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## Characteristics of an Ideal Filter (LPF, HPF, BPF and BRF)

What is a filter.

A filter is a frequency selective network, i.e., it allows the transmission of signals of certain frequencies with no attenuation or with very little attenuation and it rejects all other frequency components.

## What is an Ideal Filter?

An ideal filter is a frequency selective network that has very sharp cut-off characteristics, i.e., it transmits the signals of certain specified band of frequencies exactly and totally rejects the signals of frequencies outside this band. Therefore, the phase spectrum of an ideal filter is linear.

## Ideal Filter Characteristics

Based on the frequency response characteristics, the ideal filters can be of following types −

Ideal Low-Pass Filter (LPF)

Ideal High-Pass Filter (HPF)

Ideal Band-Pass Filter (BPF)

Ideal Band-Reject Filter (BRF)

## Ideal All Pass Filter

Ideal low pass filter (lpf).

An ideal low pass filter is the one which transmits all the signal of frequencies less than a certain frequency $\mathit{\omega_{c}}$ radians per second without any distortion and blocks all the signals of frequencies above $\mathit{\omega_{c}}$ radians per second. Where, the frequency $\mathit{\omega_{c}}$ radians per second is called the cut-off frequency . The phase function of an ideal low-pass filter is given by $[\mathit{\theta \left(\omega\right)=-\omega t_{d}}]$.

The transfer function of an ideal low-pass filter is given by,

$$\mathrm{\mathit{\left | H\left(\omega\right) \right |=\left\{\begin{matrix} \mathrm{1}\:\:\mathrm{for}\:\left | \omega\ \right|<\omega_{c} \ \mathrm{2} \:\:\mathrm{for}\:\left | \omega\ \right|>\omega_{c} \end{matrix}\right.}}$$

Therefore, the frequency response characteristics of an ideal low-pass filter is a gate or rectangular function and it is shown in Figure-1.

## Ideal High Pass Filter (HPF)

An ideal high pass filter transmits all the signals of frequencies above a certain frequency $\mathit{\omega_{c}}$ radians per second without any distortion and blocks completely all the signals of frequencies below the frequency $\mathit{\omega_{c}}$ radians per second. Here, the frequency $\mathit{\omega_{c}}$ radians per second is called the cut-off frequency . The phase function of an ideal high pass filter is given by,

$$\mathrm{\theta (\omega )=-\omega t_{d}}$$

The transfer function of an ideal high pass filter is given by,

$$\mathrm{\mathit{\left | H\left(\omega\right) \right |=\left\{\begin{matrix} \mathrm{0}\:\:\mathrm{for}\:\left | \omega\ \right|<\omega_{c} \ \mathrm{1} \:\:\mathrm{for}\:\left | \omega\ \right|>\omega_{c} \end{matrix}\right.}}$$

Figure-2 shows the frequency response characteristics of an ideal high pass filter.

## Ideal Band Pass Filter (BPF)

An ideal band pass filter transmits all the signals of frequencies within a certain frequency band $\mathit{\left(\omega _{\mathrm{2}}-\omega_{\mathrm{1}}\right)}$ radians per second without any distortion and completely blocks all the signals of frequencies outside this frequency band.

The frequency band $\mathit{\left(\omega _{\mathrm{2}}-\omega_{\mathrm{1}}\right)}$ is called the bandwidth of the band-pass filter.

The phase function of an ideal band-pass filter for the distortion less transmission is given by,

$$\mathrm{\mathit{\theta\left(\omega\right)=-\omega t_{d}}}$$

And the transfer function of an ideal band-pass filter is given by,

$$\mathrm{\mathit{\left | H\left(\omega\right) \right |=\left\{\begin{matrix} \mathrm{1}\:\:\mathrm{for}\:\left | \omega_{\mathrm{1}}\ \right|<\omega< \left | \omega_{2}\ \right| \\mathrm{0} \:\:\mathrm{for}\:\omega<\left | \omega_{\mathrm{1}}\ \right|\&\:\omega>\left | \omega_{\mathrm{2}}\ \right| \end{matrix}\right.}}$$

The figure-3 shows the frequency response characteristics of an ideal band-pass filter (BPF).

