Welcome to The STEM Sessions Podcast. I am Jarl Cody, your host and narrator.
At my day job, I moderate a working group in which engineers of varied disciplines share knowledge outside of program channels. It has successfully improved communication and learning, and is one of the inspirations for creating The STEM Sessions.
I try to lead by example, and share material often, filling in when no one else volunteers. Recently, I presented a chapter of my bus bar design guide detailing electrical isolation. In all of my presentations, I try to explain why we do something, not just what we should do. So a large portion of this was explaining the physics Paschen’s Law… which I first had to teach myself before I could explain it to the group.
And, since I put in a lot of effort and research to be able to at least somewhat adequately explain the concepts to a group of engineers, I thought I would share it here, too.
This is The STEM Sessions Podcast – Episode Six. The Physics of Electrons at Altitude
In electronics packaging, we’re often concerned with the spacing of electrical conductors, such as the leads of adjacent components on a circuit card or pins in a connector. Typically, the more densely you can package conductors, the more weight and volume you save. But dense packaging also increases the chance of electrical shorts, which can damage your hardware or harm the user. So knowing how closely can you place two conductors without an electrical current shorting between them is critical to efficient and robust packaging.
Paschen’s Law shows the relationship between conductor spacing and voltage. It’s a complicated equation taking into account the altitude and the composition of the atmosphere. Fortunately, we rarely need to use this equation, because countless graphs and tables have already been published for nearly every design environment we find ourselves in.
We simply find the graph for the atmosphere we’re working in – be it air, pure oxygen, hydrogen, etc – and look up the appropriate conductor spacing given the voltage and altitude we want to meet. This data is so readily available and experimentally verified, we take Paschen’s Law for granted without understanding the physics behind it.
Let’s say you have two parallel conductors, such as metal plates, separated by a gap containing some composition of gas molecules or even a vacuum. A voltage differential is applied to the plates. As you increase the voltage, at some point, there will be enough energy to make electrons jump from one plate to the other, crossing the air gap, and creating a short between the conductors.
Alternately, you could keep the applied voltage constant and bring the two plates closer together. At some point, the gap will be small enough that the electrons will have enough energy to jump, again resulting in a short between the conductors.
In either case, the voltage at which the electrons jump from one conductor to the other is called the breakdown voltage; a value specific to several variables such as the gas between the plates, the conductor spacing, and the altitude. To be more technical, Paschen’s Law accounts for air pressure, not altitude. But the published curves are often in terms of altitude, because that’s often the variable we’re concerned with, and for the sake of this discussion, just understand that as altitude increases, air pressure decreases. So high altitude, means low pressure.
As the gap increases, so does the breakdown voltage. This makes obvious physical sense as more energy is needed to overcome the distance.
Different gasses have different insulative properties, and as the insulative value increases so does the breakdown voltage. Again, this makes intuitive sense.
As air pressure increases, so does the breakdown voltage. This also made intuitive sense to me, or so I thought. As I dove into the details, I discovered I was correct but for the wrong reasons.
I’m a mechanical engineer, so I immediately thought about it in mechanical terms. Higher air pressure means you have a greater force pushing against the electrons, thus you need to apply more energy (or a higher voltage) to overcome the force of the air pressure keeping the electrons in place. Conversely, when you have lower air pressure, you have a lower force holding the electrons in place so the breakdown voltage is lower.
This made perfect sense in my head, but it was completely wrong. It has nothing to do with the air pressure keeping the electrons in place. In fact, that isn’t even a force you need to worry about. The electrons are much too small, and I should have realized that to begin with. the air pressure doesn’t interact with the electrons at all. Instead, it’s the gas molecules the air pressure interacts with, impacting the density, or number, of gas molecules between the plates.
So here is what really happens:
The applied electric field (or voltage) accelerates electrons across the gap between conductors. Along the way, they collide with gas molecules. The average distance between collisions is called the mean free path.
To fully jump the gap between conductors, the electric field must give the electrons enough energy to create a cascade reaction of collisions. This means the collision between the electron and gas molecule ionizes molecules freeing new high energy electrons, which in turn have enough energy themselves to cause additional ionizing collisions until electrons reach the other conductor.
But every collision randomizes the electrons’ direction of travel, meaning they do not travel in a straight line between the conductors. In fact, some collisions result in the electrons traveling backwards to the originating conductor. Further, energy is lost in each collision, meaning less energy is available to ionize the gas molecule in the next collision.
Therefore, as the number of collisions increases, a higher voltage is required to give the electrons sufficient energy to ionize all gas molecules they collide with – overcoming both the gap distance and the energy lost in the collisions themselves.
Increased air pressure means increased density of gas molecules between the plates. This means more collisions and therefore more energy is needed to overcome them; thus, the breakdown voltage is higher. Decreased pressure results in fewer molecules between the plates, which means fewer collisions and less energy required; thus, the breakdown voltage is lower.
Therefore, a better mechanical analog would be a pool table. The end rails represent the parallel conductors. The distance between them is the gap. The balls represent the gas molecules, the cue ball an electron, and the force with which you hit it is the applied voltage. The more balls you have on the table, the more energy you need to hit the cue ball with for it, or the results of the many collisions, to reach the opposite end of the table. Fewer balls results in fewer collisions, and you probably don’t need to hit the cue ball as hard for it or another ball to reach the opposite end of the table.
Air pressure is an important variable to understand, because it decreases rapidly from sea level. So an electronics design that may have sufficient conductor spacing on the ground might have problems at 50,000 feet. As an example, a connectors come with a published dielectric withstanding voltage between adjacent pins. The dielectric withstanding or test voltage is typically 75% of the breakdown voltage. A withstanding voltage of 1300 Vrms at sea level may drop to 550 Vrms at 50,000 feet and 350 Vrms at 70,000 feet. So a design voltage of 500 V has plenty of margin at sea level, but becomes iffy at 50,000 feet and insufficient at 70,000.
Fortunately, the industry has published many design guidelines over the years that provide starting points for conductor spacing. Some go beyond the relationships found in Paschen curves and include common isolating coatings such as parylene. These guidelines are based on physics and experiment, so we don’t need to start from scratch each time.
If any of you paused this episode to search for an example of a Paschen curve, you may have noticed the relationship between gap distance and breakdown voltage flips on the left side of the Paschen minimum. At those incredibly small scales, the breakdown voltage increases as the gap distance decreases.
This is another non-intuitive bit of mechanics that I’d like to briefly explain. As stated earlier, the mean free path is the average distance an electron travels between collisions. When the gap distance is below the Paschen minimum, there are a reduced number of gas molecules between the plates; they’re basically squeezed out of the gap. The electrons, therefore, have greater distances to travel between collisions (the mean free path increases), and thus a higher voltage is needed to overcome the longer distances and produce a cascade.
You might think at small gap distances, the electrons have less distance to travel, but that’s a fault in our perception or understanding of size of the electrons and gas molecules relative to the distance between conductors. As closely spaced as we can make conductors, electrons are still much, much smaller.
Thank you for listening to this episode of The STEM Sessions podcast. I do my best to always provide accurate information, but, unfortunately, I’m fallible like everyone else. So I encourage you to do your own research on the topic we discussed. Corrections and new information are always welcome.
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Do your own research. Satisfy your curiosity. And keep learning.
Design Considerations for Power Supplies in High-Altitude Applications