Filters

Department of Electronics and Communication Engineering,Manipal Institute of Technology, Manipal, INDIA

Filters

Department of Electronics and Communication Engineering,Manipal Institute of Technology, Manipal, INDIA

FiltersElectrical/Electronic filters are electronic circuits which perform signal processing functions, specifically to remove unwanted frequency components from the signal, to enhance wanted ones, or both.

Audio equalizers and crossover networks are two well-known applications of filter circuits.

Equalizers allow the amplitudes of several frequency ranges to be adjusted to suit the listener's taste and acoustic properties of the listening area. Crossover networks block certain ranges of frequencies( low-frequency signals) from reaching tweeter (high-frequency speakers).

Department of Electronics and Communication Engineering,Manipal Institute of Technology, Manipal, INDIA

Types of Filters

Electronic Filters belong one of the following types:

• Digital Filters

• Sampled-data Filters

• Continuous-time Filters(Analog Filters)

Electronic filters can also be classified as • Passive filter• Active filter

Department of Electronics and Communication Engineering,Manipal Institute of Technology, Manipal, INDIA

Types of Analog Filters

The commonly used Analog Filters belong to one of the following types :

• Low-pass(LP)• High-pass(HP)• Band-pass(BP)• Band-reject(BR)• All-pass(AP) • Amplitude Equalizer(AE)

Department of Electronics and Communication Engineering,Manipal Institute of Technology, Manipal, INDIA

Low-pass(LP) Filter

A low-pass(LP) filter is a filter that passes low-frequency signals but attenuates (reduces the amplitude of) signals with frequencies higher than the cutoff frequency.

A low-pass(LP) filter is the opposite of a high-pass(HP) filter.

Ideal LP response

Department of Electronics and Communication Engineering,Manipal Institute of Technology, Manipal, INDIA

Department of Electronics and Communication Engineering,Manipal Institute of Technology, Manipal, INDIA

Continuous-time LP Filter

An ideal LP filter completely eliminates all frequencies above the cutoff frequency while passing those below unchanged.

Ideal LP frequency response is a rectangular function, and is a brick-wall filter. The transition region present in practical filters does not exist in an ideal filter.

Department of Electronics and Communication Engineering,Manipal Institute of Technology, Manipal, INDIA

Frequency response of 1st order LP Filter

The gain-magnitude frequency response of a first-order (one-pole) low-pass filter. The voltage gain is shown in decibels .At cut-off frequency there is a 3 dB decline .Angular frequency is shown in units of radians per second.

Department of Electronics and Communication Engineering,Manipal Institute of Technology, Manipal, INDIA

Stop-band response of LP Filter

For a first-order LP filter ,the attenuation rate in the stop-band is 20 dB per decade.

A second-order filter attenuates higher frequencies more steeply. In general a second-order Butterworth filter exhibits the 40 dB per decade attenuation rate in the stop-band. Other all-pole second-order filters may roll off at different rates initially depending on their Q-factor, but approach the same final rate of 40 dB per decade.

Third- and higher-order filters are defined similarly. In general, the final rate of power roll off for a nth order LP filter is 20n dB per decade.

Department of Electronics and Communication Engineering,Manipal Institute of Technology, Manipal, INDIA

Passive RC first order LP filter

:

The combination of resistance and capacitance gives you the time constant of the filter τ = RC (represented by the Greek letter tau)

Department of Electronics and Communication Engineering,Manipal Institute of Technology, Manipal, INDIA

An active low-pass filter

This 1st-Order low pass Butterworth type filter, consists simply of a passive RC filter connected to the input of a non-inverting operational amplifier. The frequency response of the circuit will be the same as that of the passive RC filter, except that the amplitude of the output signal is increased by the pass band voltage gain of the amplifier.  

The gain in the pass band is −R2/R1

First-order Low Pass Butterworth Filter

First-order Low-Pass(LP) Butterworth Filter

Department of Electronics and Communication Engineering,Manipal Institute of Technology, Manipal, INDIA

An active low-pass filterFirst-order Low Pass Butterworth Filter

Voltage Gain for a First-order Low-Pass(LP) Filter

Where   AF = the pass band gain of the filter, (1 + R2/R1)  ƒ = the Frequency of the Input Signal in Hertz, (Hz)  ƒc = the Cut-off Frequency in Hertz, (Hz)

• A high-pass(HP) filter offers easy passage to high-frequency signal and attenuates the low-frequency signal.

