|Title of Invention||
NONSYMMETRIC SURFACE ACOUSTIC WAVE FILTER
|Abstract||ABSTRACT OF THE INVENTION Disclosed herein is a surface acoustic wave (SAW) filters, more specifically to nonsymmetric SAW filters having maximum cancellation of sidelobes due to exact overlap of positive and negative sidelobes of adjacent eigen functions, resulting in an efficient design by getting higher stopband rejection.|
The present invention relates to surface acoustic wave (SAW) filtere, more specifically to non-symmetric SAW filters.
As known in the art, a surface acoustic wave (SAW) filter consists of two interdigital transducers (IDTs), formed by finger like metal electrode patterns on a piezoelectric substrate. One of the transducers converts electrical signals into acoustic waves, which travel along the surface of the substrate and reach the other transducer, which converts back the acoustic waves into electrical signals. Thus the frequency response of the SAW filter is the multiplication of individual frequency responses of the two transducers. The frequency response of the each of the transducer is determined by the metal electrode pattern in the transducer. Fig. 1 of the accompanying drawings illustrates the surface acoustic wave filter which consists of a saw absorber 1, piezoelectric substrate 2, Apodized IDT 3, Uniform IDT 4 and Electrodes 5. The saw propagation is identified by reference numeral 6 and L is the Electrode width.
As known in the art, when all the electrode overlaps in a transducer are of equal length, the transducer is called uniform IDT and when there is variation in the electrode overlap lengths, the transducer is described as apodized IDT. When an electrical impulse is applied to the uniform IDT, each electrode overlap in the IDT generates an acoustic impulse proportional to the overlap length. Since the electrode overlaps are equal in an uniform IDT, a serious of acoustic impulses of equal amplitudes are generated. These impulses can be approximated as cosine burst for the purpose of mathematical modeling. The number of cycles in the cosine burst is equal to the number of electrode pairs in the transducer.
As known in the art, in a transducer with electrodes of constant line and gap widths, the impulse response consists of cosine burst with cycles of constant period. The spacing between the consecutive electrode pairs is equal to the product of cosine cycle period and the SAW velocity. This spacing is termed as SAW wavelength. The electrode width in a basid IDT structure is equal to one-fourth of the SAW wavelength.
As known in the art, the frequency response of a uniform transducer is obtained by taking Fourier transform of impulse response of the transducer or in other words, by taking Fourier transform of the cosine burst generated by the input impulse. The frequency response obtained is in the form of 'sinc' function, which has peak amplitude at center frequency. The center frequency is determined by the period of the cosine burst and the first nulls of the 'sinc' function are determined by the duration of the cosine burst. The 'sinc' frequency response of the uniform IDT has side lobe peak of-13 dB only and the pass band has rounded shape. Thus the SAW filter formed by two identical uniform IDT structures will have side lobe peak of -26 dB only, an inadequate side lobe rejection in most of the applications. Due to this limitation, normally the SAW filter consists of one uniform IDT and one apodized IDT, wherein the apodized IDT facilitates enhanced side lobe rejection and desired passband shaping.
As known in the art, the desired frequency response of the apodized IDT is obtained by dividing the desired filter response by the uniform IDT response. The desired frequency response of the apodized IDT is constructed by techniques such as:
a non-iterative design technique, b. computer aided iterative technique,
which are explained in the following paragraphs.
As known in the art, the computer aided iterative technique employs iterative procedures, which reduce the error between the desired and the simulated response to an acceptable limit. Both symmetric and non-symmetric frequency responses are feasible with this method. However, this technique requires substantial amount of computer memory and time, making SAW filter design very expensive. Further any design modifications using this technique become extremely cost prohibitive.
As known in the art, the non-iterative design technique comprises of window technique and eigen function (or building block) approach. In window technique, the infinite impulse response of an ideal rectangular bandpass frequency function is multiplied with a finite and smoothly varying time function (known as window function), to obtain a realizable finite impulse response. This finite response is mapped in spatial domain (by multiplying with SAW velocity), and the electrode overlaps are placed at the peaks of cosine burst to construct the apodized IDT structure. Choice of proper window function yields the desired ripple, rejection and transition width characteristics. Even though the window technique is straightforward method without involvmg any iterative procedures, there are some limitations as discussed below.
As known in the art, with the window technique, only symmetric band pass functions are feasible and all the filter parameters (ripple, rejection and transition width) are simultaneous functions of the window used. This prohibits specifying any parameter independently. On the other hand, the eigen function (or building block) aproach does not have the limitations of either computer aided iterative technique or the window technique as explained further.
As known in the art, in the eigen function approach, the desired frequency response is approximately constructed by superposition of frequency shifted basis functions. These basis functions (or eigen functions) are triangular shaped frequency functions with low side lobes and they have finite time domain responses. Thus the desired response will have closed form expressions in time and frequency domains. Both symmetric and non-symmetric bandpass functions can be constructed using this approach. The amplitudes of mdividual eigen functions are varied to obtain the desired non-symmetric passband shape. The passband ripple is minimized by adjusting the spacing between the adjacent eigen functions. The transition width depends upon the duration of the impulse function of the eigen function while the bandwidth depends upon the number of eigen functions placed. The rejection depends upon the side lobe peaks of the eigen functions employed in the design. Thus with this approach all parameters can be specified independently.
