04-12-2016

04/12/2016

Review of Capacitor and Inductor Lab

I. Introduction:

Today we spent most of our time reviewing all the knowledge we had learned in 4B class,specifically the capacitors and inductors, their relationships with currents, resistors, and voltage.

Professor Mason introduced us to rage bridge, which was the complex combination of capacitors. Due to the fact that the bridge had a large spark because the mechanical engineer designed the bridge, not an electrical engineer.

 2. Design of capacitor:

Here is our simple design of capacitor. We believed that we could design a variable capacitor by pumping in and out the dielectric oil; however, the downs side is that the dielectric oil would be dried out eventually

We knew that I=cdV/dt. P=VI=Cvdv/dt. We then take the integral with respect to t to find the total energy

Given the current graph with respect to time of a capacitor. We had to plot a graph of voltage with respect to time. Our approach was to use the formula I=c*dV/dt. therefore, V=Ict

Given the circuit with a capacitor on the top. Our goal is to find the current of i2. Since we already knew the current in the loop 1, we used mesh analysis to find the current in loop 2, therefore, we could find the voltage across resistor R2

We were given some more sinusoidal graph of voltage and triangular wave of voltage. Our goal is to find the graphs of current over time, using the fact that I=cdV/dt. We could find the corresponding graph of current over time

 II. Lab: Capacitor and Voltage in the circuit
1. Introduction:
 Our goal is to find out the relationship between the capacitor and the current pass through that capacitor over time. Using the two graphs we had derived previously for the prelab, we expected our experimental labs should look the same

The blue graph measures the voltage across the capacitor. The orange graph measures the voltage across the resistor, notice that the orange graph is a sin function, whereas the blue graph is a cos function, which indicates the voltage across the resistor has a phase shift of pi/2 

Here is the same setup but we used the 2kHz for the frequency, these are the graphs of voltage and current across the capacitor

Here is the picture of capacitor voltage waveform. We input 100Hz triangular voltage here

Here is our simple setup for the lab

Our data for the lab, we checked with the other group to make sure our data is correct. Notice that for part A and part B, the voltage across C1 is closely followed by the voltage across C2

 III. Capacitor explosion:
Professor Mason demonstrated a capacitor explosion, what he did basically applying  a large voltage a capacitor, a capacitor would be exploded

what was left after the explosion

Here is a picture of the polar capacitor.

 IV. Equivalent capacitor:
Here is a rule of thumb: equivalent capacitor is the opposite of equivalent resistor, which means that we have to add when they are in parallel and inverse when they are in series

Given a simple of capacitor, we had to find the  equivalent capacitor, which in this case we approached right to left.

Here is a short summary of all the formulas we should know

 V. Summary:
For today lab, we spent most of our time reviewed all the knowledge we had learned in 4B class. We did derive some equation using derivative and integral to get  the current and voltage across the capacitor. For the lab part, we applied different voltage sources to observe the change in current using the built in scope of the analog discovery

04/07/2016

04/08/2016: Cascaded Op ams and Temperature Measurement System Design

I. Introduction:

Today we spent most of our time studying op ams, which indicated the connection between many op ams in one circuit. The system in return would be more complex but not impossible to analyze using nodal analysis. For today lesson, we would have to use many combinations of summing amplifier op ams, inverting and so on

Here is a picture of inverting cascard op ams.

Professor Mason asked us to determine the type of op ams circuit  he put on the screen. We chose inverting for a and b due to their terminal, c is summing because has more than one op am

Here is a picture of cascaded op ams. We found the V1 using the formula we nodal analysis, and using the same approach to find V_2, notice that they were all determined by Vs and those resistors

We plugged the numbers into the formulas we had derive previously solving for V_2 and i_0

II. Temperature Measurement System Design
1. Introduction:
For this lab, we used the wheatstone bridge circuit to convert resistance to a voltage change. The change in resistance was determined by the thermistor. The change in voltage was the change Voutput on the side of the op am

For this picture, my lab partner Carlos derived the expression for Vab, 

Here is the drawing for our circuit, it took us 15 mins to decide our values for the resistors, we also went around to check with other groups

The last equation is the most important equation for this lab, for this part, we used Maple to solve for Vo symbolically

Here is my setup for the wheatstone. 

Here is the direct view of my wheatstone design

d

Last but not least, here Professor Mason introduced use to use bit representation for the resistors, except that the power would be negative instead of positive, made them a fraction

IV. Summary:

After many experiments, we believe nodal analysis worked best compared to other techniques that we have learned so far. For today lab, we spent most of our time understanding the cascaded circuit. We derived many formulas for summing amplifiers, difference op ams, and so on. For the lab, we only did the wheatstone lab, but it took us a lot of time to figure out the right design, the good thing about the wheatstone is that we could use it to convert the change in resistance to the change in voltage

04/05/2016

04/05/2016: Phase Shift and Continue with Op Ams

I. Introduction:

Today, we started out with a simple graph of sinusoidal wave. The question is how would the function change if shift the graph to stay totally positive. We spent part of our time to do some op am circuit, including the inverting, non-inverting, summing, and difference.

First, I wrote down the general equation. I missed the sin there so it should be Asin(kx+wt). The second graph is exactly the first one except its amplitude is 25 and it shifts up 2.5 unit.

