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.
- 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.
- They are limited by the amplifiers’ band-with, and noise
- They need power supplies
- They dissipate more heat than a passive circuit.
- 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.
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.
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.
- 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.
- 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.
First order Band Stop filter Circuit:
- 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.
- A low pass filter allows lower frequency signals to pass through but attenuates higher frequency signals.
- 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.
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