Lightning Strike

[mbrooke]

Why do lightning strikes travel or propagate in a wave? Does it have to do with the way the electric field distributes over a mile wide area and then sharply increases in gradient potential as the discharge finalizes and then starts to occur- low to high bleed to ground at the strike point? Or something to do with the high frequency nature of lighting causing back EMF in a conductor?

https://cdn.ymaws.com/www.kmunet.org/resource/resmgr/Presentations_Misc_Docs/4a_-_Overcurrent_Protection_.pdf

 

[GoldDigger]

Because of the interaction between the electric and magnetic fields associated with high frequency current, modeling of current flow along any path really needs to analyze each path as a transmission line with a characteristic impedance. That line is usually not terminated at the characteristic impedance, leading to reflections and standing waves along the path.

 

[mbrooke]

Because of the interaction between the electric and magnetic fields associated with high frequency current, modeling of current flow along any path really needs to analyze each path as a transmission line with a characteristic impedance. That line is usually not terminated at the characteristic impedance, leading to reflections and standing waves along the path.

I see... how exactly does the characteristic impedance result in reflection?

 

[GoldDigger]

It is hard to describe clearly without the math behind it. But the theory says that an ideal or real world line composed of distributed series inductance and parallel capacitance acts as if it is (to first approximation) a lossless transmission line as long as it is terminated by a resistive load whose value depends on the inductance and capacitance values. And that characteristic impedance (resistance) is independent of the applied frequency.

From high school physics, the explanation of reflections is that at any termination or impedance change there must be both an incoming wave and a reflected wave whose phase and amplitude allow the boundary conditions to be met. For example, a short circuit termination requires that the voltage at that point be zero. That is satisfied by a reflected wave of identical amplitude and reversed phase (looking at voltage).
An open circuit requires that the current be zero, which is satisfied by a reflected wave of identical phase and identical amplitude (but with the current in the opposite direction, since the wave is going the other way.)
Since one condition gives an in phase reflection and the other gives an out of phase reflection, you can see that for some resistance value in between 0 and infinity there must be no reflection.

A simple experiment involves laying a long slinky stretched out on the floor, holding one end fixed and jerking the other end sideways. You see a pulse move down the slinky and move back, reflecting off the fixed end. Take the formerly fixed end and instead support it with a long string so it can move sideways freely and you see that the polarity of the reflected pulse is reversed.
Connect the fixed end to a length of identical slinky continuing on down the floor and there will be no reflection at the junction point.

 

[synchro]

It is hard to describe clearly without the math behind it. But the theory says that an ideal or real world line composed of distributed series inductance and parallel capacitance acts as if it is (to first approximation) a lossless transmission line as long as it is terminated by a resistive load whose value depends on the inductance and capacitance values. And that characteristic impedance (resistance) is independent of the applied frequency.

From high school physics, the explanation of reflections is that at any termination or impedance change there must be both an incoming wave and a reflected wave whose phase and amplitude allow the boundary conditions to be met. For example, a short circuit termination requires that the voltage at that point be zero. That is satisfied by a reflected wave of identical amplitude and reversed phase (looking at voltage).
An open circuit requires that the current be zero, which is satisfied by a reflected wave of identical phase and identical amplitude (but with the current in the opposite direction, since the wave is going the other way.)
Since one condition gives an in phase reflection and the other gives an out of phase reflection, you can see that for some resistance value in between 0 and infinity there must be no reflection.

A simple experiment involves laying a long slinky stretched out on the floor, holding one end fixed and jerking the other end sideways. You see a pulse move down the slinky and move back, reflecting off the fixed end. Take the formerly fixed end and instead support it with a long string so it can move sideways freely and you see that the polarity of the reflected pulse is reversed.
Connect the fixed end to a length of identical slinky continuing on down the floor and there will be no reflection at the junction point.

Also, the ratio of the reflected wave voltage to the incident wave voltage at a load impedance ZL which terminates a transmission line of characteristic impedance Z0 is the reflection coefficient "Gamma":

Γ = (ZL - Z0) / (ZL + Z0)
So if the the load impedance ZL equals Z0 (i.e, a matched load) then Γ=0 and there is no reflected wave. That's because the energy of the incident travelling wave is completely absorbed by the "matched" load.

 

[mbrooke]

It is hard to describe clearly without the math behind it. But the theory says that an ideal or real world line composed of distributed series inductance and parallel capacitance acts as if it is (to first approximation) a lossless transmission line as long as it is terminated by a resistive load whose value depends on the inductance and capacitance values. And that characteristic impedance (resistance) is independent of the applied frequency.

In full understanding here.

From high school physics, the explanation of reflections is that at any termination or impedance change there must be both an incoming wave and a reflected wave whose phase and amplitude allow the boundary conditions to be met.

Can you define boundary?

For example, a short circuit termination requires that the voltage at that point be zero. That is satisfied by a reflected wave of identical amplitude and reversed phase (looking at voltage).

A bit confused on this part...

An open circuit requires that the current be zero, which is satisfied by a reflected wave of identical phase and identical amplitude (but with the current in the opposite direction, since the wave is going the other way.)
Since one condition gives an in phase reflection and the other gives an out of phase reflection, you can see that for some resistance value in between 0 and infinity there must be no reflection.

But how could you have current if there is a reflected wave?

A simple experiment involves laying a long slinky stretched out on the floor, holding one end fixed and jerking the other end sideways. You see a pulse move down the slinky and move back, reflecting off the fixed end. Take the formerly fixed end and instead support it with a long string so it can move sideways freely and you see that the polarity of the reflected pulse is reversed.
Connect the fixed end to a length of identical slinky continuing on down the floor and there will be no reflection at the junction point.

How would this translate to a lightning strike though?


An ideal transmission line with series reactors and shunt capacitors is the easiest to picture. I've done some transmission line modeling at 60Hz. But how this complex impedance reacts to a lightning pulse I need more of a walk through.

Would resonance play a role in any of this?


Forgive me for asking the obvious on this concept. Lightning has always been a very hard topic for me to grasp however I intended to dedicate time to finally mastering it in 2020 .

 

[mbrooke]

Also, the ratio of the reflected wave voltage to the incident wave voltage at a load impedance ZL which terminates a transmission line of characteristic impedance Z0 is the reflection coefficient "Gamma":

Γ = (ZL - Z0) / (ZL + Z0)
So if the the load impedance ZL equals Z0 (i.e, a matched load) then Γ=0 and there is no reflected wave. That's because the energy of the incident travelling wave is completely absorbed by the "matched" load.

Perhaps an animation of charging caps and inductive field lines may help? For some reason I'm thinking series RLC circuits.

 

[GoldDigger]

Perhaps an animation of charging caps and inductive field lines may help? For some reason I'm thinking series RLC circuits.

You have to lose the R part. And when the L and C are distributed rather than lumped, there is no resonance, just a transmission line with a purely resistive characteristic impedance. Now a transmission line of the right length, terminated by other than the characteristic impedance, can appear as almost any complex impedance you want, varying with the applied frequency.

 

[mbrooke]

You have to lose the R part. And when the L and C are distributed rather than lumped, there is no resonance, just a transmission line with a purely resistive characteristic impedance. Now a transmission line of the right length, terminated by other than the characteristic impedance, can appear as almost any complex impedance you want, varying with the applied frequency.

Getting there- this part I can understand. Can you clarify "terminated by other than the characteristic impedance" (its early morning for me lol)