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Problem: Design a bandpass filter

Let us look at bandpass filters, which pass a band of desired or specified frequencies, while attenuating those outside the band. The simplest such filter can be modeled as second-order with the following general transfer function as shown in Equation 1.

where

Symbol	Description
:	Resonant Frequency (rad/s)
B :	3-dB Bandwidth (rad/s)
K:	Gain

You can create filters using both linear circuit elements like resistors, inductors, and capacitors (RLC) as well as from nonlinear circuit elements such as Op-amps and transistors. Figure 1 shows a general bandpass filter using an Op-amp circuit configuration.

Figure 1: General bandpass filter circuit schematic using an Op-amp configuration.

Sometimes the filter transfer function in Equation 1 is written in terms of the quality factor Q (i.e. Q = /B), to assist in determining the height and sharpness of the resonant peaks of the bandpass system as shown in Equation 2.

By knowing the height and sharpness of the resonant peaks of the filter, the better we can determine how well it behaves and filters the desired frequencies.

Design Criteria: Design a bandpass filter that will yield a resonant frequency of 10 kHz, with a maximum gain of 10, and a bandwidth of no more than 500 Hz.

Objective: Find the appropriate transfer function that meets the design criteria and verify your result with a frequency response plot from MATLAB.

Given: = 2p x 10 kHz, B = 2p x 500 Hz, K = 10 x B

See Solution