Active Band Pass Filter : Circuit, Types, Frequency Response, Q Factor, Advantages & Its Applications

The bandpass filter allows the signals to supply between two particular frequencies, even though separates these signals at other frequencies. These types of bandpass filters are available in various types; some of the bandpass filter design is made with external power & active components like; transistors, and integrated circuits, which are called active BPF. Likewise, some filters utilize any power source & passive components such as inductors & capacitors, called passive BPF. These filters are applicable in wireless transmitters & receivers.

A BPF in a transmitter is used for limiting the bandwidth of the output signal to the least required level and transmitting data at the ideal speed and form. Likewise, this filter in a receiver allows the signals within a favored frequency level to be decoded, while keeping absent from signals at needless frequencies. The S/N ratio of a receiver is optimized through a bandpass filter. This article provides brief information on an active band pass filter.

What is an Active Band Pass Filter?

A type of bandpass filter that uses active components like an operational amplifier, along with resistors and capacitors to form the filter is known as an active band pass filter. These bandpass filters amplify the input signal in addition to filtering, although they need an external power source.

This band pass filter is designed by cascading an HPF, an amplifier & an LPF as shown in the below figure. The amplifier circuit in between the HPF & LPF provides isolation and provides overall voltage gain. The cut-off frequency values of both filters should be maintained by least variation. If this variation is extremely small, then there is a chance of interaction between the low pass & high pass stages. Therefore, an amplifying circuit is required. to have the right levels of these cut-off frequencies.

Active Band Pass Filter Working Principle

Active bandpass filter works by attenuating frequencies above or below a range of frequencies (i.e., passband or the bandwidth of the filter). Any signal with a frequency in that bandpass range passes simply through the filter. Any frequency that is outside of the bandpass is reduced or attenuated.

Active Band Pass Filter Design

The active bandpass filter circuit is shown below. This circuit can be designed by cascading individual low-pass and high-pass passive filters together. It gives a low “Quality-factor” type filter which contains a broad pass band. The primary stage of the active band pass filter is the high pass stage which utilizes the capacitor for blocking any DC biasing from the main source.

This circuit design has the benefit of generating a fairly flat asymmetrical pass band frequency response through a single half signifying the low pass response whereas the remaining half signifies a high pass response.

The higher corner point ‘ƒH’ & the lower corner frequency cut-off point ‘ ƒL’ are calculated the same as before in the normal first-order LPF & HPF circuits.

A reasonable separation is necessary between the two cut-off points to avoid any interaction between the LPF & HPF stages. The amplifier helps in providing isolation between the two filter stages to describe the overall voltage gain of the filter circuit. Therefore, the filter bandwidth is the disparity between higher & lower -3dB points. The normalized frequency response & phase shift of an active BPF will be as follows.

Frequency Response

When the above passive-tuned filter circuit works as a BPF, then bandwidth can be fairly wide. This may be a trouble if we desire to separate frequencies with a small band. Active bandpass filter can also be designed with inverting op-amp.

Thus, by reorganizing the resistors & capacitors’ positions in the filter, we can generate a much better filter circuit. The lower cut-off -3dB point is specified by ‘ƒC1’ for an active BPF while the higher cut-off -3dB point is specified by ‘ƒC2’.

The above filter has two center frequencies HPF and LPF. The high pass filter center frequency should be lower as compared to the center frequency of the LPF.

The centre frequency of BPF is the geometric mean of upper & lower cut-off frequencies like; fr2 = fH x fL.

The gain of the active BPF is 20 log (Vout/Vin) dB/Decade.

The amplitude response is related to the LPF and HPF responses. The response curve mainly depends on the order of the cascading filter.

Q Factor

The overall width of the actual passband in between the upper & lower -3dB corner points of the active bandpass filter decides the Q-factor of the circuit. The Q factor value is lower then the bandwidth of the filter is wider. As a result, the Q factor is higher the filter is narrower.

Sometimes, the Q factor of the active bandpass filter is denoted with the Greek symbol ‘α’ and is called the alpha-peak frequency.

α = 1/Q

As the ‘Q’ of an active BPF relates to the “sharpness” of the response of the filter around its ‘ƒr’ (center resonant frequency) then it can also be known as the Damping Factor (or) Damping Coefficient because the filter has more damping then the filter has flatter response. The filter has less damping the filter response is sharper.

The damping ratio is indicated with the Greek symbol ‘ξ ‘

ξ = α/2

The quality factor of an active band pass filter is the ratio of the ƒr (Resonant Frequency) to the BW (Bandwidth) in between the higher & lower -3dB frequencies.

Active Band Pass Filter Types

There are two types of active band pass filters; wide band pass filter and narrow band pass filter which are discussed below.

Wide Band Pass Filter

If the quality factor (Q) value is below ten, the pass band is broad, and then it gives us the larger bandwidth. So this BPF is known as Wide Band Pass Filter. In a wide band pass filter, the high cut-off frequency should be larger as compared to the lower cut-off frequency.

First, the signal passes through the HPF, the output signal of this filer will tend to infinity which is given to the LPF at the end. This LPF will low-pass the higher frequency signal.

