(RACs) [4, 51, and filters with slanted transducers [4, 6,. 71 are typically used. The principle of stationary phase yields a very good approximation to the optimum ...
Optimum Design of Low Time-Bandwidth Product SAW Filters Clemens C.W. Ruppel, Leonhard Reindl, and Karl Ch. Wagner Siemens Corporate Research and Development, Munich, Germany Abstract - For years linear optimization algorithms have been used successfully in bandpass filter design. This method has been adopted for the design of pulse compression filters with low time-bandwidth products. In the bandpass filter design, the sidelobe level in the frequency domain is optimized for a fixed impulse response length. In case of the design of a low timebandwidth product filters, we optimize the sidelobe suppression in the time domain for a fixed overall bandwidth. We get the optimum time response for a given frequency bandwidth and width of the compressed pulse. The spurious time response is minimized. The corresponding optimum frequency response is split up onto expander and compressor, each consisting of two chirped and apodized IDTs.
As an example, an expander-compressor pair at 350 MHz with a 3 dB bandwidth of approximately 11 MHz, an overall bandwidth of approximately 33 MHz, and a chirp time of 1.0 ps was designed The
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sidelobe suppression in the design is better than 40 dB. The measured filters exhibit a sidelobe level close to -40 dB. Design and measurement are in excellent agreement.
I.
INTRODUCTION
T
he design of pulse compression filters with a high time-bandwidth product is well known [ 1, 2, 31. Inline configurations, reflective array compressors (RACs) [4, 51, and filters with slanted transducers [4, 6, 71 are typically used. The principle of stationary phase yields a very good approximation to the optimum solution. Only very few papers deal with the design of pulse compression filters with a low time-bandwidth product [8, 9, lo]. Due to the low time-bandwidth product it is advantageous to use for this type of filter an inline configuration.
of sidelobes in the time domain is well known. The restricted assortment of the window functions is a limiting factor for the obtainable performance of the pulse compression systems. With the introduction of optimization procedures, which are well known for the design of transversal filters, these restrictions can be overcome. As a consequence, the obtainable sidelobe suppression depends only on the width of the compressed pulse and the allowed frequency bandwidth. In addtion, for any given frequency response of an expander an optimum frequency response of the corresponding compressor can be designed. The next problem in the design of pulse compression filters is the realization of the optimum frequency responses by dispersive delay lines. Classical solutions produce filters consisting of an apodized and a uniform transducer, with one or both transducers being dispersive. In this configuration, Fresnel ripple originating from the umform transducer yields problems [9]. The apo&zed transducer has to compensate for t h ~ sFresnel ripple. To overcome this situation it is advantageous to use two weighted transducers. There are, however, some drawbacks. The linear design is difficult because the transfer function of the filter is not equal to the product of the transfer functions of both transducers in first order. Compared to configurations with one unapodized transducer, second order effects, e.g., diffraction, become more severe. For the compensation of second order effects, precise simulation tools for all relevant second order effects, e.g., diffraction, reflection, refraction are required. The procedure for the compensation of second order effects is rather complex [ 141,
The classical design procedure of pulse compression filter pairs starts with the choice of an appropriate window function. Most frequently, window functions like Hamming, Blackman-Hams, etc., are used for the first steps of the design of pulse compression filters [8, 9, 11, 12, 131. These functions are easy to implement and the relative broadening of the pulse as well as the suppression
The speclfications for the design example are a center frequency (fo) of 350 M H z and an overall bandwidth (SW) of 33.2 MHz. In our pulse compression system, the power ampllfier of the transmitter is not driven in saturation. Thus the envelope of the impulse response of the expander has not neccessarly to be constant. The bandwidth of the expander filter is chosen as 44 M H z with an almost flat amplitude response over the bandwidth of the pulse compression system. The 3 dB width of the compressed pulse is 0.05 ps and the 40 dB width (T) is 0.14 ps, respectively.
1051-0117/94/0000-0061$4.00 0 1994 IEEE
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Fig. 1: Amplitude response of the expander filter. The bandwidth of the pulse compression system is depicted by the vertical lines.
