Band Pass Filter

Signal processing is incomplete without bandpass filters, which are special-purpose devices that pass only a particular range of signals while attenuating all others that lie outside this range. These filters can be passive or active with different designs and concepts respectively. In the case of passive bandpass filters, the combination of capacitors, inductors and resistors is used while operational amplifiers are included in active filters to enhance their performance.

Exact frequency choice, noise reduction and size miniaturization are some of the benefits of using bandpass filters, however, they also suffer from limitations such as narrow bandwidth and component tolerance susceptibility. For example, telecommunication systems, medical equipment and radar technology among other applications all require accurate frequency management to operate at optimum levels.

In this article, we will be going through the definition of bandpass filters. We will talk about the topic’s filters, types of filters, working principles, construction, and applications of bandpass filters after looking at their various types. We will also discuss its advantages and disadvantages along with some FAQs.

What is a Filter?

Filters are used to change the frequency of signals. They are available in different varieties, each with a distinct function:

• Low pass filter (LPF): LPF allows signals with frequencies below a set cutoff frequency to pass through while attenuating higher frequencies.
• High Pass Filter (HPF): This filter has the opposite effect of a low-pass filter (LPF). Instead of allowing only low-frequency signals to pass through, it allows higher-frequency signals above a specific cut-off frequency.
• Band Pass Filter (BPF): BPF attenuates frequencies outside of its selected range while selectively passing signals within it. It functions similarly to a small window that only lets through a specific frequency band.
• Notch Filter: Notch filters, sometimes referred to as band-stop filters, act as barriers for particular, small frequency ranges while allowing all other frequencies to flow freely.

In this article we’ll be discussing specifically about Band pass filters

Types of Filters

What is Band Pass Filter?

A bandpass filter is a device that controls the flow of electrical signals. It allows signals within a specific frequency range to pass through, while blocking signals outside that range. This means it only allows signals with frequencies that fall within a certain spectrum while eliminating unwanted ones. Next we will be going through the different types of Band Pass Filter and go through its different types in brief.

Types of Band Pass Filters

Some of the Band Pass Filters are :

• Active Bandpass Filters
• Passive Bandpass filters
• Bandpass filters with RLC
• Wide Band Pass Filters
• Narrow Band Pass Filters

Active Bandpass Filters

• Active bandpass filters incorporate active components like operational amplifiers alongside passive components like resistors, capacitors, and inductors.
• These filters can provide both filtering and amplification, making them suitable for applications that require signal gain and frequency selectivity.
• Mathematical expression: [Tex]H(s)= \frac{K(w_o)^2}{s^2+\frac{w_os}{Q}+{w_o}^2}[/Tex]

Active Bandpass Filters

Passive Bandpass filters

• Passive bandpass filters, on the other hand, consist solely of passive components like resistors, capacitors, and inductors.
• They are relatively simple to design and do not require a power source, making them ideal for situations where amplification is not needed or where power consumption is a concern.
• Mathematical expression: [Tex]H(s)= \frac{Ks}{s^2+\frac{s}{Q}+{w_o}^2}[/Tex]

Passive Band Pass Filters

Bandpass Filters with RLC

• RLC bandpass filters, a type of passive filter, use the combination of resistors, inductors, and capacitors to create a frequency range that allows specific signals to pass through.
• These filters utilize the properties of reactive components to achieve the desired frequency response.
• Due to their versatility and effectiveness in frequency selection, RLC bandpass filters find wide application in various electronic circuits and systems.

Wide Band Pass Filters

• Wide bandpass filters allow a wide range of frequencies to pass through while blocking frequencies outside that range.
• They combine the characteristics of high pass and low pass filters.
• Dropping both high pass and low pass segments creates a WBF. Combining a first-order low pass and high pass section produces a BPF with ± 20 dB/decade attenuation.
• Similarly, two second-order filters, one low pass and one high pass, connected in series result in a BPF with ± 40 dB/decade. The order of the BPF is determined by the order of the contributing low pass and high pass filters.
• Mathematical Expression: [Tex]H(s)= \frac{Ks}{s^2+\frac{s}{Q}+{w_o}^2} [/Tex]

Wide Band Pass filters

Narrow Band Pass Filters

• Narrow bandpass filters are unique filters that allow signals within a tiny frequency range to pass through while suppressing all others.
• These filters often employ multiple feedback loops, also called multiple feedback filters due to their dual feedback paths.

