eHam

eHam Forums => Antennas and Towers and more => Topic started by: JAHAM2BE on October 29, 2012, 05:57:39 AM



Title: What's wrong with stored energy, exactly?
Post by: JAHAM2BE on October 29, 2012, 05:57:39 AM
I asked this in another thread but got no response, so I thought I'd formulate the question again independently and hopefully more clearly. I freely admit that my intuition about AC circuits is weak and influenced by my intuition about DC circuits. I suspect it is this that is preventing me from clearly seeing a simple answer to the following question.

The question is: what is the nature and quantity of loss introduced into an antenna system by increasing stored energy? Can I see this loss in a circuit simulator?

The reason I ask is because of rather unequivocal statements like "increasing the stored energy will also increase the dissipative losses: from the medium the antenna is immersed in, and the resistive losses of the antenna itself" (ref. 1) or "The more energy we store, the higher losses within the area storing energy become for fixed loss resistance values" (ref. 2). Intuitively, it makes sense, but I can't put my finger on a specific formula or phenomenon to account for the additional loss caused by added stored energy.

Specifically I'm thinking of a magnetic loop antenna with extra stored energy in the form of unnecessary series inductance (i.e. added reactance). But I think the question can be formulated more generally as follows.

Consider an ideal series LC circuit (which is what a magnetic loop antenna is), in series with a resistive load R and an AC voltage source (E volts peak) at the series resonant frequency. Since the impedance of the LC circuit at resonance is purely resistive and in the ideal case is 0 ohms, a current of E/R will flow. Regardless of the reactance of the LC components, the same current will eventually flow, even if we increase the reactance 1000-fold. I simulated this in a circuit simulator just to make sure I could see the basic behavior. In the simulator, increasing reactance predictably increases the "build up" time to the final steady-state current (as the alternating supply voltage is pushing and pulling in resonance with the sloshing of current between magnetic/electric field storage), but the final current (always the same magnitude, E/R) is always reached, regardless of how much reactance I put into the system. The voltage across the reactive components is of course higher for higher reactances, since the same current is pushing against (and overcoming) a comparatively larger "inertia" and thus building up a larger "pressure" as a result.

This is an ideal system, so it obviously is missing something that could illustrate the phenomenon of "more reactance causes more loss". But what is that "something" that causes increased reactance (and energy storage) to cause loss?

It seems at first glance that it can't be an increase in current and associated I^2 R losses, since the same current will always flow through all the series-connected components in the circuit. Is that right? Or, does increased reactance actually cause an increase in current somehow, perhaps related to an increase in reactive power caused by the increased reactance? (Though I don't see how this can happen at series resonance.) If so, where does that increased current flow, what is its magnitude, and can I see it in a circuit simulation?

Or, is some other phenomenon responsible for the increased losses associated with increased reactance and increased energy storage?

I'm sure there's a simple answer, and I look forward to hearing it. Thanks in advance for any insight.

Ref. 1: http://home.earthlink.net/~w6rmk/antenna/phased/small.htm
Ref. 2: http://www.eham.net/ehamforum/smf/index.php/topic,85149.msg622412.html#msg622412


Title: RE: What's wrong with stored energy, exactly?
Post by: AA4PB on October 29, 2012, 06:16:07 AM
As a practical matter, when you increase the inductance you increase the resistance of the wire used to make the inductor. This resistance is in series with your external resistance so the total I*I*R loss goes up.


Title: RE: What's wrong with stored energy, exactly?
Post by: W5DXP on October 29, 2012, 06:20:05 AM
The question is: what is the nature and quantity of loss introduced into an antenna system by increasing stored energy?

The energy stored in an RF system is in electric and magnetic fields. Electric energy manifests itself in voltage. Magnetic energy manifests itself in current. Higher stored electric energy increases the dielectric losses in the system. Higher stored magnetic energy increases the I^2*R losses in the system.

As an example, the higher the SWR, the greater the stored energy in the system and the higher the losses due to SWR.

OTOH, transmission lines are designed to store energy while the energy is being transferred from one end to the other.

Strangely enough, for a 1/2WL resonant dipole (a standing wave antenna) about 80% of the energy is stored in the standing waves vs about 20% of the energy being radiated, i.e. if we are radiating 100 joules/sec, the antenna is storing about 400 joules/sec of energy.


