Active Filters
#1

Abstract

A filter is a system that processes a signal in some desired fashion.
A continuous-time signal or continuous signal of x(t) is a function of the continuous variable t. A continuous-time signal is often called an analog signal.
A discrete-time signal or discrete signal x(kT) is defined only at discrete instances t=kT, where k is an integer and T is the uniform spacing or period between samples

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#2
Active Filters


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1. Introduction

In this chapter, we will deal with active filter circuits. Why even bother with active
filters? Answer: Audio. Most (99%) of audio devices have filters in them. They allow
you to separate out different frequency regimes. Your project this semester is to design
an audio amplifier. This chapter is organized as follows:
2. A Review of Complex Numbers and Introduction to Frequency Response: In this
section, I talk about why complex numbers, the standard form of a complex number,
Euler's forumla, the impedence of a resistor, capacitor etc.
3. An Overview of Filter Circuits: I discuss terms like active filters, passive filters,
low-pass, high-pass, band-pass and band-reject filters.
4. A Passive Filter Circuit - The RC low-pass filter: I will derive in detail the
expression for the frequency response of an RC circuit and show how it can be used as a
low pass filter.
5. An Active Filter Circuit - The Op-amp band-pass filter circuit: I will derive in
detail the expression for the frequency response of this circuit and show how it can be
used to construct a band-pass filter.

An Overview of Filter Circuits

A filter circuit (as the name suggests) filters stuff. In our case, the circuit allows
sinusoids of a certain frequency to appear at the output, it attenuates sinusoids at other
frequencies – that is, the circuit does not allow them to appear at the output. We will see
how in the next section. The main types of filter circuits are:

i . Low-pass filter: This circuit allows frequencies below a specific frequency to pass
through. Higher frequencies are attenuated. The RC circuit considered above is a low
pass filter circuit – we will see how in the next section.
ii . High-pass filter: Allows frequencies above a specific frequency to pass through.
Lower frequencies are attenuated.
iii . Band-pass filter: Frequencies in a specific range (or band), example: [1 kHz, 1 MHz]
pass through. Frequencies above 1 MHz and below 1kHz are attenuated.
iv.Band-reject filter: Frequencies in a specific range (or band), example: [1kHz, 1MHz]
are attenuated. Frequencies above 1 MHz and below 1 kHz are allowed to pass
through.
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