Yes, Thanks, Paul.
It is likely not enough for detailed calculations. (I forgot to ask about the quality factor, was it on the order of 7000 for these runs?) That's OK because I'm not sure how to run the calculations anyway. But it is enough to illustrate the thought and question that I want to ask about.
The thing is, the frustum is warmer at the big end than the small end so RF energy is being dissipated preferentially at the big end. Inside the frustum, doesn't that mean that the reflection coefficient is lower at the big end than the small end? If I'm reading the images right, the big end temperature rise is 6.6 K while the small end temperature is effectively unchanged. I will assume from this that the reflection coefficient at the small end is near enough to one as to make no difference while at the large end something on the order of 100 watts is being dissipated.
Now, I know that there are many ways to cause the reflection coefficient to differ end to end, one way is to use different end materials for example. Another way is to highly buff one end only. But that is not the case with this data. It seems to me from the temperature data, that another way to make the reflection coefficient differ is to operate one end of the frustum near the cut-off frequency.
The reflection coefficient is a wave phenomenon. Proceeding with the thought and using Q = energy stored/energy lost per second gives Q = power stored/power lost, so power stored = Q * power lost. With Q = 7000 and drive power (power lost) = 100W, power stored = a big number. 0.7 MW. If the reflection coefficient at the small end = 1, then the reflection coefficient at the big end seems to equal (power stored - power lost)/power stored which is (1 - 1/Q), or in this case 0.99986.
Taking a step further out on the limb, using radiation pressure, P = Ef/c (Ef is radiation intensity) and for a perfectly reflected wave, P = 2*Ef/c and introducing the reflection coefficient, Γ, calculate the internal pressures on the ends of the frustum as:
Pressure Force, P = 2 *Γ *Ef/c . I have arbitrarily introduced the reflection coefficient as it seems right to me.
But I must take another step. Ef is defined as radiation intensity, in units of N/m^2 and I have E on the ends of the frustum. I'm guessing that the frustum end diameters are: inside big dia. = 0.25552668 ; inside small dia. = 0.15875 from my meep control file for the Brady cavity. Those numbers give A_be = 0.0513 and A_se = 0.0198 m^2. This gives
big end intensity, Ef_be = 1.37E+7 and
small end intensity, Ef_se = 3.54 E+7
Factoring these parameters into the pressure force equation and using differential pressure, delta P = P_se - P_be gives
delta P = 2 * ( Ef_se - Γ * Ef_be)/c . This is now in units of N/m^2 though and I need total. Maybe the best shot is simply to use total stored energy and not factor areas into then back out of the equation and call it Thrust.
Thrust = 2 * 0.7E+6* (1 - Γ ) / c
This number calculates to 0.667 micro-N. That is different than 83.6 micro-Newtons from Paul's temperature image data.
Lots of problems here. It gives the wrong answer by 2 orders of magnitude. That could be due to miss treatment of the areas of the two ends, or perhaps the Q value is wrong, or maybe the experimental force number is not the right data point to use, or maybe the temperatures were measured too long after power-off allowing too much heat to be conducted away/lost from the ends which would give the wrong ratio of reflection coefficients. Or maybe there is nothing to it at all. Lots of models can easily fit one data point. Still, I would like some input from the forum.
I found some related stuff here - https://arxiv.org/pdf/0807.1310.pdf

Proof of zero force for any shape of cavity
Despite the asymmetry of our truncated spherical cone along the z-axis, the net force from radiation pressure on its walls is zero. How can we be sure, though, that there isn’t some other shape that will yield a non-zero net force?
To see what the net force will be in a resonant cavity of a completely arbitrary shape, we need to construct the stress tensor [10] for the electromagnetic field. This can be defined as a three-by-three matrix T with components:
Tij = (ε0 / 2) [ (E2 + c2 B2) δij – 2 EiEj – 2 c2 BiBj ]
The subscripts i and j range from 1 to 3, and correspond to the Cartesian x, y and z coordinates. The symbol δij is the Kronecker delta, equal to 1 if i=j, and 0 otherwise.