## Ideal Band Rejection Filter (BRF)

An ideal band rejection filter rejects completely all the signals of frequencies within a frequency band $\mathit{\left(\omega _{\mathrm{2}}-\omega_{\mathrm{1}}\right)}$ radians per second and transmits all the signals of frequencies outside the frequency band without any distortion.

In this case, the frequency band $\mathit{\left(\omega _{\mathrm{2}}-\omega_{\mathrm{1}}\right)}$ is called the rejection band. The Band rejection filter is also called the band stop filter (BSF) or band-elimination filter (BEF). The phase function of an ideal band rejection filter is $\mathit{\theta\left(\omega\right)=-\omega t_{d}}$.

And the transfer function of an ideal band rejection filter is given by,

$$\mathrm{\mathit{\left | H\left(\omega\right) \right |=\left\{\begin{matrix} \mathrm{0}\:\:\mathrm{for}\:\left | \omega_{\mathrm{1}}\ \right|<\omega< \left | \omega_{\mathrm{2}}\ \right| \\mathrm{1} \:\:\mathrm{for}\:\omega<\left | \omega_{\mathrm{1}}\ \right|\&\:\omega>\left | \omega_{\mathrm{2}}\ \right| \end{matrix}\right.}}$$

The figure-4 shows the frequency response characteristics of an ideal band rejection filter.

An all pass filter is a frequency selective network which transmits signals of all the frequencies without any distortion. That is, the bandwidth of an all pass filter is infinite as shown in figure-5. The transfer function of an ideal all pass filter is given by,

$$\mathrm{\mathit{\left| H\left(\omega\right)\right |=\left\{\mathrm{1}\:\:\mathrm{for} \:\mathrm{all}\:\omega\right.}}$$

And the phase function of an ideal all pass filter for the distortion less transmission is $\mathit{\theta\left(\omega\right)=-\omega t_{d}}$.

Note - All ideal filters are non-causal systems. Therefore, none of them can be physically realizable.

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## What is Band Pass Filter : Circuit & Its Working

October 26, 2020 By WatElectronics

During signal processing, a device called a Band Pass Filter or BPF is needed to allow a particular range of required frequencies and to avoid unwanted frequency ranges or components. By this filtering noise signal can be reduced by eliminating frequencies that are not required. Different types of filters like linear and nonlinear, analog, digital, active and passive, etc. are available to use based on the requirement. This article discusses an overview of Band Pass Filter.

## What is Band Pass Filter?

The bandpass filter is defined as a device that allows the frequencies which are within the required frequency range and reject the remaining frequencies which are not in that specific range. Coming to high pass filter , this filter will attenuate signals which are below the cut-off frequency and low pass filter will attenuate the signals which are having frequencies higher than the cut-off frequency. But if we only require a particular range of frequencies and want to eliminate the frequencies which are out of that range, another filter can be formed by cascading high pass filter and low pass filter which can be called a bandpass filter.

There are two cuts off frequencies in this bandpass filter, one is from the high pass filter and its high cut off frequency. This will be the highest frequency limit of that band. There is another cut-off frequency from the low pass filter and its second cut off frequency known as the lower cut off frequency which decides the low-frequency range of that band.

This bandpass filter only allows the particular band and attenuates all the remaining signals above or below that cut off frequencies.

## Band Pass Filter Circuit

This is the circuit diagram of the RC passive bandpass filter.

Band Pass Filter

The cascading or the combination of high pass filter and low pass filter forms a bandpass filter as it allows a particular band of frequencies and will attenuate the signals which are higher and lower than cut off frequencies. This bandpass filter will allow the input signals without distortion and Noise. The width of this band of frequencies is called bandwidth. To clearly define bandwidth, it is the particular frequency range that lies in between two cut-off points i.e. high cut-off frequency and low cut-off frequency.

