CPE160P-4 FILTERS

frequency filter

A _____________ also known as a frequency selective circuit is a special type of a circuit, which is used for filtering out some of the input signals on the basis of their frequencies. A ________ circuit passes some frequency signal's without any attenuation (Reduction in amplitude) or with some amplification, & attenuate other frequency depending on the types of the ______.

PASSBAND

The band of frequencies of the input signal that pass through the filter without any attenuation is called ________. Usually, the _______ has no gain considering the filter is a passive filter. In active-filters, the ______may have some gain depending on the configuration of the circuit.

STOPBAND

The band of frequencies of the input signal that are blocked or attenuated in the filter is called __________. The gain at the stop is usually taken to be less than -3db of the input.

-3db gain is considered for the 1st order filter. 2nd order filter has -6db gain, which decreases with the order of the filter.

CUTOFF FREQUENCY

The passband & stopband are distinguished from each other by the _____________ or corner frequency. The output signal's voltage at the cutoff frequency is 70.7% of the input signal's voltage. It is also known as "-3db frequency" because -3db represents half power. And it is the frequency where the power of the output signal becomes half the power of the input signal.

Lower Cutoff Frequency

The lower frequency at which the gain of the filter is half or -3db. It is denoted by f1. Bandpass filter allows frequency after this point, whereas the band stop filter blocks it.

Upper Cutoff Frequency

The upper frequency at which the output power is reduced by ½ 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.

CENTER FREQUENCY

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.

fo = (f1 + f2) / 2

Formula for CENTER FREQUENCY

BANDWIDTH

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. The width of the frequencies before (in case of low pass filter) or after (in case of high pass filter) the cutoff frequency is called __________.

It is the difference between both cutoff frequencies of the band pass or band reject filter.

Β = f2 - f1

Formula of bandwidth

ROLL-OFF RATE

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).

The ________of nth order filter is 20n dB/decade or 6n dB/octave & n is the order of the filter. The per-decade means with a 10 times increase in frequency & the octave means a 2 times increase in frequency.

PASSIVE FILTERS

As the name suggests, _____________ are made up of passive components, such as resistors, capacitors & inductors.

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.

Although its design is simple but connecting a load to this filter impacts on its characteristics. Cascading the ___________ for higher order filter affects the characteristics of the filter.

Active Filters

The ________________ can filter very low-frequency signals but it cannot process very high-frequency signal.

They may have a little bit of complex design but they provide very high input & low output impedance. That is why; the load impedance does not affect the characteristics of the _________.

Cascading Configuration

To increase the order of the filter, active filters are used in _____________ without worrying about the loss of input signals power.

LOW PASS FILTER

_______________ allow low-frequency signals without any attenuation (decrease in power) but it rejects any high-frequency signals. The ___________ has a reactive component, whose reactance varies with the input frequency. The variation in the reactance causes the voltage drop to increase or decrease inside the circuit. if the voltage drop is larger at the output, the signal will be passed, otherwise, it is rejected by the filter. The passband & stopband frequencies are defined by the cutoff frequency of the filter. Any frequency less than the cutoff frequency is passed without any attenuation. While any other higher frequency signal then the cutoff frequency will be blocked.

HIGH PASS FILTER

The type of filter that allows the high-frequency signals to pass without any attenuation in its amplitude & blocks (rejects) any low-frequency signal is called __________.

Any signal with a frequency lower than the cutoff frequency of the filter gets blocked. While any signal with a frequency higher than the cutoff frequency passes with full amplitude.

BAND PASS FILTER

This type of filter allows a specific band of frequencies & blocks any other frequencies lower or higher than its passband frequencies. This type of filter has two cutoff frequencies i.e. lower & upper cutoff frequency.

__________ blocks low frequencies & high frequencies, while allows the frequencies in between known as the passband frequencies. Any input signal having frequency belonging to the passband frequencies will get passed without any attenuation.

BAND REJECT FILTER

This type of filter attenuates the signal whose frequencies lies in a fixed band of frequencies. It is also known as Band Stop filter or Notch Filter. 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. It also has lower & upper cutoff frequencies. And any signals having frequency in-between these cutoff frequencies are rejected by the filter.

Tuner

Application of filter where the bandpass filter in the _____ of the radio allows a fixed frequency to the output speaker.

Treble & bass of the speaker

Application of filter the bass has lower frequencies & treble has higher frequencies. They are separated using high pass & low pass filter and are separately routed to corresponding_________ for clear music.

Anti-Aliasing

Application of filter where a low pass filter that filters out the high-frequency components from a signal before sampling. It prevents the aliasing component form being sampled.

Notch Filter

Application of filter where they are band rejects filters with a narrow bandwidth that filter out any interfering signal

Power Supply Smoothing

Application of filter where 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.

Noise suppression

Application of filter where they are used in communication systems for noise removal from the received signals.

PASSIVE HIGH PASS FILTER

A type of high pass filter that is made up of only passive components such as resistor, capacitor & inductor is called ________ filter. ___________ filters do not need any external source thus they have no gain i.e. the output signal amplitude is always equal to or less than the input signal amplitude.

