Author Topic: Quantity chickens sacrificed for 433MHz antenna?  (Read 17788 times)

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Offline chipwitchTopic starter

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Quantity chickens sacrificed for 433MHz antenna?
« on: March 15, 2016, 04:32:01 pm »
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.
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Offline CatalinaWOW

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #1 on: March 15, 2016, 05:07:06 pm »
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.
 

Offline chipwitchTopic starter

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #2 on: March 15, 2016, 05:30:16 pm »
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.
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Offline chris_leyson

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #3 on: March 15, 2016, 05:58:54 pm »
Hi Chipwitch, what rx/trx pair are you using ?
 

Offline donmr

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #4 on: March 15, 2016, 06:04:19 pm »
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.
 

Offline chris_leyson

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #5 on: March 15, 2016, 06:23:35 pm »
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.
 

Offline chipwitchTopic starter

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #6 on: March 15, 2016, 06:57:14 pm »
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:

Quote
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. :)

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Online PA0PBZ

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #7 on: March 15, 2016, 07:37:24 pm »
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?
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Offline chipwitchTopic starter

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #8 on: March 15, 2016, 08:20:59 pm »
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!
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Online PA0PBZ

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #9 on: March 15, 2016, 08:41:59 pm »
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?
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Offline Howardlong

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #10 on: March 15, 2016, 10:20:09 pm »
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

 

Offline Howardlong

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #11 on: March 15, 2016, 10:35:26 pm »
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.
 

Offline Marco

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #12 on: March 15, 2016, 11:19:04 pm »
Do the helical antennas glued down on a spindle perform much better than the loose wires ones?
 

Offline chipwitchTopic starter

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #13 on: March 15, 2016, 11:58:13 pm »
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.

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Offline chipwitchTopic starter

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #14 on: March 16, 2016, 12:05:24 am »
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?
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Offline JimRemington

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #15 on: March 16, 2016, 12:40:16 am »
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.
 

Offline vk6zgo

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #16 on: March 16, 2016, 01:08:04 am »
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.
 

Offline chipwitchTopic starter

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #17 on: March 16, 2016, 02:02:29 am »
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
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Offline vk6zgo

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #18 on: March 16, 2016, 02:08:19 am »
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
Quote
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.

.
 

Offline Howardlong

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #19 on: March 16, 2016, 08:17:24 am »
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.
 

Offline Howardlong

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #20 on: March 16, 2016, 09:59:23 am »
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.
« Last Edit: March 16, 2016, 09:43:48 pm by Howardlong »
 

Offline chipwitchTopic starter

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #21 on: March 16, 2016, 12:46:21 pm »
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.
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Offline KM4FER

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #22 on: March 16, 2016, 01:36:43 pm »
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...
 

Offline chipwitchTopic starter

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #23 on: March 16, 2016, 02:22:14 pm »
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.

Quote
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.

Quote

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?

Quote
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?
Quote
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.

Quote
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.
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Offline borjam

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #24 on: March 16, 2016, 02:37:40 pm »
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

 

Offline borjam

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #25 on: March 16, 2016, 03:18:56 pm »
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. :)
The text is indeed chaotic :)


Alright, let me try the intuitive path.

There are some key points you need to take into account. I think it would help to grasp some

First, the length of an antenna matters. An antenna must resonate in some way, and it depends on its dimensions and the frequency you wish to use.

Second, transmissions take a bandwidth necessarily greater than 0, which is why that paragraph you quote mentions "Q" and problems derived from antennas with narrow bandwidth.

For example: a voice transmission on HF (short wave) as used by hams takes about 2 KHz of bandwidth. So, if you are transmitting SSB on, say, 7.100 MHz you are actually radiating energy from 7100 to 7102 KHz. So, your antenna must work well not only for 7100 KHz, but for 7102 as well :)

If you are using the 433 MHz transmitters for digital data, you need some way to modulate the radio signal with the data. There are so many ways to do it. Morse code is the oldest, just switching the radio signal (called carrier) on and off. But it's not particularly well suited for digital data, so other methods are commonly used.

A simple to understand digital modulation method (which was mentioned in another post) is called "FSK", which uses two signals. One of them is a digital "1", the other one a digital "0". The frequency differences range usually from 170 Hz (typical in amateur radio transmissions) to almost 1 KHz.

Higher speeds require of course much more bandwidth. WiFi transmissions can require between 20 MHz and 160 MHz of bandwidth.

And how do you increase the bandwidth of a simple antenna?

