May 16, Tuesday (The day-late ides of May)
Today we denuded phasors of their complexity (yes, I just wanted to use the word denude). Today we arrived about 30 minutes late. Today we read a bit of a book I think Mason would like to read (but probably can't, he's a busy dude), called Happy City_Transforming Our Lives through Urban Design. Yes I did use an underscore to denote a subtitle. Last night we slept poorly. Tomorrow we'll sleep better. Joke's on me, as was the coffee. How much do I need to drink to get addicted? I've read that I can safely consume 500mg of caffeine a day. Think I've passed that yet? I'm on my 4th (5th?) cup of coffee today. We did some nonsense with phasors and impedance today. Luckily for me, I have a handy dandy calculator that does complex plane calculations. The world is full of these little wonders.
f.lux is conveniently turning my screen yellow to reduce blue light (which keeps you awake), and to remind to use the computer at night less. Thanx f.lux.
Impedance is actually really easy, esp. with phasors. It's like a complex resistance that changes with frequency for inductors and capacitors. We use some bold and capital letters to differentiate between the time and phasor domains with their impedances and whatnot. And that's impedance IANS.
LAB: Passive RL Circuit Response
a. Show that the amplitude gain and phase difference between the input voltage and the input current are as shown in equations (4) and (5). R b. The cutoff frequency for the circuit of Figure 2 is given to be c =. Calculate the cutoff L frequency for the circuit of Figure 2 if L = 1mH and R = 47. c. Determine the gain and phase difference for the RL circuit for frequencies co 0, co , and co =co c if L = 1mH and R = 47. d. Do your low and high frequency gain results in part (c) agree with your expectations based on the inductor’s low and high frequency behavior? (e.g. calculate the inductor impedance at low and high frequencies, substitute these impedances into the circuit of Figure 2, calculate the response of the resulting resistive circuit, and compare to the results of part (c).)
Use your function generator to apply a sinusoidal input at vIN(t). Use your oscilloscope to display both vIN(t) and vL(t). Use the oscilloscope’s math operation to display the input current, iIN(t), as provided by equation (6). Record the amplitude of vIN(t) and iIN(t) and the time delay between vIN(t) and iIN(t) for the following input voltage frequencies: = c /10 (low frequency input) = 10*c (high frequency input) = c (corner frequency input) b. Calculate the measured gains and phase differences between iIN(t) and vIN(t) for the three frequencies listed in part (b) above. Compare your measured results with your expectations from the pre-lab. Comment on your results.
a. Show that the amplitude gain and phase difference between the input voltage and the input current are as shown in equations (4) and (5). R b. The cutoff frequency for the circuit of Figure 2 is given to be c =. Calculate the cutoff L frequency for the circuit of Figure 2 if L = 1mH and R = 47. c. Determine the gain and phase difference for the RL circuit for frequencies co 0, co , and co =co c if L = 1mH and R = 47. d. Do your low and high frequency gain results in part (c) agree with your expectations based on the inductor’s low and high frequency behavior? (e.g. calculate the inductor impedance at low and high frequencies, substitute these impedances into the circuit of Figure 2, calculate the response of the resulting resistive circuit, and compare to the results of part (c).)
Use your function generator to apply a sinusoidal input at vIN(t). Use your oscilloscope to display both vIN(t) and vL(t). Use the oscilloscope’s math operation to display the input current, iIN(t), as provided by equation (6). Record the amplitude of vIN(t) and iIN(t) and the time delay between vIN(t) and iIN(t) for the following input voltage frequencies: = c /10 (low frequency input) = 10*c (high frequency input) = c (corner frequency input) b. Calculate the measured gains and phase differences between iIN(t) and vIN(t) for the three frequencies listed in part (b) above. Compare your measured results with your expectations from the pre-lab. Comment on your results.
Phase offset:
Current as function of time:
Prelab & Calculations
Circuit:
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