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# e-book Analog Filters

Mechanical Equivalent of an Inductor is a Mass The mechanical analog of an inductor is a mass.

### Analog Filter Demo

The voltage across an inductor corresponds to the force used to accelerate a mass. The current through in the inductor corresponds to the velocity of the mass. From the defining equation for an inductor [Eq. In other words, magnetic flux may be regarded as electric-charge momentum.

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Transfer Function Since the input and output signals are defined as and , respectively, the transfer function of this analog filter is given by, using voltage divider rule ,. Impulse Response In the same way that the impulse response of a digital filter is given by the inverse z transform of its transfer function , the impulse response of an analog filter is given by the inverse Laplace transform of its transfer function, viz.

The Continuous-Time Impulse The continuous-time impulse response was derived above as the inverse- Laplace transform of the transfer function. In this section, we look at how the impulse itself must be defined in the continuous-time case. A simple valid definition is. Driving Point Impedance By inspection, we can write. Transfer Function The transfer function in this example can similarly be found using voltage divider rule:. Poles and Zeros From the quadratic formula , the two poles are located at. Impulse Response The impulse response is again the inverse Laplace transform of the transfer function. Expanding into a sum of complex one- pole sections,. This pair of equations in two unknowns may be solved for and.

The impulse response is then. Relating Pole Radius to Bandwidth Consider the continuous-time complex one-pole resonator with -plane transfer function. This shows that the 3- dB bandwidth of the resonator in radians per second is , or twice the absolute value of the real part of the pole. Denoting the 3- dB bandwidth in Hz by , we have derived the relation , or. The most natural mapping of the plane to the plane is.

### The Two-Pole Circuit to the Rescue

Quality Factor Q The quality factor Q of a two- pole resonator is defined by [ 20 , p. By the quadratic formula , the poles of the transfer function are given by.

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Relating to the notation of the previous section, in which we defined one of the complex poles as , we have E. Since the imaginary parts of the complex resonator poles are , the zero-crossing rate of the resonator impulse response is crossings per second. Moreover, is very close to the peak-magnitude frequency in the resonator amplitude response. If we eliminate the negative-frequency pole, becomes exactly the peak frequency.

It introduces the reader to the elegant theory in the development of analog filters. Although some of the mechanical steps for generating filters are covered, the book stresses the mathematical bases and the scholastic ingenuity of analog filter theory. It should be helpful to nonspecialist electrical engineers to gain a background perspective and some basic insight to the development of real-time filters.

In many modern advances in signal processing, their concepts and procedures have close links to analog filters.

## Digital Signal Processing/Analog Filter Design

The material in this book will provide engineers with a better perspective and more penetrating appreciation of many modern signal-processing techniques. JavaScript is currently disabled, this site works much better if you enable JavaScript in your browser. Free Preview. Buy eBook. Buy Hardcover. Buy Softcover. Sign In.

Access provided by: anon Sign Out. Systematic method to convert of analog filters to digital filters Abstract: The analog filters are usually converted to IIR digital filters using appropriate transformation of system function from s-domain to z-domain.

Recently another approach of converting an analog filter described by a diagram or a netlist to a digital filter has been proposed. In this paper, we present a systematic state-space SS based approach that provides an automatic procedure to convert an analog filter described by a diagram or a netlist to a digital filter described in system function form.