Control Systems: Open vs Closed Loop

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Questions and Answers

Which control system relies on a human operator to adjust the input for achieving the desired output?

  • Manual Control System (correct)
  • Automatic Control System
  • Open Loop Control System
  • Closed Loop Control System

Which of the following control systems does NOT use feedback to determine if the desired output has been achieved?

  • Manual Control System
  • Automatic Control System
  • Open Loop Control System (correct)
  • Closed Loop Control System

Which term defines the difference between the process variable and the set point after the system has stabilized?

  • Rise Time
  • Steady State Error (correct)
  • Settling Time
  • Overshoot

Which of the following is most closely associated with closed-loop control systems?

<p>Dependency on the generated output (B)</p> Signup and view all the answers

In control systems, what does 'overshoot' refer to?

<p>The maximum amount the response exceeds the final steady-state value. (C)</p> Signup and view all the answers

Which of the following describes 'rise time' in the context of control systems?

<p>The time for a response to increase from 10% to 90% of its final value. (B)</p> Signup and view all the answers

Which of the following is the correct formula for calculating Steady State Error?

<p>setpoint - final value (C)</p> Signup and view all the answers

What role does the 'Actuator' play in the described open loop system?

<p>Adjusts the valve opening and motor speed according to the controller signal. (D)</p> Signup and view all the answers

In an open loop system designed to control flow rate, what is the primary function of the 'controller'?

<p>To generate a signal that dictates valve opening and motor speed to achieve the required flow without feedback. (D)</p> Signup and view all the answers

In a closed-loop system, what is the main function of the PID controller?

<p>To compare the setpoint to the actual output, generate a control signal to minimize the error. (A)</p> Signup and view all the answers

Which component is unique to closed-loop systems when compared to open-loop systems?

<p>Sensor (B)</p> Signup and view all the answers

Which of the following is true of open-loop control?

<p>Control action is independent of the output. (B)</p> Signup and view all the answers

Why is it necessary to disconnect the circuit to connect the ammeter in series with the consumer when measuring current?

<p>To ensure the same current flows through both the ammeter and the consumer (D)</p> Signup and view all the answers

What is the purpose of connecting a voltmeter in parallel with a component when measuring voltage?

<p>To avoid affecting the voltage across the component. (C)</p> Signup and view all the answers

What does 'Accuracy' refer to in the context of measurement instruments?

<p>How close a measurement is to the true or accepted value. (D)</p> Signup and view all the answers

What is the definition of 'Tolerance' as it relates to measurement and instrumentation?

<p>The allowable variation from a specified value. (B)</p> Signup and view all the answers

What does the acronym 'NTC' stand for in the context of resistors?

<p>Negative Temperature Coefficient (C)</p> Signup and view all the answers

What happens to the resistance of an NTC thermistor as the temperature increases?

<p>It decreases (D)</p> Signup and view all the answers

Which of the following best describes a Light Dependent Resistor (LDR)?

<p>Its resistance decreases with increasing light intensity. (B)</p> Signup and view all the answers

What is the typical behavior of a PTC resistor as temperature increases?

<p>Resistance increases (B)</p> Signup and view all the answers

What is the 'dark resistance' of a Light Dependent Resistor (LDR)?

<p>The resistance when the LDR is in complete darkness. (D)</p> Signup and view all the answers

Which component is used to measure level on the PCT-100?

<p>Magnetostrictive transducer (D)</p> Signup and view all the answers

How does a platinum resistance thermometer (PRT) operate?

<p>By measuring changes in electrical resistance of platinum wire due to temperature. (C)</p> Signup and view all the answers

What is the function of a turbine flow meter?

<p>Measuring the rotational speed of a rotor caused by fluid flow. (B)</p> Signup and view all the answers

In a voltage divider, if $V_{in}$ is the input voltage, and $R_1$ and $R_2$ are the resistors, what is the output voltage $V_{out}$ across $R_2$?

<p>$V_{out} = V_{in} * (R_2 / (R_1 + R_2))$ (D)</p> Signup and view all the answers

What is a potentiometer primarily used for?

<p>Creating an adjustable voltage divider (B)</p> Signup and view all the answers

What does the term 'loading effect' refer to in the context of sensors?

<p>The impact of the measurement process on the system being measured. (C)</p> Signup and view all the answers

Why is a voltage follower used as a buffer?