Title: RE: What's wrong with stored energy, exactly?
Post by: W8JI on October 29, 2012, 07:10:01 AM
Consider an ideal series LC circuit (which is what a magnetic loop antenna is), in series with a resistive load R and an AC voltage source (E volts peak) at the series resonant frequency. Since the impedance of the LC circuit at resonance is purely resistive and in the ideal case is 0 ohms, a current of E/R will flow. Regardless of the reactance of the LC components, the same current will eventually flow, even if we increase the reactance 1000-fold. I simulated this in a circuit simulator just to make sure I could see the basic behavior. In the simulator, increasing reactance predictably increases the "build up" time to the final steady-state current (as the alternating supply voltage is pushing and pulling in resonance with the sloshing of current between magnetic/electric field storage), but the final current (always the same magnitude, E/R) is always reached, regardless of how much reactance I put into the system. The voltage across the reactive components is of course higher for higher reactances, since the same current is pushing against (and overcoming) a comparatively larger "inertia" and thus building up a larger "pressure" as a result.

If you increase Q by increasing reactance with the same real part of impedance, you either increase voltage or you increase current, or you increase both. Neither is  desirable.

Your idea that resistance remains constant is flawed in the real world. Loss resistance has to increase, unless the additional reactance has infinite Q. If you add something that increases series inductance, you also add loss resistance. The resistance increases not just from the extra inductance, but system resistance also will generally increase just from the fact the capacitance decreases. Fields inside the capacitor are more concentrated.   

Q is, after all, the ratio of stored energy to working energy. This means increases unloaded Q with fixed loaded Q increases losses. After all, the ratio of unloaded Q to loaded Q is one way to determine efficiency.

Of course if we add magical zero-loss reactances, then your assumptions are correct. I'll take a box of those, if you really have them. :-)

73 Tom


Title: RE: What's wrong with stored energy, exactly?
Post by: JAHAM2BE on October 29, 2012, 07:53:28 AM
If you increase Q by increasing reactance with the same real part of impedance, you either increase voltage or you increase current, or you increase both. Neither is  desirable.

In the specific case of a series RLC circuit in series with an AC voltage source at the resonant frequency, I can see how added reactance causes voltage to increase (as observed in the simulator and justified above), and how increased voltage (across a capacitor) can increase dielectric losses as W5DXP pointed out.

But I don't see how, in this case of series resonance, added reactance (and its accompanying loss resistance) can increase current since everything is in series, the reactances "cancel" at resonance, and the same current flows through all series-connected elements in the circuit. In fact adding loss resistance by means of added inductance would seem to decrease the overall current flowing in the circuit.

Can added reactance increase current in a series RLC circuit? If so, how? If not, what is an example where added reactance increases current?

I think I'm overlooking something simple, but I can't quite see the case of increased current.


Title: RE: What's wrong with stored energy, exactly?
Post by: N3OX on October 29, 2012, 10:57:34 AM
Quote
Can added reactance increase current in a series RLC circuit?

It cannot (in the specific case of always re-resonating!) .  Your analysis is correct: in the ideal case the current at resonance stays the same no matter the reactance, end of story for THAT system.

Quote
This is an ideal system, so it obviously is missing something that could illustrate the phenomenon of "more reactance causes more loss". But what is that "something" that causes increased reactance (and energy storage) to cause loss?

Well first of all, some of this is the imprecision of language used to describe mathematical things. 

When someone says "more reactance causes more loss," what are they assuming stays the same vs. your assumptions?  Do they really mean "adding pure reactance causes loss" or do they mean "in all real-world cases, for best efficiency you should minimize the reactive power circulation." 

I think they usually mean the latter even if that's imprecise and seems to imply the former... for the former, though, it's straightforward, as you've done, to find counterexamples.  You should also be able to find some series-parallel circuit examples where increasing reactance of some components alone increases the loss, but I don't really think that's what people mean.

I agree that a lot of the PRACTICAL issues are related to what AA4PB says.  We're always talking resonant antennas, so adding reactance always implies adding inductance (as well as increasing cap. reactance), and all inductive structures are really pretty awful in terms of how closely they can approach an ideal inductor.

In my opinion, it's often counterproductive to treat plain-language statements about antennas as if they have precise mathematical meaning.  I'm glad you don't trust them, but don't feel too baffled if you easily find contradictions using ideal circuits.  A lot of the time plain-language statements about antennas should be thought of as practical engineering advice that always assumes things like non-ideal components, or that might use the word "always" when they mean "almost always except in extremely difficult to realize situations". 

===

If you want to find a circuit where increasing stored energy by increasing pure reactances actually increases the loss, I would start by incorporating parallel elements.  Parallel reactances can be used to transform fixed resistances to a wide range of values depending on the reactance.  For example:

http://n3ox.net/files/trap_Z.jpg

I call that a "trap" because it's similar to a real-world trap where the lion's share of the resistance is in the inductor.

The resistance of the equivalent circuit with a 1 ohm resistor can be anything from the 1 ohm value if X_L is low and X_C is high, to practically nothing when the capacitive reactance is very low and shunting current around the inductor leg, to hundreds of thousands of ohms or more if the circuit is at resonance and R is small (omega*L = omega*C*(R^2+omega^2*L^2), making the imaginary part zero and the denominators equal to R^2.

