Electronic filter design pdf

We will assume that the given filter specification is presented in the form shown in figure 1. The interpretation of the diagram is the following:.

The transfer function G f is almost invariably given in units of dB. Within the passband, the magnitude of the transfer function may vary between zero and G p. When it enters the stop band, the magnitude of the transfer function should decrease to G s or less as the frequency f s is reached.

A possible transfer function, in the form of the smooth curve, is shown in figure 1. We plan on realizing the filter using a linear analog-circuit. Such circuits have transfer functions whose magnitude squared is an even polynomial in the frequency variable f. Therefore the first step in the design process is to find a polynomial transfer-function that will satisfy the specifications.

Many different well-known polynomial transfer-functions are used for approximating filter specifications. Because of time constraints, however, our attention will be confined entirely to Butterworth and Chebyshev polynomial realizations. They have the advantage of having over the years acquired extensive tabulations.

But it must be understood at the outset that additional polynomial realizations exist, and that with each is associated a set of advantages and disadvantages which are discussed in the literature.

We will now address the question of how to fulfill the specification of the filter by using Butterworth and Chebyshev transfer functions. Back to top EE Index. At the outset we observe that Butterworth filters have the magnitude characteristic given by. This class of filters has a monotonically decreasing amplitude characteristic.

It has no ripples in the passband, in contrast to Chebyshev and some other filters , and is consequently described as maximally flat. In order to fully specify the filter we need an expression for determining n as well as a method for computing the f c needed in 1.

To reach this goal we substitute the filter specifications at f p and f s into 1. The example which follows will illustrate the use of the above equations. Substituting the specifications given into 1. We need an integer exceeding that given in 1. We now simply need to find the value of f c needed to finish specifying 1. The last two equations produce the two results for f c ,.

With n fixed at 4 and f c fixed at 3. Comparing the above results to the original specification we find that the specifications are exceeded. We therefore have some latitude in our design to compensate for tolerances of component values. The filter specifications, as well as a sketch of a Chebyshev filter response, are shown in figure 1. As can be seen in the diagram, this class of filters has an amplitude characteristic which has ripple in the passband, in contrast to the maximally flat Butterworth filters.

The end of the passband, the frequency f p , is also the cutoff frequency f c appearing in the equations which are presented below. Chebyshev filters have an amplitude characteristic given by. They also have the nonpolynomial forms, given below, which are very convenient for hand calculation. As can be seen from the following equations, there is one form for the passband and one form for the stopband. Examination of 1. As a consequence we conclude from 1.

The above is the magnitude of the ripple in the passband. The upper bound corresponds to 0 dB. The lower bound corresponds to G p dB. If we could obtain an expression for calculating the value of n needed in 1. To attain this objective we substitute the filter specifications at f s and f p using f p for f c , as well as 1.

Solving for n in the above we obtain. Since n has to be an integer exceeding that given in 1. We can either increase f c or decrease the ripple in the passband. We choose, quite arbitrarily, to decrease the ripple in the passband to 0.

A band-stop filter can also be called a band-reject or notch filter. A filter is characterised by the following parameters:. As we know, filters consist of inductances and capacitances, and their response changes with frequency.

Resolving this equation we can find the position of the roots on the s-plane where imaginary components are vertical, and the real component is horizontal. If all the roots are on the left side of the plane, then the filter is stable. It helps us to work with two important parameters of the filters, that were mentioned above: F C cutoff frequency and , quality factor.

F C cutoff frequency is a frequency where the filter response is down 3dB from the pass band. You can see the quality factor graphs in the Analog Devices datasheets, for example. So what do these parameters mean?

They play an important role in the definition of the transfer function and characterisation of the filter. Here the quality factor Q , has a special meaning. The difference F H — F L is a bandwidth. The band-pass filter can be narrow and wide.

The narrow band-pass filter is a classical one. One T network is made up of two resistors and a capacitor, while the other uses two capacitors and a resistor.

There are several ways to make the notch filter. One way is to subtract the band pass filter output from its input. Procedure: 1. Connections are given as per the circuit diagram. Set the desired input voltage. By varying the frequency note down the corresponding output.

Calculate the voltage gain and gain in db using respective formulas. Plot the graph between gain in db and frequency and get the corresponding bandwidth. Practice Questions 1.

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