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Design options for SAW IF filters used in wireless applications.

With the wireless industry poised for exponential growth, the trend in the various wireless equipment is toward miniaturization. Thus, components used in this equipment are under constant pressure to become smaller. SAW filters that are used invariably in RF and IF stages of wireless handsets need to be miniature.

This article discusses the various requirements of SAW filters used in the IF stages of wireless handsets designed for use with different standards and presents several design options using eigen functions to realize the SAW filters. A brief discussion is presented on the earlier methods using eigen functions.


SAW filters are used invariably in both RF and IF stages of a cellular or cordless telephone, as shown in Figure 1. However, each of the various telephone standards have unique requirements for signal bandwidths and RF/IFs. For example, IFs in the Global System for Mobile communications systems range from 45 to 259.5 MHz with a signal bandwidth of 0.16 MHz. The Advanced Mobile Phone System/Extended Total Access Communications System standard requires an IF filter at 86.85 MHz with a signal bandwidth of 0.03 MHz. The Digital Enhanced Cordless Telecommunications (DECT) system, which is growing as a popular standard for cordless telephones in Europe, has IFs at 110.592 and 112.32 MHz requiring a bandwidth of 1.13 MHz. The personal handyphone system standard for cordless telephones, a standard prevalent in Japan, has IFs at 248.45 and 243.95 MHz with a bandwidth requirement of 0.4 MHz.

In the US, a new cordless telephone standard that operates in the industrial, scientific and medical frequency band is gaining predominance. For this standard, the IF filters are required to operate at 49.05 and 70 MHz for a signal bandwidth of 0.03 MHz. The rejection requirements for these SAW filters typically range from 30 to 60 dB. The low cost versions usually are available in miniature sizes with moderate rejection levels, whereas the professional devices demanding higher performance need larger packages. An important common factor among all the IF filter requirements of the different standards is that they require narrowband filters with fractional bandwidths less than two percent. This article describes various options suitable for these narrowband SAW filters.


The eigen function design approach used to realize SAW filters is noniterative and the pass band shapes of the transfer functions can be manipulated easily by varying the coefficients of the eigen functions. Thus, both symmetric and nonsymmetric bandpass functions can be realized with ease. Eigen functions for the SAW filter design (first used by DeVries[1]) were simple sinc functions in the frequency domain whose inverse Fourier transforms were cosine bursts of particular durations. High side lobes (-13 dB) of sinc functions limit their utility as efficient eigen functions. A three-term cosine function in the time domain that produces low side lobes of the order of 76 dB in the frequency domain with a main lobe width of[+ or -]3/T was proposed.[2]

A design procedure for realizing the SAW filters using this eigen function has been described previously.[2] This procedure can be used for two types of interdigital transducers (IDT): compensated and uncompensated. For the uncompensated IDT design, the output IDT response is ignored. For the compensated design, the sinc response of the output IDT is compensated by raising the amplitudes of the eigen functions with respect to the amplitude of the eigen function at the center.

In the case of the uncompensated IDT design, the output IDT is a broadband type using a small number of fingers. This type of design relies only on the input IDT response for its stop rejection requirements. This method cannot be adopted for narrowband SAW filters that normally are used in wireless applications for two reasons. First, since the output IDT uses a few fingers, the insertion loss will be quite high for quartz substrates (with a low coupling coefficient) usually employed in narrowband SAW filters. Second, since only the input IDT contributes to rejection and the eigen function described decays slowly, a long impulse duration is required to achieve the desired shape factor.

The compensated IDT design can be adopted for narrowband SAW filter designs with limited success. In this case, since the output IDT also contributes to the rejection and shapes the pass band, the net transfer function decays faster, producing a steeper transition width and flat pass band.

The increasing demand for smaller filter sizes for wireless applications emphasizes that the impulse duration of the transfer function should be kept to a minimum, which, in turn, dictates that a minimum number of possible eigen functions be employed to realize the desired response. In the compensated design approach, at least three eigen functions are incorporated, including one at the center that is used as a reference for varying the amplitudes of the eigen functions on either side. However, this approach cannot be used for designs demanding only two eigen functions.