That circuit in series with another resistor with inductance chosen to be near resonance of the "trap" can give a circuit where the fraction of the power dissipated in the "trap" resistor can be greater or less than the fraction of the power dissipated in the other series resistor.  If you call the series resistor "the radiation resistance" there's an example of a circuit where increasing only inductive reactance can decrease the antenna efficiency.




Title: RE: What's wrong with stored energy, exactly?
Post by: W5DXP on October 29, 2012, 11:50:36 AM
Can added reactance increase current in a series RLC circuit?

In the real world, when a coil becomes large enough to exhibit transmission line effects (easily observed at microwave frequencies) under certain conditions, added reactance can certainly increase (or decrease) current in a series RLC circuit which, in the real world, is not an ideal lumped-circuit.


Title: RE: What's wrong with stored energy, exactly?
Post by: STAYVERTICAL on October 29, 2012, 11:52:09 AM
N30X, Dan

+1 best answer of the day.
Clear, succint, and answered the question.
Thanks for lifting the fog.

73 - Rob


Title: RE: What's wrong with stored energy, exactly?
Post by: W8JI on October 29, 2012, 05:38:03 PM
Well first of all, some of this is the imprecision of language used to describe mathematical things. 

When someone says "more reactance causes more loss," what are they assuming stays the same vs. your assumptions?  Do they really mean "adding pure reactance causes loss" or do they mean "in all real-world cases, for best efficiency you should minimize the reactive power circulation." 

As I recall, this thread stems from a conversation where he was cautioned to keep leads short and to make a capacitor "boxy" instead of having a long path through the capacitor.

Any unnecessary series inductance in the capacitor, by using poor form factor, increases losses. This is not only because of the longer path, but also because the capacitor starts to behave increasingly like a transmission line. This is especially important in small loops because subtle changes insignificant in many typical resonant circuits (where load or source resistances are pretty high) cause large problems in a small loop (where the load, radiation resistance, is very low).

Also, any extra lead length that is not in the perimeter of the loop can cause deleterious changes in the radiation resistance of the loop.

The actual problems go far beyond a small ideal RLC circuit, because workings of a small loop system do not come close to either an ideal (or even a real) RLC circuit. One similar example is a typical antenna tuner. It handles nicely treating things as a simple network with real lumped components with modest load impedances. Stick a 10-ohm load on it, and things people don't even think about (like lead lengths and sizes) start to be major problems.

73 Tom


Title: RE: What's wrong with stored energy, exactly?
Post by: JAHAM2BE on October 30, 2012, 04:51:32 AM
Thank you all, gentlemen, for the highly informative responses. The various explanations all make sense and are very useful facts and analysis techniques to keep in mind when trying to move from ideal circuits into the real world. Having now understood the nature of stored energy loss, I can finally sleep at night again! Until the next baffling question arises, that is...

system resistance also will generally increase just from the fact the capacitance decreases. Fields inside the capacitor are more concentrated.

I'm getting my feet wet with electromagnetic field simulation software (using the FDTD method) and have successfully simulated current flow over a series of butterfly capacitor plates and am on my way to calculating the inductance and loss of the structure. Eventually I hope to simulate an entire small transmitting loop antenna and observe current flow differences such as the increased fields (and consequently, I assume, increased current density) inside the capacitor compared to the rest of the loop. Based on the time it takes to simulate the capacitor alone (with mm-level resolution), I imagine simulating an entire loop antenna at the same resolution could take days, if not longer.

Any unnecessary series inductance in the capacitor, by using poor form factor, increases losses. This is not only because of the longer path, but also because the capacitor starts to behave increasingly like a transmission line.

That is indeed one issue I find interesting because it's not addressed directly by most amateur small loop construction articles that I've seen (and I've seen a few). For my current small loop construction project, I am building a loop similar to the Midnight Loop design (ref. 1), which is a circular loop made of a wide sheet of aluminum sheet metal (flashing), with the ends of the flashing bent downwards and into the loop to form two large capacitor flaps. In my particular case, the sheet metal will be made of copper and will be 36cm wide, formed into an octagon 3.5m in "circumference". As a first test, I plan to make the capacitor plates 36cmx36cm with around 1mm separation to give me more than enough capacitance to achieve the ~500pF capacitance (this value is from memory, but I think that's what I calculated) required to cover 40m. The plates will be separable at the bottom in a hinged flap fashion to vary the capacitance and to cover hopefully up to 10m.

