03/10/2016

03/10/2016: More on Mesh Current

I. Introduction:

We continued where we left with on Tuesday, which was about Mesh Current.

Here we were asked to solve the circuit using Mesh analysis. We took a look of the inner meshes, which were 3 of them. We set up the equations to solve the 3 unknowns

i1, i2, and i3 are respectively -2.57A, -.342A, and 0.428A

II. Compared the node voltage method with Mesh analysis

There would be some situations where meshes produce less equations compared to the nodal analysis; therefore, easier to solve. However, nodal would be more powerful for parallel circuit.

Another example of three meshes, three equations and three unknowns, our goal is to find the voltage across the 6.8kOhm

While Sam was setting the circuit, I was doing the every circuit to make sure that our work was correct, which it was

II. Experiment:
1. Experiment 1:
Here we were given 4 resistors as shown below. Our goal was to verify that our pre-lab calculation was correct using Analog Discovery

Here were our recorded values for each of the resistors, with color code next to it

The voltage is 5v, and current is 0.332mA, which matched up with our pre-lab values

Here was the close view of the set up

Here was our data

The difference of error is 3 percent, which was in the acceptable range 

Here is a close view of diode ,which is a semiconductor allowing the flow of current in one direction only

III. BJT Tracer:

We already had Beta, which was about 50, we solved for IB=165 micro A. Then we plugged it back to solve V_o

Using the lab manual, we set up the scale for graph we were going to collect

A close view of the circuit with the 2N304 transistor

IV. Conclusion;

Today, we kept going with the mesh analysis. We spent some of our time setting up the circuit and test for many parts, such as the voltage and current across a specific resistor. We learned the concept of the diode- which was a semi-conductor. And transistor, which collects the current and gives a greater output

03-17-2016

03-17-2016: Thevenin Equivalent, Norton Equivalent

I. Introduction:

Here was the idea of Thevenin problem- if we changed one component in the circuit, it would make us to redo the whole calculation. The idea of Thevenin is that we can treat part of the circuit we don't need to know, and replace it with a voltage source and a resistor.

Using the everycircuit to check our work, which turned out to be correct

II. Thevenin equivalent concept:

If we just need to focus on element in the circuit (eg a resistor), then we have to redo the calculation for the circuit every time we make that decision,but with Thevenin, founded by Thevenin, a French engineer, we could replace our circuit with a voltage source (or current source if a Norton equivalent) and a resistor.

For thevenin equivalent, to find Vth, we open circuit that branch. To find ith, we short circuit that branch. To find Rth, we could take Vth/ith or we could use the test source method ( for this method, we keep the dependent source, for the independent current source, we open circuit, for the independent voltage source, we short circuit)

Here we were trying to find the Rth. We short circuit the voltage source and open circuit the current source. and find the Rth

II. Practicing finding the Rth equivalent using the combining Requi

We were practicing finding th Rth of the circuit. By following the rules as shown above, it would be faster using this method comparing to find the Isc in thevenin.

III. Power Load Part 1:
1. lab
We obtained many ressitors, to set up the thevenin circuit given by Professor Mason in the lab manual

Before we actually did the work, we checked the perecent error of all the resistors, which usually less than +-5%

We used the everycircuit to check the result of our lab.

Our data for percent comparing between the theoretical result to the experimental results

The formula for P=V^2/R. We used the "pot" to vary our resistance, we found 10 data points and ajjust

Here is our data table, the nax power is associated with the highest power

IV. Conclusion and Summary
For today lab, we spent most of our time learning about Thevenin equivalent, including finding the Thevenin voltage, resistance, and Norton current. We spend the other half of our time doing the lab work to verify with our results. The numbers had some small errors due to the fact that those resistors had their percentage resistance error

03-15-2016

03-15-2016: Lab: Input wave in different form, change the voltage ratio

I. Introduction:

We depicted the behavior of the wave due to its geometry over the course of time

For this lab, we were going to put sinusoidal voltage wave, square wave, and triangular wave and observe the change in the amplitude of the wave

We recorded and compared the values of the theoretical and experimental value of two different resistors.

After some offset, we were able to have a better look at the graph

The shape of the square waves were different, here the amplitude was 2.5V, which was what we had expected

Here was the set up of the circuit, we used the red wire for 5V and yellow wire for 3V

Using the voltage division to find out the output voltage

II. Continue with Mesh Analysis:

We were asked to find the current in loop 1 and loop 2. There were two loops and two unknowns, we can solve the problem

To verify our work, I performed the mesh analysis to find the total current, while Sam used the nodal analysis, the results were the same, which means our answers were correct

II. Lab:

We set up the same circuit and used the Analog Discovery to verify that our result was correct

Here was close view of our set up. We were measuring the voltage across one of our resistors to make sure that we had a closed circuit

We combined the resistors to find the R_eq. It is actually better to see if we redraw the combination of the resistors

III. Source Transformation:
The concept here was bout turn in parallel current source to voltage source in series, and vice versa, but we should not modify the branch that we want to find.