Let's begin with the simple antenna you are considering, which is just a length of wire. That antenna can be considered unidimensional. And it's possible to make an antenna that resonates on different frequencies just connecting together different lengths of cable. Some hams do it in order to cover several HF bands. So, imagine you add together three different wires: you have three lengths availalable, right?

Now imagine that you make your antenna bidimensional. For example, rather than a simple wire you use a rectangular or triangular piece of copper sheet. What happens now? Your bidimensional object can now be seen as the sum of many unidimensional pieces, which is "a collection of different lengths".

I hope it serves as a starting point to somewhat grasp the intuitive aspect of it.
 

Offline CatalinaWOW

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #26 on: March 16, 2016, 04:22:38 pm »
A comment and a question to try to help you along.

You are having trouble conceptually with bare wires into nowhere.  Maybe if you start first with a DC circuit.  In that case you will have an electric field that once established consumes no power. There is no current.  If the voltage is then changed some charge flows and the change in field propagates out at the speed of light.  If you rapidly change voltages back and forth there will be charge flowing in and out of the antenna, and the field strength viewed at varying distances will go up and down based on the history of voltage change.  Note that the charge flowing in and out will induce a magnetic field and this magnetic field will interact with the electric field.  The details of that interaction are described by Maxwell's equations.  These fields have energy and thus power.  So power is flowing into the wire and out into the world in the form of EM waves.  While this is a fairly easy conceptual start, directly solving these fields from Maxwell's equations is somewhat challenging even with the simplest geometries, and effectively impossible for most real world situations.  For this reason simplifications have been developed, which include viewing an antenna as a resonant circuit.  An R an L and a C.  Q is just another way of saying how small the R is.

The question.  Although your current interest is in the antenna and antenna coupling, are you sure that is where the problem lies?  There are many places a radio link can fail, and it seems unlikely that your antenna would be bad enough to cause the magnitude of failure you are observing.  It may be worthwhile checking the rest of the system just so that you can be sure that your experiments with antenna configuration provide results that are actually due to changes you are making in the antenna.  A simple check would be to directly connect the Rx and Tx through an appropriate resistive attenuator.  Say 1000:1 or more to prevent overload in the receiver.  Which brings up another possibility.  At the distances you are describing it is possible your antennas are working too well, the receiver is saturating and therefore nothing is getting through.
 

Offline chipwitchTopic starter

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #27 on: March 16, 2016, 05:02:08 pm »
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

Wow... that's a huge resource.  The reviews look pretty good except for one moron who gave it one star (who's never read the book) because they are unhappy with the kindle version being only a buck less than the paper version.  :--

At $600 bucks  :o, it looks like I will have to forego ever owning a VNA. 
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Offline chipwitchTopic starter

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #28 on: March 16, 2016, 05:23:11 pm »
So power is flowing into the wire and out into the world in the form of EM waves.  While this is a fairly easy conceptual start, directly solving these fields from Maxwell's equations is somewhat challenging even with the simplest geometries, and effectively impossible for most real world situations.  For this reason simplifications have been developed, which include viewing an antenna as a resonant circuit.  An R an L and a C.  Q is just another way of saying how small the R is.
So, the wave is a by-product of the same force that makes a motor armature turn?  Electric current in a magnetic field?

Quote
The question.  Although your current interest is in the antenna and antenna coupling, are you sure that is where the problem lies? 
Nope, not at all.  In fact, Howard has all but convinced me that it's likely NOT the problem.   While the antenna may not be at the heart of the problem I'm currently experiencing, it's hard to deny the importance of antennas in radio communication (that's an understatement).  I've seen lots of electronics tinkerers in videos and blogs that gloss over the antenna aspect.  It's obvious that they do so because they lack the knowledge.  I guess being a difficult subject, they are often content with a less than cursory understanding of them.  I'm trying to avoid that.
Quote
A simple check would be to directly connect the Rx and Tx through an appropriate resistive attenuator.  Say 1000:1 or more to prevent overload in the receiver.  Which brings up another possibility.  At the distances you are describing it is possible your antennas are working too well, the receiver is saturating and therefore nothing is getting through.
Sorry.  I don't know what that means.  Like I said earlier, the software is likely an issue as well.  Since the MCU is simply turning the oscillator on and off something within the MCU (an interrupt for example) could be breaking up the transmission sequence.  Same goes for the receiver end.  The program I have has no filtering no error checking etc.  I only just started playing with these little devices so there are PLENTY of weak points in the system.  No doubt.
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Offline chipwitchTopic starter

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #29 on: March 16, 2016, 05:42:21 pm »
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. :)
The text is indeed chaotic :)


Alright, let me try the intuitive path.