Though I'm concerned about the loss (and effects on current distribution) from the large capacitor plates, I've chosen to proceed with this design because it is mechanically easy to create and is probably (admittedly, by gut feeling alone) at least as efficient as other 1m-diameter small-diameter-tubing loops that amateurs can use, with effort, on 40m. The Midnight Loop design on 20m reportedly achieved efficiency on par with the MFJ loop antenna offering, based on field strength comparisons taken in the clear.

Ref. 1: http://midnightdesignsolutions.com/MidnightLoop/index.html


Title: RE: What's wrong with stored energy, exactly?
Post by: STAYVERTICAL on October 30, 2012, 01:36:34 PM
JAHAM2BE,

Hi again.
The fact you are going to use copper will give you a huge advantage over a similar loop which uses aluminium.
If you keep the capacitor losses low, with the dimensions you indicate, you will blow the MFJ and midnight loop out of the water.
Copper almost doubles the efficiency of a STL antenna compared to aluminium, due to reducing the losses.

If the MFJ were copper, or copper coated it's performance would be much better, especially on 40m.

There is an antenna manufacturer in Italy which uses the system you describe to cover 40m to 10m commercially.
They make a range of loops from what they call the "baby" to a monster loop.
Have a look at their web page for some good ideas at least.
If nothing else it is eye candy for magloop enthusiasts.

http://www.dxzone.com/cgi-bin/dir/jump2.cgi?ID=11310

I see you are going for very large diameter strip etc in your loop project.
I have tried this as well, and can vouch that it works well.
Directivity and pattern is the same as for a tubular loop in my experiments.
One thing I have found which is important in keeping the SWR low and consistent is to maintain symmetry.
When I lost symmetry due to having the tuning capacitor offset from the centre slightly, getting a consistent low SWR was difficult.
It does not have to be millimetre perfect, but avoid any obvious asymmetry.

Remember that increasing the diameter of a magloop will have far more effect than changing the tubular/strip diameter.
So, if you are using a thinner tube, it can be more than compensated for by increasing the diameter somewhat.
I have looked at some of your experiments, and am impressed by your persistence and patience in taming those vast sheets of aluminium.

As a fellow loop enthusiast who has tried about every combination of materials and format, I would suggest considering a tubular loop.
I know you want something which can be disassembled, but I believe that a copper tube of 20mm diameter in two sections (or four) would work well for you.
If you were to take two or four segments of 20mm soft copper tube, flatten the ends, drill a hole in them and put in a brass bolt, you would form a low resistance connection.
It would also be able to be disassembled easily for storage.

I use magloops as my only H.F. antennas, so I speak with experience on a daily basis.
Frankly, I love the small magloop antenna.
It's still amazing to me that it can be at head height (mounted vertically), tune 40m to 10m, maintain a consistent pattern, have a built in antenna tuner/preselector and give low angle to high angle radiation in such a small package.
This is only because it is an electrically small antenna - something an electrically small dipole would also do.
Of course efficiency is the trade-off.
But good construction, and mathematical modelling will give real world performance based on fact, not fantasy.

My next project is a small rotator to move the loop through 90 degrees.
It is no beam of course, but in my experience the orthogonal null is a real problem when in net's and the like.
Stations broadside to the magloop suffer both in receive and transmit, and having a small rotator sure saves my door hinges running in and out to shift the magloop.

Sorry about the long over, but Magloops tend to produce excitement in their users similar to the malady affecting Mac user's.

73 - Rob


Title: RE: What's wrong with stored energy, exactly?
Post by: JAHAM2BE on October 30, 2012, 03:28:06 PM
I see you are going for very large diameter strip etc in your loop project.
I have tried this as well, and can vouch that it works well.
Directivity and pattern is the same as for a tubular loop in my experiments.
One thing I have found which is important in keeping the SWR low and consistent is to maintain symmetry.
When I lost symmetry due to having the tuning capacitor offset from the centre slightly, getting a consistent low SWR was difficult.
It does not have to be millimetre perfect, but avoid any obvious asymmetry.

Excellent. Thank you for that piece of advice. I was considering a non-symmetrical capacitor arrangement for possibly easier construction: Instead of two capacitor flaps running inward toward the center of the loop, I was considering simply overlapping one end of the loop strip on top of the other, along the loop circumference, and lifting/lowering the top flap to change the capacitance. I was worried about loop symmetry, and your experience seems to confirm that symmetry is indeed something to worry about. Back to the flaps-running-toward-the-center idea.

The next question is whether I will really be able to achieve a 40m-10m tuning range with large capacitor flaps that are hinged at the top (a "book capacitor"). G8JNJ designed a similar capacitor arrangement for his tubing loop and only achieved 9-25 MHz - which is still not bad, but I'd really like an all-in-one loop that can operate 40-10m. I know the best solution is a vacuum variable capacitor, but I can't get my hands on one locally.


