Day 9 3/22 Max power applications source modeling

At the beginning of the class, we first learn about max power transfer

The Thevenin equivalent is useful in finding the maximum power a linear circuit can deliver to a load. We assume that we can adjust the load resistance R_L .

In this photo, if the entire circuit is replaced by its Thevenin equivalent except for the load, as shown, the power delivered to the load is the equation we write on the whiteboard. Then we make a sketch of the power as a function of load resistance.

In this photo, to find the point of  maximum power transfer, we differentiate p in the equation above with respect to R_L and set the result equal to zero. And in the end we find that Rth=RL.

Maximum power is transferred to the load when the load resistance equals the

Thevenin resistance as seen from the load (R_L = R_Th ).

Then we did an example about max power.

In this photo,we  obtain the Thevenin equivalent at terminals a-b and Find R_L for maximum power

In this photo, we did an example to find the Rth=0.0527 ohms Pmax=732W

In this photo, we find the value R_L for maximum power transfer .

Lab: Maximum Power Transfer

Purpose: to attempt to maximize power transfer to a load by modifying the source circuit. Also, we will see that this approach is inappropriate; the maximum power transfer theorem does not apply in reverse.

The professor didn't let us do the pre-lab, but do the lab instead.

In this photo, here is our set up.

In this photo, we use Rs= 4.6 kohms.

In this photo, we change the value of RL and make a table about Vout and the power and we find that max power is 1.33*10^-3 when RL=5K ohms, which is same as Rs=4.7k ohms.

Then we learn about source modeling

In this photo, we did an example to calculate the source voltage v s and internal resistance R s . Then we determine the voltage when an 8-Ohm load is connected to the source.

Summary:

Today, we learn maximum power transform. It is important to transfer maximum power to the load. In order to do that, the load resistance should equal the Thevenin resistance. We also learn that souce modeling, power sources contain an internal resistance and how to calculate the resistance.

DAY7 3/15 Superposition and Source Transformation

Lab1: Time-varying Signals

Purpose: We need to get familiar of suing wave form generator to generate time varying signals and use oscilloscope to measure it.

In this photo, it is the graph we need to connect and measure. We choose R1=R2=1000ohm.

Pre-lab question:

In this photo, we draw graphs of sinusoidal, triangular and square wave with amplitude A and period T

In this photo, we measure the true value of these two resistors and compare with theo values.

 In these two photos, we uses input voltage 5 Vwith 2kHz frequency. Here is the set up and we measuere the Vout=2.5V

In this photo,it is the graph of sin wave.  As the picture shows,the frequency and period are its original value but the amplitude become half 

 In this photo,it is the graph of  triangular  wave.  As the picture shows,the frequency and period are its original value but the amplitude become half

In this photo, it is the graph of square wave.  The frequency and period are its original value. The amplitude become half. 

Next,we learn about Linearity Property

In this photo, we use mesh circult to find I0=0.316A

 In the next, we learn about superpostion.

In this photo, we did an example about superposition and check it with nodal analysis.

 LAB2 : Superposition 

Purpose: Learn how to analy build and tese a circuit containing multiple sources. Use circuit reduction techniques in conjunction with superpostion to determine the response of a circuit with multiple sources.

Pre-lab Question:

In this photo, we first with the 3V source replaced with a short circuit and find the V= 0.71V and then we with the 5V source replaced with a short circuit and find the V=2V, so the total V=2.71V

In this photo, we measure the 5 different resistors and compare with their theo values.

In this photo, we set up the circult and measure that the V=2.71, which is same with what we calculate.

In this photo, we make a table, it is the measured voltage V due to the 5V source alone.  The expected value of the voltage due to the 5V source.  The measured voltage V due to the 3V source alone. The expected value of the voltage due to the 3V source. The measured voltage V due to both sources. The expected value of the voltage due to both sources from your pre-lab

Then we learn about Source Transformation

In this photo, we use the soure transformation to use current in the end find the I0=2.9A

But in this photo, professor use the voltage in the end and fing the I=1/9 A

Summary:

Today, we first did the lab of Time-varying signals and know the different of the graph sina, tranigal and square.Then we learn about Linearity Property and superpostion. And we did another lab about superposition. In the end of the class, we learn soure transformation.

Day8 3/17 Theveninb

Today, in class, we first learn about Thevenin's Therorem.

