Thevenin Resistance

[Ratchit]

MrAl,

"I almost forgot to mention that it looks like this circuit might belong in the "Theoretical Only" section of our libraries. That's because it looks like with even the smallest DC offset voltage present at the input the circuit could ramp to an infinite response, which would mean it would latch up to the highest or lowest possible operating voltage and stick there. You could look at this too if you wish."

Although the independent current source symbol in the circuit schematic is presented as a DC source, the fact that reactance values are given for the capacitors implies that it is really an AC source at some definite frequency. If it were a DC source, both capacitors would blow out because the voltage across them would eventually exceed their voltage ratings. This would happen without any external attachment to the circuit. If any voltage is attached to a-b, the capacitor across a-b will be locked at that voltage, but the capacitor in series with the independent current source would eventually blow.
Ratch

 

[MrAl]

Hi Ratch,

I am not sure what you are trying to imply there, but just to clear one thing up i never said that the current source was a DC source, i was just pointing out that a DC offset of even a small amount anywhere in the circuit could cause a ramp up (or down) to the max (or min) available supply voltage.

It's very hard to create a perfect AC source with no DC offset and that includes an AC source with only slightly higher amplitude positive half cycles than the negative half cycles. Even a capacitor in series with a supposedly AC source would have leakage current that could introduce a little DC current into the circuit. So it might be impossible to use this circuit in a real life application without some sort of DC offset correcter circuit added on.

We also see this kind of thing in power converters that have output transformers. The power converters can not generate a perfect AC sine source even not a perfect PWM sine so we end up with some DC current in the primary unless we use an offset current correcter circuit. Without the correcter circuit the transformer makes more audible noise which can be quite annoying.

 

[Ratchit]

MrAl,

In post #20 you talked about an offset voltage at the input, which I assume are terminals a-b. In post #22 you expand the location to it "anywhere" in the circuit. If there is a voltage source in series with the independent current source, then it will not affect the circuit because the current source will adjust its voltage to keep sqrt(2) current existing, thereby nullifiying the voltage source. The calculations were made with ideal theoretical components. If other factors are to be considered, then a new circuit should be submitted.

Ratch

 

[MrAl]

Hello,

Well the main idea and simplest is to think of it as having a small DC offset at the input a,b terminals. That is the simplest to show where the trouble starts. But the type of offset varies with the source it's not restricted to a given type of source.

The sqrt(2) current source does not need to have a DC "voltage" offset, it can have a DC current offset. That may cause a problem as well, and you can look at that if you wish.

 

[Ratchit]

MrAl,

Well, as I said in post #21, if a small constant voltage is put across the a-b terminals, then the capacitor will be locked at that voltage, and the current will bypassed by the zero impedance of the voltage source. The DC offset current can be modelled by a DC source in parallel with the AC source.

Ratch

 

[MrAl]

Hello Ratch,

Yes that's true, but that is only if the voltage source has low enough series impedance.

Also true about the current source, and i think it may be hard to design an AC current source with a perfectly zero offset. Might be possible though, but you see the point now.

This also comes up in the primary of transformers where even a tiny offset voltage like 0.1v with a very low primary resistance like 0.1 ohm causes a full 1 amp DC already.