If we have a small area whose unit normal vector is n, then the force per unit area due to the electromagnetic field in a region that n points away from is equal to Tn, where we multiply the matrix T and the vector n in the usual way. A careful analysis of any scenario involving an electromagnetic field will yield a force in agreement with this formula [11] (but note that there are other sign conventions in use, where T is defined to be the opposite of the matrix given here, and the force is measured across a surface element facing in the opposite direction).
Now, suppose we take one of the rows of T, and, treating it as a vector field, compute its divergence. For example, if we take the first row:
div T1 = ∂T11 / ∂x + ∂T12 / ∂y + ∂T13 / ∂z
It’s a tedious but straightforward calculation to evaluate this as:
div T1 = ε0 [ – E1 (div E) + E2 (curl E)3 – E3 (curl E)2 – c2 B1 (div B) + c2 B2 (curl B)3 – c2 B3 (curl B)2 ]
We get similar results for the divergence of the other rows, and we can package all three results quite compactly as:
div T = ε0 [ E × (curl E) + c2 B × (curl B) – (div E) E – c2 (div B) B ]
where “×” here indicates the vector cross product.
Maxwell’s equations tell us that div B is zero everywhere, and that in the absence of charges (as in the interior of our cavity) div E is also zero. The curls of B and E, in the absence of currents (which again holds true in the interior of our cavity), are linked to the rates of change of E and B:
c2 curl B = ∂E / ∂t
curl E = –∂B / ∂t
So we have:
div T = ε0 [ –E × (∂B / ∂t) + B × (∂E / ∂t) ]
= –ε0 ∂[E × B] / ∂t
= –(1/c2) ∂S / ∂t
where S = c2 ε0 E × B
The vector field S is known as the Poynting vector, and it describes the rate of flow of energy per unit area in an electromagnetic field. The quantity S/c2 gives the momentum per unit volume contained in the field.
If we apply Gauss’s Theorem to the integral over the walls of an arbitrarily-shaped cavity of any one of the rows of T, say Ti, we obtain:
(Net force)i = ∫wall Ti · dA = ∫interior div Ti dV = –(1/c2) ∫interior (∂Si / ∂t) dV
If the cavity contains a standing wave, then the fields will have a harmonic time dependence of the form sin(ωt) or cos(ωt), and over one complete cycle of the mode, a period of 2π/ω, all the fields will return to their origin values. So at each point in the interior of the cavity, we will have:
∫cycle (∂Si / ∂t) dt = Si(t0+2π/ω) – Si(t0) = 0
So, averaged over a complete cycle in the same way, each component of the net force on the wall will sum to zero.
Yes, Thanks, Paul.
It is likely not enough for detailed calculations. (I forgot to ask about the quality factor, was it on the order of 7000 for these runs?) That's OK because I'm not sure how to run the calculations anyway. But it is enough to illustrate the thought and question that I want to ask about.
The thing is, the frustum is warmer at the big end than the small end so RF energy is being dissipated preferentially at the big end. Inside the frustum, doesn't that mean that the reflection coefficient is lower at the big end than the small end? If I'm reading the images right, the big end temperature rise is 6.6 K while the small end temperature is effectively unchanged. I will assume from this that the reflection coefficient at the small end is near enough to one as to make no difference while at the large end something on the order of 100 watts is being dissipated.
Now, I know that there are many ways to cause the reflection coefficient to differ end to end, one way is to use different end materials for example. Another way is to highly buff one end only. But that is not the case with this data. It seems to me from the temperature data, that another way to make the reflection coefficient differ is to operate one end of the frustum near the cut-off frequency.