Fig. 3: Compressed pulse of the ideal dispersive filters. The absolute delay time is eliminated. In a second step the amplitude response Hz(f) of the compressor filter is designed. The same design procedure as for the frequency response of the expander filter may be used. Only the role of frequency and time domain are exchanged. Instead of minimizing the stopband attenuation in the frequency domain, the level of spurious signals in the time domain is minimized by linear programming (equ. 1). The amplitude response of the expander filter must be accounted for. There are no limitations on the achievable levels of the spurious signals in the time domain. The broader the frequency bandwidth of the compressed pulse c(t) (equ. 2) is, the lower the obtainable level of spurious signals in the time domain becomes.
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Fig. 2: Amplitude response of the compressor filter. The bandwidth of the pulse compression system is depicted by the vertical lines.
The design problem can be described in the following way: m
Minimize L
where T is the width of the compressed pulse and
11.
LINEAR DESIGN
The linear design of the frequency responses of the expander and compressor filter consists of four steps. Firstly, the amplitude response H,(Qof the expander filter is designed. Any standard design procedure for the design of transversal SAW filters can be used, e.g., the linear programming technique 115, 161. The characteristic can be chosen almost arbitrarily. Only the bandwidth of the pulse compression system has to be accounted for. In the design example, we have chosen a frequency response with an amplitude response which is flat almost over the complete bandwidth BW of the pulse compression system (figure 1). This frequency response has to be accounted for in the second step of the linear design.
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c(t):=
F-'(H,(f)H,(f)).
(2)
H,(f) is the amplitude response of the expander, that has already been determined, and H, (f) is band limited. The optimum frequency response of the compressor is depicted in figure 2.
So far no dispersion has been introduced. In the third step of the design procedure the desired chirp is specified and the amplitude responses of the expander and compressor filter are multiplied with the corresponding complex valued exponential functions. The compressed pulse of these two dispersive frequency responses is depicted in figure 3. The sidelobe level is approximately -40d B . In a fourth step, the frequency responses have to be realized by SAW filters. We have chosen SAW filters
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Fig. 4:
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Compressed pulses of all iterations of the compensation procedure. The final result is the solid line, all other results are broken lines.
Relative transition width
Suppression of sidelobes
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Fig. 6: Frequency responses for compressor filters with different widths of the cosine roll-off of the expander. The transition widths are 0 %, 10 %, 20 %, and 30 YOof the overall bandwidth. Distance between Broadening of the Suppression of the first zeros 3 dB bandwidth sidelobes
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Table 5: Influence of the relative transition width on the achevable optimum suppression of sidelobes. with two dispersive and amplitude weighted IDTs. The sharing out of the frequency response onto the two weighted IDTs is done using the square root method [ 141. This is not optimum but deviations are compensated for in the compensation procedure for second order effects.
111. COMPENSATION OF SECOND ORDER EFFECTS The compensation of second order effects [ 141 is iterative. For the simulation of second order effects, an extended angular spectrum of straight crested waves model [ 17, 18, 191 was used. The number of necessary iterations depends on the specifications of the dispersive delay line. In the presented example a maximum number of 8 iterations was used. The compressed pulses of all iterations are depicted in figure 4. As can be seen, the shape of the compressed pulse is obtained after a few iterations. The following iterations are necessary for the compensation of effects that cause a degradation of the suppression of spurious signals in the time domain. The solid line represents the last iteration and the suppression of spurious signals is close to 40 d B .
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-10.71 -26.81 -39.30 -52.81 -64.23 -78.55
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Table 7: Suppression of sidelobes in the time domain versus relative 3 dB bandwidth.
IV. DESIGN VARIATIONS The overall performance of a pulse compression system depends on the choice of the expander and the compressor filter for a given bandwidth. In table 5, the influence of the transition width of the expander is given. In this example, the expander is chosen constant with a cosine roll-off. The 3 dB bandwidth of the compressed pulse is fixed. The relative transition width of the cosine rolloff is varied from 0 % to 15 %. If the transition width of the expander varies, the frequency response of the optimum compressor has to vary too in order to obtain a good compressed pulse. In figure 6, the frequency responses for Merent relative transition widths are depicted.