Department of Electronics and Communication Engineering,Manipal Institute of Technology, Manipal, INDIA

High-pass Filter

Passive High-pass(HP) Filter

Department of Electronics and Communication Engineering,Manipal Institute of Technology, Manipal, INDIA

Department of Electronics and Communication Engineering,Manipal Institute of Technology, Manipal, INDIA

Frequency response of 1st order HP Filter

The cutoff frequency for a high-pass filter is that frequency at which the output voltage equals 70.7% of the input voltage. Above the cutoff frequency, the output voltage is greater than 70.7% of the input, and vice versa.

Department of Electronics and Communication Engineering,Manipal Institute of Technology, Manipal, INDIA

First-order High Pass Butterworth Filter

First-order High-Pass(HP) Butterworth Filter

Voltage gain of a first-order High-Pass(HP) FilterWhere  AF = the Pass band Gain of the filter, (1 + R2/R1)  ƒ = the Frequency of the Input Signal in Hertz, (Hz)  ƒc = the Cut-off Frequency in Hertz, (Hz)

Department of Electronics and Communication Engineering,Manipal Institute of Technology, Manipal, INDIA

Band-pass(BP) filter

The Band-Pass(BP) filter passes a selected range or band of frequencies that can be either narrow or wide while attenuating all those outside of this range.

The Band-Pass(BP) filter can be of two types:

• Broad-band Band-Pass filter• Narrow-band Band-Pass filter

Department of Electronics and Communication Engineering,Manipal Institute of Technology, Manipal, INDIA

Band-pass(BP) filter

Frequency Response of a 2nd order Band-Pass(BP) FilterThe term "bandwidth" refers to the difference between the lower cut-off frequency(ƒcLOWER) and the upper cut-off frequency (ƒcUPPER) points.

Department of Electronics and Communication Engineering,Manipal Institute of Technology, Manipal, INDIA

Band-pass(BP) filter

2nd order Band-Pass(BP) Filter

A band-pass(BP) filter arrangement commonly consists of a combination of a Low-pass (LP) and a High-pass(HP) filter.

Active Band Pass Filter Circuit

Department of Electronics and Communication Engineering,Manipal Institute of Technology, Manipal, INDIA

Wide-band and narrow-band BP Filter

The "Q" of a BP filter is the ratio of the Resonant Frequency, (ƒr) to the Bandwidth(BW) and is given as:

:

:                                 

In BP Filter, the width of the pass-band between the upper and lower-3dB corner points determine the Quality Factor(Q-point) of the circuit. This Q Factor is a measure of how "Selective" or "Un-selective" the band pass filter is towards a given spread of frequencies. The lower the value of the Q factor the wider is the bandwidth of the filter and consequently the higher the Q factor the narrower and more "selective" is the filter.

Department of Electronics and Communication Engineering,Manipal Institute of Technology, Manipal, INDIA

Band-Reject(BR) FilterA band-stop filter or band-rejection filter passes most frequencies unaltered, but attenuates those in a specific range to very low levels. It is the opposite of a band-pass filter.

A notch filter is a band-stop filter with a very narrow stop band.(high Q factor).Notch filters are used in live sound reproduction(Public Address systems, also known as PA systems) and in instrument amplifier(especially amplifiers or preamplifiers for acoustic instruments such as acoustic guitar, mandolin etc.) to reduce the noise and unwanted frequencies.e.g., Anti-hum filter is used to filter out the mains hum from a 50 Hz power line, though its higher harmonics could still be present. The filter passes all frequencies, except for the range of 49–51 Hz.

Department of Electronics and Communication Engineering,Manipal Institute of Technology, Manipal, INDIA

Frequency response of BS filter

Department of Electronics and Communication Engineering,Manipal Institute of Technology, Manipal, INDIA

All-pass Filter

The all-pass filter is an important building block in audio signal processing systems. It is called all-pass because all frequencies are passed equally.

In other words, the amplitude response of an all-pass filter is any nonzero constant at each frequency, but filter changes the phase relationship between various frequencies.

Generally, the first-order all-pass filter is described by the frequency at which the phase shift crosses 90°

Department of Electronics and Communication Engineering,Manipal Institute of Technology, Manipal, INDIA

Phase response of 1st order All-pass Filter

For 1st order all-pass filter ,the amplitude response is flat (within the bandwidth limitation of the amplifier), and there is a 90 degree phase shift at the "corner" frequency.

Department of Electronics and Communication Engineering,Manipal Institute of Technology, Manipal, INDIA

All pass filters are most often used for following:

• for matching phase in systems where phase is important

• for producing delays in circuits that need to delay a signal

• for creating 90o shifts for quadrature modulators

Applications of All-pass Filters

Department of Electronics and Communication Engineering,Manipal Institute of Technology, Manipal, INDIA

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