As known in the art, SAW filter is a sampled data structure, in the sense that the impulse response of the desired bandpass function is sampled at instants corresponding to the electrode overlap positions. In a basic IDT structure where the impulse response is sampled, at 1 / 2fo, interval by the electrode overlaps, the resulting frequency response will be periodic with the original function repeating at the mterval 1 / 2fo, where fo is the center frequency of the bandpass function. Thus the original bandpass function at fo and its Hermitian conjugate at - fo, overlap each other when sampled at 1 /2 fo. This overlapping is called aliasing and when the band pass function is symmetric, aliasing will not result in the distortion of the function. However, when the desired function is non-symmetric, sampling at 1 /2 fo results in aliasing of non-symmebic response with its mirror image (Hermitian conjugate), and the non-symmetric function gets distorted to a symmetric function (refer Fig.2).
As known in the art, in order to avoid aliasing and to retain original non-symmetric shape of the bandpass function, it is necessary to increase the sampling frequency to at least 2fm, where fn, is the maximum frequency of interest in the bandpass function. Normally the sampling frequency is chosen as 4fo which is higher than 2fm and the electrode width will be one-eighth of SAW wavelength (corresponding to center frequency f©), and it is well known that at this electrode width, inter-electrode reflections cancel to a maximum extent resulting in minimum ripple at and around the center frequency.
However, there are some limitations with the prior art described above.
a. In the construction of desired frequency response using eigen function approach,
there is no attempt to minimize side lobe level in the prior art, thereby the filter
design becomes inefficient, in the sense that, if higher rejection is needed, one is
forced to use eigen functions with lower side lobes which require longer impulse
duration and hence longer IDT structure.
b. The sampling frequency chosen in the non-symmetric SAW filter design of the
prior art, is four times the center frequency, due to which inter-electrode
reflections and hence ripple around center frequency are minimized. This design
is satisfactory when the frequency of peak amplitude (in the passband) is close to
the center frequency, however in many non-symmetric bandpass functions, the
frequency of peak amplitude is invariably away from the center frequency,
resulting in partial cancellation of reflections, which in turn result m the higher
ripple m the passband.
These limitations of prior art are addressed and successfully resolved in the non-symmetric SAW filter design of the present art, as described below.
a. In the non-symmetric SAW filer design of the present art, the side lobe
characteristics of various eigen functions are carefully studied, and it is found that
only odd and even cosine series functions have side lobes with constant lobe
width of 1/T, where T is the impulse duration of the cosine series function. These
functions are then placed at spacing of 1/T, which results in complete overlap of
positive side lobe of one function with the negative side lobe of the adjacent
function. This results in maximum cancellation of side lobe amplitudes,
minimizing the side lobe levels and hence higher rejection (refer Fig.3)
b. In the non-symmetric SAW filter design of the present art, the sampling
frequency is four times the frequency of peak amplitude (fk) in the passband of
non-symmetric function. This choice makes the electrode width of the IFT to be
one eighth of SAW wavelength at fk, which results in maximum cancellation of
inter-electrode reflections at and around fk resulting in minimum ripple in the
passband. Fig.4 shows how the inter-electrode reflections cancel when the
electrode width is one-eighth of SAW wavelength.
1. Surface Acoustic Wave (SAW) filter consisting of two interdigital transducers
(IDTs) formed by rectangular metal electrode patterns on a piezoelectric
substrate such that one of the IDTs is apodized and the other is unapodized,
means for obtaining the electrode overlap pattern by first determining the time
domain function by performing fourier inverse transform on the desired non
symmetric frequency response by placing the frequency domain eigen
functions which are cosine series functions, at 1/T frequency spacing, where T
is time duration of the time domain function, and means for sampling and
mapping the time domain function into spatial domain, the sampling of the
time domain function being performed at time interval l/4fk, corresponding to
the sampling frequency 4fk, where fk is the frequency of the peak point in the
desired non-symmetric frequency response.
2. Surface acoustic wave (SAW) filter, as claimed in claim 1, wherein non-symmetric surface acoustic wave filter is used.
3. Surface acoustic wave (SAW) filter, as claimed in claims 1 and 2, wherein the inter-electrode reflections at the peak of bandpass function are cancelled and the ripple in the bassband are minimized by sampling the non-symmetric bandpass function at a rate of four times the peak frequency, 4fk.
4. A method of constructing non-symmetric surface acoustic wave filter comprising the steps of:
(i) placing the eigen functions which are cosine functions, at at l/T apart, where T is the impulse duration, resulting in maximum cancellation of side lobes, due to exact overlap of positive and negative side lobes of adjacent eigen functions, resulting in an efficient design by getting higher stop band rejection; and
(ii) minimizing the ripples in the passband by sampling the nonsymmetric bandpass function which is four times the peak frequency, 4fk to minimize the inter-electrode reflections.
|Indian Patent Application Number||700/MAS/1999|
|PG Journal Number||08/2007|
|Date of Filing||02-Jul-1999|
|Name of Patentee||BHARATH ELECTRONICS LIMITED|
|Applicant Address||116/2, RACE COURSE ROAD, BANGALORE 560 001|
|PCT International Classification Number||H03H 9/00|
|PCT International Application Number||N/A|
|PCT International Filing date|