Title: RE: What's wrong with stored energy, exactly?
Post by: STAYVERTICAL on October 30, 2012, 04:30:07 PM
Hi Jaham2be,

You should be able to get 7-30 Mhz if you have the loop small enough, otherwise it will be difficult.
If you look at that Italian commercial loop site link, it shows the "baby" (1 meter wide) loop which tunes from 40 to 10m.
They achieved this by having the capacitor bolted to both ends of the loop and then squeezing the loop to mesh the capacitor.
In this way at the extreme low end of the capacitance range the blades are edge on and so there is not much area to give capacitance.
I think this is the secret to getting a good range.
Even vacuum variable capacitors work the same way to get good range except that they have concentric cylinders, not square "fingers" meshing.
At their lowest capacitance, the cyclinders are edge to edge as well.

The Italian loop site also have "midi" and "maxi" loops.
The Maxi loop tunes from 1.8 to 7Mhz, is 4 metres wide and made of 140mm wide aluminium tube - a sight to behold.
They all seem to use the "squeeze" a box capacitor at the top type of system, and have a hinge at the bottom to facilitate movement.
I am not promoting these, or suggesting you buy one, just indicating that they are true works of art and inspirational for us magloop builders.

I have a 1 metre wide 20mm copper loop ready to try this myself.
I will simply make up two "book" type capacitor blocks, solder them to the ends of the loops and build a piston/motor squeezing mechanism for the loop.
Care has to be taken that it does not skew and cause the capacitor fingers to touch, but I have that problem sorted with the aid of Polyethylene chopping board material.

One thing I have made which makes all this experimentation much easier is a 1 metre "spine" of fibreglass (Old crappy pole lowest section) with a couple of PE chopping board sections attached.
This makes mounting both the top of the loops, capacitor and feed loop much easier - a prototyping setup.
A camera tripod completes the system.

I am not saying you should do any of this, but I am just sharing what has made life easier for me to progress with magloop construction and experimentation.

Have fun,

73 - Rob
 


Title: RE: What's wrong with stored energy, exactly?
Post by: JAHAM2BE on October 30, 2012, 05:16:52 PM
They achieved this by having the capacitor bolted to both ends of the loop and then squeezing the loop to mesh the capacitor.
In this way at the extreme low end of the capacitance range the blades are edge on and so there is not much area to give capacitance.
I think this is the secret to getting a good range.

I had originally planned to make a no-compromises, maximum efficiency, 40m-10m loop with 10cm-diameter (i.e. 100mm-diameter) copper tubes formed by rolling flashing (0.2mm thickness, more than 5 skin depths at 7 MHz) into a tubular shape, then soldering 8 such tubes together into an octagon, and finally to use some sort of capacitor plates mounted on the loop ends and a loop-deforming piston or pulley arrangement to push the loop (and the capacitor plates) apart, while being careful to keep the piston and control lines well away from the capacitor to avoid balance problems.

I realized that this is just a bit too mechanically complex for me right now to tackle - and also, someone suggested to me that with 10cm-diameter tubing, the loop would not be easily deformable as much as required (I estimated at least a 1mm-50mm deformation range would be needed for 2 capacitor plates to cover 7-28 MHz; for meshing multi-plate capacitor blocks, probably more). I would hate to go through all the trouble of cutting the flashing, rolling and soldering the individual tubes, and soldering the separate tubes together, only to find out at the end that the loop is too stiff to be deformed for a wide-spacing, minimum-capacitance arrangement required for 10m. So I put that idea on hold for now, though I still think it could have worked. The flat strip loop shape has, in my estimation, a greater chance of succeeding, so it's a safer bet for the expensive copper investment.

Of course, for someone with the time, money, parts, and skills, the best would be using huge-diameter tubular conductors with tapering connections to a vacuum variable capacitor. One can dream...


Title: RE: What's wrong with stored energy, exactly?
Post by: STAYVERTICAL on October 30, 2012, 06:09:38 PM
They achieved this by having the capacitor bolted to both ends of the loop and then squeezing the loop to mesh the capacitor.
In this way at the extreme low end of the capacitance range the blades are edge on and so there is not much area to give capacitance.
I think this is the secret to getting a good range.

I had originally planned to make a no-compromises, maximum efficiency, 40m-10m loop with 10cm-diameter (i.e. 100mm-diameter) copper tubes formed by rolling flashing (0.2mm thickness, more than 5 skin depths at 7 MHz) into a tubular shape, then soldering 8 such tubes together into an octagon, and finally to use some sort of capacitor plates mounted on the loop ends and a loop-deforming piston or pulley arrangement to push the loop (and the capacitor plates) apart, while being careful to keep the piston and control lines well away from the capacitor to avoid balance problems.