The reflection coefficient is a wave phenomenon. Proceeding with the thought and using Q = energy stored/energy lost per second gives Q = power stored/power lost, so power stored = Q * power lost. With Q = 7000 and drive power (power lost) = 100W, power stored = a big number. 0.7 MW. If the reflection coefficient at the small end = 1, then the reflection coefficient at the big end seems to equal (power stored - power lost)/power stored which is (1 - 1/Q), or in this case 0.99986.
Taking a step further out on the limb, using radiation pressure, P = Ef/c (Ef is radiation intensity) and for a perfectly reflected wave, P = 2*Ef/c and introducing the reflection coefficient, Γ, calculate the internal pressures on the ends of the frustum as:
Pressure Force, P = 2 *Γ *Ef/c . I have arbitrarily introduced the reflection coefficient as it seems right to me.
But I must take another step. Ef is defined as radiation intensity, in units of N/m^2 and I have E on the ends of the frustum. I'm guessing that the frustum end diameters are: inside big dia. = 0.25552668 ; inside small dia. = 0.15875 from my meep control file for the Brady cavity. Those numbers give A_be = 0.0513 and A_se = 0.0198 m^2. This gives
big end intensity, Ef_be = 1.37E+7 and
small end intensity, Ef_se = 3.54 E+7
Factoring these parameters into the pressure force equation and using differential pressure, delta P = P_se - P_be gives
delta P = 2 * ( Ef_se - Γ * Ef_be)/c . This is now in units of N/m^2 though and I need total. Maybe the best shot is simply to use total stored energy and not factor areas into then back out of the equation and call it Thrust.
Thrust = 2 * 0.7E+6* (1 - Γ ) / c
This number calculates to 0.667 micro-N. That is different than 83.6 micro-Newtons from Paul's temperature image data.
Lots of problems here. It gives the wrong answer by 2 orders of magnitude. That could be due to miss treatment of the areas of the two ends, or perhaps the Q value is wrong, or maybe the experimental force number is not the right data point to use, or maybe the temperatures were measured too long after power-off allowing too much heat to be conducted away/lost from the ends which would give the wrong ratio of reflection coefficients. Or maybe there is nothing to it at all. Lots of models can easily fit one data point. Still, I would like some input from the forum.
I found some related stuff here - https://arxiv.org/pdf/0807.1310.pdf
I came across this a couple of weeks ago. I don't remember if I ever saw it brought up on the forums and the math is way beyond me, but the author's conclusion is that the radiation pressure always ends up canceling out once all of the factors are accounted for.
Might be worth it for you to take a look at if you're headed down this particular rabbit hole
http://www.gregegan.net/SCIENCE/Cavity/Cavity.htmlQuoteProof of zero force for any shape of cavity
Despite the asymmetry of our truncated spherical cone along the z-axis, the net force from radiation pressure on its walls is zero. How can we be sure, though, that there isn’t some other shape that will yield a non-zero net force?
To see what the net force will be in a resonant cavity of a completely arbitrary shape, we need to construct the stress tensor [10] for the electromagnetic field. This can be defined as a three-by-three matrix T with components:
Tij = (ε0 / 2) [ (E2 + c2 B2) δij – 2 EiEj – 2 c2 BiBj ]
The subscripts i and j range from 1 to 3, and correspond to the Cartesian x, y and z coordinates. The symbol δij is the Kronecker delta, equal to 1 if i=j, and 0 otherwise.
If we have a small area whose unit normal vector is n, then the force per unit area due to the electromagnetic field in a region that n points away from is equal to Tn, where we multiply the matrix T and the vector n in the usual way. A careful analysis of any scenario involving an electromagnetic field will yield a force in agreement with this formula [11] (but note that there are other sign conventions in use, where T is defined to be the opposite of the matrix given here, and the force is measured across a surface element facing in the opposite direction).
