First Order Filter: Design and Analysis - Essay Example

F I R S T O R D E R F I L T E R D e s i g n a n d A n a l y s i s By HERE] A Report Submitted to the School of Engineering and Built Environment Napier University, Edinburgh in Partial Fulfillment of the Requirements for the Degree of [DEGREE NAME]. November 2008 I N T R O D U C T I O N The word filter refers to the removal of an undesired portion of a frequency spectrum (Carpenter, Roden and Savant; “Electronic Design: Circuits and Systems” 527). Filters are classified, according to technology, into passive and active. Passive filters consist of combinations of resistors, inductors and capacitors. These filters do not depend upon an external power supply thus they are considered passive. Active filters, on the other hand, are implemented using a combination of passive and active (amplifying) components, and require an outside power source. These filters produce gain and usually consist only of resistors, capacitors and operational amplifiers. The most common classes of filters that can either be passive or active are the low pass, high pass, band pass, and band stop filters. Ideal low pass filters allow frequencies up to a given limit to pass and attenuate frequencies above that limit. Ideal high pass filters on the other hand, pass frequencies above a specified limit and attenuate those below. Ideal band pass filters allow only a particular band of frequencies to pass and attenuate the remaining frequencies. Ideal band stop filters are the reverse; this class of filters rejects frequencies within a specified band and passes those frequencies outside it. A filter that is important to note is the universal first order filter. It has a pole and at the same time a zero thus it is also called a bi-linear filter. D E S I G N A N D T H E O R E T I C A L A N A L Y S I S The figure below can be interpreted as first order active filters connected in series. By cascading a 20 dB-gain first order bi-linear filter and another first order bi-linear filter with unity-gain, we can construct a low pass filter whose frequency response is that in Figure 1. When universal filters are cascaded, they form a shaped filter. Figure 1 Filter Specification The analysis of the aforementioned filter is relatively simple. Its transfer function is obtained by multiplying the transfer functions of each of its components: that of the 2 bi-linear filters. It is specified that the output signal MUST NOT BE INVERTED. Notice that the transfer function of a bi-linear filter includes a NEGATIVE sign. When two bi-linear filters are cascaded, this eliminates the negative sign thus there is NO NEED for an inverter. C A L C U L A T I O N S Universal First Order Filter I This filter has a low frequency ( Read More