### Analog Filters

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This removing of unnecessary parts of the signal is called as filtering process. These signal processing filters are classified into various types such as electronic filters , digital filters, and analog filters. Analog filter is typically used in electronics and is considered as a basic building block of signal processing.

These analog filters are used to separate audio signals before applying to loudspeakers. To separate and to combine several telephone conversations onto a single channel can be done using analog filters. To select a particular radio station from the radio receiver by rejecting all other channels can be done using analog filters. The continuously varying signals analog signals can be operated using passive linear electronic analog filters which are composed of passive elements such as resistors, capacitors, and inductors. These analogue filters are frequently used for allowing particular frequency components by rejecting other from analog or continuous time signals.

## Analog Filters Using MATLAB

The linear analog filters can be listed as network synthesis filters, image impedance filters, and simple filters. The analog filter design includes analog filter transfer functions, poles and zeros of analog filters, frequency response of analog filters, output response, and different types of analog filters. The Butterworth or maximally flat magnitude filter has a flat mathematically as much as possible frequency response. If we increase the order of the Butterworth filter, then the Butterworth filter design cascaded stages also gets increased.

The following chapters will show some of the techniques involved in designing analog filters, and transforming analog filters from one type to another. The section will culminate on a chapter on the bilinear transform, which transforms the mathematical representation for an analog filter into the equations for an equivalent digital filter. There are many different types of spectral transformations and there are many mappings from analog to digital filters. Butterworth ensures a flat response in the passband and an adequate rate of rolloff.

A good "all rounder," the Butterworth filter is simple to understand and suitable for applications such as audio processing. Three types of analog filters are commonly used: Chebyshev , Butterworth , and Bessel also called a Thompson filter. Each of these is designed to optimize a different performance parameter.

The complexity of each filter can be adjusted by selecting the number of poles , a mathematical term that will be discussed in later chapters.

The more poles in a filter, the more electronics it requires, and the better it performs. Each of these names describe what the filter does , not a particular arrangement of resistors and capacitors.

For example, a six pole Bessel filter can be implemented by many different types of circuits, all of which have the same overall characteristics. For DSP purposes, the characteristics of these filters are more important than how they are constructed.

Nevertheless, we will start with a short segment on the electronic design of these filters to provide an overall framework. Figure shows a common building block for analog filter design, the modified Sallen-Key circuit. This is named after the authors of a s paper describing the technique.

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The circuit shown is a two pole low-pass filter that can be configured as any of the three basic types. Table provides the necessary information to select the appropriate resistors and capacitors. The particular op amp use isn't critical, as long as the unity gain frequency is more than 30 to times higher than the filter's cutoff frequency. This is an easy requirement as long as the filter's cutoff frequency is below about kHz. Four, six, and eight pole filters are formed by cascading 2,3, and 4 of these circuits, respectively.

## Filters - Analog filter | Dewesoft Training Portal

For example, Fig. Bessel filter created by cascading three stages. Each stage has different values for k 1 and k 2 as provided by Table , resulting in different resistors and capacitors being used. Need a high-pass filter? Simply swap the R and C components in the circuits leaving R f and R 1 alone. The problem is, it is difficult to make resistors directly in silicon.

## Digital Signal Processing/Analog Filter Design

The answer is the switched capacitor filter. Figure illustrates its operation by comparing it to a simple RC network.

If a step function is fed into an RC low-pass filter, the output rises exponentially until it matches the input. The voltage on the capacitor doesn't change instantaneously, because the resistor restricts the flow of electrical charge.

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The switched capacitor filter operates by replacing the basic resistor-capacitor network with two capacitors and an electronic switch. The switch alternately connects the small capacitor between the input and the output at a very high frequency, typically times faster than the cutoff frequency of the filter.

When the switch is connected to the input, the small capacitor rapidly charges to whatever voltage is presently on the input. When the switch is connected to the output, the charge on the small capacitor is transferred to the large capacitor.

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In a resistor, the rate of charge transfer is determined by its resistance. In a switched capacitor circuit, the rate of charge transfer is determined by the value of the small capacitor and by the switching frequency.

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This results in a very useful feature of switched capacitor. This makes the switched capacitor filter ideal for data acquisition systems that operate with more than one sampling rate. These are easy-to-use devices; pay ten bucks and have the performance of an eight pole filter inside a single 8 pin IC.

Now for the important part: the characteristics of the three classic filter types.