# Band-Pass Filter: Circuit Diagram, Frequency response with Transfer function

In signal processing applications there is a very high chance for the circuit to be affected by noise signals. There the many ways to remove noise from a circuit, the most important one is called a Filter Circuit. As the name suggests, this circuit filters out the unwanted signals (noise) from the desired signal. There are many types of filter circuits, but the most commonly used and effective one is the Band Pass Filter which can be easily designed using a pair of resistors and capacitors.

A band-pass filter is a circuit designed to pass signals only in a certain range of frequencies while attenuating all the signals outside this range. The parameters of interest in a bandpass filter are the high(fH) and low(fL) cut-off frequencies (fH>fL), center frequency FC,  bandwidth (BW), center-frequency gain, and the selectivity or Q. Selectivity is also called a figure of merit or quality factor.

There are basically two types of bandpass filters

Wide band pass filter(Q<10)

Narrow band pass filter(Q>10)

There is no set dividing rule between the two. However, a bandpass filter worked as a wide bandpass if quality factor Q <10 while the bandpass filters with Q > 10 worked as the narrow bandpass filters. Thus Q is a measure of selectivity of filter, means higher the value of Q, the filter is more selective or the narrower is its bandwidth (BW).

The relationship between selectivity Q, 3-dB bandwidth, and the center frequency Fc is given by an equation

Q=fc/BW   ;   where BW=(FH-fL)

Q = fc/(fH-fL);

Centre frequency in case of wide band pass filter is given as

fc=√(fH.fL);

fH = high cutoff  frequency (Hz);fL=low cut off frequency(Hz)of wide bandpass filter.

Table of Contents

## Wide Band pass Filter

Fig.1 Circuit diagram

From the figure A1,A2 are the dual operational amplifiers

A wide band-pass filter is simply designed by cascading a high-pass and lowpass circuits in series. This configuration provides design simplicity and good performance. Although this circuit can be realized by a number of possible circuits. To achieve a ± 20 dB/ decade bandpass section, a first-order high-pass and first-order low-pass sections are cascaded; for a ± 40 dB/decade bandpass filter, it requires a second-order high- pass filter and a second-order low-pass filter are cascaded in series, and so on. It means that the order of the bandpass filter order depends on the order of the high-pass and low-pass filter circuits. A ± 20 dB/decade wide bandpass filter composed of a first-order high-pass filter and a first-order low-pass filter, is shown in fig. (1). its frequency response is illustrated in fig. (2).

Fig.2 frequency response

## Transfer function of band pass filter:

The transfer function of band pass filter is given as

H(s) = H0ω02 / [s2+ s. (ω0/Q) + ω02];

Whereω0= frequency of the filter at which gain of the filter attains peak value.

ω0=2 п Fc;

H0 is the circuit gain and it is defined as H0=H/Q;

Selectivity Q = Fc/(fH-fL);

Center frequency Fc=√(fH.fL) ;

s    =σ +jω

ω= angular frequency(rad/sec);σ=Neper frequency (NP/s)

## Narrow Bandpass Filter

Fig 3.Circuit diagram

Fig 4.frequency response

This filter consists of only one operational -amplifier, as shown in figure 3. In comparison to all the above-discussed filters, this filter has some unique features as follows.

It consists of two feedback paths, and this is the reason that.it is called a multiple-feedback filter.

Here the op-amp is used in the inverting mode. The frequency response of a narrow band -pass filter is shown in fig(4).

Generally, the narrow bandpass filter is designed for precise values of center frequency FC and Q or FC and BW. The circuit components are determined from the following relationships. For simple design calculations, each ofC1and C2may be taken equal to C.(C1=C2=C3)

R1 = Q/(2∏ fc CAF)

R2 =Q/(2∏ fc C(2Q2AF))

and R3 = Q /(∏ fc C)

HereAF, is the gain at centre frequency fc.

And it is given as AF = R3 / 2R1

The gain AF must satisfy the following condition

AF<2 Q2.

The center frequency Fc of the multiple feedback filter can be changed to a new frequency FC’ without changing, the gain or bandwidth due to an advantage of multiple feedback filter. This is simply achieved by changing R2 to R’2 so that

R’2 = R2 (fc/f’c)2

Note: The above-discussed band pass filter is also known as an active band pass filter because it is designed with active components like Transistors and Op-amps.WhereasPassive Band Pass Filter is designed by cascading passive low pass and passive high pass filter circuits.(By using R, L, C passive components)This arrangement will also provide selective filtering which passes only certain frequencies.

Fig.Passive Band Pass Filter

The cut-off frequency of the circuit can be given as follows.

fC = 1/(2πRC)​

Band Width of the circuit is given  by the frequencies ‘fH and fL‘.

BW = fH – fL

Where fH high cut of frequency; fH= 1/2 п R1C1

fL low cut of frequency; fL= 1/2 п R2C2

## Band pass filter applications

These are utilized in remote correspondence medium at transmitter and collector circuits.

Utilizations of Band Pass Filter are utilized to improve the sign to commotion proportion of the recipient.

Utilizations of Band Pass Filter are utilized in optical correspondence region like LIDARS.

Applications are utilized in a portion of the methods of shading sifting.

These are additionally utilized in clinical field instruments like EEG.

In telephonic applications, at DSL to part telephone and wideband signals.