Narrow Band Pass filters

Working Principle of Band Pass Filters

Given Below is the Block Diagram of the Band Pass Filters

Working of Band Pass Filter

• A low-pass filter (LPF) and a high-pass filter (HPF) are combined to form a bandpass filter. These filters are connected together so that they permit exclusively only some specific frequencies, called the passband. This implies that all other frequencies beyond this range get attenuated.
• For example, in a circuit diagram, the bandpass filter is usually presented with an arrangement where the output of the low-pass filter is linked to the input of the high-pass filter. The input signal goes into the input of LPF, which allows just low-frequency components to go through it. Afterward, low pass filters output will be fed as input to HPF allowing only high-frequency components to be passed.
• This results from having combined filters is called passband, which is between cutoff frequency points for LPF and HPF. Frequencies within this passband experience minimum attenuation while those outside this region are attenuated.
• In essence, however, it should be noted that bandpass filter circuit functions as an apparatus for letting signals at particular ranges go while preventing any other range from passing through it.
• By combining low pass and high pass filter, we can create a bandpass filter that allows frequencies within a certain range (between Fl and Fh) to pass through relatively unattenuated, while frequencies outside of this range are filtered out.
• The center frequency (Fc) of the bandpass filter is the geometric mean of the high-pass and low-pass cutoff frequencies:

[Tex]Fc=\sqrt{Fh*Fl}[/Tex]

• The bandwidth (BW) of the bandpass filter is the difference between the high-pass and low-pass cutoff frequencies:

BW= Fh-Fl

Circuit Diagram of Band Pass Filters

Given Below is the circuit Diagram of the Band Pass Filters

Circuit Diagram

Passive bandpass filters are made up of a combination of resistors, inductors, and capacitors. Usually, they consist of a resistor connected in parallel with an inductor and series capacitor forming a resonant circuit. This configuration allows the filter to selectively pass signals inside its designated range while attenuating frequencies outside of it. Capacitor and inductor values in bandpass filters are precisely tuned to achieve a specific operating frequency. A resistor complements this by limiting the frequency range and suppressing undesirable resonances. Passive bandpass filters, characterized by their simple design and affordability, are commonly employed in various electronic applications.

Band Pass Filter Equation

Depending on the particular kind of filter circuitry being used, the general equation for a bandpass filter can change. But in its simplest form, the transfer function H(s) of a second-order bandpass filter can be represented as:

H(s)=[Tex] \frac{K(w_n)^2}{s^2+\frac{w_n*s}{Q}+{w_n}^2}[/Tex]

Where:

• H(s) is the transfer function.
• s is the complex frequency variable.
• K is the gain factor.
• [Tex]w_n[/Tex] is the center frequency
• Q is the quality factor

Important Terminologies

• Cutoff Frequency: The point where a bandpass filter begins to reduce signal strength.
• Pass band: The frequency range within which a bandpass filter allows signals to pass without significant weakening.
• Stop band: The frequency range outside the passband where a bandpass filter blocks signals.
• Bandwidth: The bandwidth of a bandpass filter refers to the range of frequencies that it allows to pass through without significant attenuation.
• Center Frequency: The center frequency of the passband is the midpoint of this frequency range.
• Attenuation: The decrease in signal amplitude or strength caused by a bandpass filter applied to frequencies that are not in the passband.
• Q Factor: A measurement of the frequency response curve sharpness or selectivity of a bandpass filter.
• Resonant Frequency: The frequency at which the reactive elements of a bandpass filter resonate, improving the filtering characteristics of the filter inside the passband.

Band Pass Filter Transfer Function

Now let’s go through Transfer Function of the first and Second order Band Pass Filter Transfer Function

First order Band Pass Filter

An RC circuit or an RL circuit can be used to create a first-order bandpass filter. The transfer function H(s) of a first-order bandpass filter can be expressed as:

H(s)= [Tex]\frac{Ks}{s^2+\frac{w_os}{Q}+{w_o}^2}[/Tex]

Where:

• H(s) is the transfer function.
• s is the complex frequency variable.
• K is the gain factor.
• w_o is the center frequency of the passband.
• Q is the quality factor, which determines the bandwidth and sharpness of the filter’s response.