Bw= fH – fL

The difference between the lowest cut-off frequency and the highest cut-off frequency is known as bandwidth.

To be an ideal bandpass filter, the filter has to filter or attenuate certain frequencies that even lies within the band because to eliminate noise. Bandpass filters are also known as second-order filters due to the factor that there exist two capacitors, reactive components within the single circuit. One capacitor in the high pass circuit and another capacitor in the low pass circuit.

Please refer to this link for Band Pass Filter MCQs

## Different Types of Bandpass Filters

These bandpass filters are mainly categorized into two types of filters. They are

Wide Band Pass Filter

## Narrow Band Pass Filter

The circuit diagram of the wide bandpass filter is shown below. Several practical circuits exist in this wide bandpass filter circuit. As we discussed this wide bandpass filter can be formed by cascading the two sections i.e. high pass and low pass.

For the formation of + or – 20db/decade bandpass filter, two sections first order high pass section and first-order low pass section are cascaded, in the same way for the formation of + or – 4odb/decade bandpass filter second order high pass section and second-order low pass section is connected. It implies that the order of low pass and high pass filters will govern the order of the bandpass filter.

BPF Characteristics

The above-shown image is the characteristics of the bandpass filter. Here wide bandpass filter composed of first-order high pass filter and first-order low pass filter is demonstrated in the figure.

Here in this diagram, a narrow bandpass filter employing multiple feedbacks is shown. Only one OP-Amp is employed in this filter. Compare to other filters, this filter has some unique features which are very useful.

- It is called a multiple feedback filter due to two feedback paths.
- OP-Amp here existed is used in inverting mode
- We can see the frequency response of the narrow bandpass filter in the above figure. The designing of a narrow bandpass filter is done for specific values of fc or Q & BW.

For the calculation purpose

C1 = C2 = C

R1 =Q/2π fc CAf

R2= Q/2πfc C(2Q2-Af) &

R3= Q/πfc C

Here the gain at center frequency is defined as Af

Fc can be changed to fc’ without changing bandwidth or gain .this can be formed by simply changing R2 to R2’

R’2= R2[fc/f’c]2

## Bandpass Filter Calculator Calculation

This is the passive bandpass filter circuit and the bandpass calculations can be done through this circuit.

BPF Calculation

By using the formula we can find out the required frequency in this passive bandpass filter.

For high cut off frequency = 1/2ΠR1C1

For low cut off frequency = 1/2ΠR2C2

Even we can also calculate required frequencies for the different bandpass filters like active inverting op-amp BPF and active non inverting op-amp BPF

## Applications of Bandpass Filter

The bandpass filter has a wide range of applications

- It is used in optics like LIDARS, LASER, etc.
- These filters are widely used in wireless transmitters and receivers.
- In audio signal processing, these bandpass filters play a vital role by allowing the particular frequencies and removing the unwanted.
- These bandpass filters are also used in instruments and applications of medical and seismology. One of the best applications of bandpass filters is audio amplifier circuits. We can observe simply as the speakers will play the desired range of frequencies and will attenuate the remaining.
- The bandpass filter is effectively used in optimizing Signal to Noise ratio, S/N ratio, and even the sensitivity of the receiver.
- As these bandpass filters are specially designed to allow a particular band of frequencies, so it is widely used in communication systems.

Please refer to this link to know more about FIR Filter MCQs and High Pass Filter MCQs .

Thus, this is the overview of bandpass filters , its circuit, types & its applications. The bandpass filter has a wide range of applications in the present world. Here is a question for you, what is the RLC bandpass filter and RLC band-reject filter?

