## Filter specifications

The first step in designing analog filters is to obtain the filter specification. The specification is developed based on the technical requirements to the filter and the possibility of hardware realization.

Analog filters are types of hardware that pass through signals with some frequency components while rejecting other frequency components. The frequency ranges in which signals pass through are named filter pass-band, and frequency ranges in which signals are rejected are named stop-band. In practical filters, signals attenuate in the pass-band as well as in the stop-band. The signal attenuations in the pass-band should not exceed some low level. In the stop-band, signal attenuations must not be smaller than the determined level.

A filter specification is a technical specification that determines the pass-band and stop-band frequency ranges and acceptable attenuations in those ranges. There are four basic types of filter specifications, one for each of the four basic filter types: low-pass, high-pass, band-pass and band-stop. Generally, filter specifications determine pass band and stop band frequency ranges, desirable signal attenuations (gains) at those ranges, approximation methods for the filter design, and hardware implementation requirements.

### Low-pass specifications

Ideal low-pass filters pass low frequency signals up to a determined cutoff frequency, and attenuate signals beyond it. Ideal low-pass filters are unrealizable due to the fact that when frequencies change from pass band to the stop band, the gain(reflection) is a jump that results in a discontinuous transition. Practical low-pass filter specifications specify the transition band where filter gain (attenuation) continuously changes from pass band gain to stop band gain.

#### Practical low-pass filter design specification.

#### Ap,As - passband and stopband attenuations.

#### 0 < f < Fp - passband

Fp < f < Fs - transition band

f > Fs - stopband

The practical low-pass filter specification is determined by four parameters: . Pass band edge frequency describes a frequency below which the signal must pass through a filter with attenuation that does not exceed . Usually, the attenuation in the pass band changes in the range . All frequency components above stop band edge frequency must be attenuated. The attenuation in the stop band must be at least . The attenuation for high quality low-pass filters can be 60 - 80 db. The behavior of the system in the transition band is not specified. The shorter the transition band, the better the practical filter is.

#### Fig 2.1 The low-pass filter specification panel intoduced in FAZA.

To design a low-pass filter using the FAZA software tool, the following parameters must be set up:

Magnitude units - decibels or linear

Frequency units - {Hz, KHz, MHz, GHz}.

Approximation methods - Butterworth approximation, Chebyshev approximation, Inverse Chebyshev approximation or elliptic approximation

- Pass band edge frequency

- Pass band attenuation (or gain)

- Stop band edge frequency

- Stop band attenuation (or gain)

Matheonics Technology Inc, 2009

### High-pass specifications

Ideal high-pass filters attenuate frequency components up to a determined cutoff frequency, and pass signals beyond it well. Ideal high-pass filters are unrealizable due to the fact that when frequencies change from stop band to the pass band, the gain(attenuation) is a jump that results in a discontinuous transition. Practical high-pass filters specify the transition band where filter gain (attenuation) continuously changes from stop band gain to pass band gain.

#### Practical high-pass filter design specification.

#### Ap,As - passband and stopband attenuations.

#### 0 < f < Fs - stopband

Fs < f < Fp - transition band

f > Fp - passband

The practical high-pass filter specification is determined by four parameters: Ap, Fp, As, Fs.
The frequency components below the stop band edge frequency Fs must be attenuated. The attenuation in the stop band must be above As. The attenuation for high quality high-pass filters must be at least 60 - 80 db. All frequency components above pass band edge frequency Fp must pass well. Usually, pass band attenuations for practical filters do not exceed 1 db.
The behavior of the system in the transition band is not specified. The shorter the transition band, the better the practical filter is.

#### Fig 2.2 The high-pass filter specification panel intoduced in FAZA.

Magnitude units - decibels or linear

Frequency units - {Hz, KHz, MHz, GHz}.

Approximation methods - Butterworth approximation, Chebyshev approximation, Inverse Chebyshev approximation or elliptic approximation

- Pass band edge frequency

- Pass band attenuation (or gain)

- Stop band edge frequency

- Stop band attenuation (or gain)

Matheonics Technology Inc, 2009

### Band-pass specifications

Ideal band-pass filters pass signals from certain lower to upper frequency points well, and attenuate signals outside of that range. Since ideal filters can not be realized in hardware, practical bandpass filters introduce transition ranges adjacent to the frequncies which determine pass band.

#### Practical band-pass filter design specification.

#### Ap - passband attenuation.

#### As1, As2 - stopband attenuations.

#### 0 < f < Fs1, f > Fs2 - stopbands

Fp1 < f < Fp2 - passband

Fs1 < f < Fp1, Fp2 < f < Fs2 - transition bands

The practical band-pass filter specification is determined by seven parameters: As1, Ap, As2, Fs1, Fp1, Fp2, Fs2. The pass band is determined by edge frequencies Fp1, Fp2 and pass band attenuation Ap. The left stop band is determined by attenuation As1 applied to the frequencies in the range 0 < f < Fs1. The right stop band is determined by attenuation As2 applied to the frequencies in the range f > Fs2 .

#### Fig 2.3 The band-pass filter specification panel introduced in FAZA

Magnitude units - decibels or linear

Frequency units - {Hz, KHz, MHz, GHz}.

Approximation methods - Butterworth approximation, Chebyshev approximation, Inverse Chebyshev approximation or elliptic approximation

- Left stop band attenuation (or gain)

- Left stop band frequency edge

- Pass band attenuation (gain)

- Left pass band frequency edge

- Right pass band frequency edge

- Right stop band attenuation (or gain)

- Right stop band frequency edge

Matheonics Technology Inc, 2009

### Band-stop specifications

Ideal band-stop (or band-reject) filters are used for attenuating (rejecting) the frequency components in a certain range. Outside of that range, signals pass with no attenuation. Practical band-stop filters introduce transition bands adjacent to frequncies which determine the stop band.

#### Practical band-stop filter design specification.

#### Ap1,Ap2 - passband attenuations.

#### As - stopband attenuation.

#### 0 < f < Fp1, f > Fp2 - passbands

Fs1 < f < Fs2 - stopband

Fp1 < f < Fs1, Fs2 < f < Fp2 - transition bands

The practical band-stop filter specification is determined by seven parameters: Ap1, As, Ap2, Fp1, Fs1, Fs2, Fp2.
The stop band is determined by edge frequencies Fs1, Fs2 and attenuation As. The left pass band is determined by attenuation Ap1 applied to the frequencies in the range 0 < f < Fs1 . The right pass band is determined by attenuation Ap2 applied to the frequencies in the range f > Fp2 .

#### Fig 2.4 The band-stop filter specification panel introduced in FAZA

Magnitude units - decibels or linear

Frequency units - {Hz, KHz, MHz, GHz}.

Approximation methods - Butterworth approximation, Chebyshev approximation, Inverse Chebyshev approximation or elliptic approximation

- Left pass band attenuation (or gain)

- Left pass band frequency edge

- Stop band attenuation (gain)

- Left stop band frequency edge

- Right stop band frequency edge

- Right pass band attenuation (or gain)

- Right pass band frequency edge

Matheonics Technology Inc, 2009