Second Order Band Pass Filter

There are several ways to implement a second-order bandpass filter, including using active filters and multiple RC stages. The transfer function H(s) of a second-order bandpass filter can be expressed as

2nd order Band pass filter

[Tex]z_1=R_1+\frac{1}{jwc_1}[/Tex]

[Tex]z_2=R_2||\frac{1}{jwc_2} [/Tex]

[Tex]z_2=\frac{R_2\frac{1}{jwc_2}}{R_2+\frac{1}{jwc_2}}[/Tex]

[Tex]H(jw)= -\frac{z2}{z1} [/Tex]

[Tex]= – \frac{\frac{R_2}{jwc_2}}{(R_2+\frac{1}{jwc_2})(R_1+\frac{1}{jwc_1})} [/Tex]

[Tex]= – \frac{jR_{2wc_1}}{(1+jwc_2R_2)(1+jwc_1R_1)} [/Tex]

[Tex]= – \frac{jwT_3}{(1+jwT_2)(1+jwT_1)} [/Tex]

[Tex]Where , T_1=\frac{1}{w_1} , T_2=\frac{1}{w_2} , T_3=\frac{1}{w_3} [/Tex]

Ideal Band Pass Filter

It is an example of a filter that completely attenuates or blocks signals outside of the passband while flawlessly passing signals inside the specified passband, or frequency range.

• The characteristics of the perfect bandpass filter include:
• Perfect Passband Transmission
• Complete Rejection Outside Passband
• Sharp Transition
• Zero Phase Distortion
• Infinite Stopband Attenuation

Band Pass Filter Cutoff Frequency([Tex]F_{cutoff}[/Tex])

A bandpass filter’s cutoff frequency is the frequency at which signals outside of its designated passband start to be attenuated or blocked. Generally speaking, a bandpass filter has two cutoff frequencies:

• The frequency below which the filter starts to attenuate signals is known as the lower cutoff frequency([Tex]F_l[/Tex]). It designates the passband’s lower boundary.
• The frequency above which signals are first attenuated by the filter is known as the upper cutoff frequency ([Tex]F_h[/Tex]). It denotes the passband’s upper boundary.
• The difference between the upper and lower cutoff frequencies is known as the bandpass filter’s bandwidth([Tex]F_h – F_l[/Tex]).
• The center frequency([Tex]F_c[/Tex]) of the band pass filter is the geometric mean of F_h and F_l.
• [Tex]F_{cutoff} = F_L + \frac{1}{2}BW[/Tex]
• [Tex]F_{cutoff} = F_c ± \frac{1}{2}BW[/Tex]

Band Pass Filter Bode Plot

A Bode plot is a graphical depiction of a system’s frequency response that includes bandpass filters, among other filters. Here are concise steps to construct a bode plot:

• Transfer Function: Analyze the transfer function of a second-order bandpass filter.
• Identify key parameters: natural frequency and damping ratio.
• Frequency Response: Derive equations for phase and magnitude responses as functions of frequency.
• Graphical Representation: Create two graphs.
• Magnitude Response Graph: Plot magnitude response (in dB) versus frequency (logarithmic scale).
• Phase Response Graph: Plot phase response (in degrees) versus frequency (logarithmic scale).
• Use the Bode plot to identify crucial properties such as the delay (phase shift), amplification (gain), operational range (bandwidth), and the frequency where the filter performs best (center frequency).
• Behavior Outside the Passband: Analyze the Bode plot at low and high frequencies to determine how the filter functions beyond its intended operating range. This is known as asymptotic behavior. It provides insights into the filter’s magnitude and phase responses outside of its passband.

Difference Between Narrow and Wide Band Pass Filter

Narrow Band Pass Filter	Wide Band Pass Filter
Passes only a narrow range of frequencies.	Passes only a wide range of frequencies.
Provides high SNR within passband.	Allows more noise due to wider passband.
High Q- factor.	Lower Q- factor.
It has higher selectivity, attenuates frequencies outside the passband	It has lower selectivity, allows frequencies outside the passband.
Used where precise frequency control is required	Used where a broad range of frequencies needs to be passed

Advantages and Disadvantages of Band Pass Filter

Given below are some of the advantages and disadvantages of Band Pass Filter

Advantages of Band Pass Filter

• The bandpass filters allow signals with only specific frequencies to go through, and this makes it possible for signal processing to be done in a precise way.
• Improving the quality of signals by reducing noise interferences, band pass filers block those frequencies which are outside the passband.
• Bandpass filters on the other hand amplify signals within the passband thus boosting desired frequencies and attenuating unwanted ones.
• Bandpass filters can also be designed smaller thus enabling their integration into small electronic devices and systems.
• They are used in various fields such as telecommunications, audio processing, medical devices and radar systems among others indicating how versatile they are.

