April 30 LEC circuit response

This lab we gonna modeling and testing of a second order circuit containing two resistors, a capacitor, and a n inductor. In this assignment, the step response of the given circuit is analyzed and tested. The measured response of the circuit is compared with expectations based on the damping ratio and natural frequency of the circuit. 

Pre lab
measured experimental value 2.9Ω resistor, a 48.6 Ω resistor, a 10.1 uF capacitor and a 1 uH inductor. 47 ohm resistor and the inductor are in series while they are in parallel with the other components in the circuit.

Lab circuit.

input signal

output signal 

calculations.for alpha. 

experimental value of α to be 3588.7, while our theoretical value is 1063.8. It has a precent difference of -237.4%. 

Summary:

We learn how to analyze the RLC circuit. we need to identify the circuit among over damped, underdamped, or critically damped. We also do a lab about RLC circuit response. In this lab we get large percent error between theoretical and experimental values. It may result from not measuring the data correctly and not correctly inputting the values. 

In this lab the experiment value is significantly different from the theoretical value, that may due to the approximation we made during calculation and inaccurate measured time and total resistance. 

April 28. Series RLC circuit step response

Prelab
we calculated the values we need, and measured the capacitor and resistor we used in lab. The experimental value for R is 3 and for C is 414uF.We are not able to measure the inductance. We assume it is correct. 
we can see that our circuit is underdamped. We also calculated the value we need to make it critically damped. 

This is the circuit we are going to build

true circuit

output function. We can see it is under damped. 


From the measurements, time between two peak is 120us, so the wd=2PI/t=5*10^4.which has almost 90% difference from the value we calculated before.

Summary:

Today, we learn how to solve source free RLC circuit. We also learn how to determine  whether the circuit is over damped, underdamped, or critically damped. We do a lab of a underdamped circuit, and we get a big percent difference which is almost 100%. Possible causes of error could be the way we measure the circuit, or could from our input value. 

The results are significantly different from what we expected, that may due to the difficult of measure time, the resistance of inductor, we observed that the small change of resistor could significantly change the results since the resistance in this set up is so small. 

April 14. Capacitor Voltage-current Relations

Prelab

n this lab we measure the relationship between the voltage and current across a capacitor. To get a better understanding of the relationship we will use three different time-varying signals: sine waves, triangle waves, and square waves as voltages applied to the capacitor. Due to the fact that our measurement tool (Analog Discovery) doesn't measure current we will use the formula:I(c)=C(dv/dt)

We predicted the resulting output based on each input signal below. 

we use a 1uF capacitor with a 100 Ohm resistor in the circuit drawn below.

Below is date for C1(top) A=1.032V across resistor,  C2(under)  A= 1.626V the voltage across the capacitor,  M1(mid)  the current through the resistor,  when f=1kHz, A=2V, and Offset=0V

Below is date for C1(top) A=1.452V the voltage across resistor,  C2(under) A=1.178V the voltage across the capacitor,  M1(mid)  the current through the resistor,  when f=2kHz, A=2V, and Offset=0V

Below is date for C1(top) the  the voltage across resistor,  C2(under)  the voltage across the capacitor,  M1(mid)  the current through the resistor,  when f=100Hz, A=4V, and Offset=0V

Lab Circuit

More practice with inductor. 

Summery
we seeing the relationship between the voltage and current across a capacitor in this lab. We were successful at our analysis that I(c)=C(dv/dt) holds true. We can see as frequency increase the voltage across the capacitor decrease, we will learn why that happens in the future i believe. We also got more experience using the Math Channel to analyze current using Analog Discovery. 
After that, we see the DEMO of inductor lab, unfortunately we don't have time to do it myself. 

April 21. Inverting Differentiator

Pre-Lab

Prediction

We determine the Vo, V1, V3 

and resistor and capacitor used in this lab

Lab measurements

For three different frequency we measure the Vout anc compare to the expected value.

 circuit

f=1kHz, A=1V, offset=0V, The display the waveforms for Vo A= 1.144V and Vin A=1V.

f=500Hz, A=1V, offset=0V, The display the waveforms for Vo A= 0.586V and Vin A=1V.

f=2kHz, A=1V, offset=0V, The display the waveforms for Vo A= 2.204V and Vin A=1V.


Summary:
 In this lab, we learned  the output voltage has a relationship respect to the time of the input to the circuit. With a higher frequency the the op amp will have a higher gain for the output, and with a lower frequency the op amp will have a lower gain for the input.
The percentage difference is quite small in this lab, no more than 9%, so we consider this lab is successful. The error may due to the opamp is non-ideal. so the experimental value is little bit off from we expected.