Quantity chickens sacrificed for 433MHz antenna?

[chipwitch]

In case the subject line escapes you, it is a reference to voodoo... Because that's exactly what antennas seem like to me.  Maybe I should be posting this in the Beginner forum? 

For me personally, learning happens by first possessing some general concept of the thing being learned.  Then, slowly heaping on technical aspects.  Without a modest grasp of the concept, the technical aspect might as well be in a foreign language.  My eyes glaze over, my pulse quickens and beads of perspiration will form on my neck just before I fall asleep. 

My first foray into RF is experimenting with the cheap 433MHz rx/tx modules.  That's is where I'm at.  I've attached 17mm copper wires to the antenna hole, wired them up to a breadboard and failed to achieve even my low expectation of the results.

There's tons of info on antennas on the net, but most of it is technical.  It doesn't help that many of the tutorials (arduino) about these modules, lacking adequate datasheets, are simply recipes for how to make them work, though not particularly well.  Further, all of the ones I've read are generally by people with no real knowledge of RF.  Many are written by people whose ambition is to make something work, not to actually learn.  I'm the latter.

So, for now, I'm just hoping you know of some nice "Antennae for Idiot" sources that you like.  I've found some for "dummies" but alas, I guess I'm not that smart.

[CatalinaWOW]

Don't know what floats your boat, but the ARRL publications generally start slow and then build.

But more fundamentally, you appear to be aiming for a 1/4 wave antenna.  That should be about 17 centimeters long.  If your post accurately states that you used 17 millimeters you would expect poor performance.

[chipwitch]

Your understanding of the OP is correct.  I got that number from numerous sites regarding this particular tx/rx pair.  Without an understanding of antenna theory, I am relegated to recipe following myself.  The current antenna configuration will only extend 1 or 2 meters, mostly a product of the antenna I suspect.  The software however, is also primitive and partly to blame for poor communication.  There isn't much filtering of noise.

[chris_leyson]

Hi Chipwitch, what rx/trx pair are you using ?

[donmr]

The length of an antenna is related to the wave length of the signal.

The wave length is the speed of the signal divided by the frequency.

In the wire the speed is about 95% of the speed of light in a vacuum (3*10^8 m/s) or about 285*10^6 m/s

So the wave length of 433 MHz is 0.658m.  1/4 wave length is 0.164m or 16.4 cm.

[chris_leyson]

Hi donmr, in wire the propagation speed is 100% light speed, 3E8 m/s, if you have a dielectric around the wire like in coax then it slows down to maybe 75% depending on the dielectric.

[chipwitch]

Hi Chris... just the standard cheap China 433MHz set.  No internal protocols or anything.  Antenna is just a bare copper wire. 

But, I'm not particularly looking for information on how to make it work, per se.  I'd rather learn why it doesn't work well.  That requires at least a better understanding of antenna theory.  I get hung up on the verbage at some point.  For instance, I read http://electronicdesign.com/passives/welcome-antennas-101 and it was all good for about half the article.  Then, I get down to about here and I'm completely lost:

If an antenna acts like a tuned circuit, how can I be sure it has the necessary bandwidth?
Antennas are resonant, so they have a Q and related bandwidth (BW). For most antennas, this bandwidth is roughly 10% to 15% of the resonant frequency. It’s important that the antenna has a broad enough response to pass all of the necessary sidebands to avoid distortion. Most antennas are selective so they can get rid of noise and some harmonics, but you don’t want sideband clipping. If you’re using a commercial antenna, look at the selectivity or BW specification to see that it fits. In antenna construction, the physical dimensions affect BW.

The text in red is like listening to Charlie Brown's parents.  I can define the words, but haven't a tangible grasp on the concepts as they pertain to antennae.  That's why I'm looking for some good remedial introductions on antennae.  Then maybe I can ask some intelligent questions.

[PA0PBZ]

I googled "Antennas for dummies" and this is the first (maybe not the best) link: http://www.comportco.com/~w5alt/antennas/notes/ant-notes.php
Can you show one of the sites where they mention 17mm?