<p>Both C and D (B)</p> Signup and view all the answers

In an inverting amplifier configuration with an op-amp, what is the phase relationship between the input and output signals?

<p>The signals are 180 degrees out of phase. (A)</p> Signup and view all the answers

In analogue electronics, what does "inverting" signify regarding the input and output signals of a circuit?

<p>A phase shift of 180 degrees between input and output. (D)</p> Signup and view all the answers

In an inverting operational amplifier circuit, which input terminal of the op-amp is connected to ground potential?

<p>The non-inverting input (+) (C)</p> Signup and view all the answers

Given an inverting amplifier circuit with an input resistor $R_1$ and a feedback resistor $R_2$, what is the voltage gain ( A ) of the amplifier?

<p>$A = - R_2 / R_1$ (A)</p> Signup and view all the answers

An operational amplifier is configured as a summing amplifier. If all input resistors are identical and equal to ( R_1 ), and the feedback resistor is ( R_2 ), what is the output voltage ( U_2 ) in terms of input voltages ( U_{in1} ), ( U_{in2} ), ..., ( U_{inn} )?

<p>$U_2 = - (R_2 / R_1) * (U_{in1} + U_{in2} + ... + U_{inn})$ (B)</p> Signup and view all the answers

In a summing amplifier, if you want each input to contribute equally to the output, what relationship should exist between the feedback resistor (( R_2 )) and the input resistors (( R_{1x} ))?

<p>All input resistors should be equal to the feedback resistor. (B)</p> Signup and view all the answers

A sensor's output is connected directly to a high impedance data acquisition system. What circuit configuration is best to use between the sensor and the acquisition system to minimize the measurement error due to loading effect?

<p>A voltage follower (A)</p> Signup and view all the answers

In a voltage follower circuit based on an operational amplifier, what is the relationship between the input and output voltages?

<p>Output voltage equals the input voltage. (A)</p> Signup and view all the answers

Which of the following is the most important consideration when utilizing sensors or instruments to monitor or control various physical parameters?

<p>Considering any loading effect. (A)</p> Signup and view all the answers

You have a sensor with a high output impedance that needs to be connected to a low impedance load. Which amplifier is best suited to minimize signal attenuation?

<p>Voltage follower (C)</p> Signup and view all the answers

Which of the following is the greatest advantage of using a voltage follower in a circuit?

<p>Impedance matching (D)</p> Signup and view all the answers

You are tasked with designing a circuit that sums three different voltage signals. Which operational amplifier configuration is most suitable?

<p>Summing amplifier (D)</p> Signup and view all the answers

Your temperature sensor has a non-linear response. To linearize the output, you decide to use a circuit that applies a mathematical function to the sensor's output. Which type of amplifier circuit is most suited for this task, assuming you need to both linearize and scale the response?

<p>A Logarithmic Amplifier followed by a Summing Amplifier (B)</p> Signup and view all the answers

Given that instrumentation sensors often exhibit sensitivity drift. Considering these factors and the need for minimal interaction., which single strategy will result in the MOST robust long-term performance for a critical system?

<p>Implementing an adaptive, closed-loop control system that relies on redundant sensors and a Kalman filter (D)</p> Signup and view all the answers

Flashcards

Manual Control System

A system where a human operator manually controls the input to achieve the desired output.

Automatic Control System

A system that regulates itself to maintain a desired output without continuous human intervention.

Open Loop Control System

A system where the output depends on the input but does not use feedback.

Closed Loop Control System

A system where the controlling action depends on the generated output, using feedback.

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Overshoot

The maximum amount by which the response exceeds the final steady state value.

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Steady State Error

The final difference between process variable and set point.

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Rise Time

The time taken for the response to increase from 10% to 90% of its final value.

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Settling Time

The time taken for the response to reach its final steady state value within tolerance.

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Input, setpoint

The required flow rate in a control system.

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Controller

Generates a signal to control the valve opening and DC motor speed without measuring the output.

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Actuator

Opens and closes the valve according to the controller's signal.

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Output

The actual flow rate in a control system.

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Process

Controls the flow rate and filling the tank.

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PID Controller

Compares the setpoint to the actual output measured and generates control signal.

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Accuracy

The degree to which a measurement correctly represents true value.

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Tolerance

The allowable variation from a specified value.

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NTC (Negative Temperature Coefficient)

Resistors with a negative temperature coefficient.