Whenever the HPF is cascaded through LPF then the simple BPF can be obtained. To understand this filter, the order of the LPF and HPF circuits should be similar.

Cascading one first-order LPF and HPF provides us with the second-order BPF. By cascading two first-order LPFs with two HPFs form a fourth-order BPF.

Because of this cascading, the circuit gives a low-quality factor value. The capacitor within the first-order HPF blocks any DC biasing from the i/p signal.

At both the stop bands, the gain rolls off is ± 20 dB per decade in the second-order filter case. The LPF and HPF must be only in first order.

Likewise, whenever the two filters are in the second order, the gain roll-off at both the stop bands is approximately ± 40dB/Decade.

Expression:

The expression for bandpass filter voltage gain is given as:

Vout/Vin = Amax * (f/fL) / √(1+(f/fL)² (1+(f/fH)²

It is attained by the individual gains of both LPF and HPF, so both the filter’s gains are given as;

Voltage Gain for HPF

Vout/Vin = Amax1 * (f/fL) / √[1+(f/fL)²]

Voltage Gain for LPF

Vout / Vin = Amax2 /√[1+(f/fH)²]

Amax = Amax1 * Amax2

Where ‘Amax1’ is the gain of the HPF stage & ‘Amax2; is the gain of the LPF stage.

The wide-band filter response is shown below.

Narrow Band Pass Filter

If the quality factor value is higher than ten, the pass band will be narrow & passband bandwidth is also less. So this filter is known as the Narrow Band Pass Filter.

This filter only uses one active component like op-amp instead of two. The op-amp used in this circuit is in an inverting configuration. The op-amp gain in this filter is maximum at the ‘fc’ center frequency.

The narrow bandpass filter circuit is shown below. The input is provided to the inverting input terminal of the op-amp then the op-amp is known as in inverting configuration. This narrow BPF circuit gives a narrow BPF response.

The voltage gain of this filter circuit is AV = – R2 / R1

The cut-off frequencies of this filter circuit are;

fC1 = 1 / (2π*R1*C1)

fC2 = 1 / (2π*R2*C2)

Advantages and Disadvantages

The advantages of an active band pass filter include the following.

• This filter helps in sending or transmitting a preferred frequency range signal, thus it helps in saving energy.
• This bandpass filter assists in filtering signals between two frequency ranges.

The disadvantages of active bandpass filters include the following.

• An active bandpass filter allows only a preferred range of frequencies to pass through.
• They can be overly restrictive, particularly whenever utilized with a narrow bandwidth. So this results in losing significant frequency content to make the sound feel hollow or thin.
• These filters are expensive.
• These filters have a complex control system.
• They have a limited range of frequency.

Applications

The applications of active bandpass filters include the following.

• Active bandpass filter is used in many optical applications like; satellite communications, telecommunications & data transfer in light modulation.
• These filters are used in audio equipment to isolate frequencies that are in the audible range from 20 Hz to 20 kHz.
• Active BPF is used in wireless communication systems to filter out unwanted signals & noise to enhance the excellence of the communication.
• These filters are used in the tuning & high-speed mode locking of EDF ring lasers.
• This type of BPF is used to level the o/p spectrum of EDF super fluorescent sources.
• This filter is used in the signal transmitter and signal receiver in a wireless communication system.
• These are used in current audio systems like the stereo system, Distributed Speaker systems, Dolby Music System, etc.
• This type of filter is used for frequency control in audio equalizer circuits, LASER, LIDAR & SONAR communication systems.
• This is used in medical devices like ECG and in neuroscience to collect & analyze data.

Where is Active Band Pass Filter Used?

The active bandpass filter is used in the telecommunication field and also used within the audio frequency range from 0 kHz to 20 kHz for modems & speech processing. These are used commonly in wireless transmitters & receivers

What is the Difference between Active and Passive Band Pass Filter?

Active filters operate with a power source whereas passive filters don’t need a power source. The passive filter output changes with the load while the active filter maintains its performance regardless of the connected load.

What is the transfer function of a bandpass filter?

The band-pass filter behavior can be mathematically described with a transfer function. This is a complex function connecting the input & output signals of the filter. So the T.F is given by H(ω) = Vout(ω) / Vin(ω).

What is a Filter Transfer Function?

The filter transfer function is the Z-transform of its impulse response. It includes whole quadratic equations within both the numerator & denominator. It provides the base to implement low-pass, high-pass, single-frequency notch & band-reject realization characteristics.

Y(z) = H(z)X(z) =( h(1)+h(2)z−1+⋯+h(n+1)z−n)X(z).

Thus, this is an overview of the active bandpass filter, circuit, working, types, and applications. Active band-pass filters are important components within electronic circuits to pass a certain range of frequencies selectively while attenuating others. These filters provide several benefits like high precision & gain. Active BPFs are used commonly in communication systems as well as signal processing-based applications wherever stability & high precision are necessary like in radio receivers. These are used In a variety of applications, audio, biomedical engineering & radio communications. Here is a question for you, what is a passive bandpass filter?