Determination of theoretical frequency of oscillation

Thread Starter

mjuric03

Joined Jun 19, 2023
7
Hi, I really need some help with this. So, my paper presents the principle of the 12V DC voltage to 220V AC voltage converter, based on RL-astable. A mains transformer is used in the opposite connection of the primary and secondary, where the coils of the secondary form the reactive components of the astable. I need to do analysis of the operation of circuit and simulation of the circuit.

First step is to determine theoretical frequency of oscillation of this circuit. I couldn't find anywhere this equation, so if someone knows, please can you share it with me.

I attached below my "final circuit" (this is just principle I need to explain, but in simulation I will need some new parameters like diodes, resistors etc. and of course consumer - picture 1). Also, I will need some simulation of the output voltage (I attached below the circuit from which I need to do simulation - picture 2).

Thank you for help in advance :)
 

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Thread Starter

mjuric03

Joined Jun 19, 2023
7
Yes, it should be.. the output won't be so "clean" so I assume I will need some capacitors, but that's not important in this moment. I really can't find anywhere about this circuit..
 

Marley

Joined Apr 4, 2016
501
Are L1 and L2 the primary windings of the transformer?
To set a frequency, you would probably need to add a capacitor between the collectors of the transistors. Forming a resonant circuit.
But there are many shortcomings with this circuit:
  • What is the primary inductance? Need to know this to determine the value of the capacitor required.
  • This inductance will be effected by the load so the frequency will not be accurate or stable.
  • The transistors will need to be high current, high power types and are need to be driven correctly.
  • For a 50Hz or 60Hz inverter, the frequency needs to be accurate and stable so a separate oscillator (frequency probably derived from a quartz crystal via a divider chain) is required.
  • The power transistors need to be correctly driven - MOSFETs would be better actually.
  • PWM to obtain pseudo sine wave.
  • And a whole lot of other things!
 

Ya’akov

Joined Jan 27, 2019
8,534
Hi, I really need some help with this.
Welcome to AAC.

Your thread has been moved to the Homework Help forum.

AAC rules constrain the sort of help that can be given with coursework. So, to prevent confusion about the nature of such a question, they must be posted to the Homework Help forum.

Nothing else is changed aside from the forum it is located in.

[Moderation]
 

MrAl

Joined Jun 17, 2014
10,909
Hi, I really need some help with this. So, my paper presents the principle of the 12V DC voltage to 220V AC voltage converter, based on RL-astable. A mains transformer is used in the opposite connection of the primary and secondary, where the coils of the secondary form the reactive components of the astable. I need to do analysis of the operation of circuit and simulation of the circuit.

First step is to determine theoretical frequency of oscillation of this circuit. I couldn't find anywhere this equation, so if someone knows, please can you share it with me.

I attached below my "final circuit" (this is just principle I need to explain, but in simulation I will need some new parameters like diodes, resistors etc. and of course consumer - picture 1). Also, I will need some simulation of the output voltage (I attached below the circuit from which I need to do simulation - picture 2).

Thank you for help in advance :)
Hi,

This circuit looks so symmetrical it is very possible it would never work in pure theory or might work in a very unexpected way, although in real life there would be an imbalance of some sort that could help to start it up.

The simplest approach seems to be to assume that at t=0 both transistors are off but just after that only one turns on fully, the first transistor. That means the inductor on that side starts to conduct current. At some point the current in that inductor goes up so high that it pulls the associated transistor out of saturation, meaning the collector voltage rises, and that means that at some point the second transistor turns on and that turns off the first transistor. The same thing would occur for the second transistor until the first transistor turns on again, and that is the end of one complete cycle. Thus, the half cycle time is the time from when an inductor first starts to conduct to when the other transistor turns on. The full cycle would be twice that.
 

Audioguru again

Joined Oct 21, 2019
6,442
A cheap and old inverter had an output squarewave and used a similar simple oscillator like yours. It can light incandescent light bulbs or feed heaters. But the peak voltage of the squarewave is too low to power modern electronic products.

Modern inverters use a modified squarewave that is almost a sinewave made up with "steps".
 

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RoofSheep

Joined Mar 7, 2023
36
Remember that average voltage across each inductor must be zero in the steady state. Can the voltage across the inductors go negative in this circuit?
 

Irving

Joined Jan 30, 2016
3,548
All astable multivibrators require this imbalance, either through deliberate component selection or just sheer luck. Typically this would be an RC network as shown above. but I don't think an R-L astable will be possible - at least not at that low a frequency. Pulling the driving transistor out of saturation wouldn't be sufficient to flip it. Maybe a current monitor on the emitter switching the other side might do it...
 