I realized that this is just a bit too mechanically complex for me right now to tackle - and also, someone suggested to me that with 10cm-diameter tubing, the loop would not be easily deformable as much as required (I estimated at least a 1mm-50mm deformation range would be needed for 2 capacitor plates to cover 7-28 MHz; for meshing multi-plate capacitor blocks, probably more). I would hate to go through all the trouble of cutting the flashing, rolling and soldering the individual tubes, and soldering the separate tubes together, only to find out at the end that the loop is too stiff to be deformed for a wide-spacing, minimum-capacitance arrangement required for 10m. So I put that idea on hold for now, though I still think it could have worked. The flat strip loop shape has, in my estimation, a greater chance of succeeding, so it's a safer bet for the expensive copper investment.

Of course, for someone with the time, money, parts, and skills, the best would be using huge-diameter tubular conductors with tapering connections to a vacuum variable capacitor. One can dream...

Roger that.

The best magloop for you is the one you can build with your available resources and skills.
In any case, visualisation brings reality in my experience.
I am sure that whatever you need will eventually come your way - it certainly always has for me.

A quote from Johann Wolfgang Von Goethe I have found is very true if embraced is:-

"Until one is committed, there is hesitancy, the chance to draw back, always ineffectiveness. 
Concerning all acts of initiative and creation,
there is one elementary truth the ignorance of which kills countless ideas and splendid plans: 
that the moment one definitely commits oneself, then providence moves too. 
All sorts of things occur to help one that would never otherwise have occurred. 
A whole stream of events issues from the decision, raising in one's favor all manner of unforeseen incidents,
meetings and material assistance which no person could have dreamed would have come his or her way. 
Whatever you can do or dream you can, begin it. 
Boldness has genius, power and magic in it. Begin it now."

- Goethe

73 - Rob



Title: RE: What's wrong with stored energy, exactly?
Post by: STAYVERTICAL on October 30, 2012, 08:57:03 PM
Hi JAHAM2BE,

I just had another thought about your strip based magloop.
You will probably wonder what the equivalent tubular dimensions are for a particular strip of copper.
From my investigations online, and looking up books and articles, it seems that the equivalence is around 4 to 1.
So a 200mm wide copper strip would be about equivalent to a 50mm diameter tube.

I came across a book online called:
"Electrically small, superdirective, and superconducting antennas" (Wiley publishing 2006) , by R.C. Hansen which had this and more information.

Another thought is that if your loop is too large for resonating with a practical capacitor, it is possible to add a parallel loop.
If you space a 20mm tube for example, around 4 inches (100mm) away from the first loop and put it in parallel, the overall inductance will drop.
This is of course the well known inductors in parallel formula.
You will then be able to use a higher value capacitance to resonate it at the high end of the frequency spectrum.

I tried this, and it did work, giving me 10 metres where I was only able to get to 12m formerly.
Unfortunately it will mean your capacitor must have enough excess to resonate the combo loop at your lower end (40M).

The reason I said to space 20mm tubing 100mm is that this spacing is one that has been found to minimise proximity effect but still give good results.
Technically, it should be 80mm, but I used 100mm and it worked well.
The spacing is determined by the number of parallel loops and their diameter tubing.
In a nutshell - for two parallel loops the centre to centre spacing should be 4 times the loop tube diameter.
I obtained this information from:
"The proximity effect in systems of parallel conductors and electrically small multiturn loop antennas" (Office of Naval Research) by Glenn Smith.

So, as you can see there is certainly hope for getting a wide range of bands with a little ingenuity.

Happy experimenting,

73 - Rob


Title: RE: What's wrong with stored energy, exactly?
Post by: JAHAM2BE on October 31, 2012, 04:08:25 AM
I just had another thought about your strip based magloop.
You will probably wonder what the equivalent tubular dimensions are for a particular strip of copper.
From my investigations online, and looking up books and articles, it seems that the equivalence is around 4 to 1.
So a 200mm wide copper strip would be about equivalent to a 50mm diameter tube.

W9CF has done some of the most thorough analysis of strip conductivity at RF that I've seen available freely online. At the following links you can see, respectively, a formula and approximation for the diameter of a tubular conductor having equivalent RF resistance to a given flat strip conductor; a Java applet that computes this equivalent diameter with (it appears) more accuracy than the approximate formula; and a formula for the diameter of a tubular conductor having equivalent inductance to a flat strip conductor.

http://fermi.la.asu.edu/w9cf/articles/equiv/index.html
http://fermi.la.asu.edu/w9cf/equiv/index.html
http://fermi.la.asu.edu/w9cf/articles/conform/index.html

From memory, for some various and plausible width:thickness ratios that I tried, I got equivalent-resistance diameters anywhere from 1/5th to 1/3rd of the strip width, which is in the ballpark of the 1/4th figure you mention from your reference.

