- #1
Emspak
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Homework Statement
I have a problem where the circuit is as follows: (pic attached I hope) but if you can't see it it's just a power source (AC), resistor and inductor with 2 terminals across the inductor (from were you measure the voltage).
I want to derive the response function, and I am trying to see if I did something off. I am doing it in terms of frequency, rather than [itex]\omega[/itex].
Homework Equations
So I know that the resistance in an inductor is [itex]Z_L = iL\omega[/itex]
Resistance from a resistor is just R
Response function [itex]H ( \omega) = \frac{V_{out}}{V_{in}}[/itex]
The Attempt at a Solution
So I take the whole circuit and see these are in series. So the total resistance ([itex]Z_{total} = R + iL\omega [/itex].
That means the current in the circuit is [itex]\frac{V_{in}}{R + iL\omega }[/itex]
and the [itex]V_{out} = \frac{V_{in}R}{R + iL\omega } [/itex] because we are measuring the voltage across the inductor.
Substitute omega with f/2pi and we get
[tex]V_{out} = \frac{V_{in}R}{R + iL\frac{f}{2\pi} } \rightarrow \frac{V_{out}}{V_{in}} = \frac{2\pi R}{2\pi R + iLf} = H ( f)[/tex]
Is there anything wrong with this? I ask because I'm doing a lab and even accounting for experimental error my Bode plot diverges a lot from the measured numbers. The shape of the curves is all good; just the one I plotted above seems moved to the right and up a bit from the values I got. Same shape exactly, tho. Not a big deal I guess, but I wanted first and foremost to make sure I did this right.