frequency ( ƒL ) and the higher frequency ( ƒH ) whilebcas.du.ac.in/wp-content/uploads/2020/04/B.ScElec_Sem4...The narrow band reject filter is also called a notch filter. Because

Dr. Inderbir Kaur Operational Amplifier and Applications Covid 19Week -3(30 March-04April2020) Reference Study Material

Band Pass filter

The principal characteristic of a Band Pass Filter, is its

ability to pass frequencies relatively unattenuated over a

specified band called the “Pass Band”.

This band or range of frequencies is set between two cut-

off or corner frequency points labelled the “lower

frequency” ( ƒL ) and the “higher frequency” ( ƒH ) while

attenuating any signals outside of these two points.

There are basically two types of band pass filters, wide

band pass and narrow band pass filters.

Wide Band Pass Filter

A band pass filter is defined as a wide bandpass if its figure of

merit or quality factor Q is less than 10

Narrow Band Pass Filter

The band pass filters with Q > 10 are called the narrow band

pass filters.

What is Q ?


Q is a measure of selectivity, meaning the higher the value of

Q the more selective is the filter, or the narrower is the

bandwidth (BW).

Or we can say it defines the selectivity of the filter in passing

the centre frequency and rejecting other frequencies The

relationship between Q, 3-db bandwidth, and the centre

frequency fc is given by an equation

Q = fc / Bandwidth = fc / (fh -fl ) (1)

For wide band pass filter the centre frequency can be

defined as

Fc = √ (2)

In narrow wide band pass filter, the output voltage peaks at

the centre frequency.


Designing of wide Band Pass Filter

A wide Band Pass Filter can be easily made by

cascading together a single Low Pass Filter with a single

High Pass Filter as shown

The cut-off or corner frequency of the low pass filter (LPF)

is higher than the cut-off frequency of the high pass filter

(HPF) and the difference between the frequencies at the -

3dB determines the “bandwidth” of the band pass filter

while attenuating any signals outside of these points.



Voltage gain magnitude of band pass filter is equal to the

product of the voltage gain magnitude of the high pass and low

pass fiters.

│VO / Vin │ = [ AFT (f / fl )] / √ [ { 1+( f / fl )2 } { 1+( f / fh )

2 } (3)

Where AFT = Total pass band gain

And f is the frequency of the input signal

For eg. If we want to design a filter with pass band gain of 4, we

can set the gain of the high pas section and low pass section

as 2.


Designing of Narrow Band Pass Filter

Narrow Band Pass filter employs only one opamp. The circuit

diagram and gain frequency response given below


In comparison to all the filters discussed so far, this filter has

some unique features that are given below.

1. It has two feedback paths, and this is the reason that it

is called a multiple-feedback filter.

2. The op-amp is used in the inverting mode.

The narrow band pass filter is designed for specific values of

centre frequency fc and Q or fc and Bandwidth (see equation 1).

The circuit components are determined from the following

relationships. For simplification of design calculations each

of C1 and C2 may be taken equal to C.

R1 = Q/2∏ fc CAf

R2 =Q/2∏ fc C(2Q2-Af)

and R3 = Q / ∏ fc C

where Af, is the gain at centre frequency and is given as

Af = R3 / 2R1

However gain must satisfy the relation

Af < 2 Q2.


Advantage of multiple feedback filters

The centre frequency fc of the multiple feedback filter can be

changed to a new frequency fc„ without changing, the gain or

bandwidth. This is achieved simply by changing R2 to R‟2 so

that

R’2 = R2 [fc/f’c]2


Band Reject filter

The band pass filter passes one set of frequencies while

rejecting all others. The band-reject filter does just the

opposite. It rejects a band of frequencies, while passing

all others. This is also called a band-stop or band-

elimination filter.

Like bandpass filters, band-reject filters can also be

classified as (i) wide-band reject ( Q< 10) and (ii) narrow

band reject ( Q> 10) filters.

The narrow band reject filter is also called a notch filter.

Because of its higher Q, which exceeds 10, the bandwidth

of the narrow band reject filter is much smaller than that of

a wide band reject filter.