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PTC (Positive Temperature Coefficient)

Resistors with a positive temperature coefficient.

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Photoresistors, Light Dependent Resistor (LDR)

Reduce resistance as light intensity increases.

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Description of PCT 100 unit

Composed of the process tank, digital LCD displays and indicator lights.

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Temperature Measurement

Electrical resistance of platinum changes with the temperature.

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Flow Measurement

Turbine rotor placed in the path of flowing water is measured.

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Level Measurement

Achieved using a magnetostrictive transducer, float travel up and down.

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Voltage Divider Circuit

Open supply voltage by multimeter.

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Voltage Divider

Electronic circuit that divides voltage into two or more parts.

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Potentiometer

3 terminal with sliding contact that forms adjustable voltage divider.

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Operational Amplifier as Non-Inverting Amplifier

Maintaining the same polarity, typically amplify.

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Op-Amp Non-Inverting Amplifier

Electronic circuit used Op Amp.

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Operational Amplifier as Inverting Amplifier

Phase shift of 180 between input and output signal. Positive voltage becomes negative one.

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Operational Amplifier as Voltage Follower and Summing Circuit

Test the loading effect of one circuit by another.

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Voltage Follower

Fundamental consideration when using sensors or instruments to monitor.

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Loading Effect

Act of measuring or sensing quantity has an impact on the system.

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Voltage to Current Converter

A summing amplifier can be used to sum up.

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Solution for Loading Effect

High input impedance of amplifier

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Study Notes

Laboratory Experiment 1: Control Systems

  • The semester is Spring 2024/2025
  • The course is Measurement and Instrumentation with course code MET222
  • The notes are for engineering students
  • The lab experiment was performed at the Sharjah Maritime Academy
  • Performed on 22/01/2025, from 12:30 to 14:20 in room 11-03
  • The experiment is worth 4 marks and there are 8 papers
  • Understand the concept of open and close loop systems and compare their performance
  • The PCT 100 is used in this experiment
  • Control can be manual or automatic.

Manual Control System

  • A human operator manually controls the input to acheive the desired output

Automatic Control System

  • A system that regulates itself to maintain a desired output and does not require continuous human intervention.

Open Loop Control System

  • The output relies on the input, lacking feedback mechanism.

Closed Loop Control System

  • A system where, the controlling action relies on the generated system output, using feedback to control system states.

Overshoot

  • The maximum amount by which the response exceeds the final steady state value of the process variable and can be a percentage.

Steady State Error

  • The final difference between the process variable and the set point

Rise Time

  • The time it takes for the response to rise from 10% to 90% of its final steady state value.

Settling Time

  • The time required for the response to reach and remain within a specified tolerance band around its final steady state value eg 5% tolerance.

Open Loop Procedure

  • Switch on the computer and PCT 100 unit.
  • Open the training program on the computer and select an open loop.
  • Set the input to step function with SP = 40% and start the measurement.
  • Save the output after it reaches a steady state.
  • From the result find the parameters below: (0.75 Mark)
  • Overshooting: maximum point higher than setpoint – setpoint =0
  • Settle time: when it becomes stable, settling time = 6 s
  • Steady State Error: setpoint – final value = 2 -1.8 = 0.2 L/min
  • Draw the response time for open loop controller.
  • Draw a block diagram showing components and describe the open loop process

Open Loop Process Parameters

  • Input (Setpoint): Required flow rate
  • Controller: Generates a signal to control valve opening and DC motor speed according to the required rate without measuring the output.
  • Actuator: Opens/closes the valve based on the controller signal, adjusts motor speed to control pump speed.
  • Output: Actual flow rate.
  • Process: Controls the flow rate and filling of the tank.

Close Loop Procedure

  • Close the open loop and set the system to close loop which is flow control in PCT unit.
  • Set the value of PG to 4 and SP to 1.5.
  • Disable I & D parameters.
  • Start measurement and save the graph.
  • From the graph get the below values: (0.75 Mark)
  • Overshooting: maximum point higher than setpoint – setpoint 1.63 – 1.5=0.13 L/min
  • Settle time: when it becomes stable, settling time = 4.4 s
  • Steady State Error: setpoint – final value = 1.5 – 1.4= 0.1 L/min
  • Draw the time response for close loop controller.
  • Draw the block diagram and briefly describe each parameter for the close loop.