Now, suppose we take one of the rows of T, and, treating it as a vector field, compute its divergence. For example, if we take the first row:
div T1 = ∂T11 / ∂x + ∂T12 / ∂y + ∂T13 / ∂z
It’s a tedious but straightforward calculation to evaluate this as:
div T1 = ε0 [ – E1 (div E) + E2 (curl E)3 – E3 (curl E)2 – c2 B1 (div B) + c2 B2 (curl B)3 – c2 B3 (curl B)2 ]
We get similar results for the divergence of the other rows, and we can package all three results quite compactly as:
div T = ε0 [ E × (curl E) + c2 B × (curl B) – (div E) E – c2 (div B) B ]
where “×” here indicates the vector cross product.
Maxwell’s equations tell us that div B is zero everywhere, and that in the absence of charges (as in the interior of our cavity) div E is also zero. The curls of B and E, in the absence of currents (which again holds true in the interior of our cavity), are linked to the rates of change of E and B:
c2 curl B = ∂E / ∂t
curl E = –∂B / ∂t
So we have:
div T = ε0 [ –E × (∂B / ∂t) + B × (∂E / ∂t) ]
= –ε0 ∂[E × B] / ∂t
= –(1/c2) ∂S / ∂t
where S = c2 ε0 E × B
The vector field S is known as the Poynting vector, and it describes the rate of flow of energy per unit area in an electromagnetic field. The quantity S/c2 gives the momentum per unit volume contained in the field.
If we apply Gauss’s Theorem to the integral over the walls of an arbitrarily-shaped cavity of any one of the rows of T, say Ti, we obtain:
(Net force)i = ∫wall Ti · dA = ∫interior div Ti dV = –(1/c2) ∫interior (∂Si / ∂t) dV
If the cavity contains a standing wave, then the fields will have a harmonic time dependence of the form sin(ωt) or cos(ωt), and over one complete cycle of the mode, a period of 2π/ω, all the fields will return to their origin values. So at each point in the interior of the cavity, we will have:
∫cycle (∂Si / ∂t) dt = Si(t0+2π/ω) – Si(t0) = 0
So, averaged over a complete cycle in the same way, each component of the net force on the wall will sum to zero.
I respect Greg Egan, and I am familiar with the quoted paper. In this case the statement - quoting
"If the cavity contains a standing wave, then the fields will have a harmonic time dependence of the form sin(ωt) or cos(ωt), and over one complete cycle of the mode, a period of 2π/ω, all the fields will return to their origin values. So at each point in the interior of the cavity, we will have:
∫cycle (∂Si / ∂t) dt = Si(t0+2π/ω) – Si(t0) = 0
So, averaged over a complete cycle in the same way, each component of the net force on the wall will sum to zero."
does not agree in the general case with the paper
arXiv:0807.1310v5 [physics.class-ph] 21 Nov 2008
The Lorentz Force and the Radiation Pressure of Light
Tony Rothman∗ and Stephen Boughn†
Which I linked. Again https://arxiv.org/pdf/0807.1310.pdf
Check equation 2.3 and figures 2 and 3 of this link. The authors show that the pressure parallel to the z-axis averages to zero only in the special case where the phase angle equals pi/2. Even in that case, there is a non-zero average force in the off-axis direction. But if you read the linked paper from the beginning you will quickly understand why knowledgeable people with training in EM physics make this mistake.
Indeed, that 'they quietly fade away' is not a good sign. I would say it is because making the microwave system work is difficult enough, but setting up a good experiment to measure the forces reliably and doing clever measurements and report about them in a clear way, is even harder.
I work on it until i'm frustrated and sick of it, then I usually take a break for a couple of weeks. Other pauses are that I don't have the time because of other projects or vacation.
I'm dealing with two issues right now before I can continue: more natural convection and an antenna self-resonating problem.
Adding the insulation to the draft enclosure greatly reduced the natural convection. But as the on-board electrical components begin to heat up, they cause natural convection of ~3uN after about 15 minutes. So most recently I've added a hefty heatsink to the on-board computer and moved it to the top of the torsional pendulum beam rather than attached to the side. I also want to add a better heatsink to the RF amplifier - perhaps even use the same phase change wax NASA is using. I also need to wrap all the aluminum below and to the sides of the pendulum arm with insulation, which I will probably do today.