After 4 source transformation, we ended up with one circuit, which was much easier to solve

IV. Conclusion:
Today we spent half of our time to do the prelab(mostly about the mesh analysis) and with the square wave, triangular and sinusoidal wave, we observed that their amplitudes behaved tge same. We also learned about the source transformation, which was an easy on solving, but it took a great amount of time to redraw those circuits. We also did some labs to verify our results were correct in the prelab.

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03/08/2016

03-08-2016: Keep Going With Nodal Analysis

I. Introduction:

Last week, we were introduced to some nodal analysis problem, which had some more advantages over the Kirchoff's Law we did back then in 4B. Next. we were given a problem introducing the concept of super node

Today we were given the problem about super node. The concept was little hard to understand at first- if there was volt meter between the two essential nodes, we can treat at one super node and write one more restriction equation. After a few practices, we got better at it

Here is Professor Mason work for the super-node problem

V_1 is the voltage across the resistor on the left, V2 is across the bottom, and V3 is across the right hand side

We were asked to find the uncertainty in range measurement. We did that by choosing V2 and V1 to be maximum, then  set it to be minimum to find the output of the calculation. Fortunately, the change is not really significance (if we use 3 significant figures, then there is no change)

II. Lab:
We were asked to set up the same circuit using analog discovery to analyze. The 3V source would come from the yellow wire- wave function generator

Our recording of the three resistors

Setup and results to prove that our pre-lab calculation is correct

A close view of how we set up. Notice that the yellow wire stands for the 3V source

here is calculation for the percent error, which was about 4.36 percent and in the acceptable range

III. Mesh Analysis:
We were introduced to the mesh analysis, which was sort of the opposite way of solving problem compare to nodal analysis. We defined the loops inside to be mesh 1 and mesh 2, therefore, we should have two equations

We wrote down two equations of i1 and i2, then we used freemat to solve for i1 and i2

We used every circuit to check our result. It took us a while to figure out we had to ground the circuit to run it

At the very last moment, Professor Mason asked us the color code of the resistors we learned in 4B. The one we used are 4 band, with the 3rd band is the exponent, and the last one is percent error.

V. Conclusion:

Today we spent most of our time learning the supernode method and did some more practices for the nodal analysis. Then we did the lab to verify our number, which was correct. Then, we learned the concept of the mesh current, which was the opposite method to solve the circuit compared to the nodal analysis. Lastly, we reviewed the color code for the resistors we learned in 4B

03/03/2016

03/03/2016: Temperature Measurement System

I. Introduction:

For today lab, we were going to desing a circuit whose output voltage provides a temperature measurement. A thermistor- a device with resistance changes with temperature- is used to sense the temperature. There were three things about this lab we had to pay attention to:

-5V input voltage to the system

-output voltage varies by a minimum of 0.5 V over a temperature range of 25 to 37 degree celcius

-output voltage must increase a temperature increases

here we had 8 bit machine, therefore, there were a total of 256 values. the voltage resolution would be 5/255 =0.01996V. Since delta V=0.5, we would have 25 counts

II. Calculation:

Here we were back to the voltage divider. We know that Vout/5= 5/(R_th+R). And we were given delta Vout as 0.5 Solve the quadratic equation, we came up with two values for R. We picked the lower resistance to be our choice of resistance

III. Setting up the circuit

The circuit was easy to set up since everything was in circuit to each other.

We picked the blue resistor to be our resistor (there was some random resistor, we had to double check to make sure we got the right one. We let the circuit sit in the room temperature (25) and read the measurement, which was about 1.51V. Then we firmly pressed the thermistor, the voltage increased to 2.04V, we found the experimental delta V to be 0.53V, which was bout 6% percet error

V. Post Lab Question:
Using the thermistor provided in this lab, we had to design a temperature measurement system which meets the following requirements:
1. The output must increase as the temperature increases
2. The output sensitivity of the device must be at least 0.1V/degree Cel

Vmax here is Vout. V max must be 44.4V or V=0.563, which is impossible to implement given all the lab device

IV. Node Voltage Method:
Applied the voltage method to annalyze the circuit

Here we chose the ground to be the lower node. Applied node voltage to essential nodes, we were able to find the V1, V2 respectively

VI. Summary:

Today we spent most of our time on temperature measurement system lab. The percent error was 6 percent, which was acceptable. We also learned the new techique to annalyze and solve for circuit element using node method. Node method is utilized to take away one variable in the system of equations, which makes it easier to solve for.