I am now in a position where I mostly understand the math of AC power, although I could not easily replicate it. So I am broadly ok with the Euler Equation, and P=V x I and all the sine wave and phase angle complications and real and reactive power, P and Q diagrams and phase angle and power factor, etc etc. I can even broadly understand phasors and phasor algebra. The problem I always had (until recently) was understanding why or how power (energy flux) actually flowed, and in what direction. I never found P=V x I and its units Watts, Volts and Amps very intuitive. And because I don't know the Maxwell equations I cant relate it all. What finally got me going in the right direction was learning about the Poynting Vector, which I had NEVER heard about before. Basically I believe the Poynting Vector is related to the Maxwell equations and basically says that energy flux is basically the cross product of the electric and magnetic fields, and once I played with this a bit, I could see how the AC voltage and current waves (and their corresponding electric and magnetic fields, at right angles) could show that power flows in one consistent direction (oscillating of course at twice the line frequency) and if the phase angle shifted into another quadrant, the cross product reverses direction and power goes the other way. So on the PQ diagram this is why in two quadrants the power is positive and in the other two is negative and all that describes in the direction of energy flux in the line. The thing about the Poynting Vector is that its usually used to describe power flow in wireless transmission, but I am sure it also applies to wired power, AC or even DC.
Even most practicing antenna engineers don't get the deep connection between reactive circuits and reactive fields.
The Poynting vector is S=E x H, and it's just a vector generalization of the power law. Volts times amps equals watts for "1-D" power in a circuit. E-field is volts/meter. H-field is amps/meter. So the Poynting vector is S = E x H = volts/meter x amps/meter = watts/meter-squared. In 1-D settings, for instance on a transmission line or plane waves interacting at normal incidence in free space, it's the same as P = V I.
Power factor and quality factor are also profoundly important parameters, if you want to understand how antennas behave. This paper explains that connection. A background in microwave circuits and particularly Smith Charts is helpful to understand the big picture, but even with just AC circuits under your belt, you're in a good position to appreciate how this all fits together.
Thanks, I will take a look at this. I have asked dozens of EEs how power flows and in what direction and very few are able to explain it. Power Factor is equally misunderstood and poorly explained, it took me forever to understand it, but its really just the easy stupidest thing ever- its just the phase angle shift between the V and I waves and which 90 degree quadrant in the possible 360 degrees (or 180 forwards and 180 backwards) it exists in. Once I got that, I usually now only visualize phase shifts by viewing two overlapping sine waves in my head.
Basically my issue is I am a Mech Eng, lots of experience, originally in aerospace, and now for some time in AC electric power. I did have some course in electricity and magnetism in junior college and electric power and instrumentation in university, but for whatever reason I never really understood or became very familiar with the Maxwells Equations.
Maxwell certainly had the benefit of knowing the speed of light, thanks to Gustav Kirchhoff's measurements. But I don't think Weber's approach - using velocity-dependent action-at-a-distance force laws - were much of a help to Maxwell.
I am now in a position where I mostly understand the math of AC power, although I could not easily replicate it. So I am broadly ok with the Euler Equation, and P=V x I and all the sine wave and phase angle complications and real and reactive power, P and Q diagrams and phase angle and power factor, etc etc. I can even broadly understand phasors and phasor algebra. The problem I always had (until recently) was understanding why or how power (energy flux) actually flowed, and in what direction. I never found P=V x I and its units Watts, Volts and Amps very intuitive. And because I don't know the Maxwell equations I cant relate it all. What finally got me going in the right direction was learning about the Poynting Vector, which I had NEVER heard about before. Basically I believe the Poynting Vector is related to the Maxwell equations and basically says that energy flux is basically the cross product of the electric and magnetic fields, and once I played with this a bit, I could see how the AC voltage and current waves (and their corresponding electric and magnetic fields, at right angles) could show that power flows in one consistent direction (oscillating of course at twice the line frequency) and if the phase angle shifted into another quadrant, the cross product reverses direction and power goes the other way. So on the PQ diagram this is why in two quadrants the power is positive and in the other two is negative and all that describes in the direction of energy flux in the line. The thing about the Poynting Vector is that its usually used to describe power flow in wireless transmission, but I am sure it also applies to wired power, AC or even DC.
Any comments?
Even most practicing antenna engineers don't get the deep connection between reactive circuits and reactive fields.
The Poynting vector is S=E x H, and it's just a vector generalization of the power law. Volts times amps equals watts for "1-D" power in a circuit. E-field is volts/meter. H-field is amps/meter. So the Poynting vector is S = E x H = volts/meter x amps/meter = watts/meter-squared. In 1-D settings, for instance on a transmission line or plane waves interacting at normal incidence in free space, it's the same as P = V I.
Power factor and quality factor are also profoundly important parameters, if you want to understand how antennas behave. This paper explains that connection. A background in microwave circuits and particularly Smith Charts is helpful to understand the big picture, but even with just AC circuits under your belt, you're in a good position to appreciate how this all fits together.
https://www.researchgate.net/publication/358618589_The_Schelkunoff-Smith_Chart_and_How_Near_Fields_Work
Thanks, I will take a look at this. I have asked dozens of EEs how power flows and in what direction and very few are able to explain it. Power Factor is equally misunderstood and poorly explained, it took me forever to understand it, but its really just the easy stupidest thing ever- its just the phase angle shift between the V and I waves and which 90 degree quadrant in the possible 360 degrees (or 180 forwards and 180 backwards) it exists in. Once I got that, I usually now only visualize phase shifts by viewing two overlapping sine waves in my head.
Wow, I am super happy I found you. I am keen to learn and have lot of pending questions!
Super happy to have you here. Looking forward to your questions.
Basically my issue is I am a Mech Eng, lots of experience, originally in aerospace, and now for some time in AC electric power. I did have some course in electricity and magnetism in junior college and electric power and instrumentation in university, but for whatever reason I never really understood or became very familiar with the Maxwells Equations.
So, do field theories imply an ether - some background substance to spatial dimensions - or not?
Yes. Probably. More on that in a couple of weeks.
Excellent. Can't wait.
Maxwell certainly had the benefit of knowing the speed of light, thanks to Gustav Kirchhoff's measurements. But I don't think Weber's approach - using velocity-dependent action-at-a-distance force laws - were much of a help to Maxwell.