**Passive Band Pass Filter** are the combination of low pass filter and high pass filter. In this tutorial we will learn about** passive band pass filter**, its basic circuit, functionality, frequency response, applications and many more and we are already discuss Passive Low Pass Filter. Passive band pass filter is a combination of low pass and high pass filters. The names of filter itself indicate that it allow only pass a certain band of frequencies and block all the remaining frequencies.

In audio application, sometime we need to pass the certain frequencies but this frequency range in start from 0 Hz or not end to high range of frequency but these frequencies are within a certain range either narrow or wide and the bands of frequencies are known as a Bandwidth.

## Passive Band Pass filter

The passive band pass filter is the cascaded from of passive low and high pass filter. This type of arrangement will allow a selective range of frequency. This RC filter circuit can able to allow the narrow and wide range of frequencies. The cut off frequency of upper and lower is depends upon the design of filter. This type of frequency is simply use a frequency selector.

One of the common uses of passive filter is in a audio amplifier or circuit such as in loudspeaker crossover filters or pre-amplifier tone controls. In audio amplifier, sometime we need a certain range of frequency that not start from 0 Hz and not a higher frequency, but we need a certain range of frequency of band of frequencies, either it is narrow or wider range.

By cascading a single low pass filter or high pass filter circuit, we produce a different type of passive RC filter that only passes selective band of frequencies that can be either is wide or narrow while attenuating all those outside of this range.

The above circuit diagram show the passive band pass filter circuit. At the input terminal we give a sinusoidal signal. The arrangement of circuit element is the series combination of RC and another of RC is parallel combination.

This filter is a second order filter because of two reactive components. In circuit one capacitor is belongs to low pass filter and one capacitor is belongs to high pass filter. Without any changement of input this band pass filter is allow certain range of frequencies. Band pass filter does not produce any extra noise in meaning full signal.

The cut-off frequency can be calculated by using given formula:

f_{C} = 1/(2πRC)

The frequency range of band pass filter is in between of cut-off frequency of high pass and low pass filters. This filter allow two cut off frequencies one is lower cut-off frequency ‘ f_{L}‘ and another is higher cut-off frequency ‘f_{H}’. This range of frequency passes through filter is called bandwidth of this filter. In general the bandwidth is the difference of two frequencies and it is denoted by “BW”

BW = f_{H} – f_{L}

Where ,

“f_{H}”→ The cut-off frequency of the high pass filter

“f_{L}”→ The cut-off frequency of the low pass filter.

“BW” → Bandwidth of the filter.

## Band Pass Filter Circuit

Unlike the low pass filter allow the low frequency signal and high pass filter allow the high frequency of the signal but band pass filter only pass the certain range of frequency without any distortion. This range of frequencies can be any width and it is commonly known as the filters **Bandwidth**.

The term bandwidth is the range of frequency that exists between two specified frequency cut-off points ( ƒc ), that are 3dB below the maximum center or resonant peak while attenuating or weakening the besides the outside of these two points. The band pass fitter is use in isolate or filter out certain frequencies that lie within a certain band of frequency.

### BPF using R, L and C components

The can also be design with the help of RLC components. The circuit diagram of band pass filter using inductor, capacitor and resistor is given below

The resonant peak or center frequency is calculated by formula which is given below.

f_{c} = 1/2π√(LC)

Where,

L → Inductance of an inductor and its units is Henry (H).

C → Capacitance of a capacitor and its units is Farad (F).

We can also design band pass filter using inductor but we know reactance of the capacitors is high. The design of filter with RC elements is more advantage than RL circuits.

### Frequency Response of Band Pass Filter

The maximum gain of frequency is equal to pole frequency approximately. The frequency response curve of **BPF** is shown below: The ideal characteristics and practical characteristics of **BFP** are different because of the input reactance of the circuit.

The input signal gain to be calculated by taking 20 log (V_{out} / V_{in}). This range is quit larger because inherent characteristics of the circuit. The low frequencies is attenuated when the output increasing at a slope of +20 dB until frequency reaches to lower cut off frequency ‘f_{L}’

At this frequency the gain value is 1/√2 = 70.7%.

The output will increase after the cut-off frequency ‘f_{L}’ at -20 dB per decade and attains maximum gain and this gain is constant until it reaches the higher cut off frequency ‘f_{H}’ After the higher cut-off frequency the output decreases at a slope of -20dB/decade or -6dB/octave.

Earlier we noticed that the first order filter shift is 90 °. We know that the band pass filter is a second order filter so the phase shift is double is 180 °. The phase angle will vary with increasing frequency. In the center of the output frequencies and input signals.

Below the resonant frequency output signal leads the input signal and above the resonant frequency output delayed input signal. The amplitude of input signal is always higher than output signal. In order to maximize circuit benefits the resistance R1 must be higher than resistance at R2.

