Filters Flashcards
is a special type of a circuit, which is used for filtering out some of the input signals on the basis of their frequencies.
frequency filter/frequency selective circuit
The band of frequencies of the input signal that pass through the filter without any attenuation is called_____.
Passband
The band of frequencies of the input signal that are blocked or attenuated in the filter is called _______.
Stopband
The passband & stopband are distinguished from each other by the_______ or ______.
cutoff frequencyorcorner frequency
The output signal’s voltage at the cutoff frequency is 70.7% of the input signal’s voltage. It is also known as _________ because ____ represents half power. And it is the frequency where the power of the output signal becomes half the power of the input signal.
-3db frequency
Two cutoff frequencies
- Lower cutoff frequency
- Upper cutoff frequency
The lower frequency at which the gain of the filter is _____ or _____. It is denoted by f1. Bandpass filter allows frequency after this point, whereas the band stop filter blocks it.
half or -3db
Upper Cutoff Frequency
The upper frequency at which the output power is reduced by _____. of the input power. It is denoted by f2. Bandpass filter does not allow frequency after this point, whereas the band stop filter allows it.
½
The frequency that lies at the center of the passband or stopband in a bandpass filter or band reject filter respectively is called ___________. It lies in-between the two cut-off frequency i.e. lower & Upper cut-off frequency. In fact, it is the arithmetic mean of both cut-off frequencies.
center frequency
Center frequency formula
f0= (f1+ f2) / 2
The range of frequencies that are passed (in case of bandpass filter) without any attenuation or the frequencies that are attenuated (in case of band reject filter) is called the _______ of the filter
bandwidth
Bandwith formula
Β = f2– f1
It is the rate of change of gain/ output power, the drop rate of gain of the filter is called the ________. it is expressed as a gain loss per decade (ten times increase in frequency) or per octave (two-time increase in frequency).
roll-off rate
Two types of filters (based on construction)
- Passive filters
- Active filters
It does not need any external source of energy. Therefore there is no voltage gain in these filters. The output voltage is always less than its input voltage.
It can easily filter a high-frequency signal but it cannot process any low frequencies.
PASSIVE FILTERS
As the name suggests, passive filters are made up of passive components, such as ______, ______, and _____.
resistors, capacitors & inductors
can filter very low-frequency signals but it cannot process very high-frequency signal.
active filters
In addition to theresistor&capacitor, Active filter uses anactive componentsuch as an ______, _______, etc.
operational amplifier,transistors
Types of filters (based on frequency)
- Low Pass Filter
- High Pass Filter
- Band Pass Filter
- Band Reject Filter
allow low-frequency signals without any attenuation (decrease in power) but it rejects any high-frequency signals.
Low pass filter
allows the high-frequency signals to pass without any attenuation in its amplitude & blocks (rejects) any low-frequency signal
high pass filter
allows a specific band of frequencies & blocks any other frequencies lower or higher than its passband frequencies.
Band pass filter
Band pass filter has two cutoff frequencies:
lower and upper cutoff frequency
Bandpass blocks low frequencies & high frequencies, while allows the frequencies in between known as the ________.
passband frequencies
This type of filter attenuates the signal whose frequencies lies in a fixed band of frequencies.
It works completely opposite to the bandpass filter. It allows low-frequency signal & high-frequency signals. But it does not allow a fixed band of frequencies in between.
BAND REJECT FILTER
band reject filter is also known as
Band Stop filterorNotch Filter
Application of filters
- The tuner in radio
- Treble & bass of the speaker
- Anti-aliasing
- Notch filter
- Power supply smoothing
- Noise Suppression
The bandpass filter in the tuner of the radio allows a fixed frequency to the output speaker.
The tuner in radio:
it is a low pass filter that filters out the high-frequency components from a signal before sampling. It prevents the aliasing component form being sampled.
Anti-Aliasing:
The bass has lower frequencies & treble has higher frequencies. They are separated using high pass & low pass filter and are separately routed to corresponding bass speaker & treble speaker for clear music.
