The history of piezoelectricity evolution is over 120 years which was discovered by brothers Curie in 1880. They were Pierre Curie (1859-1906) and Jacques Curie (1855-1941). During the study of the generation surface electrical charge by applying pressure on some material, they found out an unusual phenomenon which was a voltage of opposite polarity was generated by pressure was applied on the crystalline minerals such as quartz. The amplitude of the generated voltage was proportional to the applied load [1]. The phenomenon was named as “piezoelectric” and the effect called as “piezo effect” [2]. In the following year, the inverse piezo effect was proposed by Lippman which was basing on the fundamental thermodynamic principles. The brothers
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Roll-off
In the graph of the amplitude against the frequency, roll-off represents as the gradient of the graph line [12]. The characteristic of filters can be determined by roll-off of the gain. For ideal filters, the gradual roll-off of the gain is from 1 to 0 [18]. Generally, the roll-off is measured in units of decibels (dB) on a logarithmic scale.
Quality factor 'Q'
The quality factor is a measure of the selectivity of the circuit. Higher the value of Q, the more selective the circuit but narrower the bandwidth. The quality factor is inversely proportional to the bandwidth of the frequency. If the quality factor is equal or greater than 10, the circuit can be considered as high-Q circuit [19].
Generally, filters are classified based on their order or their specific design type. Higher order of filter provides sharper roll-off at cut-off frequency.
Figure 2. 11: Ideal and Actual Frequency Response of Four Types of Filter: (a) A Lowpass Filter (b) A Highpass Filter (c) A Bandpass Filter (d) A Bandstop Filter [19]
2.3.2.1 Butterworth
Roll-off
In the graph of the amplitude against the frequency, roll-off represents as the gradient of the graph line [12]. The characteristic of filters can be determined by roll-off of the gain. For ideal filters, the gradual roll-off of the gain is from 1 to 0 [18]. Generally, the roll-off is measured in units of decibels (dB) on a logarithmic scale.
Quality factor 'Q'
The quality factor is a measure of the selectivity of the circuit. Higher the value of Q, the more selective the circuit but narrower the bandwidth. The quality factor is inversely proportional to the bandwidth of the frequency. If the quality factor is equal or greater than 10, the circuit can be considered as high-Q circuit [19].
Generally, filters are classified based on their order or their specific design type. Higher order of filter provides sharper roll-off at cut-off frequency.
Figure 2. 11: Ideal and Actual Frequency Response of Four Types of Filter: (a) A Lowpass Filter (b) A Highpass Filter (c) A Bandpass Filter (d) A Bandstop Filter [19]
2.3.2.1 Butterworth