[chipwitch]

I didn't realize it until I saw it in your post... 17mm is ridiculous of course...

17cm.    See... told you "dummy" was too smart for me!

[PA0PBZ]

So you have a TX module and a RX module, both with ~ 17cm antennas and you only get 1-2M range?
Are the antennas oriented the same way? So like |  |  and not like | _ ?
It could be that you have something else on that exact frequency that spoils the fun, but not very likely.
Are these FSK units or OOK or anything else? Can you post a link to the modules?
How did you test the range?

[Howardlong]

If you are after plans for antennas, in particular directional ones at 433MHz, look up "Cheap Yagis" by Kent Britain. Unlike the vast majority of antenna recipes, these are designed to be reproducible by mere mortals. While they might not squeeze out the very best last fraction of a dB in gain, that is not the point: fundamental in the design is that you don't need an antenna range, anechoic chamber or VNA to make them work reasonably well, just make sure you adhere to the specifications in element lengths and diameters.

http://www.wa5vjb.com/yagi-pdf/cheapyagi.pdf

[Howardlong]

On a more general note to the OP, it took me many years to really think I had any grasp of antennas despite a huge amount of effort during that time and several shed loads full of bent aluminium. The day the penny really dropped was the day I used a VNA, everything just sank into place in a matter of minutes. You can do stuff without a VNA, but it's a bit harder and often much more time consuming. The visual nature of it and the immediate feedback adds so much value to the understanding.

Luckily nowadays you don't have to remortgage your house to get a VNA, there are USB based devices commonly available.

Note that a VNA will only tell you about impedance matching and resonance, not radiation patterns.

Doing antennas is a life long class, it's such a big subject that most aficionados tend to specialise in a particular area.

[Marco]

Do the helical antennas glued down on a spindle perform much better than the loose wires ones?

[chipwitch]

So you have a TX module and a RX module, both with ~ 17cm antennas and you only get 1-2M range?
Are the antennas oriented the same way? So like |  |  and not like | _ ?
It could be that you have something else on that exact frequency that spoils the fun, but not very likely.
Are these FSK units or OOK or anything else? Can you post a link to the modules?
How did you test the range?

Here is why the OP is NOT asking for help getting my radios to work... I had to LOOK up OOK and FSK.  I don't have a link as I bought them a year or so ago.  They're like 99 cents.  Arduino switches the oscillator, so I'm guessing, in my limited comprehension of radios, that they can be made AM or FM as a result.  I'm less interested in making them function than I am in learning about antennas at the moment.  I appreciate the willingness to help me get them working, but I'd rather "learn to fish" as they say.

[chipwitch]

On a more general note to the OP, it took me many years to really think I had any grasp of antennas despite a huge amount of effort during that time and several shed loads full of bent aluminium. The day the penny really dropped was the day I used a VNA, everything just sank into place in a matter of minutes. You can do stuff without a VNA, but it's a bit harder and often much more time consuming. The visual nature of it and the immediate feedback adds so much value to the understanding.

Luckily nowadays you don't have to remortgage your house to get a VNA, there are USB based devices commonly available.

Note that a VNA will only tell you about impedance matching and resonance, not radiation patterns.

Doing antennas is a life long class, it's such a big subject that most aficionados tend to specialise in a particular area.

I really appreciate the story.  It was helpful... up until the "VNA" part.  What the hell is that?     I'm guessing something something analyzer?  I'm probably overstating my knowledge of radios when I say I don't really know much about them. 

If VNA's can be had for little money, what you describe sounds like a HUGE help for me.  Right now, I don't know what the impedances of the Rx, the Tx or my antennae are.  That's one of the disconcerting things for me.  I know what impedance is in terms of ac circuits, but when I look at my 6 inches of copper wire, all I see is 0 ohms resistance.  How do I get to 50 from there?  See why I need the basics.  I don't even know enough to ask what I don't know?