Even and odd cosine series functions in the time domain that are used as eigen functions for SAW filter realization have been described.[3] As the number of terms (N) in the functions increase, the side lobe levels decrease and the main lobe width increases. Thus, the order N is chosen to obtain the desired side lobe level in the eigen function. A procedure to design SAW filters using these functions has also been described. In this approach, one of the ITDs is apodized using the odd-series cosine functions; the other ITD is apodized using the even-series cosine functions to take advantage of the orthogonality of the odd- and even-series functions. (Apodization refers to the unequal overlap of the fingers in the IDT.) Thus, the side lobe maxima of one function coincides with the side lobe nulls of the other function, producing the net minimum side lobe levels in the stop band. However, since both IDTs are apodized, this approach implicitly assumes that multistrip couplers (MSC) are to be used. The MSC designs are adopted only for high coupling coefficient ([K.sup.2]) material such as lithium niobate, which is used for moderate/broad bandwidth SAW filters. Narrowband SAW filters are realized on quartz due to its superb temperature coefficient characteristic. However, quartz, with its low coupling coefficient, requires a prohibitively large number of electrodes in the MSC for efficient energy transfer from the input IDT track to the output IDT track. Therefore, this design approach is limited to moderate or broad bandwidth SAW filters.

This article describes a procedure that is suitable for narrowband SAW filter designs. The procedure uses two eigen functions to realize the input IDT transfer function. The eigen functions used are given as[3]

[h.sub.N1], (t,T) =

[summation of] [a.sub.n] cos (2n[Pi]t/T) where n=0 to N-1 [multiplied by] rect (t/T) (1)

[h.sub.N2] (t, T) = [summation of] [b.sub.n] cos [(2n + 1)[Pi]t/T] where n=0 to N-1 [multiplied by] rect (t/T) where n = 0 to N - 1


rect (t/T) = 1 for [absolute value of t] [less than or equal to] T/2 and 0 for [absolute value of t] [greater than] T/2

and their Fourier transforms are given as

[H.sub.N1] (f, T) = T/2 [summation of] [a.sub.n][sin ([Pi]fT - n[Pi])/[Pi]fT - n[Pi] where n=0 to N-1 + sin([Pi]fT + n[Pi])/[Pi]fT + n[Pi]] (3)

[Mathematical Expression Omitted] (4)


[h.sub.N1] (t,T) = odd-series cosine functions in time domain

[h.sub.N2] (t,T) = even-series cosine functions in time domain

[a.sub.n] and [b.sub.n] = coefficients determined by minimizing the side lobes

The output IDT is uniform and its sinc transfer function is selected to minimize the net side lobe levels of the filter and to achieve an acceptable ripple level (less than [+ or -]0.5 dB) in the pass band.

For [H.sub.11] or [H.sub.12] (that is, N = 1), the side lobes are of uniform width 1/T with alternating signs, as shown in Figure 2. Thus, when the functions (either [H.sub.11] or [H.sub.12]) are placed 1/T apart, the positive side lobes of the first function overlap completely with the negative side lobes of the second function, resulting in the minimized side lobes for the input IDT transfer function. Further side lobe reduction is achieved when the output IDT sinc transfer function is selected such that its first nulls are placed on the first maxima of the input IDT transfer function. Using [H.sub.11], which has a side lobe level as high as -13 dB, a filter transfer function with a -44 dB side lobe level is achieved. A stop band rejection better than 54 dB is obtained using eigen function [H.sub.12]. The limitation of this approach is that only bell-shaped pass bands can be realized. However, for many IF requirements in wireless applications (such as in DECT systems) bell-shaped pass bands are acceptable while short impulse durations are essential.

The need for a flat bandwidth stipulates that the condition of a complete overlap of side lobes with alternate signs must be dispensed with, resulting in lower levels of rejection. To improve the stop band rejection, higher order eigen functions must be employed. The output IDT sinc transfer function is still used to cancel the first prominent maxima of the input IDT transfer function. The sinc roll-off of the output IDT transfer function in the pass band is now compensated by the critical placement of the two eigen functions on either side of the center so that the net response will have a flat pass band. The transfer functions of the input and output IDTs and the net transfer function are shown in Figure 3. In the transfer function plot, two [H.sub.21] functions are used to realize the input transfer function. This technique, unlike that described by Vasile,(2) requires only two eigen functions, which can be chosen according to their required specifications.

Two parameters, [Q.sub.1] and [Q.sub.2], are used to inter-relate the spacing between the eigen functions, their impulse duration and the bandwidth of sinc response. The parameters are defined as

[Q.sub.1] = BT (5)

[Q.sub.2] = [B.sub.o]/B (6)

For a given impulse duration T, [Q.sub.1] determines the separation B between the two eigen functions and [Q.sub.2] determines the null-to-null bandwidth [B.sub.o] of the output IDT transfer function. By determining the proper values for [Q.sub.1] and [TABULAR DATA FOR TABLE I OMITTED] [Q.sub.2] with the help of computer iterations, a flat bandwidth with an acceptable ripple level (usually less than [+ or -]0.5 dB) and good stop band rejections are achieved. Values of [Q.sub.1] and [Q.sub.2] for various eigen functions are determined. The corresponding frequency response plots are shown in Figure 4. The normalized frequency (f- [f.sub.o]) is plotted along the x-axis and the spacing between eigen functions B is 1 MHz. Table 1 lists various selectable design options depending on the specifications to be achieved, such as shape factor, side lobe level and impulse duration (chip size). Note that the impulse duration provided includes the impulse durations of both the input and output IDTs.