There are some key points you need to take into account. I think it would help to grasp some

First, the length of an antenna matters. An antenna must resonate in some way, and it depends on its dimensions and the frequency you wish to use.

Second, transmissions take a bandwidth necessarily greater than 0, which is why that paragraph you quote mentions "Q" and problems derived from antennas with narrow bandwidth.

For example: a voice transmission on HF (short wave) as used by hams takes about 2 KHz of bandwidth. So, if you are transmitting SSB on, say, 7.100 MHz you are actually radiating energy from 7100 to 7102 KHz. So, your antenna must work well not only for 7100 KHz, but for 7102 as well :)

If you are using the 433 MHz transmitters for digital data, you need some way to modulate the radio signal with the data. There are so many ways to do it. Morse code is the oldest, just switching the radio signal (called carrier) on and off. But it's not particularly well suited for digital data, so other methods are commonly used.

A simple to understand digital modulation method (which was mentioned in another post) is called "FSK", which uses two signals. One of them is a digital "1", the other one a digital "0". The frequency differences range usually from 170 Hz (typical in amateur radio transmissions) to almost 1 KHz.

Higher speeds require of course much more bandwidth. WiFi transmissions can require between 20 MHz and 160 MHz of bandwidth.

And how do you increase the bandwidth of a simple antenna?

Let's begin with the simple antenna you are considering, which is just a length of wire. That antenna can be considered unidimensional. And it's possible to make an antenna that resonates on different frequencies just connecting together different lengths of cable. Some hams do it in order to cover several HF bands. So, imagine you add together three different wires: you have three lengths availalable, right?

Now imagine that you make your antenna bidimensional. For example, rather than a simple wire you use a rectangular or triangular piece of copper sheet. What happens now? Your bidimensional object can now be seen as the sum of many unidimensional pieces, which is "a collection of different lengths".

I hope it serves as a starting point to somewhat grasp the intuitive aspect of it.

 :o

Thanks for trying.  I got the first part down to just past "Second."  Then, it was like listening to someone with a heavy accent where you get every other word or so.  lol.  You made me realize one thing for sure... I've been conflating (in my mind) bandwidth with data bandwidth.  Maybe they're related?  I don't know.  Morse code is how I think of my little carrier.  In my mind, it's the model I'm trying to use.  Transmit, don't transmit.  By varying the time of transmission against a clock at either end, time on, time off in terms of clock cycles, I could create my own comm protocol.  I'm sure there are more sophisticated ways, but this was my first endeavor. 

So, bandwidth is the difference between the lower and upper frequency used.  So that's FM, no?  Does AM also have bandwidth?  It doesn't seem to me that it would.  My little 433MHz transmitter doesn't have the ability to transmit AM, right?

I might be wrong about my little transmitter now that I think about it.  There are three terminals, besides the antenna.  Vcc, Gr. and data.  Is data doing more than turning the oscillator on and off?  Is it transmitting a slightly different frequency when it's high or low?
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Offline donmr

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #30 on: March 16, 2016, 06:34:40 pm »
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.

Its gets down to values like 75% with coax, but a single insulated wire is more like 95%.
And as vk6zgo says its really even more complicated with parasitic Ls and Cs.

But we are getting into fine details and here we should mostly be giving the overall idea: you can quickly calculate the approximate length for a single frequency.
« Last Edit: March 16, 2016, 06:41:47 pm by donmr »
 

Offline mikerj

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #31 on: March 16, 2016, 06:41:22 pm »
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. 

A mismatched antenna impedance results in power being reflected back down the feeder and into the output of the transmitter.  When you have a transmitter with very low outputs like the 433MHz modules then you are very unlikely to cause any damage this way.  However, as TX output power goes up, the amount of reflected power increases proportionally so matching becomes more critical not only from an efficiency point of view, but also to prevent your power output stage disappearing in a puff of smoke.
 

Online PA0PBZ

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #32 on: March 16, 2016, 06:52:42 pm »
So, bandwidth is the difference between the lower and upper frequency used.  So that's FM, no?  Does AM also have bandwidth?  It doesn't seem to me that it would.  My little 433MHz transmitter doesn't have the ability to transmit AM, right?

I might be wrong about my little transmitter now that I think about it.  There are three terminals, besides the antenna.  Vcc, Gr. and data.  Is data doing more than turning the oscillator on and off?  Is it transmitting a slightly different frequency when it's high or low?

