Passive Filters

Group members: Norman Bo, Kelvin Leung, David Ritter

This document outlined the procedures in designing a band-pass filter for RF circuits using RLC components.

An important block of communication systems is the electronic filter. Here, we will investigate the implementation of passive filters using resistors, capacitors and inductors. These filters work well at high frequencies, however, in low-frequency applications (dc to 100kHz), the required inductors are large and physically bulky, so they are difficult to implement.

There are four major types of filter, high-pass filter, low pass filter, band-pass filter and band-stop filter.

Diagram 1. Schematic Diagram of Band-pass filter

Diagram 2. Schematic diagram of High-pass filter

Diagram 3. Schematic diagram of Low-pass filter

In our circuit design, we are especially interested in using a band-pass filter. A band-pass filter is used to filter out unnecessary signals and noises at the non-desired frequency. During modulation, a lot of high harmonic noises (which is at higher frequency) are created.

Lets analyze the frequency response diagram of a band-pass filter.

Diagram 4. Frequency response of a band-pass filter.

In our project, our carrier frequency is 800kHz. Therefore,

w o= 2 * pi * f = 1/(LC)^1/2

L*C = 4 * 10 ^ -14

We picked a 22uH inductor since this is a standard value which can be obtained easily. Therefore, we need a 1800pF capacitor. To determine the Q factor and the value of resistor, we can,

Q = 2* pi * f * C * R

We would like to have a Q factor of 10, therefore, the calculated R is 1.1kOhm, which again, is a standard value of resistors.

After we confirmed our components value for the band-pass filter, we calculated the w 1, w2 values according to the equations on the frequency response diagram. We found that f1 and f2 is equal to 761kHz and 841kHz.

Therefore, a band-pass filter is created with a center frequency at 800kHz by using a 1.1kOhm resistor, 1800pF capacitor and a 22uH inductor.

Reference:

Sedra/Smith Mircoelectronic Circuits 4th Edition, Oxford.