[JimRemington]

The cheap 434 MHz modules work very well with a balanced dipole, like those shown below. Connect one end of the dipole to ANT and the other to GND on each module.

I used the antenna design program MMANA-GAL to optimize the dipole and for #12 gauge copper wire, it came out to be 32.8 cm end-to-end. The impedance is calculated to be 74 Ohms at the feedpoint, but who knows what the modules have for output impedance?

I easily get over 300 meters line of sight range with the setup, even with only 3.5V on the transmitter.

[vk6zgo]

Hi donmr, in wire the propagation speed is 100% light speed, 3E8 m/s, if you have a dielectric around the wire like in coax then it slows down to maybe 75% depending on the dielectric.

The 95% thing isn't to do with speed of propagation --it is due to an antenna characteristic known as "end effect".

A quick Google for end effect won't be incredibly productive,if you are shy about theory.

It seems that an antenna cut to formula (300/f in MHz) turns out to be slightly inductive.
We normally want the antenna impedance to be resistive only,so cutting a bit off the antenna adds capacitance,cancelling the inductance.

Most of us just say :-"Yeah,we have to allow for end effect",& do so,without thinking much more about it.

For simplicity,just use the formula,then cut the antenna until resonance is reached.
The length should be around the 95% mark.

[chipwitch]

The cheap 434 MHz modules work very well with a balanced dipole, like those shown below. Connect one end of the dipole to ANT and the other to GND on each module.

I was wondering if that would work.  Thanks for the tip and photo

[vk6zgo]

On a more general note to the OP, it took me many years to really think I had any grasp of antennas despite a huge amount of effort during that time and several shed loads full of bent aluminium. The day the penny really dropped was the day I used a VNA, everything just sank into place in a matter of minutes. You can do stuff without a VNA, but it's a bit harder and often much more time consuming. The visual nature of it and the immediate feedback adds so much value to the understanding.

Luckily nowadays you don't have to remortgage your house to get a VNA, there are USB based devices commonly available.

Note that a VNA will only tell you about impedance matching and resonance, not radiation patterns.

Doing antennas is a life long class, it's such a big subject that most aficionados tend to specialise in a particular area.

I really appreciate the story.  It was helpful... up until the "VNA" part.  What the hell is that?     I'm guessing something something analyzer?  I'm probably overstating my knowledge of radios when I say I don't really know much about them. 

If VNA's can be had for little money, what you describe sounds like a HUGE help for me.  Right now, I don't know what the impedances of the Rx, the Tx or my antennae are.  That's one of the disconcerting things for me.

A "VNA" is a "Vector Network Analyser".
What is nice about it,is that it shows both amplitude & phase  changes with frequency.
It can thus,show impedance

I know what impedance is in terms of ac circuits, but when I look at my 6 inches of copper wire, all I see is 0 ohms resistance.  How do I get to 50 from there?  See why I need the basics.  I don't even know enough to ask what I don't know?

It all depends upon your viewpoint---- replace your transmitter with a DMM on resistance range,& your piece of wire will read as "infinity".

To RF,your length of wire when used as a part of an antenna possesses both inductance & capacitance,as well as
resistance.

At resonance ,the inductive & capacitive reactances cancel,leaving you with real resistance,& "Radiation Resistance"
This is not a real physical resistance,but looks like one to the external circuit.

Many people get "all bent out of shape" trying to get their heads around radiation resistance,but things which are not real resistors,but act like one are common in Electrical Theory.

One such is internal resistance in a Dry or a Wet Cell,where the internal chemical reaction decreases in activity as the cell becomes flat,looking to the external circuit like an increase in resistance.

Another is in an Electric motor .

Running unloaded,it looks like a high Inductive Reactance,& draws a small current,lagging the input voltage.
Apply a mechanical load,& the current increases,with the lag decreasing towards the resistive case.
It looks like a resistance in parallel with the motor inductance,but is really caused by the mechanical load.

In the same manner,the act of radiating electromagnetic waves from an antenna looks like a resistive loss,in phase with that caused by the real resistance,but is,of course,the whole object of the device.

