Unit – 2: Wave form generators and Filters

BSc in Physics 6th
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PHY C16 – T: Electronic Instrumentation & Sensors Unit – 2: Wave form generators and Filters
Notes by Mr. Chandrakantha T S, Dept. of PG Studies & Research in Electronics Kuvempu University, Jnanasahyadri Shankaraghatta,2023-24
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For more Notes visit :https://sites.google.com/view/chandrakanthats/teaching
PHY C16 – T: Electronic Instrumentation & Sensors(Theory)
Unit – 2: Wave Form Generators and Filters
INTRODUCTION
Waveform/Signal/Function Generators:
 Waveform/Signal/Function Generators are electronic instruments that create electrical
signals with various shapes (waveforms such as sine, square etc..) and frequencies.
 These signals can be periodic, such as sine, square, triangle, and sawtooth waves, or
arbitrary, allowing the user to define custom waveforms.
 It is also called an oscillator, since it produces periodic signals.
 These generators are crucial for testing, development, and troubleshooting of electronic
devices and circuits.
 The versatility of waveform generators lies in their ability to produce both analog and
digital signals, making them indispensable in fields such as audio engineering,
telecommunications, and digital signal processing.

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Applications of Wave Form Generators
1. Electronics Testing and Development
o Circuit Design: Engineers use waveform generators to simulate inputs for testing
circuit responses.
o Component Testing: Verify the performance of individual components like
resistors, capacitors, and transistors.
2. Communications
o Signal Analysis: Test the integrity and quality of communication signals.
o Modulation and Demodulation: Simulate different types of modulation schemes
to evaluate communication systems.
3. Audio Engineering
o Sound Equipment Testing: Calibrate and test audio equipment like amplifiers,
speakers, and microphones.
o Synthesizers: Create and manipulate audio signals for music production.
4. Medical Devices: Generate signals to test medical devices such as ECG and EEG
machines.
5. Education and Research
o Teaching: Demonstrate fundamental concepts in electronics and signal processing
to students.
o Research: Facilitate experiments in fields like physics, electronics, and materials
science.
6. Defense and Aerospace: Generate signals to test radar and sonar systems.
7. Consumer Electronics
o Product Testing: Evaluate the performance of consumer electronics like TVs,
smartphones, and gaming consoles.
o Quality Control: Ensure products meet specified performance criteria before
shipment.

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Basic Principle of Standard AF Signal Generator
 A standard Audio Frequency (AF) signal generator is used to produce sine wave signals
over a wide range of frequencies, from a few Hertz (Hz) to several Giga-Hertz (GHz)
usually 20 Hz to 20KHz.
 They can be categorized into fixed-frequency and variable-frequency generators.
1. Fixed-Frequency Generators: These generators produce signals at a constant, pre-
set frequency. They are often used when a specific, unchanging frequency is
required for testing or calibration purposes.
2. Variable-Frequency Generators: These allow users to adjust the output frequency
over a wide range. They are versatile tools used in scenarios where the frequency
needs to be tuned according to the testing requirements.
Basic Standard Sine Wave Generator
The basic structure of a sine wave generator consists of two main components: an oscillator and
an attenuator.
1. Oscillator:
 The oscillator is responsible for generating a precise and stable frequency. Its performance
determines the accuracy, stability, and distortion-free nature of the output signal.
 The oscillator uses an LC tank circuit (inductor-capacitor circuit) to maintain a constant
output frequency over the desired range.

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 Frequency stability and control are achieved through range switching, typically by
selecting appropriate capacitors.
2. Attenuator:
 An attenuator is an electronic device used to reduce the amplitude (or power) of a signal
without significantly altering its waveform.
 It adjusts the signal's strength to the desired level, ensuring that the output voltage is
controllable and accurate.