Close Loop Process Parameters

  • Input (Setpoint): Required flow rate.
  • PID Controller: Compares the setpoint to the actual output measured by sensor and generates the control signal based on the error between setpoint and actual output to minimize the error.
  • Actuator: Opens/closes the valve according to the controller signal and adjusts the motor speed to operate the pump.
  • Output: Actual flow rate.
  • Process: Controls flow rate and tank filling.
  • Sensor: Flow rate sensor

Comparison of Open loop and Closed loop System

  • Open loop system is independent of the output vs Close loop which depends on the output for control action
  • Open loop is simple with Controller+valve+dc motor component vs Close loop is complex with Controller+valve+dc motor+sensor components
  • Open loop is affected by disturbance vs Close loop is not

Laboratory Experiment 3: Specifications of Measuring Instruments

  • The semester is Spring 2024/2025
  • The course is Measurement and Instrumentation with course code MET222
  • Performed at the Sharjah Maritime Academy
  • Performed on 12.02.2025, from 12:30 – 14:20 in room 11-11
  • Worth two marks, there are 5 papers

Objective

  • To measure resistance using current and voltage circuits

Instruments & Equipment

  • Electronic Circuits Board
  • Resistors
  • Multimeter

Theory

  • Electrical quantities (Voltage and Current) require measuring devices.
  • Voltage measurement needs parallel connection while current measurement occurs in series
  • Current measurement needs circuit disconnection to connect in series, ensuring same current flow for consumers and measuring devices.
  • The ammeter shows the current flowing on the internal resistance of the voltmeter and in the resistor R

Current and Voltage Measurement

  • Voltage measurement connects Voltmeter in parallel
  • Current measurement connects Ammeter in series

Voltage Measurement Formula

  • VR = U * (R / (Ri + R))

Error Formula

  • Error (%) = (True value – Measured value) / True value

Measuring device characteristic

  • Accuracy:measurement, calculation, represents true value or reality directly
  • Tolerance: variation or deviation allowable
  • Precision: difference between a measured value and the arithmetic mean value

Procedure

  • Connect the circuit and set U = 5 V
  • Connect the circuit and set U = 5 V
  • Use a multimeter to measure the value of R, and enter readings in the table.
  • Measure the current and voltage for both consumers and enter the readings in the table.
  • Calculate error between measurements

Measuring resistor

  • Current circuits results in smaller errors when compared to voltage circuit in order to calculate the value of the low resistor (33 Ω)

Error analysis (2% tolerance)

  • If the first current circuit's error is less than 2%, the value complies with tolerance.
  • The second measurement value is a higher error than acceptable tolerance.
  • Current and voltage circuits provide the same error value to calculate the value of the high resistor (22 KΩ)

Maximum voltage measure

  • with multimeter is 1000V

Voltage error Measurement

  • Assuming minimum value is 40mV with a voltage reading at 22K Ω
  • Calculate
  • ± 0.5% of reading (4.99V)
  • ± 0.1% of FS, then +0.15% of span

Current Voltage Measurements

  • Input different voltage (V) given in tables
  • Mesaure current and voltage readings
  • Find precision value

Calculations

  • Use current circuit and 22Ω to find Ohm's Law, (R = V/I) and Precision.
  • Calculate Mean and Standard Deviation

Experiment 5: Resistors Sensors PTC, NTC and LDR

  • The semester is Spring 2024/2025
  • The course is Measurement and Instrumentation with course code MET222
  • Conducted at the Sharjah Maritime Academy
  • Performed on 05.03.2025, from 10:25 – 11:45 in room 11-11
  • 3 marks and has 4 papers

Objective:

  • To study the characteristics of NTC and PTC thermistor resistors.
  • To study and analyze the characteristics of LDR resistor.