A resonant 1/2 wavelength dipole is (in free space) about 70 Ohms,that of a1/4 wavelength vertical,half of that.

There is nothing magical about 50 Ohms,it is a standard coaxial cable impedance,& luckily,many practical antennas are closer to that value than the theoretical one.
50 Ohms has become the standard for RF interconnections,as it makes it a lot easier to measure signal levels,etc.

.

[Howardlong]

Do the helical antennas glued down on a spindle perform much better than the loose wires ones?

Axial or normal mode helix? What frequency and what is the material and dimensions of the spindle?

The reason I ask is that the spindle can have a dielectric effect and (a) detune the antenna (b) introduce losses and (c) affect the radiation pattern.

[Howardlong]

As I mentioned earlier, you can spend a lifetime studying antennas. There are a lot of abstract conceptual things to understand if you want to go the theory way. Equally, there are an awful lot of rules of thumb to learn if you go the empirical/practical way. Typically most antenna gurus have a hybrid understanding, in its simplest for there's the calculation for a dipole resonant length... and then the 95% end effect thing would be a rule of thumb.

The antenna itself is just one part of the equation. The matching of the antenna is a whole topic in its own right, but it's a key part of any antenna design, so here's a worked example for a simple dipole.

The dipole is a reasonable starting point except that it's a balanced antenna, and most (but not all) presentations are 50 ohm unbalanced (ie, coaxial). Coaxial is generally favoured over balanced twin-lead because it's easier to route physically and its performance isn't affected by other adjacent objects, like other feeders, pipes or walls for example. To terminate (ie connect the coax to the antenna), you could simply put the outer of the coax feed to one side of the dipole and the inner to the other side, and in practical it will usually work apparently reasonably well. The downside is that because you're feeding a balanced antenna with an unbalanced feeder, some of the power will also be radiated back along the coax outer as well as the antenna itself, affecting the radiation pattern. To fix this, you use a balun which is simply a high frequency isolating transformer, with two windings, one you put across the coax and the other goes to your dipole. This can be a simple off the shelf part you can mount on a PCB for low power applications.

All that is great but there's one other thing... a dipole has an impedance at resonance of round about 75 ohms, but your transmitter and coax feeder is 50 ohms, so you won't achieve an optimum match, resulting in some of the power being reflected back to the transmitter, rather than absorbed and radiated by the antenna. This is not black magic, this is all about maximum power transfer, you can do the same experiment at DC with resistors, and maximum power is transferred when the impedance of the load (antenna) is the same as the supply (transmitter).

Practically speaking, just like the balanced/unbalanced thing, you might well have difficulty in telling any difference in most circumstances, as the impedances aren't a million miles away from each other, but frequently that is not the case, and anyway it's bad form from an engineering perspective to throw away power. So to fix the impedance mismatch, you could use a 25 ohm series resistor couple of resistors to convert that 50 ohms to 75 ohms at the antenna... but then resistors will throw away that power as heat, we want to transfer all the power to the antenna. So a better way is either to use an inductor/capacitor matching network, or as you're already using a balun, use a balun with a different windings ratio, ie 1.5:1 instead or 1:1. Typically to reduce losses, if it's economically effective, I'd rather use a single part than several.

Say, though, you do want to match 50 ohms to 75 ohms in a relatively lossless way at a given frequency with an LC network rather than a balun, how do you do that? The internet is at your service! There are plenty of online calculators for this, for example http://leleivre.com/rf_lcmatch.html

I plugged in a frequency of 433MHz, source impedance of 50 ohms and load impedance of 75 ohms. We are only interested at resonance, so in theory there is no reactive component on source or load, so we set the j ohm entries to zero. (Note that the j notation is to do with complex numbers: don't worry about this for now as it'll just confuse the issue, but if you do want to understand antennas in any depth you'll have to engage with the topic at some point.)