The way to use W9CF's resources to design a small loop is: pick the desired sheet dimensions (width, thickness, and length), compute the equivalent tubular diameter for resistance, calculate the RF resistance of the equivalent-resistance tube having the previously-chosen length (by using either a small loop calculator program/formula, or by directly computing the RF sheet resistance of the equivalent-resistance-tube's surface area - they will be the same), compute the equivalent tubular diameter for inductance, compute the RF resistance of the equivalent-inductance tube, make a note of the additional RF resistance between the equivalent-inductance tube (which will be lower) and the equivalent-resistance tube (which will be higher), and finally to use a small loop calculator program or formula with the equivalent-inductance tube dimensions and the just-calculated additional RF resistance to determine final values for the loop efficiency, resonating capacitance, loop current, etc.

By doing the above, you will at the end be calculating the small loop values for a tubular conductor that has the same RF resistance and the same inductance as the flat sheet, according to W9CF's approximations (which he says were documented at least in part in previous literature; see http://fermi.la.asu.edu/w9cf/articles/update/index.html).

If you find my explanation difficult to follow, N3OX also explains the same thing here: http://forums.qrz.com/showthread.php?317014-Magnetic-Loop-Calculations&p=2361920#post2361920

Having gone through the quite interesting calculations as described above for my particular strip dimensions, and comparing the efficiency at 7 MHz of the flat strip used flat vs. the flat strip rolled into a tube, I can say that the difference was small enough not to matter to me - less than half a dB (in favor of the tubular conductor) as I recall. That possible half-dB improvement didn't outweigh the increased constructional challenges of making the tube-based loop.

This all of course ignores any calculation of capacitor losses. Electromagnetic field simulation or field strength measurements of the completed loop-and-capacitor assembly seem to be the only way to get an idea of these.

Your suggestion about an additonal loop is indeed interesting, but I feel the issues surrounding multi-turn or multi-conductor loops are a bit too hairy to tackle right now. Since coming to the recent realization that it's actually entirely feasible to home-fabricate gigantic-diameter copper tubing by rolling flat sheet metal into tubes, I'll probably (one day) pick up on the large-diameter-tubing loop idea before I venture into multiple conductors.

The nice thing about starting with the flat-strip design is that I can re-use the same material to form copper tubes, whenever I feel like tackling that.


Title: RE: What's wrong with stored energy, exactly?
Post by: STAYVERTICAL on October 31, 2012, 12:01:46 PM
Thanks for the info and the websites.
I will certainly investigate them and see what else I can learn (a lot I am sure).

A few notes from the trenches:

From my experiments, it does not seem to matter much whether you use strip or tubular conductors, taking into account the equivalences.
My large copper strip loop (almost a foot wide strip) worked well.
It had about 90 percent greater bandwidth at 12m than a single 20mm conductor.
At the lower end (10Mhz) it had about a 20 percent wider bandwidth.
So there was a difference, but I determined the difference was not great enough to warrant the extra effort in my case.
This was because I already had a pretty efficient system/capacitor to begin with.

As you imply, the benefits of large diameter conductors/strips is primarily evident at 40m and 30m.
Above that the incremental benefit is not that great if you have an optimised 20mm copper tubular system.
From my experiments the two things which deliver the greatest increase in efficiency are:

1. Using copper rather than aluminium.
2. Making the loop circumference/span greater.

Also, I found that it is best to avoid wires for interconnecting capacitors.
Using 12mm copper tube to directly connect the capacitor to the main loop/loops gave me far better results.
It is a case of the weakest link causing the whole structure to become inefficient.
That's about it for small loops.
They really are just a big tuned circuit with losses in the form of R.F. radiation (in addition to the other dissipative losses).

Happy experimenting,

73 - Rob


Title: RE: What's wrong with stored energy, exactly?
Post by: JAHAM2BE on October 31, 2012, 09:50:46 PM
My large copper strip loop (almost a foot wide strip) worked well.
It had about 90 percent greater bandwidth at 12m than a single 20mm conductor.
At the lower end (10Mhz) it had about a 20 percent wider bandwidth.
So there was a difference, but I determined the difference was not great enough to warrant the extra effort in my case.
This was because I already had a pretty efficient system/capacitor to begin with.

Your results bring to light an interesting subtle aspect. The strip exhibits wider bandwidth. Why? Because it has less self-inductance per unit length than the tube. In other words, it has less inductive reactance, leading to lower Q=X/R and broader bandwidth.

And as we see in this thread, less inductive reactance means less energy storage and - that's right - less loss!

