2nd order circuit continue...

We continue to learn more about 2^nd order  circuits.

Step response of series RLC circuit: the step response is obtained by the sudden application of a dc source. It has the source free equation with an addition term for the Voltage supply. The solution to the differential equation above has two components: the natural response v _n (t) and the forced response v _f (t).

We did following problem of series step response RLC circuit.

The natural response is the solution when we set V _s = 0 and is the same as the one obtained for the source free circuit.

v _n (t) = V_s + A ₁ e^s1t + A ₂ e^s2t  (Overdamped)

v _n (t) = V_s +  (A ₁ + A ₂ t)e^−αt     (Critically damped)

v _n (t) = V_s + (A ₁ cos ω _d t + A ₂ sin ω _d t)e^−αt    (Underdamped)

The values of the constants A ₁ and A ₂ are obtained from the initial conditions: v(0) and dv(0)/dt.

RLC Circuit Response LAB:  we tested and analyzed step response of the following circuit shown in the picture. 

Then we learned about parallel step response RLC circuit. It  is pretty much the same process. Natural response is the same as what we did before.

Following is an example we did in class for parallel Step Response RLC circuit.

From the above differential equation we estimated the damping ratio and natural frequency of the circuit. R1= 4.7 ohm and R2= 1.1 ohm 

Our % Difference was 81.9% for omega and 42.8% for alpha. This % error could have caused by the Resistors and capacitor we used. We might not have used correct decimal points to get exact answer.

FollowinWe input 500Hz square wave at 2VDC into the circuit,and above graph is the outputg is the graph of the circuit from the oscilloscope. The circuit is underdamped. 

Data obtained from the graph  shows the higher and lower peak, we calculated period, omega, and alpha

Summary: 

In this lab we obtained large percent error between theoretical and experimental values. Which could have caused from not measuring the data correctly and inputting the values correctly.