## What is a Band Pass Filter? Circuit Diagram, Types, and Applications

In signal processing , filters are one kind of devices used for allowing required frequency components as well as removes unwanted frequency components. Filtering can be defined as; the interfacing signal background noise can be diminished by removing some frequencies. The circuit of the filter can be used for uniting the LPF and HPF properties into an only filter which is termed as a band pass filter. There are different kinds of filters available such as analog/digital, active/passive, linear/nonlinear, time-variant/time invariant. This article discusses an overview of the band pass filter with applications

## What is Band Pass Filter?

The definition of the band pass filter is a circuit which permits the signals to flow among two particular frequencies, although divides these signals at other frequencies. These filters are available in different types; some of the BPF- band pass filter design can be done with an external power as well as active components such as integrated circuits, transistors , which are named as an active band pass filter . Similarly, some of the filters use any kind of power source as well as passive components like capacitors and inductors , which are named as a passive band pass filter.

These filters are applicable in wireless transmitters as well as receivers. In a transmitter, a BPF can be used to limit the output signal’s bandwidth toward the minimum necessary level & transmitting data at the preferred speed & form. Similarly, in a receiver, this filter lets the signals in a favored frequency range to be decoded, whereas keeping away from signals at unnecessary frequencies. The signal to noise (S/N) ratio of a receiver can be optimized by a BPF.

## Band Pass Filter Circuit

The best example of a band pass filter circuit is the RLC circuit that is shown below. This filter can also be designed by uniting an LPF and HPF. In BPF, Bandpass illustrates a kind of filter otherwise procedure of filtering. It is to be differentiated from passband that refers to the real section of the influenced spectrum. An idyllic bandpass filter doesn’t have gain and attenuation, so it is totally level passband. That will totally attenuate every one of frequencies exterior the passband.

Practically, the bandpass filter is not ideal and doesn’t attenuate every one of frequencies outside the preferred frequency choice totally. Particularly, there is a section just outside the proposed pass band wherever frequencies are attenuated, however not discarded which is called like the filter roll-off, & usually, it is specified in dB of attenuation for every octave otherwise decade of frequency. In general, the filter design looks to build the roll-off as thin as feasible, therefore letting the filter to do the proposed design. Frequently, this can be attained at the expenditure of passband ripple otherwise stopband ripple.

The filter bandwidth can be defined as the dissimilarity among the upper frequency as well as lower frequency. The form factor is the fraction of bandwidths calculated with two dissimilar attenuation values for determining the cut-off frequency, For example., a form factor of 2:1 at 20/2 dB means the bandwidth calculated among frequencies at 20 dB attenuation is double that calculated among frequencies at 2 dB attenuation. Optical BPFs are commonly used in photography as well as lighting work in theatre. These kinds of filters take the outline of a clear colored film otherwise sheet.

## Different Types of Band Pass Filters

The categorization of the bandpass filter can be done in two types such as wide bandpass filter as well as narrow band pass filter .

## Wide Band Pass Filter

A WBF or wide bandpass filter (WBF) can be formed by dropping low pass as well as high pass segments which is normally a different circuit intended for simple design & act.

It is recognized with a number of practical circuits. A bandpass filter with ± 20 dB/ decade can be formed by using the two sections like a 1st order low pass as well as high pass sections can be dropped. Similarly, a bandpass filter with ± 40 dB/ decade can be formed by connecting two second-order filters in series namely low pass and high- pass filter (HPF). This means the order of the bandpass filter (BPF) is ruled with the order of the low pass & high pass filters . The bandpass filter graph is shown below.

A bandpass filter with ± 20 dB/decade can be is composed of a 1st order HPF (high pass filter) . A 1st order LPF (low-pass filter) is shown in the following figure by its frequency response.

## Narrow Band Pass Filter

Generally, a narrow bandpass filter uses several feedbacks. This bandpass filter using an op-amp as shown in the following circuit diagram. The main features of this filter mainly include the following.

Another name of this filter is a multiple feedback filter because it includes two feedback lanes

An op-amp is utilized in the inverting mode

The frequency response of this filter is shown in the following figure.

Usually, the designing of this filter can be done for exact values of center frequency (fc) & bandwidth or center frequency & BW. The components of this circuit can be determined by the following relationships. Each of the C1 and C2 capacitors can be taken to C for the simplifications of design calculation.

