Ohms Law Limits

vk6kro

3 GHz is 1 cm, so any circuit element larger than 1 cm is 100% "distributed" and not "lumped" while at 300 MHz (1/10 3 GHz), 1 cm sized circuit elements are still "lumped" to a good approximation. In the in-between of 300 MHz-3Ghz, things get dicey because some aspects are lumpy enough while other aspects are distributed.

A case in point: all square wave or "pulse-y" waveforms have odd harmonics to make them "square". Basically all digital waveforms. So you need "sufficient" harmonics to get a square-ish edge on any digital waveform. The rule of thumb from this is digital waveform edges (rising or falling edge time) require bandwidths that 10x the clock rate.

So if your clock rate is 300 MHz, then you need 3 GHz for the edges. If you are at 3 GHz, you need 30 GHz for the edges. This is actually central to why microprocessor clocks hit a brick wall around 2000: how big is that average microprocessor die, diagonal corner to corner? ~1 cm. So you have edge issues already that are distributed rather than lumped.

And that's a problem: the entire concept of digital logic 0 or 1 is itself a lumped model on top of the analog lumped model that approximates Maxwell's equations. If the foundation turns to quick-sand, then the building itself will start having problems.

The wavelength of a 3 GHz radio wave in air is close to 10 cm or about 4 inches. (³⁰⁰/₃₀₀₀ * 100 cm)This is quite a lot bigger than the average computer CPU chip.

Transmission line effects cause apparent Ohm's Law violations all the time.
If you connect a quarter wavelength of 50 ohm transmission line to a 100 ohm resistor, at the other end of the line it will appear to be 25 ohms.
Put 100 volts across it (at the right frequency for that wavelength) and it will draw 4 amps. That is 400 watts and the resistor will get 400 watts too, (ignoring losses), but at 200 volts and 2 amps.
Ohms Law still applies locally, but transmission line effects make it look as if it doesn't apply.
After all, you put 100 volts in and the resistor drew 2 amps, that is only 200 watts, so where did the other 200 watts go?

sophiecentaur

I don't see that any of this relates to Ohm's Law at all. There's nothing inherently non linear about any of these effects and that's all Ohm's Law tells you. It deals specifically with resistance and doesn't concern any transforming effects of distributed components. In all these examples, doubling the Volts will double the Current. So where's any violation?

vk6kro

That was the point I was making. You can get apparent anomalies, but Ohm's Law continues to apply.

If fact, I cringe when I hear talk of "non-ohmic" resistors. Just because the resistance of a resistor changes (due to temperature, for example) does not mean Ohm's Law no longer applies.
A small change in voltage still produces a small change in current and the ratio of these two still gives the resistance of the resistor.

sophiecentaur

It would have been better if they had called it 'Ohm's Behaviour', perhaps.

Nevertamed

ohms law fails when the resistance of the conductor increases as it gets hot by electron friction

phinds

That doesn't seem to make sense. All you are saying is that the resistance varies with temperature. Whatever the resistance is, Ohms Law should still hold.

sophiecentaur

You obviously haven't read what Ohm's Law says.

Nevertamed

in Ohm's law as resistance is proportional to voltage, then: temperature is a limitation, resistance varies with temperature, and depending on materials and room temp, it can vary a lot. unless we state that temp is constant we can secure the lineality of the ecuation

vk6kro

It depends on the definition of Ohm's Law.

There is the one we all saw on day 1 of Electricity at school. Graph voltage vs current and if it is a straight line then you can work out the resistance.

According to that version, even a rheostat would be regarded as non ohmic because it can change.

It leads to the strange situation where a lamp filament is "non-ohmic" if you measure its voltage and current curve slowly (and give it time for the temperature to change) but "ohmic" if you change the voltage rapidly. The current in a lamp filament with 60 Hz AC on it is close to sinusoidal, meaning the resistance is close to constant because the temperature is fairly constant and the resistance is also stable.

Much more useful is the incremental one which assumes that Ohm's Law always applies and you can work out the resistance at any point on a V vs I curve by taking a small change in voltage and observing the small change in current that results.

This small signal resistance is very real and it can be measured as the actual impedance of a circuit. It may be quite different to the ratio of DC voltage to DC current that applies at that point.

sophiecentaur

Ohm's Law is its own definition. The condition for V/I being constant is for the temperature to be constant. Measurement with a 'probe', low level AC of a filaments lamp will reduce the temperature fluctuation and give a value of dV/dI that is not resistance. The resistance is still V/I for the particular point on the temperature dependent VI curve that you will get using DC.

The only time that Ohm's Law truly fails for a metal is for enormous current flux when there are just no more conduction electrons available and the conductor becomes .non linear.

es1

I wonder though: It is Ohm's Law that is failing or that the device (or circuit) in question is no longer well modeled by an ideal resistor in the examples given? I would argue Ohm's law isn't breaking, the ideal resistor model is.

If one replaced the ideal model in Ohm's law with a new model that also took temp, time, etc., into consideration, wouldn't Ohm's law still hold? I think it does.

I agree with Sophie and the only thing that really breaks it is current density and possibly arc'ing across the geometry of the element. Because if the function for R had to take current or voltage as an independent variable then equation we would be left with would be self referencing and I think this would count as a new beast.

sophiecentaur

But, as with many so called laws of nature, Ohm's Law has no 'authority' to make things behave a certain way. It doesn't punish them if they don't conform. Ohm's law is merely a description of what happens under a particular set of circumstances. If one reads the wording carefully (actually, it's blindingly obvious that you should always do that) then there isn't much to disagree with and there's certainly no reason to hop about saying "Ohm got it wrong". Add some extra factors and metals will behave differently - so what?

I would say that the only time a metal stops obeying Ohm's law is when it is under such extreme conditions that it can almost not be classed as a metal because its very structure will have changed (metallic bonding won't even be the same). George O. can't really be blamed for not having put a codacil on his Law to take account of this.

Nevertamed

wonderful answer

Kholdstare

Can anyone quote the exact statement given by Ohm with web reference. Just being curious.

Given a constant temperature current will be equal to voltage multiplied by resistance. - correct
Given a constant temperature current will be proportional to voltage. - wrong

vk6kro

The history of Ohm's Law is covered in the Wikipedia article:
http://en.wikipedia.org/wiki/Ohms_law

sophiecentaur

?????
If you get your history right, you will realise that Ohm only introduced Resistance as the constant of proportionality for a linear relationshipbetween two quantities that he could actually MEASURE. They didn't sell Ohmmeters at the time!

Nevertamed

dude could u explain wtf are u talking about? under that condition voltage follows current proportionally: CORRECT

I= V R: WRONG