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F. Kung


Introduction to Filter
A filter is a network that provides perfect transmission for signal with frequencies in certain passband region and infinite attenuation in the stopband regions. Such ideal characteristics cannot be attained, and the goal of filter design is to approximate the ideal requirements to within an acceptable tolerance. Filters are used in all frequency ranges and are categorized into three main groups:
• Low-pass filter (LPF) that transmit all signals between DC and some upper limit c and attenuate all signals with frequencies above c.
• High-pass filter (HPF) that pass all signal with frequencies above the cutoff value c and reject signal with frequencies below c.
• Band-pass filter (BPF) that passes signal with frequencies in the range of 1 to 2 and reject frequencies outside this range. The complement to band-pass filter is the band-reject or band-stop filter.

In each of these categories the filter can be further divided into active and passive type. The output power of passive filter will always be less than the input power while active filter allows power gain. In this lab we will only discuss passive filter. The characteristic of a passive filter can be described using the transfer function approach or the attenuation function approach. In low frequency circuit the transfer function (H()) description is used while at microwave frequency the attenuation function description is preferred. Figure 1.1a to Figure 1.1c show the characteristics of the three filter categories. Note that the characteristics shown are for passive filter.


Realization of Filters
At frequency below 1.0GHz, filters are usually implemented using lumped elements such as resistors, inductors and capacitors. For active filters, operational amplifier is sometimes used. There are essentially two low-frequency filter syntheses techniques in common use. These are referred to as the image-parameter method (IPM) and the insertion-loss method (ILM). The image-parameter method provides a relatively simple filter design approach but has the disadvantage that an arbitrary frequency response cannot be incorporated into the design. The IPM approach divides a filter into a cascade of two-port networks, and attempt to come up with the schematic of each two-port, such that when combined, give the required frequency response. The insertion-loss method begins with a complete specification of a physically realizable frequency characteristic, and from this a suitable filter schematic is synthesized. Again we will ignore the image parameter method and only concentrate on the insertion loss method, whose design procedure is based on the attenuation response or insertion loss of a filter.

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