Figure 1: Block diagram of a function generator.

What is Function Generator?

A function generator is a signal source that produces various waveforms, such as sine, square, triangular, sawtooth, and pulse signals. The frequency, amplitude, and waveform type can often be controlled, making it versatile for different applications. These waveforms can be adjusted to specific requirements, depending on the use case.

Block Diagram of a Function Generator

The block diagram (like the one provided in your image) typically consists of the following components:

1. Frequency Control Network: This stage determines the frequency of the output waveform, which can be controlled manually or externally. External frequency control enables precise adjustment for synchronization.
2. Upper and Lower Constant Current Sources: These sources are responsible for generating a current that charges or discharges a capacitor to produce ramp-like signals for triangular and sawtooth waveforms.
3. Integrator: Converts the current into a voltage signal. By controlling the charging and discharging rates, different waveform slopes can be achieved.
4. Voltage Comparator and Multivibrator: This block compares the voltage from the integrator with a reference voltage, converting it into square waveforms or pulse signals.
5. Resistance-Diode Shaping Circuit: Used to shape the triangular or square waves into sine waves through nonlinear distortion.
6. Output Amplifiers: Amplify the generated waveforms and provide multiple outputs for driving different devices.

Types of Function Generators

Function generators can be classified into various types based on technology and usage:

1. Analog Function Generators: These use analog circuitry to generate signals and include components like operational amplifiers, resistors, capacitors, and diodes. Analog generators are cost-effective and reliable for basic applications.
2. Digital Function Generators: Digital function generators use digital signal processing (DSP) techniques to create waveforms. They offer greater precision, programmability, and flexibility in generating arbitrary waveforms.
3. Arbitrary Waveform Generators (AWGs): AWGs are advanced versions of digital function generators. They allow users to generate custom waveforms stored as data points in memory, making them highly versatile for specialized applications.
4. RF Function Generators: These are designed to operate at high frequencies, typically in the radio frequency (RF) range, for applications like communication testing.

Advantages of Function Generators

1. Versatility: Capable of producing multiple waveform types and frequencies.
2. Ease of Use: User-friendly interfaces with precise control over frequency, amplitude, and phase.
3. Cost-Effective: Basic analog models are affordable for educational and general-purpose use.
4. Integration: Many modern function generators include features like frequency counters and arbitrary waveform generation.
5. Wide Range of Applications: Suitable for R&D, production testing, educational labs, and more.

Disadvantages of Function Generators

1. Accuracy Limitations: Analog function generators have limited accuracy compared to digital models.
2. Complexity in Arbitrary Waveform Generation: Designing custom waveforms on arbitrary waveform generators may require specialized knowledge.
3. Frequency Range Limitations: Certain function generators may not cover very high or very low frequencies.
4. Distortion: At extreme ranges, waveforms may become distorted, impacting accuracy.

Applications of Function Generators

Function generators are essential tools in many fields. Some key applications include:

1. Testing and Debugging: Used to test circuits by simulating input signals. Debugging faults in communication, audio, and control systems.
2. Signal Simulation: Mimics real-world signals in systems like sensors and transducers.
3. Education and Training: Found in physics and electronics labs to demonstrate waveform characteristics.
4. Calibration: Serves as a reference signal source for calibration of other equipment.
5. Research and Development: Generates complex waveforms for experimental analysis and prototyping.
6. Communications: Produces modulated signals for testing communication systems.

Working of a Function Generator

1. Signal Generation: The frequency control network sets the base frequency. Current sources generate charging and discharging cycles for capacitors, which are processed to produce triangular, sine, and square waves.
2. Shaping Circuits: The resistance-diode shaping circuit converts triangular signals to approximate sine waves by manipulating voltage curves.
3. Output Delivery: Amplified waveforms are sent to the output terminals for use in external circuits.

Difference between Analog and Digital Function Generators

Conclusion

Function generators play a critical role in modern electronics, providing the flexibility to create, modify, and analyze signals in various domains. Their versatility, coupled with continuous advancements in technology, ensures their relevance in scientific research, industrial applications, and education. Understanding their design and operation allows engineers and students to harness their full potential effectively.

