Active Band Reject Filters Information

Band reject or band stop filters (also known as notch filters) allow the passage of all frequencies with the exception of a frequency band that is attenuated or rejected.

A notch filter can be built by passing the input signal through both a low pass filter and a high pass filter simultaneously. The resulting signal is the sum of the outputs of both filters. The following figure shows a block diagram of a typical band reject filter.

The frequency response is shown below.

For detailed information on the theory and design of filters in general, please visit the Electronic Filters Specification Guide.

Specifications

The most important parameters when selecting a notch filter include the following. Many of these parameters are illustrated in the frequency response figure above.

Cutoff or center frequency. A filter's type determines the specified frequency (fc). For band reject filters, the specified frequency is the center frequency.

Bandwidth. Bandwidth (BW) is the range of frequencies that notch filters pass with maximum attenuation. (In the case of all other filter types [low pass, high pass, and band pass], bandwidth represents the frequency passed with minimal attenuation.)

Power dissipation. Power dissipation is the total power consumption of the device. This value is generally expressed in watts or milliwatts.

Order. This represents the number of poles in a filter design. Filter order is based on the transition band, or the range (fs - fc) of frequencies between the critical and cutoff frequencies. The slope or steepness of the transition region is related to the number of poles in the transfer function of the response. A pole is a root of the denominator of the transfer function. For a standard Butterworth filter every pole adds  -20  dB/decade or -6 dB/octave to the slope of the response. The slope of the line is called the roll-off of the transition. A pole represents one RC (resistor-capacitor) stage in the filter circuit. A filter that has only one RC network it is called a single-pole or order-one filter; one with two RC circuits is a 2-pole or second order filter, and so on.

Filter characteristics. This is the shape and behavior of the frequency response. Common filter classifications by frequency response are listed below.

• Bessel filter. Bessel filters are active filters with a passband that maximizes the group delay at zero frequency, thus showing a constant group delay in the passband. Group delay represents the time it takes for a signal to move between two points in a network. A constant group delay in the passband implies that for all signals with frequencies in the passband, the time delay will be the same. This fact is important in many situations, especially audio, video, and radar applications.
• Butterworth filter. Butterworth filters are designed so that the frequency response is flat in the passband.
• Chebyshev filter. Chebyshev filters feature a very steep roll-off, but have ripples in the passband.
• Elliptic filter. Elliptic (or Cauer) filters exhibit equalized ripple in both the passband and the stopband.
• Gaussian filter. Gaussian filters produce no overshoot in response to an input step and optimize the rise and fall times.
• Legendre filter. Legendre filters are designed to produce the maximum roll-off rate for a given order and a flat frequency response in the passband.

Circuits Today