Day 14 - First Order Circuits

Topics Discussed

On day 14 of the ENGR 44 course, we were introduced to first order circuits. These circuits are known as either RL or RC circuits (resistor-inductor or resistor-capacitor, respectively). These circuits contain the passive elements such as resistors, capacitors, and inductors, and one active element being the operational amplifier. We discussed several relationships to the voltage or current through a capacitor or inductor, and how we can essentially model the behavior of these elements in such a circuit. We did example problems that included deriving an equation for the voltage across a capacitor and the time constant tau associated with the equation. (Fig. 1, Fig. 2, & Fig. 3) "The time constant of a circuit is essentially the amount of time required for the response to decay by a factor of 1/e." (Mason- Lecture Notes). For capacitors, it is RC and for inductors it is L/R. We also did work with inductors in example problems and modeled the current through it as a function of time. (Fig. 4)

Fig. 1 

Fig. 2

Fig. 3

Fig. 4

Passive RC Circuit Natural Response Lab

In lab, we sought to create a simple RC circuit and observe its natural response when an input voltage is applied. We would first model the circuit in a schematic and estimate the time constant. This would allow us to create a theoretical value for how long the capacitor would take to discharge. We would use the oscilloscope trigger to determine the response of the capacitor when voltage was disconnected, or when a square wave was applied. We first created the schematic and made our predictions. (Fig. 6) Once this was done, we created the actual circuit. (Fig. 7)

Fig. 6

Fig. 7

Upon creation of the circuit, we hooked up our analog discovery device and set up an oscilloscope window to observe the specific changes occurring within the capacitor. Perhaps the most difficult aspect of this lab was properly setting up the trigger, which would ultimately determine whether or not we could get a good reading from the oscilloscope window. We found our reading. (Fig. 8) We found that our value for Tau compared to our calculated value was very close and exhibited a percent error of roughly 10%. (Fig. 9)

Fig. 8

Fig. 9

Passive RL Circuit Natural Response Lab

Although we did not necessarily get a chance to complete this in class, we recreated a similar circuit to the when mentioned above, only this time we used an inductor. We again created the schematic and made predictions for the general equaion describing the current as a function of time (Fig. 10) Prior to leaving class, we quickly assembled the circuit and ran a quick trial to observe the response of the inductor. (Fig. 11) 

Fig. 10

Fig. 11

Summary

We were able to successfully assemble and verify our models for the natural response of an RC and RL circuit today in lab. Considering our only measured and recorded trials, the RC circuit exhibited only a rough 10% error in tau when compared to our calculated value. By understanding the process by which these circuits operate, we will be able to create more complex and versatile circuits in the future.