Disadvantages of Bandpass Filter

• These limits restrict them to particular frequency areas over which an effective transmission is possible
• Optimum performance of band pass filters may require careful calibration as slight alterations in values of elements significantly affects their performance.
• Moreover, some forms of distortions may be introduced by bandpass filter sometime due to effect from the edges of the passband hence resulting in a change of reality or truthfulness on signal’s part.
• For example, designing accurate characteristics for bandpass filters is complex since it entails knowledge in filter design and analysis.
• Consequently, highly specified high-performance band-pass filters can have relatively high costs because of special components required and manufacturers’ techniques.

Applications of Bandpass Filter

• Bandpass filters are crucial for separating different channel frequencies and separating positive signals from noise.
• Band pass filters are used in crossover networks and audio systems for equalization and tone control.
• By using band pass filters in a radar system, superfluous frequencies can be removed.
• They have the ability to separate out particular frequency components of signals that are utilized by medical imaging devices like ultrasound and magnetic resonance imaging machines for diagnostic purposes.
• These kinds of filters are used by science and measurement instruments and other signal processing equipment to pick relevant data from the desired frequency range.
• These band-pass filters are used in modern wireless communication systems with multiple frequency bands assigned for transmission or reception to separate Wi-Fi, Bluetooth, cellular networks, etc.
• Bandpass filters are used in audio effects processing units, synthesizers, and music production equipment to generate a range of sound effects.
• Seismic monitoring systems employ bandpass filters to isolate and examine particular frequency bands within seismic signals.
• In medical signal analysis (e.g., EEG, ECG), bandpass filters are used to extract specific frequency ranges from bioelectric signals.
• Bandpass filters are also employed in environmental monitoring systems.

Band Pass Filter Design Example

A basic passive bandpass filter using a RLC circuit. A second-order bandpass filter with a 500 Hz bandwidth and a 1 kHz center frequency is designed (assuming quality factor=1).

Formula used:

• Bandwidth (BW) = Fh – Fl
• Quality Factor (Q) = Fc / BW
• Lower Cutoff Frequency (Fl) = [Tex]\frac{\ Fc}{\sqrt{2^{\frac{1}{Q}\ }\ \ -1}}[/Tex]
• Upper Cutoff Frequency (Fh) = [Tex]Fc* \sqrt{2^\frac{1}{Q}-1}[/Tex]

lower cutoff frequency:

Fl = [Tex]1000 / \sqrt{2^{\frac{1}{1}\ }\ \ -1}[/Tex]≈ 707.11 Hz

upper cutoff frequency:

Fh = [Tex]1000 * \sqrt{2^{\frac{1}{1}\ }\ \ -1}[/Tex] ≈ 1414.21 Hz

Inductor (L): 680 mH (for lower cutoff)

Capacitor (C): 0.1 µF (for upper cutoff)

Conclusion

In summary, bandpass filters are crucial components for many electronic systems as they attenuate certain frequency ranges and permit selective transmission of others. These filters come in a range of configurations, including passive and active versions, each with special advantages and disadvantages. Passive bandpass filters typically consist of resistors, capacitors, and inductors, whereas active filters incorporate amplifiers to process signals. Their working principle is based on resonance phenomena, in which certain frequencies are transmitted while others are suppressed.

As bandpass filters have limited bandwidth and insertion loss, they are not ideal for selecting frequencies. Nonetheless, because precise frequency control is essential in biomedical devices, audio processing, and telecommunications, they are widely utilized in these fields. All things considered, bandpass filters are essential for modifying signals in a variety of industries and enabling effective signal processing and transmission.

Band Pass Filter – FAQs

What is used to make a bandpass filter?

Typically, passive bandpass filters consist of capacitors, inductors, and resistors; active designs may also incorporate amplifiers.

Is noise removed by a band pass filter?

By selectively letting through only the desired frequency band and attenuating others, bandpass filters can effectively eliminate noise.

How far does the band pass filter go?

A bandpass filter can be made to target particular frequency bands within the entire spectrum, depending on how it is designed.