The calculator came out with two solutions (13nH & 3.5pF or 39nH & 10.4pF) and two "Nan" (not a number, ie unsolvable) solutions which simply can't be made with the topologies given. For the two solutions provided, you could use either one, but for this I'd choose the one with the most practical of components and easiest to fabricate, which would be the second one. Why? It's easier to fabricate the second one because parasitics (inductance and capacitance from PCB and other construction effects) on those larger value parts will be relatively less than on the first option. Sometimes though, there may be an engineering reason to choose the first option, for example you might want a DC path which you get with the first option. Particularly at UHF and higher, rather than using "lumped" parts frequently you can fabricate the matching on the PCB itself, using those parasitic characteristics to your advantage, but that's yet another topic.

As with many engineering topics, knowing what matters and what doesn't in a practical sense is frequently a matter of experience, and no matter how many theory classes you do, you'll never know what can be discounted and what's really important, how things interact, and how to prioritise things given a set of design criteria.

[chipwitch]

I know what impedance is in terms of ac circuits, but when I look at my 6 inches of copper wire, all I see is 0 ohms resistance.  How do I get to 50 from there?  See why I need the basics.  I don't even know enough to ask what I don't know?

It all depends upon your viewpoint---- replace your transmitter with a DMM on resistance range,& your piece of wire will read as "infinity".

Am I to understand you're saying only attach one lead of the DMM?  Otherwise, I don't see how you get infinity. 

To RF,your length of wire when used as a part of an antenna possesses both inductance & capacitance,as well as
resistance.

At resonance ,the inductive & capacitive reactances cancel,leaving you with real resistance,& "Radiation Resistance"
This is not a real physical resistance,but looks like one to the external circuit.

Many people get "all bent out of shape" trying to get their heads around radiation resistance,but things which are not real resistors,but act like one are common in Electrical Theory.

One such is internal resistance in a Dry or a Wet Cell,where the internal chemical reaction decreases in activity as the cell becomes flat,looking to the external circuit like an increase in resistance.

Another is in an Electric motor .

Running unloaded,it looks like a high Inductive Reactance,& draws a small current,lagging the input voltage.
Apply a mechanical load,& the current increases,with the lag decreasing towards the resistive case.
It looks like a resistance in parallel with the motor inductance,but is really caused by the mechanical load.

In the same manner,the act of radiating electromagnetic waves from an antenna looks like a resistive loss,in phase with that caused by the real resistance,but is,of course,the whole object of the device.

A resonant 1/2 wavelength dipole is (in free space) about 70 Ohms,that of a1/4 wavelength vertical,half of that.

There is nothing magical about 50 Ohms,it is a standard coaxial cable impedance,& luckily,many practical antennas are closer to that value than the theoretical one.
50 Ohms has become the standard for RF interconnections,as it makes it a lot easier to measure signal levels,etc.

I am guilty of being unable to get my head around it.  Unlike the examples you site, motor reactance, battery resistance etc, difficult as they are for a newbie to wrap their head around, those things don't exist outside of a circuit!  Antennae require a whole new concept where one end of a wire is simply dangling free.  The "resistance" or impedance of that antenna isn't quite so obvious.  In fact, I'd venture that antennas would probably be an easier concept in which to get ones head around, if they were taught that before possessing conceptual knowledge of circuits.

[KM4FER]

Chipwitch,

You say you want to learn not just follow a recipie  Great, I'm with you on that.

My suggestion is that you start at the beginning.  A good way to do that would be to study to obtain an amateur radio license.  In doing that you will learn the very basics of rf and antenna theory.  Also I would build an oscillator that runs at about 1 MHz which you could tune in on a standard AM radio.  Then if you have your license you could change the oscillator frequency to one you are allowed to transmit in and play around with antennas.

This won't be fast but it will give you the understanding to answer your original question.

Earl...