Treble & bass of the speaker:
they are band rejects filters with a narrow bandwidth that filter out any interfering signal.
Notch Filter:
The output of the power supply which is a rectifier has an AC ripple in it. These frequencies are filtered out using a low pass filter which results in smoothing the output signal.
Power Supply Smoothing:
They are used in communication systems for noise removal from the received signals.
Noise suppression:
Types of High pass filters
PASSIVE and ACTIVE high pass filter
TYPES OF PASSIVE HIGH PASS FILTER:
- FIRST ORDER PASSIVE HIGH PASS FILTER
- SECOND ORDER PASSIVE HIGH PASS FILTER
First order filters contain only one reactive component i.e. either capacitor or inductor. It is the simplest form of filter made from only two components with resister being common in both designs i.e. RC & RL.
FIRST ORDER PASSIVE HIGH PASS FILTER:
In order to understand a filter, you need to study its frequency response. Frequency response or bode plot is a graph of a circuit which shows its gain on the vertical axis with respect to the frequency on the horizontal axis.
However, the frequency response contains some key terms which need to be discussed to fully understand it. Here is a frequency response of First-order High Pass filter.
FREQUENCY RESPONSE AND TERMS USED IN IT:
The frequency at which the gain of the filter is ½ or -3db or the output amplitude is 70.7% (1/√2) of the input is known as __________ it is denoted by fc. It is the boundary between passband & stop band of a filter.
CUT OFF FREQUENCY OR CORNER FREQUENCY
The ________ is the band of frequencies that is blocked by the filter. in a high pass filter, the frequency that is lower than the cutoff frequency fcis the stop band frequency.
Stop band
The band of frequency that gets passed through the filter without attenuation is ________. The frequency above the cutoff frequency fcis the passband frequency of a high pass filter. It is clearly shown in the frequency response graph above.
passband
The width of the frequency allowed by the filter is called the ______ of the filter.
bandwidth
Gain of filter formula
Gain = Vout/Vin
The ________ is the rate of change in gain or steepness of the curve in the stop band of a filter.
roll off rate
The roll of rate depends on the order of the filter & it is given by;
20n dB/decade or 6n dB/octave
In this design of high pass filter, a capacitor is connected with a resistor in series. The input signal is applied through the capacitor.
RC FIRST ORDER HIGH PASS FILTER
The reactance of the capacitor is very high at low frequency. It acts as an open circuit to low frequency signals. Thus the low-frequency input signal gets blocked and it never makes it to the output terminal as the whole signal appears across the capacitor.
OPERATION
At the _______, the resistance and the capacitive reactance of the circuit are equivalent
cutoff frequency
This filter is designed by combining a resistor with an inductor.
RL FIRST ORDER HIGH PASS FILTER
First order filters contain only one reactive component i.e. either capacitor or inductor. It is the simplest form of filter made from only two components with resister being common in both designs i.e. RC & RL.
SECOND ORDER PASSIVE HIGH PASS FILTER:
KEY FEATURES OF SECOND ORDER FILTER
- ROLL OFF RATE
- GAIN AT CUTOFF FREQUENCY
It is the phenomenon of low signal drop at the load circuit due to its low impedance than the source circuit.
LOADING EFFECT
The _________ is a type of filter that comprises of one or more than one active component such as transistors, amplifiers or OP-Amps. In contrast to passive filters, ________ have an amplification factor which can be modified. They have high input impedance and low output impedance which nullifies the loading effect that occurs in passive filters.
active filter
TWO TYPES OF LOW PASS FILTERS
PASSIVE LOW PASS FILTER
ACTIVE LOW PASS FILTER
It is a simple filter that is made of only one reactive component i.e Capacitor along with an active componentOp-Amp. A resistor is used with the Capacitor or Inductor to form RC or RL low pass filter respectively.
FIRST ORDER ACTIVE HIGH PASS FILTER
Op-Amp can be used in the following configurations:
> Non-Inverting (voltage follower) Configuration
Buffer (Unity gain)
Inverting Configuration
the standard configuration implies the use of Op-amp as a separate amplifier at the output of a traditional RC Low Pass filter circuit.