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Working Principle of a Toggle Switch

The working of a toggle switch is simple and involves mechanical movement:

1. The lever or handle of the switch is moved manually to change its position.
2. Depending on the switch type (e.g., SPST, SPDT), the movement of the lever either connects or disconnects the electrical circuit.
3. Internally, the movement aligns contacts to allow or interrupt the flow of current, completing or breaking the circuit.

Types of Toggle Switches

Advantages of Toggle Switches

1. Ease of Use: Simple design allows for easy operation.
2. Durability: Built to withstand frequent switching.
3. Versatility: Available in multiple configurations for varied applications.
4. Compact Size: Saves space in electronic devices.
5. Reliability: Provides consistent performance over time.

Disadvantages of Toggle Switches

1. Mechanical Wear: Frequent use may cause wear and tear over time.
2. Limited Current Capacity: Not suitable for high-current applications without proper design.
3. Manual Operation: Requires physical intervention for switching.
4. Design Constraints: Limited customization in aesthetic applications.

Applications of Toggle Switches

1. Home Appliances: Used in lighting systems, fans, and other household devices.
2. Automotive Industry: Controls lights, horns, and other functions in vehicles.
3. Industrial Equipment: Manages power and operational modes in machinery.
4. Aerospace: Found in control panels for aircraft systems.
5. Consumer Electronics: Incorporated in audio systems, computers, and gaming consoles.
6. Marine Applications: Used in boat control panels for navigation and lighting.
7. Testing and Prototyping: Commonly used in laboratories and test setups for circuit control.

Conclusion

Toggle switches are versatile, reliable, and widely used electrical components that provide a straightforward way to control circuits. With their various configurations and types, they cater to a broad range of applications, from household devices to industrial machinery. Proper maintenance and usage ensure their longevity and effectiveness.

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Working Principle of Thermistor

Thermistor have a Negative Temperature Coefficient (NTC) i.e. resistance decreases as the temperature increases. The materials used in the manufacture of thermistors include oxides of cobalt, nickel, copper, iron, uranium and manganese. The thermistor has very high temperature coefficient of resistance of the order of 3 to 5% per ºC. The resistance at any temperature T is given by,

\[{{R}_{T}}={{R}_{0}}\text{ exp }\beta \text{ }\left( \frac{1}{T}-\frac{1}{{{T}_{0}}} \right)\]

Where,

R_T – Thermistor resistance at temperature T (K)

R₀ – Thermistor resistance at temperature T₀ (K)

β – A constant determined by calibration

At high temperature, equation (1) reduces to,

\[{{R}_{T}}={{R}_{0}}\text{ exp }\left( \frac{\beta }{T} \right)\]

Working & Symbol of Thermistor

Figure 1.

The resistance-temperature characteristics is shown in Fig. 1 (b) and symbol in Fig. 1 (a). The curve is non-linear and the drop in resistance from 500Ω to 100Ω occurs for an increase in temperatures from 20 to 100ºC. The temperature of the device can be changed internally or externally. An increase in current through the device will raise its temperature carrying a drop in its terminal resistance. Any externally applied heat source will result in an increase in its body temperature and drop in resistance. This action tends itself well to control mechanisms.

Types of Thermistor

Figure 2: Various configurations of thermistor.

The thermistors are available in various configurations such as beads, disc, rod, washer as shown in Fig. 2. The smallest thermistors are made in the form of beads. Some are as small as 0.15 mm in diameter. And where greater power dissipation is required, thermistors obtained are in disc, washer or rod forms.

Advantages of Thermistor

1. Small size and low cost.
2. Fast response over narrow temperature range.
3. Good sensitivity in the NTC region.

Disadvantages of Thermistor

1. Non-linearity in resistance versus temperature characteristics.
2. Unsuitable for wide temperature range.
3. Very low excitation current to avoid self-heating.
4. Need of shielded power lines, filters etc. due to high resistance.

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When the anode terminal of a diode is connected to the negative terminal of voltage source and cathode to the positive terminal then the diode is reverse biased as shown in Fig. 1 (a) and its symbolic representation in Fig. 1 (b).

Operation of Reverse Biased PN Junction Diode

Figure 2: Reverse biased effect on layer and barrier voltage.