[chipwitch]

Howard, I would have never presumed to expect lessons in antenna theory from this forum as I'm sure it's already been replicated elsewhere... numerous times.  I just haven't been able to find the one that clicked, for me.  I feel a little guilty that you should spend so much time trying to teach me here, in a forum before I've had ample time to absorb some of the basics.  I certainly appreciate the effort and I have to say, it hasn't been entirely in vain.  Like you say, a lifetime of learning antenna theory... I don't doubt that.

As I mentioned earlier, you can spend a lifetime studying antennas. There are a lot of abstract conceptual things to understand if you want to go the theory way. Equally, there are an awful lot of rules of thumb to learn if you go the empirical/practical way. Typically most antenna gurus have a hybrid understanding, in its simplest for there's the calculation for a dipole resonant length... and then the 95% end effect thing would be a rule of thumb.

Well observed and stated.  I am familiar with the theory/practical dichotomy.  The hybrid approach is my typical MO with all things in which I enjoy some measure of success.  Kudos to you for recognizing that.  I'm not an EE, though it was my major, briefly.  But I do find a general understanding of theory helps me understand (perhaps remember) the practical side of things better.  I remember my Calc I professor in college.  The first day of class, I had NO CLUE what calculus was.  It was intimidating.  But, I was fortunate to have one of those really great teachers.  When he merely mentioned the concept of the sum of an infinite number of approximated segments under a curve to determine the area under the curve, it opened the floodgates for all the rest calculus had to offer.  To me, that was the key.  Memorizing derivation and integration rules and employing them by rote is a recipe for failure in my opinion.

The antenna itself is just one part of the equation. The matching of the antenna is a whole topic in its own right, but it's a key part of any antenna design, so here's a worked example for a simple dipole.

Excellent.  I didn't want to bring up the latter part.  I recognize the two parts.  Measuring the resistance and how to "tune" it, are both mysteries to me.  I read an article (might have been a video that accompanied it) about how to make the device to measure antenna impedance using a scope, signal generator and a whet bridge.  It's a pretty detailed article, but then he doesn't really explain how the "tuning" part is done.  Measuring impedance is a pretty useless activity without the ability to alter it.

The dipole is a reasonable starting point except that it's a balanced antenna, and most (but not all) presentations are 50 ohm unbalanced (ie, coaxial). Coaxial is generally favoured over balanced twin-lead because it's easier to route physically and its performance isn't affected by other adjacent objects, like other feeders, pipes or walls for example. To terminate (ie connect the coax to the antenna), you could simply put the outer of the coax feed to one side of the dipole and the inner to the other side, and in practical it will usually work apparently reasonably well. The downside is that because you're feeding a balanced antenna with an unbalanced feeder, some of the power will also be radiated back along the coax outer as well as the antenna itself, affecting the radiation pattern. To fix this, you use a balun which is simply a high frequency isolating transformer, with two windings, one you put across the coax and the other goes to your dipole. This can be a simple off the shelf part you can mount on a PCB for low power applications.

I need to digest this one paragraph at a time.  You're testing my limit of comprehension, but you're NOT way over my head.  A balun is an isolation transformer... aha moment for me.  It's a transformer.  It has inductance.  The coax (and to a lesser extent, the twin lead?) naturally has some capacitance... introduce an ac signal and that is the impedance?  We are talking about electrical impedance?  I just learned there is "wave impedance" as well.  I don't want to conflate the two.

So, the model that is forming in my mind thanks in great part to you, is this: Low energy radiation is emitted from wires with an a/c signal.  All electrified components in the "circuit" will have (generally small?) some amount of inductance and/or capacitance.  Being charged positively and negatively alternately at some frequency, creates a resistance to that change in charge, impedance.  I see a set of components in series.  Monopole antenna for simplicity, various connectors, balun if you like, cables, the pcb etc.  Because the components are in series, the flow (rather voltage) must be the same in each (Kirchhoff's law).  If the impedances of each component aren't identical, then they would be out of phase with one another (something that is impossible?) therefore, the peak charge can never reach it's full potential?  Is that too simplistic or just plain wrong?