In the image below I have the cavity removed so I can work on the antenna. Roger Shawyer thinks my antenna design, which the Polish group is also using, is self-resonating at a certain frequency rather than exciting the cavity. This makes a lot of sense as Jakub and I are both showing the same ~2.409Ghz -40dB return loss. This is highly unlikely since we have very different geometric dimensions. This was unlucky for me as the spherical end-plate frustum is designed to resonate at 2.405Ghz with mode TE013. As that may be too close to the resonate frequency of the antenna, it looks like I will need a different antenna. The antenna should still work in the flat end-plate frustum as that cavity was designed to resonate at 2.45Ghz. My simulations of Jakub's cavity show TE012 at 2.369Ghz, so he is going to try that next instead of 2.404Ghz - though it looks like the small end is a little below cut-off (second image below).
this site seems to have been updated
any views on what Richard Banduric proposes?
http://electricspacecraft.org/
I respect Greg Egan, and I am familiar with the quoted paper. In this case the statement - quoting
"If the cavity contains a standing wave, then the fields will have a harmonic time dependence of the form sin(ωt) or cos(ωt), and over one complete cycle of the mode, a period of 2π/ω, all the fields will return to their origin values. So at each point in the interior of the cavity, we will have:
∫cycle (∂Si / ∂t) dt = Si(t0+2π/ω) – Si(t0) = 0
So, averaged over a complete cycle in the same way, each component of the net force on the wall will sum to zero."
does not agree in the general case with the paper
arXiv:0807.1310v5 [physics.class-ph] 21 Nov 2008
The Lorentz Force and the Radiation Pressure of Light
Tony Rothman∗ and Stephen Boughn†
More progress on the insulation. All components have been placed back onto the torsional pendulum after some testing with the antenna indicates that it is not self-resonating, and there is a reasonable field in the cavity.
!I would still like to improve the heat sink on the main amplifier.
<sigh> I was looking at this but I'm not sure it (or something like it) may be appropriate for your device and won't introduce noise (edit: more stuff here)
?Jamie - are you using a loop antenna? Sorry but I have forgotten.
If so it can likely be analyzed as a single coil inductor - probably treated as a helical transmission line since typically above 1Ghz lumped components must usually be addressed as transmission lines. In any case it should be relatively simple to move the self resonance frequency (SRF) with a bit of capacitance (treat this as an open circuit transmission line).
If you are using a 1/4 lambda spike or wheel antenna that is somewhat different.
Herman
graybeardsyseng
Jamie - are you using a loop antenna? Sorry but I have forgotten.
If so it can likely be analyzed as a single coil inductor - probably treated as a helical transmission line since typically above 1Ghz lumped components must usually be addressed as transmission lines. In any case it should be relatively simple to move the self resonance frequency (SRF) with a bit of capacitance (treat this as an open circuit transmission line).
If you are using a 1/4 lambda spike or wheel antenna that is somewhat different.
Herman
graybeardsyseng
Herman, check out this
https://forum.nasaspaceflight.com/index.php?topic=42978.msg1698864#msg1698864
if I'm not wrong the above is the antenna Jamie is currently using


More progress on the insulation. All components have been placed back onto the torsional pendulum after some testing with the antenna indicates that it is not self-resonating, and there is a reasonable field in the cavity.
I would still like to improve the heat sink on the main amplifier.
Jamie - are you using a loop antenna? Sorry but I have forgotten.
If so it can likely be analyzed as a single coil inductor - probably treated as a helical transmission line since typically above 1Ghz lumped components must usually be addressed as transmission lines. In any case it should be relatively simple to move the self resonance frequency (SRF) with a bit of capacitance (treat this as an open circuit transmission line).
If you are using a 1/4 lambda spike or wheel antenna that is somewhat different.
Jamie - are you using a loop antenna? Sorry but I have forgotten.