When an external bias is applied to a diode, positive to cathode and negative to anode, electrons from N-side are attracted to the positive terminal and holes from P-side are attracted to the negative terminal. As shown in Fig. 2, holes on P-side of junction are moved away from the junction and electrons are also moved away from the junction on N-side. This results in the depletion region to be widened and the barrier voltage to be increased.

As the barrier voltage at the junction increases, the holes and electrons are not able to cross the junction, hence the majority charge carrier current will be zero and the junction is said to be reverse biased. There will be very small reverse current due to minority charge carrier. Because of this very small reverse current flow, a reverse biased PN junction diode offers very high resistance. As there is no possibility of majority charge carriers the current flowing across a reverse biased junction, minority carriers i.e. holes on N-side and electrons on P-side, generated on each side can cross the reverse junction. The electrons on the P-side are attracted to the positive voltage crossing the junction on the N-side. The holes from N-side flow across to the negative voltage on P-side. Due to this, small current flows through the junction. Only a very small reverse bias voltage is necessary to move all available minority carriers across the junction and if voltage bias is increased further, current will not increase. And hence this current is referred as reverse saturation current. The reverse saturation current is very small ranging from nanoamperes to microamperes. It depends on the junction area, temperature and semiconductor material.

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Figure 1.

When anode is connected to the positive terminal of a battery/voltage source and cathode to the negative terminal, then the diode is said to be forward biased as shown in Fig. 1 (a) and its symbolic representation is shown in Fig. 1 (b).

Operation of Forward Biased PN Junction Diode

Figure 2: Forward biased effect on layer and barrier voltage.

When PN junction is forward biased, the holes (being positively charged) are repelled by the positive terminal of voltage source and forced to move towards the junction. Similarly, the electrons (negatively charged) are repelled by the negative terminal of voltage source and move towards the junction. As they get some energy from the voltage source, some of the holes and electrons enter the depletion layer and recombine themselves. This results in reduction in width of depletion layer and the barrier potential with forward bias as shown in Fig. 2. Therefore, it causes a large current to flow through the diode. When the applied bias voltage is increased from zero, the barrier voltage gets decrease until it effectively disappears and majority charge carriers easily flow across the junction. The electrons from N-side are now attracted across to the positive bias terminal on P-side and holes from the P-side flow across to the negative terminal on the N-side. Thus, a majority carrier current flows and the junction is said to be forward biased. This large current due to majority charged carrier in forward biased is called as forward current.

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Figure 1: V-I Characteristics of a PN Junction Diode.

VI Characteristics of pn junction diode, is a graph between the voltage applied across the terminals of a device and the current that flows through it. Fig. 1 shows the V-I characteristics of a typical PN junction diode with respect to breakdown voltage (V_BR). The complete V-I characteristics is divided into two parts, namely forward characteristic and reverse characteristic.

Forward characteristics :

Figure 2.

Fig. 2 (a) shows the circuit arrangement for obtaining forward characteristic of a diode. In this circuit, the diode is connected to a d.c. voltage (V_AA) through the potentiometer (P) and a resistance (R). The potentiometer helps in varying the voltage applied across the diode. The resistance (R) is included in the circuit, so as to limit the current through the diode. A voltmeter is connected across the diode to measure the voltage and milliammeter to measure the current in the circuit. The positive terminal of the voltage source is connected to the anode and the negative terminal to the cathode, hence the diode is worked in forward-biased condition. Increase the voltage and record the corresponding values of diode current. The graph between applied voltage and current is plotted as shown in Fig. 2 (b).

Forward characteristics show that no current flow till the point P is reached. It is due to the fact that, applied voltage is less than the junction voltage i.e. 0.7 V for Silicon and 0.3 V for Germanium. As the voltage is increased above point P, the diode current increases rapidly. The voltage at which the diode starts conducting is called a knee voltage, cut-in voltage or threshold voltage. The knee voltage is denoted by V_R or V_γ. Its value is 0.6 V for Si and 0.2 V for Ge.

Reverse characteristics :

The circuit arrangement for obtaining reverse characteristics of a diode is shown in Fig. 3 (a). In the circuit a diode is connected in reverse biased condition i.e. cathode is connected to the positive terminal of voltage source and anode to the negative terminal. The applied reverse voltage is gradually increased above zero and the values of diode current are measured. The graph plotted between reverse voltage and current is shown in Fig. 3 (b). The curve OCD is called reverse characteristics of a diode. The reverse characteristics indicate that when applied reverse voltage is less than breakdown voltage (V_BR), the diode current is small and remains constant. This current is called as reverse saturation current (I_o).