Practically speaking, just like the balanced/unbalanced thing, you might well have difficulty in telling any difference in most circumstances, as the impedances aren't a million miles away from each other, but frequently that is not the case, and anyway it's bad form from an engineering perspective to throw away power. So to fix the impedance mismatch, you could use a 25 ohm series resistor to convert that 50 ohms to 75 ohms at the antenna... but then resistors will throw away that power as heat, we want to transfer all the power to the antenna. So a better way is either to use an inductor/capacitor matching network, or as you're already using a balun, use a balun with a different windings ratio, ie 1.5:1 instead or 1:1. Typically to reduce losses, if it's economically effective, I'd rather use a single part than several.

You make a point I've not seen elsewhere.  I've always gotten the impression that at some point, mismatched impedances will result in setting ones hair on fire.  So, it's about maximizing efficiency more so than necessity.  Does that mean my little 433MHz tx/rx isn't likely having a problem due to impedance mismatch?

Say, though, you do want to match 50 ohms to 75 ohms in a relatively lossless way at a given frequency with an LC network rather than a balun, how do you do that? The internet is at your service! There are plenty of online calculators for this, for example http://leleivre.com/rf_lcmatch.html

I plugged in a frequency of 433MHz, source impedance of 50 ohms and load impedance of 75 ohms. We are only interested at resonance, so in theory there is no reactive component on source or load, so we set the j ohm entries to zero. (Note that the j notation is to do with complex numbers: don't worry about this for now as it'll just confuse the issue, but if you do want to understand antennas in any depth you'll have to engage with the topic at some point.)

I checked out the link.  That was also a missing "link" for me as well (pun intended).  The concept of "resonance" still eludes me.  Being able to define it is not the same as comprehending the concept.  At one point I had a pretty fair grasp of reactance in ac circuitry.  So, "j" doesn't bother me... complex numbers for that matter.  I'll have to review that though.  Perhaps it will help.  Again, the part that I think bothers me about antennae is that you have a "conductor" that doesn't go anywhere.  It's a wire that needs to be attached to something.  That's the elusive part it seems.

The calculator came out with two solutions (13nH & 3.5pF or 39nH & 10.4pF) and two "Nan" (not a number, ie unsolvable) solutions which simply can't be made with the topologies given. For the two solutions provided, you could use either one, but for this I'd choose the one with the most practical of components and easiest to fabricate, which would be the second one. Why? It's easier to fabricate the second one because parasitics (inductance and capacitance from PCB and other construction effects) on those larger value parts will be relatively less than on the first option. Sometimes though, there may be an engineering reason to choose the first option, for example you might want a DC path which you get with the first option. Particularly at UHF and higher, rather than using "lumped" parts frequently you can fabricate the matching on the PCB itself, using those parasitic characteristics to your advantage, but that's yet another topic.

As with many engineering topics, knowing what matters and what doesn't in a practical sense is frequently a matter of experience, and no matter how many theory classes you do, you'll never know what can be discounted and what's really important, how things interact, and how to prioritise things given a set of design criteria.

I appreciate your thoroughness.  I thought I'd find this on the net.  I'm sure it's out there, a needle among haystacks.

[borjam]

A VNA can eliminate most of the voodoo factor. Of course, looking good on the VNA doesn't mean that the antenna will work. But an antenna looking bad on the VNA most certainly won't Moveover, mismatched antennas can damage transmission circuitry.

VNAs are really expensive instruments, but luckily there are cheap models adequate for the needs of a radio amateur. For example, I've got a miniVNA Tiny from Mini Radio Solutions (miniradiosolutions.com) and it certainly works. It can measure from 1 MHz to 3 GHz.

There is a very good introductory book on antennas. Depending on how you read (or skim through it) you can learn a lot or at least develop some intuitive knwoledge of what might work and not when designing an antenna.

http://www.amazon.com/Practical-Antenna-Handbook-5-e/dp/0071639586/ref=sr_1_1?s=books&ie=UTF8&qid=1458138978&sr=1-1&keywords=practical+antenna+handbook