So it seems for a given conductor length and sufficient strip width to ensure good conductivity, a strip is actually better than a tube! :o


Title: RE: What's wrong with stored energy, exactly?
Post by: W5DXP on November 01, 2012, 04:36:28 AM
So it seems for a given conductor length and sufficient strip width to ensure good conductivity, a strip is actually better than a tube! :o

Would that also apply to magnetic loop antennas?


Title: RE: What's wrong with stored energy, exactly?
Post by: N3OX on November 01, 2012, 07:26:46 AM
And as we see in this thread, less inductive reactance means less energy storage and - that's right - less loss!

You know, this is probably an example where lowering the reactance by itself probably doesn't lead to LESS loss, at least not in any meaningful way.

If the loss resistance and enclosed area (and hence the radiation resistance) of the two loops is the same, and they only differ in their reactance because of the extra self-inductance of the conductor, then the balance of loss and radiation will be the same.  I don't think the resistance of a good air or vacuum capacitor changes much with its reactance.

From the Jennings vacuum variable literature:
Quote from: http://www.jenningstech.com/pdf/cap_cat1.pdf
Based on actual tests, the ESR value is not affected
by change in capacity, other parameters being fixed. The value
of ESR varies over a range of 2 to 20 milliohms from 2 to
30 MHz

So tuning out some extra reactance with a good vacuum cap, for example, is simply irrelevant to the loss.  The cap adds 2-20 milliohms in series, period, no matter the capacitance.

----------------

The bandwidth will be improved with lower conductor self-inductance.  But the equivalent circuit, at least for a small loop, is more like your series LCR circuit

o--Rloss--Rrad--Cap ESR--Loop Inductance--Conductor Self-Inductance--Tuning Capacitance--o

Rrad and cap series resistance are probably about constant for a good cap, Rloss (the conductor) is chosen by choosing strip width for good efficiency, so let's say it's the same to put things on equal footing.  So there's nothing you can do with the conductor self inductance to change the power dissipated in the combination of Rloss+Rrad+Cap ESR at resonance.

In a purely series circuit the only reason to get more loss with more loading inductance is the highly non-ideal nature of an inductor; seems hard to get a weakly radiating inductive structure with a Q exceeding 1000.  But if you talk about keeping resistance equal and lowering conductor self-inductance, and you don't have some kind of parallel or distributed transformation like my example, all you will change is bandwidth.  

These bandwidth issues are kind of insidious for people who like to use bandwidth as a proxy for efficiency.  It's plausible that you can increase conductor loss resistance and self-inductance simultaneously, leading to a narrower bandwidth magloop with more loss.  It doesn't have more loss *because* you added more inductance; it has more loss because you added more resistance.  But the added conductor inductance masks the bandwidth widening you'd expect if you just added loss resistance.


Title: RE: What's wrong with stored energy, exactly?
Post by: W8JI on November 01, 2012, 09:31:08 AM
If the loss resistance and enclosed area (and hence the radiation resistance) of the two loops is the same, and they only differ in their reactance because of the extra self-inductance of the conductor, then the balance of loss and radiation will be the same.  I don't think the resistance of a good air or vacuum capacitor changes much with its reactance.

From the Jennings vacuum variable literature:
Quote from: http://www.jenningstech.com/pdf/cap_cat1.pdf
Based on actual tests, the ESR value is not affected
by change in capacity, other parameters being fixed. The value
of ESR varies over a range of 2 to 20 milliohms from 2 to
30 MHz

So tuning out some extra reactance with a good vacuum cap, for example, is simply irrelevant to the loss.  The cap adds 2-20 milliohms in series, period, no matter the capacitance.

The resistance stabilitly occurs because the capacitor is compact and has the same path length through the component, and nearly the same current distribution and density in conductors, regardless of capacitor setting.

However, the capacitor Q changes. :-)

It would take a good sized book to cover this stuff.

:-)

73 Tom


Title: RE: What's wrong with stored energy, exactly?
Post by: JAHAM2BE on November 01, 2012, 03:25:19 PM
The resistance stabilitly occurs because the capacitor is compact and has the same path length through the component, and nearly the same current distribution and density in conductors, regardless of capacitor setting.

However, the capacitor Q changes. :-)

It would take a good sized book to cover this stuff.

Might you suggest any references on capacitor analysis and design?

Here's a 2009 article that indicates some analysis techniques for inclined plate capacitors: http://www.icrepq.com/ICREPQ'09/452-barrachina.pdf


Title: RE: What's wrong with stored energy, exactly?
Post by: W8JI on November 01, 2012, 05:03:48 PM
I doubt you will find a detailed article on capacitor design, unless someone did their doctorate thesis on the topic. It is probably like RF inductor design, although there was one good inductor design paper many years ago.