When reverse voltage is increased to a large value, the diode reverse current increases as rapidly as shown by curve CD in Fig. 3. The applied reverse voltage at which large current flows through the diode is known as breakdown (V_BR) voltage of a diode.

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Working Principle of Strain Gauge

Their working principle is based on piezo-resistive effect. The piezo-resistive effect states that if a metal conductor is stretched or compressed, its length and diameter changes. Therefore its resistance also gets changed. Similarly the resistance of a metal conductor changes when it is strained.

Fig. 1 shows an unstrained wire of elastic material with length L, Diameter: D and Area of cross-section = A.

\[R=\rho \frac{L}{A}=\rho \frac{L}{(\pi /4){{D}^{2}}}\]

\[R=\rho \frac{L}{A}=\rho \frac{L}{\left( \frac{\pi }{4} \right){{D}^{2}}}\]

Where,

ρ = Resistivity of the wire in Ω – m

If this wire of elastic material (Strain Gauge) is subjected to tension, its length increases and diameter reduces. These changes in the dimensions due to applied force are shown in Fig. 2.

Let the change in length = ΔL and change in diameter = ΔD. To find the change in resistance (ΔR) due to applied force we use Poisson’s ratio.

\[\text{Using Poisson ratio (}\mu \text{) = }\frac{(\Delta D/D)}{(\Delta L/L)}\]

But,

\[\frac{\Delta L}{L}=\sigma =\text{ Strain}\]

Therefore,

\[\Delta D=\mu .\sigma .D\]

Thus the change in resistance is given by ΔR = Rσ (1+2µ).

From the above equation, we can conclude that the resistance of the wire increases due the applied force. The gauge factor (G) of a strain gauge is defined as the unit change in resistance per unit change in length. Therefore,

\[G\text{= }\frac{(\Delta R/R)}{(\Delta L/L)}\] (Ranges from 1.5 to 1.7)

Types of Strain Gauge

The two types of strain gauges as

1. Bonded Strain Gauge
2. Unbonded Strain Gauge

Bonded Strain Gauge

Fig. 3: Bonded Type Strain Gauge.

A bonded strain gauge consists of a grid of fine wire which is fixed on a base of a thin paper sheet as shown in Fig. 3. The paper sheet is bonded with an adhesive to the spot under measurement. When force is applied to the surface, to which the strain gauge is bonded, the resistance of the grid wire changes due to the change in length and diameter of the wire. This change in the resistance can be measured by connecting the strain gauge in one of the arms of the Wheatstone bridge that generates equivalent voltage. The bonded strain gauge is useful only for measuring very small displacements. To measure large displacements, the strain gauge is bonded to a flexible element like cantilever beam. The displacement can then be measured at the end of the cantilever beam.

Unbonded Strain Gauge

Fig. 4: Unbonded Type Strain Gauge.

As shown in Fig. 4, an unbonded strain gauge is constructed by fitting the gauge wire on a stationary frame having a movable armature fixed at the centre. The armature can be moved only in one direction and its travel is limited by four strain gauge wires. If an external force is applied to the strain gauge or the armature is moved, the gauge wire gets stretched showing a proportional change in its resistance value which can be measured with the Wheatstone bridge. The output voltage of the Wheatstone bridge can be calibrated according to displacement of the armature.

Advantages of Strain Gauge

1. High accuracy and reliability.
2. Small size and easy to use.

Disadvantages of Strain Gauge

1. High cost.
2. The changes in temperature may affect the output.

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Types of Summing Amplifier (Adder) Using Op-Amp

Depending on the polarity or sign of the output voltage the adder circuits can be classified into two categories as :

1. Inverting adder and
2. Non-inverting adder.

Inverting Adder or Inverting Summing Amplifier

Figure 1: Summing Amplifier.

