Transforming DC to AC: The Role of Inductors and Capacitors in RLC Circuits

[21joanna12]

I have only just found out about inductors, and am trying to figure out how a circuit with an inductor and a capacitor could change dc current to ac current.

With the set up of the circuit, would it suffice just to have the dc supply with a 'gate' that stops/allows through the dc current with a frequency of 50 Hz, and then an inductor connected to this is series and a capacitor conected to the inductor in series? Would the output be ac? I don't quite understand how to complete the circuit either...

If the above is a good way to go, is there a way to show mathematically that sinusoidal current is the output? I am still trying to get my head around this, but from what I understand the capacitor will initially be charging with a large current and the current will be decreasing. It would be decreasing exponentially, but the inductor resists the change in current so that it ends up decreasing sinusoidally, and then when the dc current is off the capacitor discharges with an initial high current which decreases exponentially, but the inductor decreases this change so that it is sinusoidal?

I have spent many hours trying to find a good YouTube video or link, but with no luck! I think it has something to do with RLC as this seemed to crop up a lot, although I don't really understand these circuits...
Thank you in advance for any help! :)

 

[davenn]

a little more involved that that

google DC to AC inverter circuits

cheers
Dave

 

[jim hardy]

see if this helps

http://www.animations.physics.unsw.edu.au/jw/LCresonance.html

it's just harmonic motion, like a spring-mass system

establish an initial condition of current through inductor or voltage across capacitor..

That's just a textbook solution though, to make useful AC you'll need more parts, as dave said...

 

[meBigGuy]

If you 50-50 gate DC into a load with a switch you get a squarewave that goes from 0 to V. It has an average value of V/2. You can think of it as a +V/2 to -V/2 squarewave sitting on top of a V/2 DC level. Put a capacitor in series with that and you block the DC, leaving the AC squarewave. Now, in reality it's a bit trickier than that since the capacitor size and the load interact with a time constant Tau=RC, which changes the waveform. But, the result is, indeed, AC.

If you put an inductor in series with the capacitor it gets Much more complicated since the energy storage of the capacitor and the inductor play against each other. They can behave in ways that are over-damped, under-damped, and critically damped, and can result in natural frequencies (ringing) that are at a different frequency than your switching frequency. That gets into the RLC circuit responses.

Jim pointed you to a good article that describes stand-alone LC circuits that resonate at a single frequency, which is indeed a sinewave.

If you think about this circuit (from http://www.facstaff.bucknell.edu/mastascu/eLessonsHTML/Circuit/Circuit4A.htm) being driven by a sweeping AC source:

The capacitor blocks low frequencies, and shifts phase in one direction, and the inductor blocks high frequencies and shifts phase in the other. In the middle range there is a frequency when the L and C have the same impedance and opposite phase shifts. As a result, their impedances "cancel" at that frequency, called the resonant frequency. That is the basic concept used by simple radio tuners. It can be called a bandpass filter.

Trying to imagine what happens when the source is 50 HZ switched DC. It can get messy. But, only AC can make it through the capacitor. That much you can count on. You don't need an inductor to remove the DC from a signal. Just a series capacitor.

 

[21joanna12]

If you 50-50 gate DC into a load with a switch you get a squarewave that goes from 0 to V. It has an average value of V/2. You can think of it as a +V/2 to -V/2 squarewave sitting on top of a V/2 DC level. Put a capacitor in series with that and you block the DC, leaving the AC squarewave. Now, in reality it's a bit trickier than that since the capacitor size and the load interact with a time constant Tau=RC, which changes the waveform. But, the result is, indeed, AC.

If you put an inductor in series with the capacitor it gets Much more complicated since the energy storage of the capacitor and the inductor play against each other. They can behave in ways that are over-damped, under-damped, and critically damped, and can result in natural frequencies (ringing) that are at a different frequency than your switching frequency. That gets into the RLC circuit responses.

Jim pointed you to a good article that describes stand-alone LC circuits that resonate at a single frequency, which is indeed a sinewave.