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 The core component of an attenuator is resistors, which are used to create the desired level
of attenuation. In a simple attenuator, resistors are arranged in a network to divide the input
signal proportionally.
 Network Topologies:
Tee Network: Uses a combination of series and parallel resistors to achieve attenuation.
It's named for the T-like arrangement of the resistors.
Pi Network: Comprises two series resistors and one parallel resistor. It resembles the
Greek letter π and provides similar attenuation but with different impedance characteristics.
Standard Signal Generator
 A standard signal generator is designed to produce known and controllable voltages,
making it a crucial tool for testing and measurement in various applications.
 It is widely used to measure gain, signal-to-noise ratio (S/N), bandwidth, standing wave
ratio, and other properties of electronic circuits. These generators are essential in the testing
of radio receivers and transmitters.

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Components and Functionality:
1. RF Oscillator: The carrier frequency is generated by a stable RF oscillator using an LC tank
circuit. This oscillator ensures a constant output frequency, which is indicated by the frequency
range control and the vernier dial setting.
2. Wide-Band Amplifier: A wide-band amplifier extends the frequency range over which the
signal generator can operate effectively. It ensures that the signal generator can produce signals
with consistent performance across a broad frequency spectrum.
3. Modulation: The signal generator can modulate the carrier frequency, either internally or from
an external source. The modulation can be amplitude modulation (AM) or frequency
modulation (FM), and it can use different waveforms, such as sine, square, triangular, or pulse
waves.
4. Buffer Amplifiers: In high-frequency oscillators, it is crucial to isolate the oscillator circuit
from the output circuit to prevent changes in the output circuit from affecting the oscillator's
frequency, amplitude, and distortion characteristics. Buffer amplifiers provide this isolation,
ensuring stable performance.
5. Output and Attenuation: The modulated carrier is delivered to an attenuator through an
output amplifier. The output voltage is read by an output meter, and the attenuator adjusts the
output setting to provide the desired signal strength.

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AF Sine and Square Wave Generator
 An AF sine and square wave generator is an instrument used to produce audio-frequency
signals, typically ranging from 10 Hz to 1 MHz.
 It employs a Wien bridge oscillator to generate high-quality sine waves, and it can also
produce square waves.
Components and Functionality
1. Wien Bridge Oscillator:
 The Wien bridge oscillator is the primary circuit used in the generator to produce
stable sine waves. It is well-suited for the audio frequency range and allows precise
frequency control.
 The frequency can be adjusted by varying the capacitance in the oscillator circuit.
Additionally, resistors with different values can be switched in to change the
frequency in discrete steps.
2. Function Switch:Directs the output of the Wien bridge oscillator either to the sine wave
amplifier or to the square wave shaper, allowing the user to select the desired waveform
(sine or square wave) at the output.

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3. Sine Wave Amplifier:Amplifies the sine wave output from the Wien bridge oscillator. The
amplitude of the sine wave can be varied from 5 mV to 5 V (rms).
4. Square Wave Shaper: Converts the sine wave output into a square wave. The output
amplitude of the square wave can be adjusted from 0 to 20 V (peak). The symmetry of the
square wave can be varied from 30% to 70%.
5. Attenuator: Adjusts the amplitude of the output signal. The attenuator is used to set the
output signal strength to the desired level.
6. Push-Pull Amplifier: Provides the final amplification stage for the output signal. For sine
waves, it delivers the output with a low impedance of 600 ohms, suitable for various
applications.
7. Front Panel Controls:
o Frequency Selector: Allows selection and continuous variation of the frequency
across different ranges, with a non-linear scale covering 5 decades (10 Hz to 1
MHz).
o Frequency Multiplier: Expands the frequency range in 5 decades, enabling precise
frequency adjustments.
o Amplitude Multiplier: Provides attenuation of the sine wave in 3 decades (×1,
×0.1, and ×0.01), enabling fine control of the amplitude.
o Variable Amplitude: Continuously adjusts the amplitude of the sine wave output.
o Symmetry Control: Adjusts the symmetry of the square wave from 30% to 70%.
o Amplitude Control: Continuously adjusts the amplitude of the square wave
output.
o Function Switch: Selects between sine wave and square wave outputs.
o Output Available: Provides access to either the sine wave or square wave output.
o Sync Terminal: Allows synchronization of the internal signal with an external
signal for precise timing and coordination.
8. Power Requirements: The instrument operates with a power consumption of only 7 W,
typically powered by a 220 V – 50 Hz supply.