Design of wide Band reject filter

The summing of the high pass and low pass filters means

that their frequency responses do not overlap, unlike the

band-pass filter. This is due to the fact that their start and

ending frequencies are at different frequency points.

For example, suppose we have a first-order low-pass filter

with a cut-off frequency, ƒL of 200Hz connected in parallel

with a first-order high-pass filter with a cut-off

frequency, ƒH of 800Hz. As the two filters are effectively

connected in parallel, the input signal is applied to both

filters simultaneously as shown above . All of the input

frequencies below 200Hz would be passed unattenuated

to the output by the low-pass filter. Likewise, all input


frequencies above 800Hz would be passed unattenuated

to the output by the high-pass filter. However, and input

signal frequencies in-between these two frequency cut-off

points of 200Hz and 800Hz, that is ƒL to ƒH would be

rejected by either filter forming a notch in the filters output

response.

In other words a signal with a frequency of 200Hz or less

and 800Hz and above would pass unaffected but a signal

frequency of say 500Hz would be rejected as it is too high

to be passed by the low-pass filter and too low to be

passed by the high-pass filter.


Circuit of wide Band Reject Filter as shown above

consists of a low pass filter, high pass filter and a

summing amplifier.

The low cut-off frequency fL of high-pass filter must be

larger than the high cut-off frequency fH of the low-pass

filter. Also the pass band gain of both the high-pass and

low-pass sections must be equal.

Frequency response of wide Band reject filter



Narrow Band Reject Filter

The narrow Band Reject filter, also called Notch Filter, is

a highly selective, high-Q, form of the band stop filter

which can be used to reject a single or very small band of

frequencies rather than a whole bandwidth of different

frequencies.

For example, it may be necessary to reject or attenuate a

specific frequency generating electrical noise (such as

mains hum) which has been induced into a circuit from

inductive loads such as motors or ballast lighting, or the

removal of harmonics, etc.

The most common notch filter design is the twin-T notch

filter network. This is a passive filter composed of two T-

shaped networks. One T-network is made up of two

resistors and a capacitor, while the other is made of two

capacitors and a resistor.


Twin T Notch Filter

The Notch-out frequency is the frequency at which

maximum attenuation occurs and is given by

FN = 1/ 2ΠRC

One drawback of above notch filter (passive twin-T

network) is that it has relatively low figure of merit Q.

However, Q of the network can be increased significantly

if it is used with the voltage follower, as illustrated in figure

below


Active Notch Filter

Frequency Response of Notch Filter


You can also watch the NPTEL video on the following link,( Lecture 37)

https://nptel.ac.in/courses/122/106/122106025/

DISCLAIMER: This study material is only for the reference of students. No copyright infringement is

intended. This is only for the emergent situation of Covid period only where students don’t have

access to other reading material.

References : 1 Opamps and linear integrated circuits technology : Ramakatnt A. Gayakwad 2 linear integrated circuits by D. Roy Chaudhary and Shail Jain 3 https://nptel.ac.in/courses/117/107/117107094/ 4 www. Circuitstoday.com

5 https://www.electronics-tutorials.ws/filters



https://www.electronics-tutorials.ws/filters


All pass filters

An all-pass filter is that which passes all frequency components

of the input signal without attenuation but provides predictable

phase shifts for different frequencies of the input signals. The all-

pass filters are also called delay equalizers or phase correctors.

Where do we use All Pass filters ?

These filters are most commonly used in communication. For instance,

when signals are transmitted over transmission lines (such as telephone

wires) from one point to another point, they undergo change in phase.

To compensate for such phase changes, all-pass filters are employed.

Designing of an All Pass Filter The circuit of an All Pass filter is similar to a Difference Amplifier except

that Capacitor C replaces a resistor (circuit given below). Also the two

input terminals are connected together so that Vin is applied to both.


The output voltage vout of the filter circuit shown in figure above can be

obtained by using the superposition theorem.