Next, we were given a simple op am circuit, Professor Mason to find the ratio between Vout/Vin, in this case, we have inverting op am circuit, therefore, the ratio would be R2/R1=-3

Here we were given another inverting op am circuit. Since Vs is connected to the ground, the voltage of the negative input would be equal to the Vs=0. Using nodal analysis, the would be able to find the Va and Vo. Vo is always greater than or equal to Vin for the inverting op ams

Here is the formula for non-inverting op am cicruit, we have V1=V2=Vi, using that application, we simplified it to Vo/Vi=1+Rf/Ri

Here is the formula for the summing amplifier circuit, Notice that as we add more branch of voltage, we simply need to add up more terms into the formula

II. Experiment with the inverting and summing amplifier op am circuit:

The op am circuit here is actually the combination of the summing amplifier and inverting op am circuit. Notice that the input is given the summing amplifier and the output is given by the inverting op am circuit.

Here is our set up for this lab, next time we should utilize more short wire to make it easier to debug. A good matching color with the analog discovery is also a good practice to follow

Here is our result, notice that since  we have inverting op am circuit, the output would be the opposite sign of the input we choose R1=R2 to simplify our work

For this problem, the output is more complicated than we thought. It was actually one of the mastering engineering homework assigned on that day. R4/R3 due to the fact that

Here we were given a difference amplifying circuit. By applying the nodal analysis, we actually be able to find the gain of 30.33

V. Summary:
For today lab, we spent most of the time understanding more about three more types of op ams: non-inverting, summing amplifier, and difference. With the nodal analysis approach, we were able to derive formula for all those types of ams. We also spent some of our time do the summing amplifier lab at the end to verify that our derivation is correct

03/29/2016: Op ams and its application

I. Introduction:

Professor Mason briefly introduced us to the op ams, which was internally complicated, but contained only resistors, capacitors, and transistors

After showed us how op ams works, Professor Mason asked us to restate the definition of close loop feedback and open loop feedback, close loop simply means received the op am with external feedback, and open  loop means gain of op am without external feedback

 II. More example of op ams:

We were asked to redraw an non-ieal op ams. Notice that there is a resistors between Vn and Vp. Vin is from power supply, Vout is voltage obtained from the other side. The ratio of Vout/Vin is also equal to 20k/10K resistor

We were asked to redraw this op am equivalent. We found the ratio Vs/Vo is roughly -50

 II. Experiment:
After doing some op ams practice, Professor Mason let us to do the experiment to test our results

We found the ratio of Vout/Vin =2. We obtained two resistors, R1=1.8kohms and R2=3.6kOhms to do this experiement

We had to look back the information of this op am to know how to setup the wire correctly, The setup is not hard, but understand instruction of the lab is most time consuming

Here is our table of data. Notice that at Vin=-3 and Vin=3 V we got the saturated circuit.

Here is our graph of Vin vs Vout, which is matched with what we learned about op ams today

Here is the ideal op ams. Basically, the resistance at negative terminal is too high to that no current can go through. The current at 10k and 20k is the same. Professor Mason redrew the circuit for us to make it easier to analyze

 III. Summary:
Today, we learned about the op ams circuit and the real-life application of it. There were two types of circuits we learned, the ideal one and non-ideal one. We can make op am as an ideal op am. The input resistance is very large and there is no output resistance, we can use the constraint equation Vp=Vn to solve for ideal op and i_p=i_n=0

03/22/2016

Day 03/22/2016: Max Power Delivered using Thevenin Approach

I. Introduction:

Today we were back to the Thevenin concept we learned from last lesson. Power maximizing using Thevenin circuit is what we learned today.

Using the Thevenin equivalent circuit, we find the dissipated power of the resistor, the formula is shown above. Power is directly related to cR_L but indirecly related to c/R_L^2. Combine the two graphs, we should come up with a nice bell-shaped curved. The power would be maximized at x=Rth

Here is how we proved the power would be maximized if Rth=R_l. First we got the Power eqution  int term of R_L. We replaed the R_L with x for easier referecen. Then we took the first derivate of power with respect to x and let it equal to 0 to find the x that maximized the power, which is x= Rthevenein

 II. More Example:
We concluded that max power is transfered to the load resistance if it equals Rth. Professor Mason assigned us a couple more examples to do

In this photo,we  obtain the Thevenin equivalent at terminals a-b and Find R_L for maximum power. We used the source transformation partially to find the power dissipated when R_l=24, 8 ohms respectively

 III. Real Life Problem
Professor Mason gave us a real problem of a robot design, we were asked to find the maximum power delived to the circuit.

We attemped to solve the problem by first find the Rth which in this case equivalent to Req due to the fact that there is no dependent source. And we applied maximized power theorem by letting Rload=Rth

One more example to find the Rth. In this case we redraw the circuit to find Rth first, and open circuit the RL to find the Vth. Then we applied maximized power delivered theorem

 IV. Lab: Proving the maximized power transfer theorem with numerical values:

Here is how we set up the circuit. We varied the pot (variable resistors) to obtain our desired value of resistance

Here is our data table. Notice that as we the Rl approaching the Rth, the power transfer is increasing, after that the power decreased . 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.

Here is the graph of Power vs. R. Power is maximized at Rl=5kohms

Here we had to calculate the source voltage V_s and internal resistance R_s (unideal source of voltage) . Then we determine the voltage when an 8-Ohm load is connected to the source.

V. Summary:
Today we further our learning of thevanin to find the max power transfer to the circuit. The max power transfer theorem stated that, and we already proved, that power is max delivered when RL=Rth. We also did the lab to use the numerical value to prove that max power transfer theorem is true, which was shown in the graph.