Lab Report Day Sixteen - Series RLC Circuit Step Response

 

Series RLC Circuit Step Response

This lab emphasizes modeling and testing of a series RLC second order circuit. This lab assignment will consist of two parts:

•In Part I of this assignment, the step response of a 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.

•Part II of this assignment consists of a simple design problem: the circuit of Part I is to be re-designed to make it critically damped, without changing either the natural frequency or the DC gain. Again, the circuit step response is measured and compared to expectations.

Since we do not have time, Professor Mason only ask us to do the first part and record the data. 

 

This is the circuit we are going to build. First, we are going to calculate whether the circuit is overdamped, underdamped, or critically damped. 

This is our pre-lab. Based on the value given, we can see that our circuit is underdamped. We also calculated the value we need to make it critically damped. 

This is our set up for the circuit. In the circuit, we use a 470 nF capacitor, a 1 uH inductor, and a 1.1 ohm resistor.

 

Our experiment value for capacitor is 420 nF.

Our experiment value for resist is 1.4 ohm. 

We are not able to measure the inductance. We assume it is correct. 

This is the input graph. It is a square wave at 500 Hz with 0 V offset. 

This is our output function. 

We calculate our experimental omega to be 5.15*10^4. Compared to our theoretical value 1.351*10^6, we get a percent difference 96.2%. That is really a big percent difference. 

 

When we record some data points form the graph, and have an offset by 2V, I get this graph in Excel. The plotted function is Y=3.5*e^(-8811x). We can rewrite it as V=3.5*e^(-8811t). This means that our experimental α is 8811. Compared to our theoretical α, 5.5*10^5, it is only 1.6% of the theoretical α. Possible causes of error could be the way we measure the circuit, or could from our input value. 

To calculate our experimental damping ratio, we get α/omega, and we get 0.171. 

Summary:

Today, we learn how to find boundary value, 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.