RLC Circuit Response Lab

Objective: 
We obtained the step response for RLC circuits when in series and in parallel. Also, we introduced and dealt with second order op amp circuits. In dealing with these circuits, it is important to KVL or KCL and rearranging the terms so that there is a second order differential equations. However, we keep in mind that there is a steady state response which is the final values of what is being found v(t) or i(t). The complete solutions change for overdamped, underdamped, and critically damped. The completed solution consists of the transient response and the steady state response. There is no source free do deal with which means we need to keep in mind of the voltage or current source.

Groupe Practice:
1. The problem below tells us to find i(t) for t>0. First we find i(0) and v(0) before it is opened which we get i(0-)= 0 since inductors acts like a short circuit and the capacitor has a voltage of v(0-) = 20V  when fully charged. Yet, when closed for t>0, the voltage source is disconnected and only the LC circuit remains. We have a source free series LC circuit. We then find the alpha and omega and check whether it is overdamped, underdamped, or critically damped.

Figure 1. Finding the i(t) for t>0

2. The problem below will solve for the natural response and will write the completed response in the end. Also, the coefficients will be solved. However, we first find the initial conditions of the circuit.

Figure 2. Find the initial conditions and solving for the natural response and complete solution. 

RLC Circuit Response Lab Procedures and Results: 

1. This lab requires us to find the maximum overshoot, rise time, and DC gain based on the circuit show in figure 3. We will estimate theses values and compare them to the experimental measurements. 

Figure 3. Circuit schematic for RLC circuit. 

2. For the pre lab, we first write the differential equations of the system which is seen in figure 4. the equations is seen in orange where α(neper frequency) = 1/CR2 + 1/L and ω(undamped natural frequency) = R1/R2LC + 1/LC

Figure 4. Differential equations relating to voltage output and input

3. The actual circuit setup can be seen in figure 5. The measure values for the circuit are: R1= 47Ω, R2= 2.2 ohms L = 1mH, C = 1nF. We apply a 2V step input at low frequency so that the circuit reaches steady state between pulses. Based on the graphs recorded, we will measure the input and output voltage.

Figure 5. Actual RLC circuit.

 4. We acquired an overshoot of overshoot=51.188%, voltage in = 2.0844V, voltage out =

Figure 6. Voltage input and voltage output 

Figure 7. voltage input and voltage output

Learning Outcome:
Based on the RLC circuit schematic, we can calculate the initial values, i(inductor) = Vin/R1+R2 = .04065A and the voltage at the capacitor is Vc=