Instruments & Equipment:

  • Electronic Circuits Board
  • NTC & PTC resistors
  • LDR resistor
  • Multimeter

NTC Resistors

  • Negative Temperature Coefficient
  • Resistance decreases as the temperature rises & conductivity improves when “hot”

PTC resistor

  • Positive Temperature Coefficient Commonly
  • commonly, resistance increases as temperature rises, improving conductivity when "cold"

Photoresistors

  • Light Dependent Resistor (LDR) reduces resistance as lights increases are wherever clear differences in luminance intensity need to be electronically

LDR Properties

  • An LDR comprises of a special semiconductor material.
  • In total darkness, it has a "dark resistance" of over 10MW.
  • Absorbing light increases conductivity by releasing charge carriers

Procedure

  • Connect the circuit and confirmation
  • For NTC, record voltage readings in a table as you adjust the DC source
  • For PTC, repeat voltage measurements by increasing DC valures and stable current readings in the second reading
  • For LDR, record voltage measurements with the multimeter and calculate R for value

Results

  • In NTC, as the current increases, temperature increases, but increasing current and temperature, the NTC decreases.
  • In PTC, as the current increases, temperature increases and the PTC increases
  • In LDR, as the voltage increases, the current and light intensity from the source increase. When Light Increase the LDR resistance decrease.

Laboratory Experiment 2: Sensors

  • The semester is Spring 2024/2025
  • The course is Measurement and Instrumentation with course code MET222
  • Conducted at the Sharjah Maritime Academy
  • Conducted on 05.02.2025, from 12:30 – 14:20 in room 11-11
  • 3 marks, has 9 papers

Objective

  • To study the characteristics of level, flow, and temperature transducers

Instruments & Equipment

  • Multimeter
  • PCT-100

Temperature Measurement (PCT-100)

  • The temperatures range from 10°C to 60°C
  • Platinum resistance thermometers (PRT) are used which operates on resistance of platinum which changes with temperature.
  • Electrical resistance of platinum increases approximately linearly with absolute temperature & reading converted to temperature using a calibration equation.
  • Measure voltage through the voltmeter by measuring current through the wire

Flow Measurement (PCT)

  • Turbine flow rate sensor measures water flow rate and rotational speed of the mechanical rotor, with magnets fitted to rotor blades
  • Frequency of passing rotor blades (pickup point) generates pulse
  • The higher rate of water flow increases the turn of rotors and gives high pulse numbers.

Level Measurement (PCT-100)

  • magnetostrictive transducer makes measurements, using magnetostrictive level transmitter
  • a float in transmitter stem detects the level by magnetic elements inside the float
  • Electronic circuit with specific frequency, which sends short current through the entire length
  • Torsional force that travels and it measures with time-of-flight (TOF) is precise value present in level signals.

PCT 100 main components:

  • Process tank, Digital LCD displays, Indicator lights, Heater, Pressure relief valve, One way check valve, Needle valve, 2/2 Proportional drain valve, Sump tank, Float switch, Pressure transducer, Level sensor, Overflow/Vent valve, Flow rate sensor, Cooler Unit, 2/2 Proportional control valve, 3/2 Diverter valve, Variable speed pump with filter and pressure switch & Sump tank temperature sensor (PRT)

Level Sensor Procedure

  • Switch on both the computer and PCT 100 unit.
  • On the computer, train program and select manual control
  • Tank liquid level increases by by setting pump control and flow control to 100%. Then close pump with “F2”
  • Measure the output

Flow Sensor Procedure:

  • Open the training program on the computer and select manual control
  • Then the flow rate value recorded in the table after set the flow control to 100

Temperature Sensor Procedure:

  • Liquid level increasing with pump control on 100%
  • Close it when 40% is reached with pump control on "F2.

Graph Observations:

  • Level Sensor exhibits between level and voltage relation, rising level, the voltage shows an increase.

Level measurement Graph

  • Considers two points to linear graph relation
  • Voltage at 85% determined

Flow Rate -Voltage:

  • linear relation to flow rate and voltage. If flow shows increase, the voltage shows increase.

Flow rate-voltage graphs

  • 1.25 L/m has voltage to find out graph relation

###Temperature Graph

  • Relations between temperature and voltage, if temperature increases graph relation shows increases.

Comparing Manual control to automatic

  • Required human intervention to perform actions Manual

###Manual control properties

  • High precision Accuracy and Precision
  • Fast response time Slow
  • Over than one cost
  • Highly scalable scalability

Experiment 4: Voltage Divider Circuit

  • Spring 2024/2025 Semester
  • Marine Engineering Technology Department
  • Instrumentation and Measurements/MET222 Course Code
  • By Eng. Ibtihal Ahmed
  • Performed on 19.02.2025 from 12:30 – 14:20
  • Located in 11-11 Room Number
  • The grade was 3 with 6 papers

Lab Objective

  • Connect and explore the potentiometer and voltage divider circuit

Equipment

  • Electronic Circuits Board
  • Resistors
  • Multimeter
  • Potentiometer

Voltage Divider and Potentiometer theory

A voltage divider divides voltage into two or more parts, and the voltage crosses the resistance is proportional to resistance depending in relation to resistance

The Potentiometer

Three-terminal and adjustable is called the potentiometer, it can be adjustment with manual for adjusting two fixed electrical terminals.

