Series RL circuit

[iamakda]

Hi everyone,

I have a series circuit. Inductor of 10uH is in series with 100 ohm resistor with pulse train voltage of 6.59 V with a duty cycle of 0.31 and frequency of 180 kHz. I want to calculate the total current flowing in this series circuit. Can anyone help me finding this? I will be really grateful.

Thank you.

[redwire]

Re: Series RL circuit

I suggest using LTspice to simulate the circuit.
I ran a quick sim and the inductor isn't doing much because the current is small due to the 100R resistor and L is small too.

[ratdude747]

Re: Series RL circuit

Hi everyone,

I have a series circuit. Inductor of 10uH is in series with 100 ohm resistor with pulse train voltage of 6.59 V with a duty cycle of 0.31 and frequency of 180 kHz. I want to calculate the total current flowing in this series circuit. Can anyone help me finding this? I will be really grateful.

Thank you.

Hmm... If it were a sine wave this would be easy. However, I'm a Junior studying Electrical Engineering Technology so I may have an answer.

I may be taking the wrong approach, but couldn't you use a Fourier Series to find the significant frequencies and coefficients (look in the attached image, the table I used this semester, it has a pulse train w/ duty cycle entry), and then for each (including the DC offset) find the current, both magnitude and phase , and add up the currents.

There may be a shortcut (maybe using step responses and time constants), but since this is a non-sinusoidal waveform, the what comes to mind is using Fourier to make it into sines and cosines (or in this case, a pulse train, just cosines luckily). That said, the time constant formulas (e ^(-t/τ) , etc.) are just the byproducts of Laplace transforms, so either method probably would work.

If this is for a class, what has the subject been lately? (That will clue me/us in on what the expected strategy is)

[iamakda]

Re: Series RL circuit

I suggest using LTspice to simulate the circuit.
I ran a quick sim and the inductor isn't doing much because the current is small due to the 100R resistor and L is small too.

Hi Redwire,

Yes, I agree and simulated myself as well and found the same results. Thanks for your help.

Regards.

[Longbow]

Re: Series RL circuit

This is a typical question invented by a clever professor to amaze his students. To ask for the total current, you must specify first (since the circuit is reactive) 1) current at time t=? or 2) current integrated over many cycles.

It seems obvious that in a series circuit the current is the same in all elements. To say that the inductor isn't doing anything is incorrect. It is causing the phase angle of the current to lag the applied voltage by whatever small amount (in this case). Nobody asked for the phase angle because it is not a constant.

In a practical sense - isn't that the whole point of figuring this stuff out? -we might want to know how to minimize the reactance of the circuit. Or, we could take an output voltage across L, for example. My next question to the professor would be to come up with a practical application for his question.

[momaka]

Re: Series RL circuit

I don't know if this is the right approach or not as I don't know what you're studying and what you have studied so far in that class (assuming this is for a class to begin with), but here's one way I *think* you can solve this:

You're given duty cycle (D) and peak pulse train voltage (a). The RMS value of a pulse train is a*(D)^(0.5) . See this article:
http://en.wikipedia.org/wiki/Root_me...mmon_waveforms
By knowing the RMS value, you can say the input source is a sinusoidal wave with a peak value equal to the RMS value times (2)^(0.5). Then, you can do a Laplace transform of the circuit and solve for the current by dividing the input sinusoidal voltage you just found by the total series impedance of the circuit. Convert your answer back into time domain (i.e. inverse Laplace transform) and only consider the steady-state response (ignore any transient responses). The output should be a sinusoidal waveform with a (possibly) different amplitude and phase angle. Take the amplitude and convert to RMS value, then go back to that Wikipedia article above and convert the RMS value to a triangle wave peak value. Why triangle wave? - because the current through an inductor cannot change instantaneously, so you can't really have a pulse train for the output current. This is, of course, assuming that the switching frequency is large enough that its period is much smaller than the time constant of the series RL circuit. If not, then you could have something that looks kind of like a pulse train for the output current. In that case, convert the RMS value back to a pulse train with same duty cycle as the voltage.