Fig. 1 shows the “inverting summing amplifier” configuration with three inputs V₁, V_2, and V₃. Depending on the relation between the feedback resistor R_F and the three input resistances R₁, R_2, and R₃ we can use the same circuit shown in Fig. 1 as a summing amplifier, scaling amplifier or averaging amplifier. V₁, V₂ and V₃ are three input signals applied simultaneously to the inverting terminal of the OP-AMP through resistors R₁, R₂ and R₃ respectively. V₁, V_2, and V₃ are measured with respect to ground. R_F is the feedback resistor, connected between the output terminal and the inverting input terminal of OP-AMP. The non-inverting input terminal is connected to ground. So the configuration of Fig. 1 is basically an inverting amplifier with three inputs. Let the currents through the resistors R₁, R₂ and R₃ be I₁, I₂ and I₃ respectively. For the analysis of this circuit, we assume that the OP-AMP is ideal. Hence its input resistance is R_i = ∞. Therefore the currents I_B1 and I_B2 are zero. In addition to this, Node A is at virtual ground potential.

Expression for the output voltage :

Apply KCL at node A of Fig. 1 to write,

\[{{I}_{1}}+{{I}_{2}}+{{I}_{3}}={{I}_{B2}}+{{I}_{F}}\]

But as R_i of the OP-AMP is ideally infinite, I_B2 = 0, and V_A = V_B = 0 due to virtual ground concept.

Hence,

\[{{I}_{1}}+{{I}_{2}}+{{I}_{3}}={{I}_{F}}\]

On the input side,

\[{{I}_{1}}=\frac{{{V}_{1}}-{{V}_{A}}}{{{R}_{1}}}=\frac{{{V}_{1}}}{{{R}_{1}}}\text{ as }{{V}_{A}}=0\]

Similarly,

\[{{I}_{2}}=\frac{{{V}_{2}}-{{V}_{A}}}{{{R}_{2}}}=\frac{{{V}_{2}}}{{{R}_{2}}}\]

\[{{I}_{3}}=\frac{{{V}_{3}}-{{V}_{A}}}{{{R}_{3}}}=\frac{{{V}_{o}}}{-{{R}_{3}}}\]

And on the output side,

\[{{I}_{F}}=\frac{{{V}_{A}}-{{V}_{o}}}{{{R}_{F}}}=-\frac{{{V}_{o}}}{-{{R}_{F}}}….(1)\]

Substituting these values in Equation (1) we get,

\[\frac{{{V}_{1}}}{{{R}_{1}}}+\frac{{{V}_{2}}}{{{R}_{2}}}+\frac{{{V}_{3}}}{{{R}_{3}}}=-\frac{{{V}_{o}}}{{{R}_{F}}}\]

Or,

\[{{V}_{o}}=-\left[ \frac{{{R}_{F}}}{{{R}_{1}}}{{V}_{1}}+\frac{{{R}_{F}}}{{{R}_{2}}}{{V}_{2}}+\frac{{{R}_{F}}}{{{R}_{3}}}{{V}_{3}} \right]\]

In Equation (1) if we substitute R_F = R₁ = R₂ = R₃ = R then we get,

\[{{V}_{o}}=-({{V}_{1}}+{{V}_{2}}+{{V}_{3}})\]

Thus output voltage is the negative sum of the input voltage. Therefore this circuit is called as “Inverting adder” or “Inverting summing amplifier”. Similarly, we can add any number of inputs.

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Figure 1: Voltage Follower (Buffer) Circuit Diagram.

Figure 2: Waveforms of Voltage Follower (Buffer).

Circuit diagram of Voltage Follower (Buffer) Using Op-Amp

When R₁ = ∞ and R_F = 0 the non-inverting amplifier gets converted into a voltage follower or unity gain amplifier. When the non-inverting amplifier is configured so as to obtain a gain of 1, it is called as a voltage follower or unity gain non-inverting buffer. The schematic diagram for a voltage follower is as shown in Fig. 1. The voltage follower configuration of Fig. 1 is obtained by short circuiting R_F and open circuiting R₁ connected in the usual non-inverting amplifier configuration of Fig. 1. Thus all the output voltage is fed back to the inverting input of the OP-AMP. Therefore the feedback factor of this circuit i.e. B = 1.

