How Do You Handle KVL Limitations in High-Frequency AC Circuits?

[Muhammad Usman]

Hi,

I was reading KVL and KCL and I read that KVL cannot be applicable to all the situations specially when :-

" KVL is applicable on the assumption that there is no fluctuating magnetic field linking the closed loop. While, in presence of changing magnetic field in a High Frequency but short wave length AC circuits, the electric field is not a conservative vector field. So, the electric field cannot be the gradient of any potential and the line integral of the electric field around the loop is not zero, directly contradicting KVL. That’s why KVL is not applicable in such a condition "

My Main question is how to deal with this inconsistency or in other words if we face such circuit where AC frequency is high then which method is used
for such kind of circuits to calculate the voltage and current. Many thanks

 

[anorlunda]

The PF Insights article https://www.physicsforums.com/insights/circuit-analysis-assumptions/ goes over the assumptions needed for KVL, and KCL, and circuit analysis in general. I think the key one for your question is:

The time scales of interest in CA are much larger than the end-to-end propagation delay of electromagnetic waves in the conductors.

When the frequencies are high enough so that is not true, then you can't use circuit analysis.

 

[DaveE]

KVL and KCL are tools applied to "lumped element" circuit analysis. What this means in practice is that you only consider circuit elements that are drawn in the schematic. If magnetic coupling between circuit loops is to be considered, then that should be drawn in the schematics as a circuit element(s), like a transformer between the loops, for example.
Circuit analysis is always an approximation in a purely theoretical sense. Problems often have implicit simplifying assumptions to allow us to use tools like KVL.
So, for example, you probably don't have to worry about quantum mechanics or cosmic rays, unless someone says they matter.

 

[jim hardy]

" KVL is applicable on the assumption that there is no fluctuating magnetic field linking the closed loop.

I still regard that claim as 99% sophistry.
Why cannot the induced emf be lumped and represented as just another voltage source?

Antennas , transmission lines and waveguides are a different story .
To me they're a separate field with its own textbooks and math. No place for beginners...

old jim

 

[anorlunda]

I still regard that claim as 99% sophistry.
Why cannot the induced emf be lumped and represented as just another voltage source?

It might be a semantic difference Jim, but an equivalent circuit is a different circuit. Once you have the equivalent circuit, it is analyzed using CA rules without flux and without charge. An ideal transformer in a transformer equivalent is a device that makes no reference to magnetic flux.

From the article.

The time rate of change of magnetic flux outside any conductor is zero. [$\frac{∂ϕ}{∂t}=0$]
If the initial flux at t=0 was zero, it remains zero. [So basically forget magnetic flux for CA. Forget Poynting vectors.]

The time rate of change of electric charge inside any conductor is zero. [$\frac{∂q}{∂t}=0$]