May 28. Signal with Multiple Frequency Component

Today we thought about what happens to circuit elements as the frequency increases and we got the following relationships. And we did a lab to visualize the frequency depend behaviors. 

The graphs show what happens to the impedance of those circuit elements as the frequency is increased.

Lab, 

following is schematic we used in today's lab

actual circuit 

For Part A of the experiment, we designed a custom signal whose equation is 

Following is the wave function we created. 

Following is a picture of what the signals on the circuit look like. 

Following is a picture of sweep wave in screen. As we can see, the gain in the output signal decreases as the frequency increases. Interestingly, it does so by forming a figure similar to a curvy cone. 

The input voltage is a sinusoidal sweep from 100Hz to 10 Khz in 20 msec:

Summary:
Today, we learn about frequency response. The frequency response of a circuit is determined by the variation in its behavior with change in signal frequency. The frequency depend behavior is quite complex when it comes to real circuit. As the experiment we did, the result is really hard to express and calculated mathimatically, We need learn much more in the future. 

May 26. Apparent Power and Power factor

This lab is about power and power factor to quantity the AC power delivered to a load and power dissipated by the process of transmitting this power. After this lab we are expected to get a better understanding of this subject. 

Pre-lab:

following are circuit schematic and values of elements and the pre-lab calculations.

actual circuit we build for this lab

another angle of the circuit. 

The oscilloscope screen with 10 ohm resistor

The oscilloscope screen with 47 ohm resistor

The oscilloscope screen with 100 ohm resistor

Then we add a capacitor in series with resistor. 
following is the prelab calculation for this set up. When we add a capacitor, the phase shift significantly decreased comparing to the previous part. 

the oscilloscope screen with 10 ohm resistor with a capacitor

the oscilloscope screen with 47 ohm resistor with a capacitor

the oscilloscope screen with 100 ohm resistor with a capacitor

The main source of error is the inaccurate measurements of the time difference, and the actual resistance and capacitance are little off from the theoretical values.

Summary:

Today we observe and calculate the apparent power and power factor of an AC circuit, then we add a capacitor to reduce the phase shift which is a very useful application of AC circuit since it could increase the apparent power we obtained. For the lab, the results are what we expected and we are happy about that.

May 19. Maximum Power/No actual lab

today we didn't have a formal lab, however prof Mason did show us how to determine the power that delivered by AC source.  

Following picture is handsome Prof Mason looking into the bulbs.

Following picture shows the peak of AC source is equal to the DC source, in this case the bulb powered by AC source is dimmer than the bulb powered by DC source. 

following picture shows that when the two bulbs are equally bight, the Peak voltage of AC source is about 1.44 which is roughly square root of 2 times the voltage of DC source,

The experiment is really helpful since it visualize the effect of power delivered by different sources.

May 14. Inverting voltage Amplifier. Op-amp Relaxation Oscillator.

Pre-lab:In this lab, we measured the gain and phase responses of an inverting voltage amplifier circuit, and compared the measurements with expected values.

following picture is the circuit we were use and the derivation of the formula.

Following picture including the values of capacitor and resistor we use and the theoretical value of the gain and phase shift for each given frequencies. 

following picture is the analogy screen of 100Hz input voltage.

following picture is the analogy screen of 100Hz input voltage. We can see the gain decrease and larger phase shift.

following picture is the analogy screen of 5000Hz input voltage. the gain got even smaller and phase shift is close to the one at 1000Hz.

following picture is the circuit we built for the lab.

Following picture is the measurements and calculations we made in this lab.
For the gain, the experimental values and theoretical values are close, the percentage differences are less than 5% which is quite good.
How ever for the phase shift measurement of 100Hz input, the percentage difference is quite large which is 12.7% off.
the errors in this lab may due to the actual value of elements we use are a little bit off from the theoretical value, and the incorrect measurements of the time differences between input and output signals.
All in all, the results are good!

Part2 relaxation oscillator
Prelab :
Following picture show the schematic of the lab.

following picture show the actual circuit we built for this lab.

following picture is  the formula given by the lab-book and we used it to calculate the resistor we use to produce a square wave of 155Hz since last 3 digit of my ID is 155.
We choose R1=R2=1000
After calculation we choose use 3 10K resistors connected in series to make a 30K resistor.

following picture is the analogy screen of the square wave we obtained, the frequency is 154.27hz which is very very close to our expected value. 

summary:
Today we enhance our understanding of how to use op amp, we did good job in lab and got good results from the lab. The two parts of lab were very important application of op amp which could benefit out final project design.

May 12, Phasors: Passive RL Circuit Response Phasors: Passive RL Circuit Response

Pre-Lab: 
We did a pre-lab analysis to predict the amplitude gain and phase difference with 3 different frequency: Wc, Wc/10, and 10Wc (Wc = 2.2*10^5 Hz). When W= Wc, expected amplitude gain = 0.032 and expected phase difference = -45degree. When frequency = Wc/10 expected amplitude gain = 0.045 and expected phase difference = -5.7 degree. When frequency = 10Wc expected amplitude gain =24.5*10^-3 and expected phase difference = -84 degree

When W= Wc

When W= Wc/10

When W= 10Wc

The circuit as illustrated previously in the schematic

the data for exp value. The amplitude gain is different, becaese we used  I/V to calculate the  amplitude gain in pre-lab, and we use the Vout/Vin in the final calculation. The results make sense through as f increase the V/V gain decrease. 
The percentage difference for the angle shifted is calculated as 5.6%, 6.3%, 9.2% respectively. 

Summary:

In this lab, we analyze the steady-state response from sinusoidal inputs. We can find the amplitude gain by comparing the Vin and Vout. We also learn how to analyze AC circuits using different methods of analysis including nodal analysis, mesh analysis, superposition, Thevenin and norton analysis. 

The results is good since the percentage difference for angle is less than 10%, the source of error may due to the inaccurate measurement of time from the graph, and the uncertainty of frequency that analogy discovery provided. 

May 7. Impedance

Above is important formula to calculate impedance for each circuit elements.
Prelab
We determined the resistor impedance = 47 + R , the real resistor values came out 48.7 ohm and 100.1 ohm, and therefore the expected impedance for resistors = 148.8 ohm  Inductor impedance = 48.7 + 0.00628j  Capacitor impedance = 48.7 - 1711.34j 

Measurements for part A.

Circuit

This is the RR circuit at 1k frequency. Vt= 1.354 V, I=13.2 mA. 


This is the RR circuit at 5k frequency. Vt= 1.354 V, I=13.2 mA. 

This is the RR circuit at 10k frequency. Vt= 1.354 V, I=13.2 mA. 

Part2 predictions



circuit

This is the RL circuit at 1k frequency. Vt= 0.2652 V, I=40.05 mA. 

This is the RL circuit at 5k frequency. Vt= 1.0584 V, I=34.2 mA. 

This is the RL circuit at 10k frequency. Vt= 1.546 V, I =25.4 mA. 

Part3 predictions


circuit

This is the RC circuit at 1k frequency. Vt= 1.999 V, I =1.05 mA. 


This is the RC circuit at 5k frequency. Vt= 1.9774 V, I =4.955 mA. 


This is the RC circuit at 10k frequency. Vt= 1.924 V, I =9.475 mA. 

Summary:

Today, we analyze AC circuits. We find that a resistor AC circuit has no phase change between the voltage and current. The voltage leads the current by 90° in a circuit with an inductor and the current leads the voltage by 90° in a circuit with a capacitor. We learn that circuit elements can be represented as impedance.