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Oscillator Definition
An oscillator is an electronic circuit that generates a continuous, periodic signal without
requiring an external input signal. It combines an amplifier with a feedback network to produce
and sustain oscillations.
Key Components
1. Amplifier:
 Provides the necessary gain to compensate for losses in the circuit and to sustain
oscillations.
 Can be an operational amplifier, transistor, or any other active device capable of
amplification.
2. Oscillator Circuit: The oscillator circuit can be based on LC (Inductor-Capacitor) or RC
(Resistor-Capacitor) networks.
3. Positive Feedback: Ensures that a portion of the output signal is fed back to the input in phase
with the original signal, reinforcing the oscillations.
The Barkhausen Criterion States:
1. Loop Gain Condition: The product of the gain of the amplifier stage and the feedback
network must be equal to one (unity gain) at the frequency of oscillation.
where A is the gain of the amplifier and 𝛽 is the feedback factor of the network
2. Phase Shift Condition: The total phase shift around the feedback loop must be zero or an
integer multiple of 360 degrees (2π radians) at the frequency of oscillation.

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Wien-Bridge Network and Oscillator Configuration(Sine Wave Generator)
 The Wien-Bridge Oscillator is a widely used electronic oscillator circuit for generating
precise sine waves.
 It is renowned for its stability and low distortion, making it ideal for audio-frequency
applications.
 The oscillator is based on the Wien-Bridge network, which determines its frequency of
oscillation.
Wien-Bridge Network Configuration
 The Wien-Bridge network is a type of electronic circuit used in the Wien-Bridge Oscillator.
 It consists of a bridge circuit with resistors and capacitors arranged in bridge configuration.
Components of the Wien-Bridge Network:
 R1 and R2: Resistors in series, typically forming one leg of the bridge.
 C1 and C2: Capacitors in series, typically forming the other leg of the bridge.
 R3: A variable resistor or potentiometer used to balance the bridge and adjust the
frequency.
 R4: A fixed resistor connected in series with the combination of R1 and C1.

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Behavior of the Network:
 The resistance R1 and CapacitorC1 make the lag part of the circuitry and resistances R2
and capacitroC2 make the leading part of the circuitry.
 At less value of frequency, the lead circuitry operates due to the large value of reactance
of capacitor C2. With the increment in frequency and decrement in this frequency causes
the output voltages to increased.
 At a certain value of frequency, the response of lag circuitry dominates and reduces the
value of XC1 that causes the output voltage to decrease.
 The resultant curvature for the lead-lag circuitry can be seen in the above figure. This
circuitry denotes that the output voltage extreme at the frequency known as the resonant
frequency.
 At this location, the attenuation (Vout/Vin) of circuitry is 1/3 if R1 = R2 and XC1 = XC2
as described the respected expression. Vout/Vin=1/3, The output voltage (V0) will be
approximately one-third of the input value.
Frequency Determination:
 The frequency of oscillation is determined by the values of R1, R2, C1, and C2. The bridge
oscillates when the impedance of the two legs is equal, which occurs at the resonant
frequency given by:

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Wien-Bridge Oscillator Configuration
 The Wien-Bridge Oscillator is built around the Wien-Bridge network and includes
additional components to sustain oscillations and control amplitude.
 The operational amplifier is used in a non-inverting configuration and feedback form a
voltage divider network. The resistances R1 and Rf forms the part of the feedback path
which determines or facilitates to adjust the amplifier gain.
 A portion of the amplifier output is feedback through the voltage divider network (a series
combination of resistor and capacitor) to the positive or non-inverting terminal of the
amplifier.
 Also, second portion of the amplifier is feedback to the inverting or negative terminal of
the amplifier through the impedance of magnitude 2R.