#### Band Pass Filter Centre Frequency

The “Center frequency” is that frequency at which the output gain is high is known center frequency. It is also called “Resonant frequency”. The center frequency is to be calculated by Geometric mean of lower and upper cut-off frequencies.

f_{r}^{2} = f_{H} x f_{L}

f_{r} = √(f_{H} x f_{L})

Where

f_{r }– resonant frequency or centre frequency

f_{H} – upper -3 dB cut-off frequency

f_{L} – lower -3 dB cut-off frequency

### Applications of Band Pass Filter

- This filter is used in wireless communication medium at transmitter and receiver circuits. Because the transmission will pass only useful signal and reduce rest of the signal to protect noise and attenuation.
- Band pass filter is use to optimize the signal to noise ratio of the receiver.
- It is use in optical communication area like LIDARS lasers, etc.
- Band pass filter used in some of the techniques of colour filtering.
- Band pass filter is also used in medical field instruments like EEG and
**Seismology**applications - It is use in telephonic system at DSL to split phone & broad band signals.

Also read:- Passive low pass filter

## Band Pass Filter Example

** Which filter passes the certain range of frequency?**

1. Band-pass filter

2. Band-reject filter

3. Band-stop filter

4. All of the mentioned

Answer: 2

A band- pass filter having pass band between two cut-off frequencies f_{H} and f_{L}.

** Narrow band pass filters are**** **

- Q < 10
- Q = 10
- Q > 10
- None of the mentioned

Answer: 3

Quality factor (Q) is the measure of selectivity. The higher value of Q is narrower its bandwidth.

** A band-pass filter has a BW of 250Hz and center frequency is 866Hz. Find the quality factor (Q) of band pass filter?**

- 46
- 42
- 84
- None of the mentioned

Answer: 1

Quality factor of band-pass filter

= Q =f_{c}/bandwidth

= 566/250

=3.46.

**What is the center frequency of wide band-pass filter**

- f
_{c}= √(f_{h}+f_{L}) - f
_{c}= √(f_{h}-f_{L}) - f
_{c}= √(f_{h}/f_{L}) - f
_{c}= √(f_{h}×f_{L})

Answer: 4

In a wide band pass filter, the center frequency is equal to product of high and low cut-off frequency.

i.e. ( f_{c})^{2} =f_{H}×f_{L}

=> f_{c}= √(f_{h}×f_{L}).

**What is voltage gain of wide band-pass filter.**

- A
_{Ft}/ √{[1+(f/f_{h})^{2}]×[1+(f/f_{L})^{2}]} - A
_{Ft}×( f/f_{L})/√[(1+(f/f_{h})^{2}]×[1+(f/f_{L})^{2}]. - A
_{Ft}/ √{[1+(f/f_{h})^{2}]/[1+(f/f_{L})^{2}]} - [A
_{Ft}/(f/f_{L})]/ √{[1+(f/f_{h})^{2}]/[1+(f/f_{L})^{2}]}

Answer: 2

** When a second order low pass and high pass filter sections are cascaded then resultant filter will be?**

- ±80dB/decade band-pass filter
- ±20dB/ decade band-pass filter
- ±40dB/decade band-pass filter
- None of the mentioned

Answer: 3

** What is voltage gain of wide band-pass filter? Where total pass band gain is 6, input frequency 750 Hz, Low cut-off frequency 200 Hz and high cut-off frequency 1 kHz.**

- 837dB
- 36 dB
- 25 dB
- 11.71 dB

Answer: 1

Voltage gain of the filter,

|V_{O}/V_{in}|=[A_{Ft}×(f/f_{L})]/{√[1+(f/f_{L})^{2}]×[1+f/f_{L})^{2}]} =[6×(750/20)]/√{[1+(750/200)^{2}]×[1+(750/200)^{2}]}

=22.5/√(15.6×1.56) =5.519.

|V_{O}/V_{in}|= 20 log(5.519) =14.837dB.

** Find out quality factor of wide band-pass filter with low and high cut-off frequencies equal to250Hz and 950Hz.**

- 278
- 348
- 994
- 696

Answer: 4

Quality factor Q=√(f_{h}×f_{L})/(f_{h}-f_{L}) = √(950Hz×250Hz)/(9950Hz-250Hz) =0.696.

** The quality factor (Q) of a wide BPF is**

- 6
- 2
- 1
- 9

Answer: 3

A wide BFP has quality factor less than 10.

## People also ask

**What is passive band pass filter?**

A passive band pass is an electrical circuit that is use to allow the certain range of frequencies. The passive band pass filter use only passive element like R, C and L so this name is a passive band pass filter. The passive BPF is made by cascading of low pass filter and high pass filter.

**What is the difference between active and passive band pass filter?**

The passive BPF use passive element like resistance, capacitance and inductance but in case of active band pass filter use active elements like op-amp and transistor for the filtering of electronic signals.

**What does a pass band filter do?**

Band-pass filter, arrangement of electronic components that allows within a certain range, or band of frequencies to pass and attenuate all others frequency.