If so it can likely be analyzed as a single coil inductor - probably treated as a helical transmission line since typically above 1Ghz lumped components must usually be addressed as transmission lines. In any case it should be relatively simple to move the self resonance frequency (SRF) with a bit of capacitance (treat this as an open circuit transmission line).
If you are using a 1/4 lambda spike or wheel antenna that is somewhat different.
Herman
graybeardsyseng
Herman, check out this
https://forum.nasaspaceflight.com/index.php?topic=42978.msg1698864#msg1698864
if I'm not wrong the above is the antenna Jamie is currently using
I'm not sure if that is the loop Jamie is using. He did a lot of different testing with different styles. Although he should be using a
Loop antenna that couples to the magnetic field. like the loop in EagleWorks test frustum. (see attached)
It should have both ends of the loop coupled to the coax feed.
https://www.nonstopsystems.com/radio/frank_radio_antenna_magloop.htm
This is a very nice site for referencing loop antennas.
My Very Best,
Shell
In any case that antenna is NOT a loop and should not be analyzed as a loop for SRF determination. Nor is the pattern of radiation anything like a loop. Jamie - are you using a loop antenna? Sorry but I have forgotten.
If so it can likely be analyzed as a single coil inductor - probably treated as a helical transmission line since typically above 1Ghz lumped components must usually be addressed as transmission lines. In any case it should be relatively simple to move the self resonance frequency (SRF) with a bit of capacitance (treat this as an open circuit transmission line).
If you are using a 1/4 lambda spike or wheel antenna that is somewhat different.
It's a simple antenna design. The polish group is also using the same design. It had the same coupling as a standard loop in FEKO.
Jamie - are you using a loop antenna? Sorry but I have forgotten.
If so it can likely be analyzed as a single coil inductor - probably treated as a helical transmission line since typically above 1Ghz lumped components must usually be addressed as transmission lines. In any case it should be relatively simple to move the self resonance frequency (SRF) with a bit of capacitance (treat this as an open circuit transmission line).
If you are using a 1/4 lambda spike or wheel antenna that is somewhat different.
Herman
graybeardsyseng
Herman, check out this
https://forum.nasaspaceflight.com/index.php?topic=42978.msg1698864#msg1698864
if I'm not wrong the above is the antenna Jamie is currently using
I'm not sure if that is the loop Jamie is using. He did a lot of different testing with different styles. Although he should be using a
Loop antenna that couples to the magnetic field. like the loop in EagleWorks test frustum. (see attached)
It should have both ends of the loop coupled to the coax feed.
https://www.nonstopsystems.com/radio/frank_radio_antenna_magloop.htm
This is a very nice site for referencing loop antennas.
My Very Best,
Shell
Shell -
EXCELLENT reference for mag loops - I had not seen that site before but it is now in my favorites for both EMdrive and Ham Radio.
Concur completely with your comments!
I remember that open "loop" antenna (i.e. only one end connected) but as you mention I thought Jamie had decided to go with a full loop. As you said - a true loop antenna has both ends connected to the coax - one to the center conductor and one to the shield. If it is open as in
it is NOT a loop and it must be analyzed differently - probably as a vertical (or so-called spike) with a capacity hat or a primitive form of wheel antenna (with only one lobe). see below for a picture of a more common 3 lobe wheel antenna.In any case that antenna is NOT a loop and should not be analyzed as a loop for SRF determination. Nor is the pattern of radiation anything like a loop.
Normally the self resonance frequency is where the capacitance (usually parasitic) and the inductance of an inductor are in resonance such that the antenna (or any inductor really) will have a very high impedance and appear like an open circuit. I don't personally recall seeing a SRF calculated for such an antenna - I will research that as time permits.
Herman
Jamie - are you using a loop antenna? Sorry but I have forgotten.