1.) RC Circuit 2.) RL Circuit

A simple High Pass filter is designed using a resistor with a capacitor (known as 1.) _________) & with Inductor (known as 2.)____________).

FIRST ORDER PASSIVE HIGH PASS FILTER

A type of passive high filter that contain only one reactive component i.e. either capacitor or inductor. It is the simplest form of filter made from only two components with resistor being common in both designs i.e. RC & RL.

STOP BAND

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 fc is the _____ frequency.

PASS BAND

The band of frequency that gets passed through the filter without attenuation is _________. The frequency above the cutoff frequency fc is the __________ frequency of a high pass filter.

Gain = Vout / Vin

What is the formula of Gain?

Gain in dB= 20 log (Vout/Vin )

What is the formula of Gain in db?

70.7% or 1/√2

We have established that the output amplitude at the cutoff frequency is ____ of its input max amplitude.

Vout = (1 / sqrt(2)) * Vin

What is the formula of Vout in Gain at Cutoff Frequency?

ROLL-OFF RATE

The _________ is the rate of change in gain or steepness of the curve in the stop band of a filter.

20n dB/decade or 6n dB/octave

The roll off rate depends on the order of the filter & it is given by;

RC FIRST ORDER HIGH PASS FILTER

In this design of high pass filter, a capacitor is connected with a resistor in series. The input signal is applied through the capacitor. The output is taken across the resistor.

Xc = 1 / 2piFC

What is the formula of capacitive resistance?

Z=√(Xc^2+R^2 )

What is the total impedance of the RC FIRST ORDER HIGH PASS FILTER?

RL FIRST ORDER HIGH PASS FILTER

This type of high pass filter is designed by combining a resistor with an inductor. The input is applied to the resistor and the output is taken across the inductor.

Xl=2πfL

What is the formula for inductive resistance?

Z=√(Xl^2+R^2 )

What is the impedance of the RL FIRST ORDER HIGH PASS FILTER?

1.) Second Order Filter 2.) 40db/decade 3.) 12 dB/octave

So the roll-off rate of 1.) _________ is 2.)_________ or ________. This means that the curve of the 1.)__________ is steeper than a 1st order filter.

LOADING EFFECT

It is the phenomenon of low signal drop at the load circuit due to its low impedance than the source circuit.

Ideally, when evaluating the performance of a multistage filter, we do not consider the input & output impedance of each stage. Practically if the succeeding stage has equal or lower input impedance than the preceding stage, the signal drop will be low at the succeeding stage. This causes an erroneous output.

10x

To reduce the loading effect, the impedance of the succeeding stage should be at least ______ times higher than the preceding stage. It is done by scaling the resistor, capacitor & inductor in both stages of the multistage filters.

RC SECOND ORDER PASSIVE HIGH PASS FILTER

Cascading two 1st order RC high pass filters provide a ___________

SECOND ORDER RL HIGH PASS FILTER

Just like RC filter, cascading two 1st order RL high pass filter will create a ___________

Active Filter

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, _________’s 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

FIRST ORDER ACTIVE HIGH PASS FILTER

A type of high pass filter that is simple and is made of only one reactive component (i.e Capacitor) along with an active component Op-Amp. A resistor is used with the Capacitor or Inductor to form RC or RL low pass filter respectively.

-20dB/decade or -6dB/octave

What is the Roll-Off Rate of a First Order Low Pass Filter?

NON-INVERTING OR VOLTAGE FOLLOWER CONFIGURATION

As you know that in the _______, the input signal is applied at the positive terminal of the Op-Amp, the output voltage is in phase with the input voltage that is why it is called ________. But to achieve the desired result (of low pass filter), the schematic can be designed in a variety of configurations.

STANDARD OP-AMP 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. It can be realized from the schematics given below.

Gain = A = 1 + (R2/R1)

The typical formula of the gain in voltage follower configuration is?

UNITY GAIN OR BUFFER 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.

NON-INVERTING FILTER WITH AMPLIFICATION

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.

INVERTING AMPLIFIER LOW PASS FILTER

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.

SECOND ORDER ACTIVE LOW PASS FILTER

A type of low pass that are very commonly used in many applications. A ______ 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 ________ a simple method is to cascade two first-order filters.

SALLEN-KEY LOW PASS FILTER

A type of low pass topology that provide a variety of 2^nd order 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.

Quality Factor (Q)

The ________ determines the behavior of the frequency response of the system i.e. under damp, overdamp or critically damp systems.

Over Damped

If Q < ½ is called _________. 1.The system has a low-quality factor. it does not oscillate at any frequency. A low-quality filter acts as a 1^st order low pass filter.

Critically Damped

1.If Q = ½, the system is called . It does not oscillate at any frequency just like an over damped filter. But it has 40db/decade or 12db/octave roll-off rate with its cutoff frequency at -6db gain because of the steeper roll-off rate. it is a perfect case for 2nd order filter.

Under Damped 

If Q > ½, the system is called _______ having a high-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.