MrAl

Joined Jun 17, 2014
10,909
Remember that average voltage across each inductor must be zero in the steady state. Can the voltage across the inductors go negative in this circuit?
Hi,

I don't think the inductor voltages have to go negative, they would actually go more positive.

During turn on, the voltage across an inductor is + on top and - on bottom, and the (conventional) current builds in the direction of top to bottom. During turn off, the current still has to go top to bottom so the bottom will go more positive in order to keep the current flowing in the same direction. Thus, the voltage at the bottom terminal will build just like a boost converter. The DC current would have to eventually go to zero, unless there was significant ESR, and then it would not have to go to zero, but it probably should, and we could look into that more carefully.
 

MrAl

Joined Jun 17, 2014
10,909
All astable multivibrators require this imbalance, either through deliberate component selection or just sheer luck. Typically this would be an RC network as shown above. but I don't think an R-L astable will be possible - at least not at that low a frequency. Pulling the driving transistor out of saturation wouldn't be sufficient to flip it. Maybe a current monitor on the emitter switching the other side might do it...
Hi there,

Some boost converters with just one inductor work under that principle. They are made with an inductor that forces the drive transistor out of saturation. They do have a small capacitor too though to help time the 'off' time. I don't know if the other inductor could perform this function well enough, but it could be just in pure theory too where we assume some other things happen perfectly as well.
I guess now to analyze the circuit :)
 

ericgibbs

Joined Jan 29, 2010
18,234
Hi,
I do have a 50Hz square wave running on LTS, using the TS's basic circuit, but reluctant to post it as this is homework.
E
 

Thread Starter

mjuric03

Joined Jun 19, 2023
7
A cheap and old inverter had an output squarewave and used a similar simple oscillator like yours. It can light incandescent light bulbs or feed heaters. But the peak voltage of the squarewave is too low to power modern electronic products.

Modern inverters use a modified squarewave that is almost a sinewave made up with "steps".
Yes, I know that.. My consumer will probably be some bulb. And I can't use this RC astable because my converter is RL based, that is problem :)
 

ericgibbs

Joined Jan 29, 2010
18,234
Hi mj03,
As this is homework I cannot give you a complete answer, this simulation shows that the circuit does work., removed the component values.
E
EG57_ 911.png
 

Ivan12345

Joined Jun 19, 2023
1
Hi, I really need some help with this. So, my paper presents the principle of the 12V DC voltage to 220V AC voltage converter, based on RL-astable. A mains transformer is used in the opposite connection of the primary and secondary, where the coils of the secondary form the reactive components of the astable. I need to do analysis of the operation of circuit and simulation of the circuit.

First step is to determine theoretical frequency of oscillation of this circuit. I couldn't find anywhere this equation, so if someone knows, please can you share it with me.

I attached below my "final circuit" (this is just principle I need to explain, but in simulation I will need some new parameters like diodes, resistors etc. and of course consumer - picture 1). Also, I will need some simulation of the output voltage (I attached below the circuit from which I need to do simulation - picture 2).

Thank you for help in advance :)
dobar dan
 

Thread Starter

mjuric03

Joined Jun 19, 2023
7
Hi,
I do have a 50Hz square wave running on LTS, using the TS's basic circuit, but reluctant to post it as this is homework.
E
I don't know why they moved this question to section "Homework help". Maybe because I used the word "help" in my first post. But I posted here so I could hear some suggestions from you because you are obviously more experienced than me. I really don't know where to start, because my mentor expects from me to first determine frequency of oscillation theoretically based on picture 2. from above (also consider in mind basic RL circuit).. and also to do some simulation based on same picture. I did that simulation, here is result but I don't know if this is correct..
 

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Thread Starter

mjuric03

Joined Jun 19, 2023
7
So I did some simulation based on circuit on my picture 2 above, here is result of current.. Is this correct? I'm not sure what I can expect as a response and what exactly I need to analyze. They just told me to look at the response of the collector current Ic and voltage Vc (between DC current - 1 A and ground) from the picture 2. DC voltage source before inductor is 12 V.
 

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MrAl

Joined Jun 17, 2014
10,909
Hi,

I overlooked the fact that the two inductors are coupled, which makes it start to look a bit like a Royer oscillator without the extra winding.
 

ericgibbs

Joined Jan 29, 2010
18,234
I don't know why they moved this question to section "Homework help".
Hi mj03,
It was moved to Homework because you are a student and the assignment will be graded by your mentor.
As you maybe aware, we only provide guidance to students with their assignments, not final solutions.

Moderation.
 
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