Journal Of Engineering And Technology, vol. 1, no. 4, 2012.

[21] T. Moyra, S. K. Parui, and S. Das, “Design of a quasi-elliptic lowpass filter using a new defected ground structure and capacitively loaded microstrip line,” International Journal on Electrical Engineering and Informatics, vol. 3, no. 11, 2011.

[22] Chen, X.-Q., R. Li, S.-J. Shi, Q. Wang, L. Xu, and X.-W. Shi, “A novel low pass filter using elliptic shape defected ground structure", Progress In Electromagnetics Research B, Vol. 9, pp:117-126, 2008.