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 If the feedback network elements are chosen properly, the phase shift of the signal input
to the amplifier is zero at certain frequency. Since the amplifier is non-inverting which
introduce zero phase shift plus the feedback network zero phase shift, the total phase shift
becomes zero around the loop hence the required condition of oscillations.
 Therefore, the Wien bridge oscillator works as a sine wave generator whose frequency of
oscillations is determined by R and C components.
A = 1 + (Rf / R1)
 The gain of non-inverting amplifier must be of minimum 3 to satisfy Barkhausen criterion.
→1 + (Rf / R1) ≥ 3
→ (Rf / R1) ≥ 2
 Hence, the ratio of resistances Rf to R1 must be equal to or greater than 2. The frequency
of oscillations is given by
f = 1 / 2πRC
 The output is a stable sine wave with the frequency determined by the Wien Bridge
network components.
Triangular and Sawtooth Wave Generators
Triangular and sawtooth wave generators are essential circuits in electronic signal processing and
waveform generation. Both can be constructed using operational amplifiers (op-amps) and share
some similarities in design, but they serve different purposes and have distinct characteristics.

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Triangular Wave
 Ramp Up and Down: The triangular wave has a linear ramp-up (increase) and a linear
ramp-down (decrease) with equal durations. The waveform appears symmetric, with equal
time spent increasing and decreasing.
 Symmetry: In an ideal triangular wave, the ramp-up and ramp-down times are equal,
resulting in a symmetric waveform. The period of the waveform is split evenly between
the rising and falling segments.
Sawtooth Wave
 Ramp Up and Reset: The sawtooth wave has a linear ramp-up (increase) followed by a
rapid drop or reset back to the starting value. The waveform appears asymmetric with a
gradual rise and an abrupt fall.
 Asymmetry: The ramp-up period is significantly longer than the reset period. The majority
of the period is spent in the ramp-up phase, while the fall or reset period is a much shorter
duration.
Triangular Wave Generator
A triangular wave generator creates a triangular waveform, which is a piecewise linear wave that
ramps up and down. This can be implemented using operational amplifiers (op-amps) in
conjunction with a square wave generator.

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Construction:
The triangular wave generator typically involves two main components:
1. Square Wave Generator: The square wave has a constant amplitude of ±Vsat and a
specific frequency. This input is fed into the integrator.
2. Integrator Circuit: The integrator takes the square wave input and integrates it over time
to produce a triangular wave.
Working:
 When the square wave is at +Vsat, it creates a constant current through a capacitor C. This
constant current causes a linear decrease in the output voltage, producing a downward
ramp.
 When the square wave switches to −Vsat, the direction of the current through the capacitor
reverses, causing a linear increase in the output voltage, producing an upward ramp.
 The triangular wave frequency matches the square wave frequency, while its amplitude
varies inversely with frequency due to the capacitor’s reactance.
 The frequency of the Triangular Wave Generator Using Op amp wave given by
Triangular Wave Properties
 Equal rise and fall times
 Frequency same as input square wave
 Amplitude decreases with increasing frequency due to capacitor reactance

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Sawtooth Wave Generator
A sawtooth wave generator produces a waveform with a linear ramp up followed by a rapid drop
back to the starting value, creating a sawtooth shape. This can be achieved using an integrator with
a reset mechanism.
Integrator:
 Similar to the triangular wave generator, but with a different reset mechanism.
 The op-amp is configured as an integrator with a capacitor C in the feedback loop and
resistor R connected to the input.
 Integrates a constant current to produce a ramp signal.
Comparator:
 Detects when the integrator output reaches a certain threshold and generates a reset pulse.
 The comparator output is connected to the reset mechanism of the integrator.

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Reset Mechanism:
 A diode or transistor to discharge the capacitor quickly.
 Resets the capacitor when the integrator output reaches the threshold, causing the sawtooth
waveform.
 The oscillation frequency can be calculated by the following formula.
Sawtooth Wave Properties
 Linear ramp up, rapid fall
 Frequency determined by RC time constant and comparator threshold
 Harmonic rich spectrum, useful for music synthesis
Passive and Active Filters
Introduction to Filters
 Filters are electronic circuits or systems that allow certain frequencies of signals to pass
through while attenuating or blocking others.
 They are crucial in various applications, including audio processing, communications,
signal processing, and instrumentation.
 Filters are designed to modify the frequency content of signals, which is essential for tasks
such as noise reduction, signal conditioning, and frequency selection.

