Active Filters

By Mallesham Devasane|Updated : January 3rd, 2017
Active Filters: An active filter means using amplifiers to improve the filter. An active filter generally uses an operational amplifier (op-amp) within its design.
  • An electronic circuit that modifies the frequency spectrum of an arbitrary signal is called filter.
  • A filter that modifies the spectrum producing amplification is said to be an active filter.
  • Filtering components are resistance and capacitance only. Doesn’t include inductors
  • Active components like op-amp, FET, transistors etc. are used
  • It requires biasing voltage
  • Its bandwidth is limited due to active component
  • Gain is limited to the gain of active components used
  • Small in size due to resistors and capacitors are used
  • Due to active components like op-amp and FET input impedance is high
  • Output impedance is low
  • Basically used to suppress unwanted frequency components from information signals
  • The main function of filters is to filter out required frequency components from mix frequency signal. They allow
  • They allow range of frequency to pass that is known as pass band and rejects (or suppresses) other frequencies known as stop band.
  • The cut-off frequency is the parameter that separates out these two bands. So depending upon these pass band and stop band there are four types of filters: Low pass filters, High pass fliters, Band pass filters, and Band reject filters.
Active Filters Advantage of active filters:
  • They can provide gain
  • They can provide isolation because of the typical characteristic impedances of amplifiers
  • They can be cascaded because of the typical characteristic impedances of amplifiers
  • They can avoid the use of inductors greatly simplifying the design of the filters.
Disadvantages of active filters:
  • They are limited by the amplifiers’ band-with, and noise
  • They need power supplies
  • They dissipate more heat than a passive circuit.
Low pass filter (LPF): It allows to pass all the frequencies lower than its cut-off frequency and stops all other frequencies.
  • A low-pass filter has a constant gain (=Vout/Vin) from 0 Hz to a high cut-off frequency fH.
  • This cut off frequency is defined as the frequency where the voltage gain is reduced to 0.707, that is at fH the gain is down by 3 dB; after that (f > fH) it decreases as f increases.
  • The frequencies between 0 Hz and fH are called pass band frequencies, whereas the frequencies beyond fH are the so-called stop band frequencies.
  • A common use of a low-pass filter is to remove noise or other unwanted high-frequency components in a signal for which you are only interested in the dc or low-frequency components.
  • Low-pass filters are also used to avoid aliasing in analog-digital conversion (which we will encounter in a few weeks). Correspondingly, a high-pass filter has a stop band for 0 < f < fL and where fL is the low cut off frequency.
  • A simple, single-pole, low-pass filter (the integrator) is often used to stabilize amplifiers by rolling off the gain at higher frequencies where excessive phase shift may cause oscillations.
First Order Low Pass Filter Circuit: Active low pass filter-1 Transfer function of the circuit: Transferfunction-lowpassfilter-1 Gain:

K=R2/R1

Cutoff Frequency:

ωc=1/R2C

 

High pass filter (HPF): It allows to pass all the frequencies higher than its cut-off frequency and stops all other frequencies.
  • A common use for a high-pass filter is to remove the dc component of a signal for which you are only interested in the ac components (such as an audio signal).
  • A simple, single-pole, high-pass filter can be used to block dc offset in high gain amplifiers or single supply circuits.
  • Filters can be used to separate signals, passing those of interest, and attenuating the unwanted frequencies.
First Order High Pass Filter Circuit: Highpassfilter-1 Transfer function of the circuit: transferfunction-highpassfilter Gain:

K=R2/R1

Cutoff Frequency:

ωc=1/R1C

  Band pass filter (BPF):
  • It allows to pass band of frequencies between its higher cut-off and lower cut-off frequencies.
  • If a high-pass filter and a low-pass filter are cascaded, a band pass filter is created.
  • A bandpass filter has a pass band between two cut-off frequencies fH and fL, (fH > fL), and two stop bands 0 < f < fL and f > fH.
  • The bandwidth of a bandpass filter is equal to fH -fL. Recall that we used a tunable bandpass filter to do harmonic spectrum analysis several weeks ago.
  • The simplest band-pass filter can be made by combining the first order low pass and high pass filters.
Bandpass
  • This circuit will attenuate low frequencies (w<<1/R2C2) and high frequencies (w>>1/R1C1), but will pass intermediate frequencies with a gain of -R1/R2.  However, this circuit cannot be used to make a filter with a very narrow band.
Bandpassfilter-1 First order band pass filter Circuit: Bandpassfilter-2Transfer function: Transferfunction-bandpassfilter-1   Band reject filter (BRF):
  • It stops band of frequencies between its higher cut off and lower cut off frequencies.
  • A complement to the band pass filter is the band-reject, or notch filter.
  • The pass bands include frequencies below fL and above fH. The band from fL to fH is in the stop band.
Active band stop filter-1

  First order Band Stop filter Circuit:  

Active band stop filter-2

  Transfer function: Bandstopfilter-transferfunction Scaling

  • There are two ways of scaling a circuit: magnitude or impedance scaling, and frequency scaling.
  • Both are useful in scaling responses and circuit elements to values within the practical ranges.

Magnitude Scaling:

  • Magnitude scaling leaves the frequency response of a circuit unaltered.
  • Magnitude scaling is the process of increasing all impedances in a network by a factor, the frequency response remaining unchanged.

Frequency Scaling:

  • Frequency scaling shifts the frequency response up or down the frequency spectrum.
  • Frequency scaling is the process of shifting the frequency response of a network up or down the frequency axis while leaving the impedance the same.
  Passive Filter:
  • A passive filter is made up entirely of passive components such as resistors, capacitors and inductors.
  • low pass filter allows lower frequency signals to pass through but attenuates higher frequency signals.
Difference between Active and Passive Filters:
  • Passive filters consume the energy of the signal, but no power gain is available; while active filters have a power gain.
  • Active filters require an external power supply, while passive filters operate only on the signal input.
  • Passive filters are constructed using only passive components (resistors, capacitors and inductors). Active filters may contain passive as well as active components.
  • Active filters may contain passive as well as active components.
  • Only passive filters use inductors.  Active filters do not contain inductors.
  • Only active filters use elements like op-amps and transistors, which are active elements.
  • Theoretically, passive filters have no frequency limitations while, active filters have limitations due to active elements.
  • Passive filters can be used at high frequencies by using inductors.
  • For Active filters, the frequency range is dependent on the bandwidth of the amplifier. Typically, to filter high-frequency signals, passive filters are used.
  • Passive filters have a better stability and can withstand large currents.
  • Passive filters are relatively cheaper than active filters.

Comments

write a comment

Follow us for latest updates