STANDARD OP-AMP CONFIGURATION
In such configuration, the gain of the Op-Amp remains unity (one) i.e. the output signal amplitude is equal to the input signal amplitude. There is no feedback resistor, so the gain of the Op-Amp (Amplifier) becomes 1.
UNITY GAIN OR BUFFER CONFIGURATION
This type of filter uses the Op-Amp as a voltage amplifier. The amplification aspect of this configuration provides a voltage gain for any weaker input signal.
NON-INVERTING FILTER WITH AMPLIFICATION
Voltage Gain formula
Gain = Av = 1 + R2/R1
Cutoff frequency
fc = 1/2𝜋𝑅𝐶
In passive filters, the gain at cutoff frequency is considered at_
-3dB
Cutoff frequency is given by:
0db - 3db = -3db
This type of filter is made using the Operation amplifier in inverting configuration. In inverting configuration, the input signal is applied to the negative terminal of the Op-Amp & the positive terminal is grounded. The output of this filter is inverted, other than that the frequency response is the same as the non-inverting filter.
INVERTING AMPLIFIER LOW PASS FILTER
INVERTING AMPLIFIER LOW PASS FILTER cutoff frequency equation:
fc = 1/(2𝜋𝑅2𝐶)
𝐴𝑣=−(𝑅2/𝑅1 )
A second order filter has 40 dB/decade roll off or 12dB/octave roll off. Whereas the first order filter has 20 dB/decade or 6dB/octave.
To get a second order filter a simple method is to ______ two first-order filters.
cascade
Gain of filter formula
𝐺𝑎𝑖𝑛,𝐴𝑣 =𝐴𝑠1𝐴𝑠2
𝐴𝑠1=1+𝑅2/𝑅1
𝐴𝑠2=1+𝑅4/𝑅3
equation for cutoff frequency of second order filter is
𝑓𝑐=1/(2𝜋√(𝑅_𝑠1 𝑅_𝑠2 𝐶_𝑠1 𝐶_𝑠2 ))
if the resistorRs1= Rs2= R& capacitorCs1= Cs2= Cthen the equation becomes;
𝑓𝐶=1/2𝜋𝑅𝐶
______ topology filters provide a variety of 2ndorder frequency selective filters including low pass, high pass, band pass & band reject filter.
It is a form of voltage controlled voltage source (VSVS) which uses a single op Amp with two capacitor & two resistors. And off-course the two other resistors for the gain of the filter.
Sallen-Key
Sallen-Key cutoff frequency equation
𝑓𝑐=1/(2𝜋√(𝑅1𝑅2𝐶1𝐶2 ))
If the resistor R1= R2= R & Capacitor C1= C2= C, the equation of cutoff frequency becomes;
𝑓𝐶=1/2𝜋𝑅𝐶
Gain of Sallen-key formula
𝐴=1+𝑅𝑏/𝑅𝑎
The _______ determines the behavior of the frequency response of the system i.e. under damp, overdamp or critically damp systems.
quality factor Q
equation for the quality factorQof a Sallen-Key Low Pass filter is
𝑄=√(𝑅_1 𝑅_2 𝐶_1 𝐶_2 )/(𝑅_1 𝑅_2 (1−𝐴)+𝐶_2 (𝑅_1+𝑅_2))
IfQ < ½,the system is called_____. The system has alow-quality factor. it does not oscillate at any frequency. A low-quality filter acts as a 1storder low pass filter.
Over Damped
IfQ = ½,the system is called____. It does not oscillate at any frequency just like an over damped filter. But it has40db/decadeor12db/octaveroll-off rate with its cutoff frequency at-6dbgain because of the steeper roll-off rate. it is a perfect case for 2nd order filter.
Critically Damped
IfQ > ½,the system is called_______having ahigh-quality factor. Such a system oscillates at a frequency near the cutoff frequency known as peak frequency. There is a huge gain at peak frequency because of the system oscillation.
Under Damped