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Types of Filters
I)Passive Filters:
 Passive filters consist of passive components like resistors (R), capacitors (C), and
inductors (L).
 They do not require external power sources or active components (e.g., transistors or
operational amplifiers) for their operation.
 The filter's response is determined solely by the values of these passive components.
Characteristics:
 Simplicity: Passive filters are simple to design and implement.
 No Power Supply: They do not require an external power source.
 Frequency Response: The frequency response is determined by the component values.
Types of Passive Filters
1. Passive Low-Pass Filter (LPF): A passive filter that allows signals with frequencies below a
certain cutoff frequency to pass through while attenuating higher frequencies. The cutoff
frequency is determined by the values of the resistor and capacitor (or inductor) used in the
circuit.

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Construction: A simple passive low-pass filter can be constructed using a resistor (R) and a
capacitor (C). The resistor is connected in series with the input signal, and the capacitor is
connected in parallel with the output signal (across the resistor).
Working:
 At low frequencies, the impedance of the capacitor is high, which means most of the input
signal passes through to the output.
 At high frequencies, the impedance of the capacitor is low, causing the high-frequency
signals to be shunted to ground, resulting in attenuation at the output.
 Cut-off Frequency (fc): The cutoff frequency is the frequency at which the output signal
is reduced to 70.7% (1/√2) of the input signal. It is given by:
2. Passive High-Pass Filter (HPF): A passive filter that allows signals with frequencies above
a certain cutoff frequency to pass through while attenuating lower frequencies. The cutoff
frequency depends on the component values in the filter circuit.

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Construction: A simple passive high-pass filter can be constructed using a capacitor (C) and a
resistor (R). The capacitor is connected in series with the input signal, and the resistor is connected
in parallel with the output signal (across the capacitor).
Working:
 At low frequencies, the impedance of the capacitor is high, which means the signal is
blocked, resulting in attenuation at the output.
 At high frequencies, the impedance of the capacitor is low, allowing most of the input
signal to pass through to the output.
 Cut-off Frequency (f c): The cutoff frequency is the frequency at which the output signal
is reduced to 70.7% (1/√2) of the input signal. It is given by:
3. Passive Band-Pass Filter (BPF): A passive filter that allows signals within a specific
frequency range (between two cutoff frequencies) to pass through while attenuating
frequencies outside this range. This is typically achieved by combining a high-pass filter and
a low-pass filter.
Construction: A passive band-pass filter can be constructed by combining a high-pass filter
and a low-pass filter in series. Typically, this can be done using two capacitors (C1, C2) and a
resistor (R).

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Working:
 Low frequencies are blocked by the high-pass section (C1 and R1).
 High frequencies are blocked by the low-pass section (R 2and C2).
 Only frequencies within the band (between the cutoff frequencies of the high-pass and low-
pass sections) are allowed to pass through.
 The cutoff frequencies are given as:
4. Passive Band-Stop Filter (BSF): Also known as a notch filter, it attenuates signals within a
specific frequency range while allowing frequencies outside this range to pass through.

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Construction: A passive band-stop filter, also known as a notch filter, can be constructed by
combining a low-pass filter and a high-pass filter in parallel. This can be achieved using resistors
(R1, R2) and capacitors (C1, C2).
Working:
 Frequencies within the stop band are attenuated by the low-pass and high-pass sections.
 Frequencies outside the stop band are allowed to pass through.
 The cutoff frequencies are given as :
II)Active Filters:
 Active filters use active components like operational amplifiers (op-amps) along with
passive components (resistors, capacitors) to achieve desired filtering characteristics.
 They can provide amplification, which is not possible with passive filters alone.
Characteristics:
 Gain Control: Active filters can provide amplification, which allows for higher signal
strength and improved performance.
 Complexity: They are generally more complex to design and implement compared to
passive filters.
 Power Supply: They require an external power source for the active components.
Types of Active Filters
1. Active Low-Pass Filter (LPF)
Construction
 The circuit consists of a low-pass filter and an amplifier. The low-pass filter, made of a
resistor (R3) and capacitor (C1), allows low-frequency signals from Vin to pass while
blocking high frequencies.