VO1 = - Vin ( because Rf = R1 )

VO2 = (1 + Rf / R1 ) VC

= 2 VC

Therefore, vout = -vin +[ -jXC/ (R-jXC)]2Vin

Substituting for XC = = 1/ (j2∏fC) in above equation

We get on simplification

Vout / Vin = ( 1- j2∏RfC ) / ( 1+ j2∏RfC ) (1)

Where f is the frequency of the input signal in Hz. The above equation

indicates that the amplitude of vout / vin is unity.


The phase angle Φ = -2 tan-1 (2ΠfRc) (2)

( output lags the input by an angle Φ )

Equation (2) is used to find the phase angle if f, R and C are known.

Phase shift between input and output waveforms.

For fixed values of R and C , the phase angle Φ changes from 0 to -

180 degrees as the frequency is varied from 0 to ∞ . In the circuit of All

Pass Filter, if the positions of R and C are interchanged, the phase shift

between input and output becomes positive. That is output leads input.


Sample and Hold Circuit

As the name indicates, a sample and hold circuit is a circuit which

samples an input signal and holds onto its last sampled value until

the input is sampled again.

Sample and hold circuits are commonly used in analog to digital

converts, communication circuits, PWM circuits etc.

The circuit shown below is of a sample and hold circuit based on

uA 741 opamp , n-channel E MOSFET and few passive

components.

The N-channel Enhancement MOSFET will be used a switching

element. The input voltage is applied through its drain terminal and

control voltage will be applied through its gate terminal.


When the positive pulse of the control voltage is applied, the

MOSFET will be switched to ON state. And it acts as a closed

switch.

On the contrary, when the control voltage is zero then the

MOSFET will be switched to OFF state and acts as the open

switch.

When the MOSFET acts as a closed switch, then the analog signal

applied to it through the drain terminal will be fed to the capacitor.

The capacitor will then charge to its peak value. When the

MOSFET switch is opened, then the capacitor stops charging. Due

to the high impedance operational amplifier connected at the end

of the circuit, the capacitor will experience high impedance due to

this it cannot get discharged.

This leads to the holding of the charge by the capacitor for the

definite amount of time. This time can be referred as holding

period.

And the time in which samples of the input voltage is generated is

called sampling period.

The output processed by operational amplifier during the holding

period. Therefore, holding period holds significance for OP-AMPS.


The time periods of the Vs during which the voltage across

the capacitor (Vc) is equal to Vin are called sample periods (Ts)

and the time periods of Vs during which the voltage across the

capacitor C1 (Vc) is held constant are called hold periods (Th).

The output of the opamp is usually processed and observed

during hold periods.


To obtain close approximation of the input waveform, the

frequency of the sample and hold control voltage must be

significantly higher than that of the input.


Questions

1 A band-pass filter has a bandwidth of 250Hz and center

frequency of 866Hz. Find the quality factor of the filter?

2 Find the voltage gain magnitude of the wide band-pass filter?

Where total pass band gain is=6, input frequency = 750Hz, Low

cut-off frequency =200Hz and high cut-off frequency=1khz.

3 Compute the quality factor of the wide band-pass filter with high

and low cut-off frequencies equal to 950Hz and 250Hz.

4 Design a narrow band-pass filter, with fc=1kHz, Q= 13 and

AF=10 (Take C=0.1µF)

5 Design a wide Band pass filter with fl = 400 Hz and fH = 2 KHz,

and pass band gain =4. (8.27)

5 What are the Applications of Notch Filters?

-------------------------------------------------------------------------------------

DISCLAIMER: This study material is only for the reference of students. No copyright infringement is

intended. This is only for the emergent situation of Covid period only where students don’t have

access to other reading material.

References : 1 Opamps and linear integrated circuits technology : Ramakatnt A. Gayakwad 2 linear integrated circuits by D. Roy Chaudhary and Shail Jain 3 https://nptel.ac.in/courses/117/107/117107094/ 4 www. Circuitstoday.com

5 https://www.electronics-tutorials.ws/filters


https://www.electronics-tutorials.ws/filters

Documents

frequency ( ƒL ) and the higher frequency ( ƒH ) whilebcas.du.ac.in/wp-content/uploads/2020/04/B.ScElec_Sem4...The narrow band reject filter is also called a notch filter. Because