The Output

  • The output can be shown as function depend of the ratio between it and voltages with resistors

Calculate Value

Connect the given circuit, then supply is turned on with multimeter

Comparing Values

Find 470 and 1000 in value parallel to compare then use V=IR to divide values

Calculating Gain

Find gain using this circuit VBG and VCG in a specific table

###Laboratory Experiment 6: Operational Amplifier as Non-Inverting Amplifier

###Objective Learn how to use an operational amplifier to assemble a non-inverting amplifier. Examine amplifier gain and how it can be changed.

###Instruments & Equipment: Electronic Circuits Board Resistors Multimeter Potentiometers Op-Amps

###Theory An op-amp non-inverting amplifier is an electronic circuit that uses an operational amplifier (op-amp) to amplify an input signal while maintaining the same polarity as the input. This configuration is typically used to provide signal amplification and impedance matching. The output is then measured

Procedure

1 . Connect the circuits, as the value is changed for Voltage Divided 2 . Set the Volts 3 . Then calculate the values using gain from

Lab Values and Equations

Formulas:

  1. Voltage and Resistor formulas can be compared, tested, and determined

Equations:

  • U1=…

Lab Results

  1. Regarding circuits using gain it can be amplified through Voltage and Gain

###Exercising Theory

  1. Given some values in an equation, can be determine through gain the different formulas

###Laboratory Experiment 7: Operational Amplifier as Inverting Amplifier

Objective:

Understand to connect Op amp circuit so it can act as an inverting amplifier

Equipment:

  • Electronic Circuits Board
  • Resistors
  • Multimeter
  • Potentiometer
  • Op-amp

Theory:

inverting it can measure phase shift with output signals, If that measure voltage change it will have cause to voltage decreases vice versa, The Descriptive formulas use a minus symbol the inversion to know what value.

To create amp inverting

Connect the input

Procedure:

Connect figure show below from Circuits Board, Input voltages and using those measure the voltage As increase the R2 the voltage out increase

Formulas

Calculation

Voltage Resistors

Experiment 8: Operational Amplifier as Voltage Follower and Summing Circuit Objectives

  • Understand and test the loading effect of one circuit by another, which is one of the most important concerns in analogy signal conditioning.
  • Learn how to use an operational amplifier to assemble a voltage follower (buffer circuit).
  • Understand and implement the Op amp circuit connection to act as a summing amplifier. Instruments & Equipment:
  • Electronic Circuits Board
  • Resistors
  • Multimeter
  • Potentiometer
  • Op-Amp

Theory:

Voltage Follower: The loading effect in sensors refers to the impact that the act of measuring or sensing a quantity has on the system or process being measured. This effect is a fundamental consideration when using sensors or instruments to monitor or control various physical parameters. The loading effect can introduce changes or disturbances in the system, which may affect the accuracy and reliability of the measurement. The most common loading effect in sensors is electrical loading. When a sensor is connected, it often draws some current or voltage from the system being measured. This can affect the accuracy of the measurement, especially if the system's characteristics change as a result. As a solution, a voltage follower can be used as a buffer because it draws little current due to the high input impedance of the amplifier, thus eliminating loading effects while still maintaining the same voltage at the output.

Procedure:

Voltage Follower: Using the voltage divider circuit in Figure below, change the value of potentiometer and then calculate the bi-polarity range of the output voltage V_BG which is voltage 𝑉𝑑.
Range of 𝑽𝒅 = 4.85 V– 64 mV Max value of 𝑉𝑑 = 2.935 𝑉
Min value of 𝑉𝑑 = 51.5 mV Comment on these results compared to step 1 results after connecting load: When the load connected the voltage drops due to loading effect.

Graph Values

A range from 4.56 to 46mV can be recorded the measure Input and output can be relate with a relation A summing amplifier can be used to sum up any input voltages with a 180° phase shift on the output. You can expand the input side of the circuit to any number of inputs. U2: = - Uin1 + (-0.45 (4.6 V)) = - Uin1 – 2.07 V = -8.17V

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