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 This filtered signal enters the inverting input of an Op-Amp, with the non-inverting input
grounded. The amplifier's gain is set by the feedback resistors R1 and R2.
Working
Filtering Action:
 When the input signal Vin enters the circuit, it first passes through the low-pass filter
formed by R3 and C1.
 The low-pass filter allows low-frequency signals to pass through with little attenuation
while attenuating high-frequency signals. This is due to the frequency-dependent
impedance of the capacitor C1.

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 Low Frequencies: At low frequencies, the impedance of C1 is high, so most of the input
signal voltage appears across R3, passing to the inverting input of the Op-Amp.
 High Frequencies: At high frequencies, the impedance of C1 is low, causing most of the
signal voltage to drop across C1, effectively shorting high-frequency components to
ground and preventing them from reaching the inverting input of the Op-Amp.
Amplification:
 The filtered signal (mainly low-frequency components) at the junction of R3 and C1 is fed
into the inverting input of the Op-Amp.
 The Op-Amp amplifies this signal. The amount of amplification (gain) is determined by
the feedback network consisting of R1 and R2
Where:
AF = the pass band gain of the filter, (1 + R2/R1)
ƒ = the frequency of the input signal in Hertz, (Hz)
ƒc = the cut-off frequency in Hertz, (Hz)
Thus, the operation of a low pass active filter can be verified from the frequency gain equation
above as:

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Output Signal (Vout):
 The amplified signal, now composed mainly of the low-frequency components of the
original input, is available at the output Vout.
 This output signal is a filtered and amplified version of the input signal, with high-
frequency noise or unwanted components significantly reduced.
2. Active High-Pass Filter (HPF)
Construction
 The high-pass filter is made up of a capacitor (C1) in series with the input signal (Vin) and
a resistor (R3) in parallel with C1 to ground. This configuration blocks low frequencies
and allows high frequencies to pass.
 The filtered signal is fed into the inverting input of an operational amplifier (Op-Amp),
with the non-inverting input grounded. The amplifier's gain is set by feedback resistors R1
(between the output and inverting input) and R2 (between the inverting input and ground).

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Working
Filtering Action:
 When the input signal Vin enters the circuit, it first passes through the high-pass filter
formed by C1 and R3.
 The high-pass filter allows high-frequency signals to pass through with little attenuation
while attenuating low-frequency signals. This is due to the frequency-dependent
impedance of the capacitor C1.
 Low Frequencies: At low frequencies, the impedance of C1 is high, blocking the
signal and preventing it from passing through to the next stage.
 High Frequencies: At high frequencies, the impedance of C1 is low, allowing the
signal to pass through R3 to the inverting input of the Op-Amp.
Amplification:
 The filtered signal (mainly high-frequency components) at the junction of C1 and R3 is fed
into the inverting input of the Op-Amp.
 The Op-Amp amplifies this signal. The amount of amplification (gain) is determined by
the feedback network consisting of R1 and R2.

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Where:
AF = the Pass band Gain of the filter, ( 1 + R2/R1 )
ƒ = the Frequency of the Input Signal in Hertz, (Hz)
ƒc = the Cut-off Frequency in Hertz, (Hz)
Thus, the operation of a high pass active filter can be verified from the frequency gain equation
above as:
Output Signal (Vout):
 The amplified signal, now composed mainly of the high-frequency components of the
original input, is available at the output Vout.
 This output signal is a filtered and amplified version of the input signal, with low-frequency
noise or unwanted components significantly reduced.
3. Active Band Pass Filter
Active Band Pass Filter can be easily made by cascading together a single Low Pass Filter with
a single High Pass Filter as shown.

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 The cutoff frequencies are given as :
 As a result of these two reactive components, the filter will have a peak response
or Resonant Frequency ( ƒr ) at its “center frequency”, ƒc.

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4. Active Band Stop Filter
Active Band Stop Filter can be easily made by combine low and high pass filter sections to
produce a Band Stop
*******

Unit – 2: Wave form generators and Filters

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Unit – 2: Wave form generators and Filters