If so it can likely be analyzed as a single coil inductor - probably treated as a helical transmission line since typically above 1Ghz lumped components must usually be addressed as transmission lines. In any case it should be relatively simple to move the self resonance frequency (SRF) with a bit of capacitance (treat this as an open circuit transmission line).
If you are using a 1/4 lambda spike or wheel antenna that is somewhat different.
It's a simple antenna design. The polish group is also using the same design. It had the same coupling as a standard loop in FEKO.K
Jamie -
I hadn't seen your post when I answered Shell. Couple of comments - in no way was I trying to say that this isn't a good antenna (the one you and the Polish group are using). it is - I was just addressing calculation of SRF and whether or not it constituted a loop antenna. And I'm not sure why FEKO treats it as a loop. I am going to try digging deeper into this design a bit.
Herman
Jamie - are you using a loop antenna? Sorry but I have forgotten.
If so it can likely be analyzed as a single coil inductor - probably treated as a helical transmission line since typically above 1Ghz lumped components must usually be addressed as transmission lines. In any case it should be relatively simple to move the self resonance frequency (SRF) with a bit of capacitance (treat this as an open circuit transmission line).
If you are using a 1/4 lambda spike or wheel antenna that is somewhat different.
Herman
graybeardsyseng
Herman, check out this
https://forum.nasaspaceflight.com/index.php?topic=42978.msg1698864#msg1698864
if I'm not wrong the above is the antenna Jamie is currently using
I'm not sure if that is the loop Jamie is using. He did a lot of different testing with different styles. Although he should be using a
Loop antenna that couples to the magnetic field. like the loop in EagleWorks test frustum. (see attached)
It should have both ends of the loop coupled to the coax feed.
https://www.nonstopsystems.com/radio/frank_radio_antenna_magloop.htm
This is a very nice site for referencing loop antennas.
My Very Best,
Shell
Shell -
EXCELLENT reference for mag loops - I had not seen that site before but it is now in my favorites for both EMdrive and Ham Radio.
Concur completely with your comments!
I remember that open "loop" antenna (i.e. only one end connected) but as you mention I thought Jamie had decided to go with a full loop. As you said - a true loop antenna has both ends connected to the coax - one to the center conductor and one to the shield. If it is open as in
it is NOT a loop and it must be analyzed differently - probably as a vertical (or so-called spike) with a capacity hat or a primitive form of wheel antenna (with only one lobe). see below for a picture of a more common 3 lobe wheel antenna.In any case that antenna is NOT a loop and should not be analyzed as a loop for SRF determination. Nor is the pattern of radiation anything like a loop.
Normally the self resonance frequency is where the capacitance (usually parasitic) and the inductance of an inductor are in resonance such that the antenna (or any inductor really) will have a very high impedance and appear like an open circuit. I don't personally recall seeing a SRF calculated for such an antenna - I will research that as time permits.
HermanHerman,
You're spot on, better than I could have said. Although that open loop antenna design like Jamie's design will generate a Circular Wave Pattern similar to a helical but I'm not sure how the near field generation on the open loop will look or couple into the magnetic field of the frustum which is important for a TExxx mode.
That's the reason for a ~1/10 WL closed loop antenna is to couple into the TE013 H-Field in the frustum.
It needs to be a current driven coil to produce the highest magnetic fields. You externally "tune" these closed loops with a small variable capacitor. A Magnetic Loop Antenna is basically just a resonant circuit using an copper wire coil and an adjustable capacitor in this case ~ a 1-10pf (pico-farad) adjustable. If the coil has a circumference of much less than, say, 1/10th of a wavelength, then the efficiency of the antenna will suffer. If the circumference approaches Ľ of a wavelength or more the antenna is accurately characterized as an electrical loop antenna, with characteristics similar to those of a dipole.
Jamie's isn't wrong but I don't think FEKO allows you to create a "tuned circuit" current loop antenna to give you a good VWSR.
My Very Bet,
Shell
In order to minimize bandwidth and maximize information content, when quoting, one can use an ellipsis (...) to indicate the clipped material.