Lab 11 - Freemat

Freemat

Objective:

Learn how to navigate through the mathematics application program(Freemat) to solve matrices and imaginary math problems

Process:
1. Assignment 1 - Use freemat to solve Nodal Analysis Equations

Result theoretically

Result verified in Freemat I_2 = -.01857

2. Assignment 2 - Use freemat for Imaginary Numbers operations

All 4 Problems

Problem 1 in Theory

Problem 1 in Freemat

Problem 2 in Theory

Problem 2 in Freemat

Problem 3 in Theory

Problem 3 in Freemat

Problem 4 is to input Imaginary Matrix into Freemat and solve 

Freemat verified correct answer on manual I_2 = 6.12<-35.22

Conclusion:

At the completion of the Feemat lab, assignments became much more feasible to accomplish because it took out computational error. This program is extremely practical, easy to learn, and will be used for the remainder of my academic career.   

Lab 10 - Practical Integrator

Practical Integrator

Objective:

Use an oscilloscope to display time-varying signals

Process:

1. In class Professor Mason used an opened oscilloscope to showcase what is inside the electronic instrument and how it works. It consists of an electric gun accelerating electrons towards a phosphor-coated display screen. This alone only yields one dot on the screen and moves only when electrostatic deflection is applied to it. The deflection plates are orientated horizontally left to right and vertically up or down causing a continuous signal varying with time to be displayed.

2. Problem
Sketch a circuit's input and output waveform for 1kHz sine wave, triangle wave, and square wave

3. Data Collected

In class demonstration - sine wave

Thats Prof. Mason!
Noise in the background illustrated because resistor was removed

square wave

Cosine wave

Conclusion:

The overall demonstration was peculiarly interesting from start to finish. To understand the how the instrument works and follow through to the product it produces, was remarkable to see what you can actually do with the material that is taught in class. Unfortunately, our camera equipment is not up to par and therefore could not capture the measurements of the waves. Although removal of the resistor did yield scratchy waves and input of it gave more smooth ones.

Lab 9 - Second Order Circuit

Second Order Circuit

Objective:

Practice online a second order circuit

Process:

1. Problem - Solve and input answer into online program about second order circuit

2. Data Collected

Conclusion:

The objective was met through completion of the problem

Lab 8 - Capacitor Charging/Discharging

Capacitor Charging/Discharging

Objective:

To charge and discharge a capacitor

Process:

1. Problem
      Design, build, and test a charge/discharge system that utilizes a 12v DC power supply, employs a charging interval of 20seconds with a resulting stored energy of 2.5mj and then discharges that 2.5mj in2seconds.

2. Circuit Calculations

Original Circuit

Computing R_th for t <0 and t > 0 of Capacitor

Calculating the Capacitance Required

Calculations for R_discharging and Peak Power and Current for Resistances

3.Built Circuit

4. Data Collected

Final Voltage recorded and length of time it took to discharge 

Time to discharge was 5.15seconds

5. Data Analyzed

Conclusion:

Given the constraints of the problem we were able to able to identify a specified capacitance by analyzing the circuit using the Thevenin resistance and voltage at the a time before it is charged and then discharged. This process fulfilled the objective of learning the practical use of a capacitor and yielded results in the 11% error range. Due to leakage resistance our final voltage digressed completely from our calculated value.
     

Lab 7 - Practical Signal Conditioning

Practical Signal Conditioning

Objective:

Use a scaling and level-shifting circuit to process the output signal from a temperature sensor to produce temperature reading in Fahrenheit.

Process:

1. Theory
         Scaling is defined as multiplying a current by a constant to change its amplitude while level-shifting is the process of adding a constant to the current.

2. Problem
         Turn room temperature degree reading Celsius into unit reading of Fahrenheit.

3. Given
         Use Semiconductor LM35
         R_1 = 1000 ohms
         V_in = +4 to +20volts

4. Circuit Calculations

Finding R_1 and R_2

Encountered an obstacle during caluculations as we noticed that breadboards only accept input of two voltages and we needed a third for V_ref leading to redesigning of circuit

Final design for Circuit 

5. Built Circuit

6. Data collected and analyzed

Conclusion:

During lab procedure we discovered that we did not have the appropriate equipment to proceed with the experiment and therefore had to alter the original circuit given to accommodate for our third voltage input. Once that was resolved we were able to get a a voltage measurement of the room in Fahrenheit with a 10% error rate meeting, the objective of amplifying the signal from Celsius.  

Lab 6 - Op Amp

Operational Amplifiers I

Objective:

Establish a sensor to a processing agent(micro-controller) by using a signal conditioning circuit in between otherwise known as an OP Amp with given restrictions.

Process:

1. Problem
          Design a circuit that increases the voltage range of a sensor from 0-1volts to 0-10volts at the microcontroller.

2. Given Constraints
         V_in = 0-1volts
         V_out = 0-10volts
         Current through sensor = 1mAmp
         Power = 30mVolt each
         V_source of sensor = 12volts

3.  Circuit Calculations

Establishing R_i and R_f

Establishng R_x , R_y, and R_th

4. Built Circuit

5. Data Collected

Measurement of individual components

Conclusion:

The objective was met through successful connection of a sensor to op amp to micro-controller. The gain calculated to produce the desired voltage of 10volts was -10 and verified in the data collected. As the input voltage increased to 1volt so did the output voltage to 9.96volts.  Unfortunately, currents at V_1 and V_2 could not be measured to analyze if the overall circuit satisfied the constraint of not having over 30mWatts of power.

Lab 5 - thevenin equivalents

Thevenin Equivalents

Objectives:

1. Model a Power System with multiple sources and loads to evaluate how an individual Load (titled #2) impacts the rest of the system designed.
2. Apply the Thevenin process to designed circuit using resistors as the load and cables in the System. Also, specify regulated power supplies to be independent voltage sources.

Process:

1. Problem
          Determine the smallest equivalent Load #2 resistance that can be successfully used and its power consumed, given voltage across Load #2. What voltage will exist at the terminals of Load #2 if we remove it (open-circuit/highest voltage) and what short-circuit current will flow if we replace Load #2 by a short?

2. Given Assumptions
          R_c1 = 1000 ohms
          R_c2 = R_c3 = 39 ohms
          R_L1 = 680 ohms
         V_s1 = V_s2 = 9 volts
         V_Load2min = 8 volts

3. Circuit Calculations
            A: Establish open circuit voltage

            B. Compute Thevenin reistance

            C. Determine R_load2

4. Built Circuit
            A. Thevenin Equivalent Circuit

            B. Original Circuit

5. Data Collected
            A. Thevenin Equivalent

            B. Original Circuit

6. Data Analyzed

Conclusion:

          The electrical circuit equivalent of the power system was given and used for analysis in identifying the impingement of R_Load2 illustrating Objective 1. To demonstrate Objective 2, R_Load2 was isolated using the Thevinin process by reducing the network down to an equivalent source and series resistance. Intermittently, nodal analysis was used to calculate the Vth that coupled the Rth for the Thevenin circuit. Measurements were taken to test the validity of the calculated values and yielded between 8 and 14 percent error. A second circuit was built to extract the value of R_Load2 and test the maximum power effect.