FILTER• An electrical network that alters the amplitude and/or

phase characteristics of a signal with respect to frequency• Ideally, a filter will not add new frequencies to the input

signal, nor will it change the component frequencies of that signal, BUT it will change the relative amplitudes of the various frequency components and/or their phase relationships.

• Often used to emphasize signals in certain frequency ranges and reject signals in other frequency ranges

Low Pass High Pass

Bandpass Bandstop

FILTER TYPESLow Pass-blocks high frequencies

High Pass-blocks low frequencies

Bandpass-blocks high and low frequencies except in narrow band

Bandstop-blocks frequencies in a narrow band

ACTIVE FILTERS• A type of analog electronic filter that uses active components such as

an amplifier• Amplifiers included in a filter design can be used to improve the performance

and predictability of a filter, while avoiding the need for inductors• Frequently use op amps so filter may have some gain as well. • Alternative to LRC-based filters

Benefits DisadvantageProvide improved characteristics Added complexitySmaller size and weight More design effortMonolithic integration in IC Implement without inductorsLower costMore reliableLess power dissipation

2nd ORDER SYSTEM The order of a filter is the highest power of the variable s (poles) in

its transfer function. The order of a filter is usually equal to the total number of

capacitors and inductors in the circuit Higher-order filters will obviously be more expensive to build, since

they use more components, and they will also be more complicated to design.

However, higher-order filters can more effectively discriminate between signals at different frequencies

Second-Order Filter Functions

Stop Band Filters (SBF) The Band Stop Filter, (BSF) is another type of frequency selective

circuit that functions in exactly the opposite way to the Band Pass Filter we looked at before.

It passes all frequencies with the exception of those within a specified stop band which are greatly attenuated.

Name Convention: A narrow-band bandstop filter will be referred to as a Notch Filter and the wideband bandstop filter will be referred to as Band-reject Filter.

Stop Band Filters (SBF) have two cut-off frequencies, commonly known as the -3dB or

half-power points producing a wide stop band bandwidth between these two -3dB points.

Then the function of a band stop filter is too pass all those frequencies from zero (DC) up to its first (lower) cut-off frequency point ƒL, and pass all those frequencies above its second (upper) cut-off frequency ƒH, but block or reject all those frequencies in-between.

BW = ƒH – ƒL

So for a wide-band band stop filter, the filters actual stop band lies between its lower and upper -3dB points as it attenuates, or rejects any frequency between these two cut-off frequencies.

Band Stop Filter Response

Band Stop Filter Characteristics

Band Stop Filter Circuit

There are many circuit topologies that can be used for very narrow notch filters, including:• Twin-T• Fliege• Wien-bridge• State-variable.

TWIN-T NOTCH FILTER• The twin-T (or twin-tee) filter is essentially a notch

(band stop) filter.• It can still give an extremely high Q notch without the

use of any opamps.• In theory, the notch depth is infinite at the tuning

frequency, but this is rarely achieved in practice.• Notch depths of 100dB are easily achieved, and are

common in distortion analysers.• If the notch is placed at the fundamental frequency of

the applied signal, it is effectively removed completely, so any signal that is measured is noise and distortion.

• The twin-T notch requires extraordinary component precision to achieve a complete notch, and for this reason it's not often recommended. However, it is without doubt one of the best filters to use when a very deep notch is needed - especially for completely passive circuits.

EXAMPLE PROBLEM

SOLUTION

SOLUTION

ANSWER

FLIEGE NOTCH FILTER• Normally, the Fliege Filter is something of an oddity, but

it makes an easily tuned notch filter with variable Q.• Notch depth is not as good as a twin-T, but it can be

tuned with a single resistor (within limits).

ACTIVE WIEN ROBINSON NOTCH FILTER• The Wien-Robinson bridge in the figure below is a passive

band-rejection filter with differential output.• The output voltage is the difference between the potential

of a constant voltage divider and the output of a band-pass filter.

• Its Q-factor is close to that of the twin-T circuit.• To achieve higher values of Q, the filter is connected into

the feedback loop of an amplifier.

ACTIVE WIEN ROBINSON NOTCH FILTER• The active Wien-Robinson filter in the figure has the

transfer function:

ACTIVE WIEN ROBINSON NOTCH FILTER

ACTIVE WIEN ROBINSON NOTCH FILTER

ACTIVE WIEN ROBINSON NOTCH FILTER• In comparison to the twin-T circuit, the Wien-Robinson

filter allows modification of the• passband gain, A0, without affecting the quality factor, Q.• If fm is not completely suppressed due to component

tolerances of R and C, a fine-tuning• of the resistor 2R2 is required.

SUMMARY:• An ideal band stop filter has a frequency response

which is the inverse of the band-pass filter.• Band stop filters block or “reject” frequencies that lie

between its two cut-off frequency points ( ƒL and ƒH ) but passes all those frequencies either side of this range. The range of frequencies above ƒL and below ƒH is called the stop band.

• Band Stop Filters have many uses in electronics and communication circuits and as we have seen here, they can be used to remove a band of unwanted frequencies from a system, allowing other frequencies to pass with minimum loss. Notch filters can be highly selective and can be designed to reject or attenuate a specific frequency or harmonic content generating electrical noise, such as mains hum within a circuit.