In this photo, we let RL=6 ohms and use everycircuit in computer to show the 

current and voltage.

In this photo, we did another example to understand thevenin therorem. We find the thevenin equivalent by R

Lab: Thevenin's Theorem

Purpose:We need to show the work of Thevenin's Theorem. We will determine a Thevenin equivalent for a given circuit; then determine the Thevenin resistance and the open circuit voltage to create the Thevenin equivalent circuit.
Pre- lab Question:

In this photo, we first find the olad resistor Rth=RL=7.4kohm, then we use the mesh equtions to find the Vth=0.46V.

In this photo, we use every circle to check our work and we find what we get is correct.

In this photo, we measure the true value of our resistor that we use in the circuit. The differences of the resistor might be a source of errors in this experiment. 

In this photo, it is our set up of this experiment.

Then we use the set up tp measure that the Vth=0.451V

In this photo, we find the percent error of Vth is 2.17%, then we put the load resistor into the circle and find that Vth=0.2V and find the percent error is.-1.5% 

In the next, we use a potentiometer to replace the load resistor. It can provide various resistance . We measured the resistance of the potentiometer, and record the voltage across it

 In this photo, it is the set up of the circuit.

In this photo, we change the value of resistor of potentiometer and measure the V and then calculate the power.

In this photo, We get  average power is 1.13*10^-6, maximum power to be 1.84*10^-6 W, when the load resistance is 620 ohm. 

Summary:

In today’s lab, we learn about Thevenin’s Theorem, and build circuits using Thevenin’s Theorem. 

Day 6 3/10 Mesh analysis and transistors

At the beginning of the class, we did a quiz about mesh analysis. 

In this photo, we use mesh analysis and create three equations and there are three unknown and we can find the i in each loop and find the I is 1.2A.

Then we learn MESH ANALYSIS WITH CURRENT SOURCES. The key is a supermesh results when two meshes have a (dependent or independent)
current source in common. 

In this photo, we use the mesh analysis with current sources and set up 3 equations and find the i1 =-2.57A and i2=-0.34A and i3=0.428A.

NODAL VS MESH ANALYSIS

In this photo, we list some different betwwen nodal analysis and mesh analysis.

Mesh analysis:
Networks that contain many series-connected elements, voltage sources, or supermeshes. a circuit with fewer meshes than nodes is better analyzed using mesh analysis.  
Nodal Analysis:
Networks with parallel-connected elements, current sources, or supernodes are more suitable for nodal analysis.   A circuit with fewer nodes than meshes is better analyzed using nodal analysis
The key is to select the method that results in the smaller number of equations. 

Lab： Mesh Analysis 2

Pre-lab question:

Purpose: the purpose of the lab is to use mesh analysis to calculate the theoretical voltage across 6.8k ohms and current I1. Then, compare the theoretical voltage and current with the experimental values. 

In this photo, we calculate the I1=-3.22*10^-4A and V1=-5V.

In this photo, we use the everycircle to see that if our solution is right. Then we find our data is right.

In this photo,We first measured the resistors in circuit and compare them with theoretical values.

In this photo, The set up of the circuit as the picture shown.

The picture shows the experimental value of V1 which is -5V and I1=-0.33mA

In this photo, here is a summary  of data and percent differences of voltage V1  and current I1. The percent differences of the voltage  is 0. the percent differences of the i1 is 3%. The error might be caused by the inaccuracy of resistors and some resistance in the wire.

Then we learn about Circuit Analysis of Transistors 

In this photo, we did an exercise about Circuit Analysis of Transistors and we find that V0=5.175V.

Lab 2: A BJT Curve Tracer 

Purpose: we need to find the collector current, and the relationship of IC vs. collector voltage, VCE characteristics of the BJT. The kit of parts the student has will contain a number of transistors.

In this photo, we find the true value of 100Kohm resistor which is 98.2 Kohm.

In these photos,the left one is NPN transisotr. the right one, it is the set up of the experiment.

In this photo, here are our first input wave (Channel 1) and second input wave (Channel 2).

In this photo.here is the oscilloscope of the wave it detected.

Summary:

In the beginning of today's class, we take a group quiz, and later on, we finish a mesh analysis lab. we learn about dioda and talked about the Transistors (NPN and PNP).  Now, we can use a lot of ways to solving circuit problems.Then we introduce BJT, and figure out how BJT works.