Closed Loop Voltage Gain (A_VF) of Voltage Follower (Buffer) Using Op-Amp

Consider the expression for the closed loop gain of a non-inverting amplifier, that is,

\[{{A}_{VF}}=1+\frac{{{R}_{F}}}{{{R}_{1}}}….(1)\]

In above equation 1, substitute the values of R_F = 0 and R₁ = ∞ to get the closed loop gain of the voltage follower as,

\[{{A}_{VF}}=1\]

Therefore the output voltage will be equal to and in phase with the input voltage, as shown in Fig. 2. Thus voltage follower is a non-inverting amplifier with a voltage gain of unity.

Why Voltage Follower is called a buffer?

A buffer is an electronic circuit that isolates the input from the output, providing either no voltage or a voltage that is the same as the input voltage. It has a voltage gain of unity (1). A voltage buffer must have a very high input impedance and very low output impedance so that it draws a very small current from input and can supply. Since a voltage follower circuit satisfies all these requirements, it is called as a buffer.

Applications of Voltage Follower (Buffer) Using Op-Amp

1. As a buffer amplifier so as to avoid the loading of the source.
2. It is used as the output stage because of its low R_o.
3. It can be used for impedance matching.

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Figure 1: Inverting Amplifier.

Circuit diagram of Inverting Amplifier Using Op-Amp

The circuit diagram of an inverting amplifier is as shown in Fig. 1. The signal which is to be amplified is applied at the inverting (-) input terminal of the OP-AMP.

Working and Waveforms of Inverting Amplifier Using Op-Amp

The signal to be amplified (V_s) has been connected to the inverting terminal via the resistance R₁. The other resistor R_F, connected between the output and inverting input terminals is called as the feedback resistance. It introduces a negative feedback. The non-inverting (+) input terminal is connected to ground. As the OP-AMP is an ideal one, its open loop voltage gain A_v = ∞ and input resistance R_i = ∞. The negative sign for A_v is due to the inverting configuration. The input and output voltage waveforms are as shown in Fig. 2. Output is an amplified and inverted version of the input signal V_S.

Closed Loop Voltage Gain (AVF) of Inverting Amplifier Using Op-Amp

Looking at Fig. 1 we can write that,

\[{{V}_{o}}=\left| {{A}_{v}} \right|\times {{V}_{d}}\]

\[{{V}_{d}}=\frac{{{V}_{o}}}{\left| {{A}_{v}} \right|}\]

Where,

A_v = Open loop gain of OP-AMP.

As we know an open loop gain of OP-AMP is ∞.

\[{{V}_{d}}=\frac{{{V}_{o}}}{\infty }=0\]

But,

\[{{V}_{d}}={{V}_{1}}-{{V}_{2}}\]

\[{{V}_{1}}-{{V}_{2}}=0….(1)\]

As the non-inverting (+) input terminal is connected to ground, V₁ = 0. Substituting this value in Equation (1) we get,

\[{{V}_{2}}=0\]

Thus V₂ is at ground potential. Since the input resistance R_i = ∞, the current going into the OP-AMP will be zero. Therefore the current “I” that passes through R₁ will also pass through R_F as shown in Fig. 1. As the input voltage V_S is being measured with respect to ground and as V₂ is at ground potential we can say that the input voltage V₂ is voltage across R₁ and voltage across R_F is output voltage. The input voltage, V_S is given by,

\[{{V}_{S}}=I\text{ }{{R}_{1}}….(2)\]

And the output voltage Vo is given by,

\[{{V}_{o}}=-I\text{ }{{R}_{F}}….(3)\]

We can write Equations (2) and (3) because V₂ is at approximately ground potential (virtual ground).

\[\text{Closed loop gain, }{{A}_{VF}}=\frac{{{V}_{o}}}{{{V}_{S}}}\]

Substituting the expression for V_o and V_S we get,

\[{{A}_{VF}}=-\frac{I{{R}_{F}}}{I{{R}_{1}}}=-\frac{{{R}_{F}}}{{{R}_{1}}}….(4)\]

And,

\[{{V}_{o}}={{A}_{VF}}\times {{V}_{S}}\]

Conclusions from the expression for A_VF :

From Equation (4) we can draw the following important conclusions :

1. The value of closed loop voltage gain A_VF does not depend on the value of open loop voltage gain A_v.
2. Value of A_VF can be very easily adjusted by adjusting the values of the resistors R_F and R_i. Generally the feedback resistor R_F is a potentiometer to adjust the gain to its desired value.
3. The output is an amplified inverted version of input.

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