As expected, the frequency responses differ only in the range of the transition of the cosine roll-off. The higher the relative transition width, the higher the pedestal of the compressor frequency response becomes and the more di&cult it is to obtain a good suppression of spu-
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Geometry ofthe expander (top) and compressor (bottom)filter. The meander line through the active taps is depicted. lG
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rious signals in the time domain. All these solutions with a pedestal are optimum, but cannot be realized in a pulse compression system because the corresponding time window is infinite. As demonstrated in the example in this paper optimization algorithms can be used for determining optimum frequency responses without a pedestal in the frequency domain.
If window functions are used for the design of a pulse compression system, the suppression of spurious signals in the time domain depends on the choice of the window function. There are only a few well-known window functions without a pedestal, e.g., Bartlett, Hanning and Blackman window functions [20] that exhibit sidelobe
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Normalized amplitude and group response of the measured expander filter (top). Normalized amplitude of the impulse and instantaneous frequency response of the measured expander filter (bottom).
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Fig. 10: Normalized amplitude and group delay response of the measured compressor filter (top). Normalized amplitude of the impulse and instantaneous frequency response of the measured compressor filter (bottom). levels from -23 dB up to -58 dB. In the case of using optimization procedures, the obtainable suppression of sidelobes in the time domain depends, for a given bandwidth in the frequency domain, only on the allowed width of the compressed pulse. In table 7, the relative broadening of the compressed pulse, versus the suppression of sidelobes, is listed.
v.
EXPERZMENTAL RESULTS
Two dispersive filters (expander and compressor) were fabricated. The geometry of the two filters is depicted in figure 8. As a substrate material 39S0,rot-YX-
VIII. REFERENCES
0
S. Jen, "Synthesis and Performance of Precision Wideband Slanted Array Compressors," Proceedings of the IEEE Ultrasonics Symposium, p p . 3749,1991 H.M. Gerard, W.R. Smith, W.R. Jones, and J.B. Harrington, "The Design and Applications of Highly Dispersive Acoustic SurfaceWave Filters," IEEE Transactions on Sonics and Ultrasonics, Vol. SU-20, NO. 2, p p . 94-104, April 1973 M. Haspel, "Iterative Synthesis of Optimized Surface Acoustic Wave Chup Waveform Compression Filter Impulse Response,'' Proceedings ofthe IEEE Ultrasonics Symposium, p p . 209-212, 1987 W. Ruile, F. Milller, and G. Riha, "Metal-R4Cs with Track Interference Weighting," Proceeding of the IEEE Ultrasonics Symposium,
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1.8
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Time l p s l
Fig. 11: Compressed pulse determined from the measured frequency responses of the expander and compressor filter. Quartz was chosen. Both filters were mounted in TO-39 packages. The frequency responses were measured in a 50 0 system using a HP 85 10. The insertion loss is about -42 dB for both filters. In figure 9 and 10, the normalized frequency and time responses are depicted. The stopband rejection of both filters is limited by the electric feed through, which has not been gated in the time domain. The agreement between simulation and measurement is excellent.
The level of spurious signals of the compressed pulse is -39 dB and in good agreement with the value obtained in the design.
VI.
CONCLUSIONS
Using linear optimization for the design of dispersive SAW filters with a low time-bandwidth product, there are no restrictions on the obtainable sidelobe level. Limits for the sidelobe level in fabricated devices are reproducibility of manufacturing, electric feed through and inaccuracies of the models used during the compensation of second order effects. The first two effects are hard limits while the inaccuracy of a model can be overcome by improving the model or by using experimental data during the compensation procedure [2 11. Experimental and theoretical results agree well. In the design a sidelobe level of better than -40 dB was obtained. The experiment showed a sidelobe level of -39 dB.