R1 = Q/2∏ fc CAf R2 =Q/2∏ fc C(2Q2-Af) R3 = Q /∏ fc C

From the above equations, at middle frequency Af denotes the gain, so Af = R3 / 2R1

But, the Af should satisfy this statement Af<2Q2

The multiple feedback filters’ fc (center frequency) can be altered toward a novel frequency fc with no changing the bandwidth or gain. This can be attained just by altering R2 to R2’ so that

R2’ = R2 * ( fc / fc )2

## Band Pass Filter Calculator

The following circuit is the passive bandpass filter circuit. By using this circuit we can calculate the passive bandpass filter. The formula for passive bandpass filter calculator is shown below.

For low cut off frequency = 1/2∏R2C2

For high cut off frequency = 1/2∏R1C1

Similarly, we can calculate for active inverting op-amp BPF, and active non-inverting op-amp BPF.

## Band Pass Filter Applications

The applications of bandpass filters include the following.

- These filters are extensively applicable to wireless transmitters & receivers .
- This filter can be used to optimize the S/N ratio (signal-to-noise) as well as the compassion of a receiver.
- The main purpose of the filter in the transmitter is to limit the BW of the output signal to the selected band for the communication.
- BPFs are also widely used in optics such as LIDARS , lasers, etc.
- The best application of this filter is audio signal processing, wherever a specific range of sound frequencies is necessary though removing the rest.
- These filters are applicable in sonar, instruments, medical, and Seismology applications
- These filters involve communication systems for choosing a particular signal from a variety of signals.

Therefore, this is all about band-pass filter theory which includes, circuit diagram with working, types of bandpass filters and its applications. From the above information, finally we can conclude that the other fields of applications of these filters include in astronomy, these filters permit only an only section of the range of light into a device. These filters can assist in finding wherever stars recline on the major series, recognizing redshifts, etc. Here is a question for you, what is an active bandpass filter?

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## Band pass filter

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- 1. NAME: BANGUL KHAN ROLL NO: F16BM05 SUBJECT : ECD PRESENTATION TOPIC: BAND PASS FILTER SUBMITTED TO: DR SYED AMJAD ALI
- 2. OUTLINE: BAND PASS FILTER SCHEMATIC DIAGRAM WAVEFORM TYPES OF BAND PASS FILTER : APPLICATIONS OF BAND PASS FILTER SIMULATION OF BAND PASS FILTER
- 3. BAND PASS FILTER: A Band pass filter is an electronic device or circuit that allows signal between two specific frequencies to pass but that discriminates the signals at other frequencies . Band pass filter is the filter which have properties of both low pass Filter and high pas filter .
- 4. SCHEMATIC DIAGRAM:
- 5. WAVEFORM:
- 6. So in waveform: Fl : low pass filter frequency FH : high pass filter frequency Fo: geometric center frequency B : band width
- 7. Types of band pass filter: There are two types of band pass filter 1. Active band pass filter: It is a band pass filter which require an external source of power and employ active Component such as transistor and integrated circuits are known as active Band pass filter.
- 8. Circuit diagram of Active band pass filter:
- 9. 2: Passive band pass filter: The band pass filter which not use external source of power and consist only of passive components such as capacitors inductors these are called passive band pass filter
- 10. Diagram of passive band pass filter:
- 11. Applications of band pass filter: Band pass filter used in main two things which are given below. Wireless transmitter Wireless receiver. And the main function in both types are given below.
- 12. Wireless transmitter The main function of such a filter in a transmitter is to limit the bandwidth of the output signal to the band allocated for the transmission. This prevents the transmitter from interfering with other station
- 13. Wireless receiver. In a receiver, a band pass filter allows signals within selected range of frequencies to be heard or decoded, while preventing signals at unwanted frequencies from getting through other stations.
- 14. SIMULATION: 1 TO 100 HZ BAND PASS FILTER;

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## Band Pass Filter Design & Simulation

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