If you think about this circuit (from http://www.facstaff.bucknell.edu/mastascu/eLessonsHTML/Circuit/Circuit4A.htm) being driven by a sweeping AC source:

The capacitor blocks low frequencies, and shifts phase in one direction, and the inductor blocks high frequencies and shifts phase in the other. In the middle range there is a frequency when the L and C have the same impedance and opposite phase shifts. As a result, their impedances "cancel" at that frequency, called the resonant frequency. That is the basic concept used by simple radio tuners. It can be called a bandpass filter.

Trying to imagine what happens when the source is 50 HZ switched DC. It can get messy. But, only AC can make it through the capacitor. That much you can count on. You don't need an inductor to remove the DC from a signal. Just a series capacitor.

Thank you so much to everyone that has replied! I really understand the role of the capacitor and inductor now, however I am confused about the rest of the circuit. meBigGuy, could you explain what the earthing does and how it works in this circuit? There is also the circuit on this link
http://www.physics.ox.ac.uk/olympiad/Downloads/PastPapers/BPhO_Round_2_Paper_2011_%20Solutions_selectedl_answers.pdf
and the circuit is under question 2c)

If there is earthing, would the current not all just flow to the Earth when the ac has a positive voltage, and flow from the Earth when the ac has a negative voltage to completely cancel out any current? If you have any links for explanations of the role of earthing in circuits, I would also be grateful.

 

[21joanna12]

I was wondering if earthing has any analogy to the use of a reservoir in thermodynamics so that a system remains isothermic? And also why it seems like earthing always occurs through a resistor?

 

[zoki85]

Earthing in electrical schemes serves to denote the zero reference voltage point (= 0 V). Every electrical circuit can work with no earthing: all it suffices is circuit to be closed. Earthing in a real world has a multipurpose function, and doesn't always occur through a resistor.

 

[21joanna12]

Earthing in electrical schemes serves to denote the zero reference voltage point (= 0 V). Every electrical circuit can work with no earthing: all it suffices is circuit to be closed. Earthing in a real world has a multipurpose function, and doesn't always occur through a resistor.

Thank you for your reply! But I am still a bit unsure- I thought it might have something to do with completing the circuit because in the link I gave above, http://www.physics.ox.ac.uk/olympiad/Downloads/PastPapers/BPhO_Round_2_Paper_2011_%20Solutions_selectedl_answers.pdf, just having an inductor and capacitor would just give single wire and not a loop. In these circuits, like the one provided by meBigGuy, and in the link I gave, there is always earthing. It seems like it is playing a pretty important role in these circuits...

 

[jim hardy]

I was wondering if earthing has any analogy to the use of a reservoir in thermodynamics so that a system remains isothermic?

hmmm sometimes that's an okay thought, as in lightning protection

but one must be very careful to not fall into the beginner's trap of thinking Earth is some infinite sink with a magical affinity for current.
When studying circuits, Earth is "just another wire that goes nearly everywhere".
And like any other wire you can have a potential difference across a length of it.
And Kirchoff dictates any current you pull out of Earth you must return to earth, also just as with any other wire..Now - A circuit that's earthed will of course be at potential of Earth in that vicinity... So your analogy is i think okay.

 

[jim hardy]

Just be aware that in Thermo you have an absolute zero for temperature
here on Earth all potentials are relative to something on Earth ,, there's no absolute zero potential that i know of.
i think that's why students get confused about "earth", thinking of it as an infinite sink.

 

[21joanna12]

Just be aware that in Thermo you have an absolute zero for temperature
here on Earth all potentials are relative to something on Earth ,, there's no absolute zero potential that i know of.
i think that's why students get confused about "earth", thinking of it as an infinite sink.

Thank you for your replies! I see now why the analogy isn't the best... In the circuits above, there would be current flow to/from Earth, right? I am just wondering why that is significant, or necessary, in these dc to ac circuits...

 

[zoki85]

In the circuits above, there would be current flow to/from Earth, right? I am just wondering why that is significant, or necessary, in these dc to ac circuits...