VII. ACKNOWLEDGMENT The authors want to thank W.-E. Bulst for continuous encouragement. Experimental devices were fabricated by S.Berek and B. Bienert.
147-151,1986
G. Riha, H.R. Stocker, R Veith and W.E. Bulst, "RAC Filters with Position Weighted Metallic Strip Arrays," Proceedings of the IEEE Ultrasonics Symposium, pp. 83-87,1982 B.R. Potter, and C.S. Hartmann, "Surface Acoustic Wave Slanted Device Technology," IEEE Transactions on Sonics and Ultrasonics, Vol. SU-26, pp. 41 1418, 1979 H.R Stocker, W.E. Bulst, G. Eberharter, and R. Veith, "Octave Bandwidth High Performance SAW Delay Lines," Proceedings of the IEEE Ultrasonics Symposium, pp. 83-87, 1980 G.W. Judd, "Technique for Realizing Low Time Sidelobe Levels in Small Compression Ratio Chup Waveforms," Proceedings of the IEEE Ultrasonics Symposium, p p . 478481,1973 M.Kowatsch, and H.R. Stocker, "Effect of Fresnel Ripples on Sidelobe Suppression in Low TmeBandwidth Product Linear FM Pulse Compression,'' IEE Proceedings, Vol. 129, Pt. F, No. 1, pp. 41-44, Februarv 1982 [lo] M. Solai, "High Performance SAW Dispersive Delay Lines for Low Time Bandwidth Using Periodically Sampled Transducers," Proceedings ofthe IEEE Ultrasonics Symposium, pp. 175-178,1988 [ l l ] M. Kowatsch, "Suppression of Sidelobes in Rectangular Linear FM Pulse Compression Radar," Proceedings of the IEEE, Vol. 70, No. 3, p p . 308-309, March 1982 [12] AR. Reddy, "Design of SAW Bandpass Filters Using New Window Functions," IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, Vol. 35, No. 1, pp. 50-56, January 1988 [13] F.J. Harris, "On the Use of Windows for Harmonic Analysis with the Discrete Fourier Transform," Proceedings of the IEEE, Vol. 66, No. 1 , ~51-83, . January 1978 [14] C.C.W. Ruppel, C. Kappacher, L. Reindl, and G. Visintini, "Design and Compensation of Non-Equidistantly Sampled SAW Transducers," Proceedings of the IEEE Ultrasonics Symposium, pp. 19-23, 1989 [15] C.C.W. Ruppel, E. Ehrmann-Falkenau, H.R. Stocker, and R. Veith,
"Optimum Design of SAW Filters by Linear Programming,"Proceedings ofthe IEEE Ultrasonics Symposium,pp. 23-26,1983 [16] C.C.W. Ruppel, AA Sachs, and F.J. Seifert, "A Review of Optimization Algorithms for the Design of SAW Transducers," Proceedings ofthe IEEE Ultrasonics Symposium, p p . 73-83, 1991 [I71 G. Visintini, A-R. Baghai-Wadji, and 0. Miinner, "Modular TwoDimensional Analysis of SAW Filters - Part I: Theory," IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, Vol. 39,No. 1 , ~ 61-72, . January 1992 [18] G. Visintini, C.C.W. Ruppel, and R. Greening, "Angular Spectrum of
Waves Analysis of SAW Filters with Dispersive Transducers," Proceedings ofthe IEEE Ultrasonics Symposium, pp. 107-112,1989 [19] G. Visintini, C. Kappacher, and C.C.W. Ruppel, "Modular TwoDimensional Analysis of SAW Filters - Part 11: Analysis and Compensation Results," IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, Vol. 39, NO. 1, pp. 73-81, January 1992 [20] G. Kino, "Acoustic Waves: Devices, Imaging, and Analog Signal Processing," Prentice-Hall, New Jersey, p p . 389-390, 1987 [21] F. Seiferl, G. Visintii, C.C.W. Ruppel, and G. Riha, "Dfiaction Compensation in SAW Filters, " Proceedings of the IEEE Ultrasonics Symposium,pp. 67-76, 1990
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