The input IDT impulse duration is g/yen by [Q.sub.1]/B and the output IDT impulse duration is given by 2/[B.sub.o]. Using Equations 5 and 6, the total impulse duration is expressed as

[T.sub.t] = ([Q.sub.1] + 2/[Q.sub.2]) / B (7)


A prototype SAW filter at 30 MHz was fabricated on an ST-X quartz substrate using the described design procedures. The filter incorporates only two eigen functions ([H.sub.31]) placed 700 kHz apart on either side of the center frequency. A shape factor better than 2.15 was required. The values of parameters [Q.sub.1] and [Q.sub.2] were chosen to be 2.6775 and 2.2556, resulting in an impulse duration of 5.092 [[micro]seconds] and a pass and ripple of [+ or -]0.4 dB. The filter's simulated and measured plots are shown in Figure 5. Note that the two plots match in the pass band and close-in stop bands. The measured ripple is approximately [+ or -]0.6 dB, 0.2 dB higher than the theoretical value. The deviation in the farther stop bands between the measured and simulated plots is attributed mainly to second-order effects in the IDTs, including diffraction and interelectrode reflections. A simple method to minimize diffraction is to increase the IDT aperture. However, this action results in an increase in chip size.

A fixed series inductor (2[[micro]hertz]) is used instead of a tuning inductor as a matching element at the input and output ports, resulting in slightly unequal lower and higher stop bands. The insertion loss with the fixed series inductor matching is 19 dB.

An impulse duration of 7.267 [[micro]seconds] is required to achieve a shape factor better than 2.15 and a flat bandwidth of 700 kHz using Vasile's method,[2] which requires three eigen functions. Thus, the design described here produces a 30 percent reduction in impulse duration.


Requirements of SAW filters used in the IF stage of various wireless handsets have been discussed and several design options have been presented that are tailored for these requirements. Due to miniaturization demands, it is essential not to overdesign the SAW filters.


The authors wish to thank the management of Bharat Electronics for supporting this work.


1. A.J. DeVries, "A Design Method for Surfacewave Filters Using Simple Structures as Building Blocks," Ultrasonics Symposium Proceedings, 1973, pp. 441-444.

2. C.F. Vasile, "A Numerical Fourier Transform Technique and Its Application to Acoustic Surface Wave Bandpass Filter Synthesis and Design," IEEE Transactions on Sonics and Ultrasonics, Vol. SU-21, January 1974, pp. 7-11.

3. D.C. Malocha and C.D. Bishop, "The Classical Truncated Cosine Series Functions with Applications to SAW Filters," IEEE Transactions on Ultrasonics, Ferroelectronics and Frequency Control, Vol. UFFC-34, No. 1, January 1987, pp. 75-85.

4. R.G. Kulkarni, H.V. Ananda and S.K. Lahiri, "Examine the Effect of Aliasing on Nonsymmetric Filters," Microwaves and RF, Aug. 1997.

R.G. Kulkarni received his BE in electronics and communication from the College of Engineering, Gulbarga, India, and his MTech from the Indian Institute of Technology, Madras, India, in 1979 and 1982, respectively. He is employed at Bharat Electronics, where he engages in the design and development of SAW devices. In 1989, he won the company's research and development award for the development of TV IF SAW filters. Currently, Kulkarni is the manager of the company's Hybrid-Microcircuits division, where he is responsible for the development of SAW devices for consumer, professional and military applications. He is a member of the ISHM India chapter.

S.K. Lahiri received his BSc in physics from Presidency College, Calcutta, India, in 1963, and his BTech, MTech and PhD degrees from the Institute of Radio Physics and Electronics, Calcutta University, in 1965, 1966 and 1971, respectively. He joined IIT Kharagpur in November 1971 as a lecturer in the department of electronics & electrical communications engineering and became a professor in 1985. In July, he was named dean, Sponsored Research Industrial Consultancy, at lit Kharagpur. Currently, Lahiri's research activities include integrated optics, power ICs, special semiconductor films, microsensors and MEMS. He works in close collaboration with the defense and ISRO labs and industries. Lahiri has published several research papers and has served as a member of the National Microelectronics Council Technology Working Group, CSIR manpower assessment board, board of examiners of several universities and project review committees of the DoE and ISRO. He is a senior member of the IEEE.
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Title Annotation:Wireless Report; surface acoustic wave
Author:Kulkarni, R.G.; Lahiri, S.K.
Publication:Microwave Journal
Date:Jan 1, 1998
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