Forget about Earth. As said, all it suffices is the circuit to be closed. You can use a perfect wire to form a closed loop (closed circuit) instead of earth.

 

[21joanna12]

Forget about Earth. As said, all it suffices is the circuit to be closed. You can use a perfect wire to form a closed loop (closed circuit) instead of earth.

But then if you have a closed loop with this periodic dc current, an inductor and a capacitor, where in the circuit will the current/voltage be ac and where will it be dc? The supply remains dc, so you cannot have an ac current entering the power source and a dc current leaving it?

And also, if the purpose of this conversion is to produce an ac supply that can go to homes, them how can you create a complete circuit? You wouldn't have a wire going from this gated dc supply, through an inductor, through a capacitor, to a house, and back to the dc supple again... For the doc supply in this case, you should only have one wire coming out of it, and so the circuit cannot be complete! I think that is where earthing comes in, and I don't want to just ignore the earthing because I know that it is an important concept that I should try to understand...

So far, my impression is that if you have two wires coming into this gated dc supply, and you Earth the wire that is the 'input' and then the output wire goes through an inductor, capacitor and then to a house circuit and then it is earther from the house circuit, then this would form a complete circuit? Although this doesn't match the diagram given by meBigGuy- in that diagram the earther wire is after the inductor and capacitor, and also I still do not understand where in the circuit the current stops being dc and becomes ac?

EDIT: I realize that because current cannot be stored at a point in a wire, it must be ac all the way through. There cannot be a transition from gated dc to ac across some component of the circuit...

 

[zoki85]

But then if you have a closed loop with this periodic dc current, an inductor and a capacitor, where in the circuit will the current/voltage be ac and where will it be dc? The supply remains dc, so you cannot have an ac current entering the power source and a dc current leaving it?

In AC circuit parts you have AC current, and in DC parts of the circuit you have DC current. Current which leaves the power source must return to it and for this circuit must have the return path. IOW, the circuit must be closed in some way or you will have accumulation of charge and voltage increase in the circuit. Will you use Earth groundings for return path , to connect pole of the source and pole of the load, or wire is irrelevant from theoretical point of considerations (but important in practical realisations). How is AC converted to DC and vice versa in circuits is the matter of the commutation theory in electrical circuits.

And also, if the purpose of this conversion is to produce an ac supply that can go to homes, them how can you create a complete circuit?

What conversion? Dominant electrical system in most of the countries is still AC all the way, from the power plant to the residental home networks.

 

[21joanna12]

In AC circuit parts you have AC current, and in DC parts of the circuit you have DC current. Current which leaves the power source must return to it and for this circuit must have the return path. IOW, the circuit must be closed in some way or you will have accumulation of charge and voltage increase in the circuit. Will you use Earth groundings for return path , to connect pole of the source and pole of the load, or wire is irrelevant from theoretical point of considerations (but important in practical realisations). How is AC converted to DC and vice versa in circuits is the matter of the commutation theory in electrical circuits.

What conversion? Dominant electrical system in most of the countries is still AC all the way, from the power plant to the residental home networks.

If you were to generate dc current in a solar panel and want to convert it to 240V, 50Hz ac to use in homes? Or if you simply had a dc power supply and wanted to convert it to ac for some reason...

 

[zoki85]

If you were to generate dc current in a solar panel and want to convert it to 240V, 50Hz ac to use in homes?

Then, you use DC-AC converter (inverter) as the interconnection, function of which is governed by commutation laws.

 

[Svein]

And also, if the purpose of this conversion is to produce an ac supply that can go to homes, them how can you create a complete circuit? You wouldn't have a wire going from this gated dc supply, through an inductor, through a capacitor, to a house, and back to the dc supple again...

The AC input to a house consists of two (or maybe three) AC lines. Earth (ground) may or may not be supplied from the power station. If it is not supplied, it is used as a protection for human beings. Otherwise, a short circuit to the metal shell of a stove or a washing machine could become very unpleasant when you touch it.

Otherwise, in an electronic circuit you have power supply lines. Tradition has it that the supply line connected to the negative pole is called "ground" or "earth" even if it is not connected to "Protective ground". Handling "earth" in an electronic product is an art in itself, and gets harder all the time (FCC requirements to radiation play a large part here).

 

[21joanna12]

View attachment 78208

The AC input to a house consists of two (or maybe three) AC lines. Earth (ground) may or may not be supplied from the power station. If it is not supplied, it is used as a protection for human beings. Otherwise, a short circuit to the metal shell of a stove or a washing machine could become very unpleasant when you touch it.

Otherwise, in an electronic circuit you have power supply lines. Tradition has it that the supply line connected to the negative pole is called "ground" or "earth" even if it is not connected to "Protective ground". Handling "earth" in an electronic product is an art in itself, and gets harder all the time (FCC requirements to radiation play a large part here).

Thank you for your reply! So it seems like earthing is never really necessary, it is just a safety measure?

What about in this circuit though:

It seems to me like the earthing to get 0V is necessary in this circuit, even though I don't know why...

 

[jim hardy]

It seems to me like the earthing to get 0V is necessary in this circuit, even though I don't know why...

seems to me you've already fallen into the "earth as absolute zero" mental trap.

Would your fig 1.3 gizmo work in an airplane, or on that asteroid that's due to fly by here in a couple days? Sure it would.
It needs no connection to earth.
Definition of voltage is potential difference
ie between two points of your choosing.
Voltmeters have two probes for that reason.

It was a revelation for me when i learned definition of potential,
the work required to bring a unit charge from some point to wherever you are.
That "some point" is your point of reference.
The closest we EE's can come to "absolute potential" would be the work required to bring that charge from infinity to where we are.
Since we have no way to do that we do not know Earth's "absolute potential".*****
so we always use terms potential , and voltage, to mean referred to someplace nearby
There's no reservoir of charge that's at absolute zero voltage.

Practice this for a few days
"whenever I say "voltage" i will append the phrase "from (measured pointA) to (reference pointB)"
pointA being the place where i have connected my meter's red wire
pointB being the place where i have connected my meter's black wire

in saying it right you will come to think of it right.***** even though some guy got a patent on an apparatus to measure it, http://www.google.com/patents/US4839581

 

[jim hardy]

Here's the simplest way to get AC out of DC
you keep two and only edit: two switches closed at any time,
S1 & S4 for a while
S2 & S3 for the next while

motor M sees its applied voltage reverse every time you change the switches.

Now - what will your voltmeter report during each of the above "while's" if you connect its + lead to M's left side and - lead to M's right side?

While S1 & S4 closed : ?
While S2 & S3 closed : ?

Next - what will your voltmeter report during each of the above "while's" if you connect its + lead to M's right side and - lead to that bottom wire joining S2 & S4 & voltage source?

While S1 & S4 closed : ?
While S2 & S3 closed : ?

and with meter + connected to other side of motor, - to same bottom wire ?
While S1 & S4 closed : ?
While S2 & S3 closed : ?
Keep at it until your mind thinks like a voltmeter.
Then realize you've made a giant step for physics students, you no longer need that mental crutch of Earth as an electrical anchor.

If a circuit is not earthed, its voltage to Earth is indeterminate, that is it's unknown. Think on that and see what questions it brings up.
.
Good luck in your studies. Your questions are interesting; someone like you who probes the very basics can come to a most solid understanding of them.

old jim

 

[Svein]

Thank you for your reply! So it seems like earthing is never really necessary, it is just a safety measure?

Yes - and no. It depends on what type of system your local power company uses. A short explanation (caveat: I describe the European standards, I do not know the standards elsewhere). For reasons lost in the mists of time, power companies deliver three-phase power to the homes. This means that relative to an arbitrary reference potential you have three AC voltages - R, S and T - with 120° phase difference. Older power systems used just these three phases pairwise as in the figure marked "Three-wire supply". Protective ground had to be supplied locally, and regulations exist as to how to create that ground.

A newer standard is the four-wire supply. We still have R, S and T, but in addition a fourth wire ("Return") is used. Now the AC voltages are tapped between each of the phases and the Return line. In theory the Return line is at protective ground level. Another difference is the voltages at R, S and T - since we now use the voltages between each of the phases and Return, the voltages between the phases are higher than for the three-wire system. Due to the 120° phase difference, they are increased by a factor of √3.

 

[21joanna12]

Here's the simplest way to get AC out of DC
you keep two and only switches closed at any time,
S1 & S4 for a while
S2 & S3 for the next while

motor M sees its applied voltage reverse every time you change the switches.

Now - what will your voltmeter report during each of the above "while's" if you connect its + lead to M's left side and - lead to M's right side?

While S1 & S4 closed : ?
While S2 & S3 closed : ?

Next - what will your voltmeter report during each of the above "while's" if you connect its + lead to M's right side and - lead to that bottom wire joining S2 & S4 & voltage source?

While S1 & S4 closed : ?
While S2 & S3 closed : ?

and with meter + connected to other side of motor, - to same bottom wire ?
While S1 & S4 closed : ?
While S2 & S3 closed : ?
Keep at it until your mind thinks like a voltmeter.
Then realize you've made a giant step for physics students, you no longer need that mental crutch of Earth as an electrical anchor.

If a circuit is not earthed, its voltage to Earth is indeterminate, that is it's unknown. Think on that and see what questions it brings up.
.
Good luck in your studies. Your questions are interesting; someone like you who probes the very basics can come to a most solid understanding of them.

old jim

Oh! I get what you mean about the reference voltage. In the four terminal circuit the 0V just means that the Vin/out are at this potential above the bottom two. But then how on Earth do you have so many terminals of different voltages? Wouldn't the charge carriers at a higher voltage just flow down to the lower voltage so that no different voltage terminals are possible?

And with the motor circuit, would the voltage across the motor produced be sinusoidal like mains current because of a back emf? Otherwise, it seems to me like it would just have dc voltage being +v and then -v when you flick the switches...

And thank you so much for answering my questions! I'm always amazed by how generous everyone of PF is with their time and effort :)

 

[jim hardy]

And with the motor circuit, would the voltage across the motor produced be sinusoidal like mains current because of a back emf? Otherwise, it seems to me like it would just have dc voltage being +v and then -v when you flick the switches...

Indeed, the motor will see only the two DC voltages, not a sine wave.
We call that a square wave , if you graph it you'll see why.

There do exist complicated machines that pulse the switches very fast for varying durations
to generate a series of short duration rectangular voltage pulses, all the same height(V_in) but of varying widths.
With clever control of those widths one can make the applied voltage have an average value quite close to that of a sinewave, we call that PWM for pulse width modulation.

For a mind-blowing investigation into that principle see "Magic Sinewaves" by Don Lancaster
http://www.tinaja.com/glib/msintro1.pdf

most PWM sinewave approximations aren't so esoteric, though.

That four switch converter is called an "H Bridge" - what's in a name, huh ?

search on H Bridge PWM

dotted line approximates short term average of pulses (remember it's the area enclosed smoothed over time)

Can you tell which two switches are closed during each gray pulse?

There's your AC approximate sine from DC

you'd add a filter to do the physical smoothing if you wanted a cleaner sinewave, probably combination of L and C.

A motor will accept those voltage pulses though and run okay. It's a math abomination but Mother Nature tolerates it.old jim

 

[jim hardy]

And thank you so much for answering my questions! I'm always amazed by how generous everyone of PF is with their time and effort :)

You take the effort to phrase your questions well, which is showing respect for others.
A thoughtful, well turned phrase invites equally thoughtful responses.
Most folks enjoy such conversations. .

"joanna' sounds like a feminine name
so why would you be surprised that young men scurry to the aid of a perceived

who's intelligent and well spoken ?

"A question well stated is half answered"
Myself I'm just a grumpy old man who enjoys well stated questions.

Good luck in your studies -

and understand regarding that "generosity" - your consideration of others as evidenced by your attention to clarity of expression is equally appreciated.old jim