Every signal that carries information has bandwidth, so AM also. There is unfortunately no such thing as a free lunch.
Until we know what your module is designed to do it's hard to tell what its abilities are, it maybe does AM but it probably is OOK (I know you looked that one up.)
Dit you try to connect the data terminal alternately to vcc and ground and monitor the receiver?
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Offline chipwitchTopic starter

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #33 on: March 16, 2016, 07:14:34 pm »

Every signal that carries information has bandwidth, so AM also. There is unfortunately no such thing as a free lunch.
Until we know what your module is designed to do it's hard to tell what its abilities are, it maybe does AM but it probably is OOK (I know you looked that one up.)
Dit you try to connect the data terminal alternately to vcc and ground and monitor the receiver?
Is AM bandwidth still a difference between the high and low frequency?  Or is it the difference between the high and low amplitude?  I was thinking, based on this thread, that "bandwidth" is the method employed to transmit data... low end of the band would be LOW, the high end HIGH in digital terms.  Or, are you saying bandwidth is an artifact?  A property to be mitigated as much as possible?

OOK sounds about right from my understanding of my device, but I could be wrong.  I couldn't find my device online (based on the silk screening), however they seem to use the same primary chip... maybe.  In any case, mine look similar to others with similar type pcb silk screenings.  The one someone posted in a photo demonstrating a dipole antenna set up looks like the same unit as mine from a distance.

No, I didn't connect directly to vcc and gr.  I manipulated the output pin programmatically.  High for 500 mS, Low for 500 mS.  The receiver was set (through arduino board) to output the signal to my computer's serial monitor (USB).  I was clearly able to discern a series of 0's followed alternately by a series of 1's.  Turning off the tx, the numbers were random.  I should note that during transmission, there were fairly frequent out of place 1's and 0's.  That's likely a result of poor coding.  I initially just followed the tutorial here: http://arduinobasics.blogspot.com/2014/06/433-mhz-rf-module-with-arduino-tutorial.html  Part one, only.  Though, he connected the receiver to an analog pin in the tutorial, I later tried something similar with the rx attached to a digital pin.  Results were similar.  I may need a pull down resistor or something too.
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Offline Howardlong

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #34 on: March 16, 2016, 07:22:25 pm »
Yes , I think there's something more fundamental than a minor impedance mismatch, although be aware that particularly in some higher power devices, they employ foldback, which detects a bad match and protects the high power RF stuff by significantly reducing power.

Balanced think...

Twin lead
Twisted pair (there are four pairs of twisted pair in a CAT5 cable for example)
Differential

Unbalanced think...

Referenced to ground, earth, common etc.
Single ended
Coaxial connections

Common to both...

Both balanced and unbalanced connections generally have characteristic impedances. You switch between them with a balun which can be constructed in all manner of ways, it might be a transformer, either of the shelf or DIY from bits of tightly wound coax and/or ferrite for lower frequencies, or you can make them out of Ls and Cs (aka a balun filter as they also have filtering characteristics done this way). Mincircuits is frequently the go-to place for off the shelf baluns.

VNAs are not bargain basement, but compared to a decade or so ago they're about an order of magnitude cheaper if you're prepared to go USB such as the miniVNA way. Yes, you're talking about $500 or so, but for a 3GHz VNA that's awesome.

 

Online PA0PBZ

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #35 on: March 16, 2016, 08:16:48 pm »
Quote
Is AM bandwidth still a difference between the high and low frequency?  Or is it the difference between the high and low amplitude?  I was thinking, based on this thread, that "bandwidth" is the method employed to transmit data... low end of the band would be LOW, the high end HIGH in digital terms.  Or, are you saying bandwidth is an artifact?  A property to be mitigated as much as possible?

Bandwidth is always the occupied space, the difference between high and low as you will. It is not a 'method to transmit data' but yes, it's more like an artifact. As soon as you change a signal it will have a certain bandwidth, and the faster you change the signal the more bandwidth it will need/occupy. For instance, when you AM modulate a signal (carrier) with a 1KHz tone it will create 2 more signals, one 1KHz below the carrier and one 1KHz above. The harder you modulate the original signal the stronger the 2 other signals (called sidebands) get.

Low end low and high end high would be FSK, Frequency Shift Keying.

Quote
OOK sounds about right from my understanding of my device, but I could be wrong.

Yes, your module definitely uses OOK.

Quote
I initially just followed the tutorial here: http://arduinobasics.blogspot.com/2014/06/433-mhz-rf-module-with-arduino-tutorial.html  Part one, only.  Though, he connected the receiver to an analog pin in the tutorial, I later tried something similar with the rx attached to a digital pin.  Results were similar.  I may need a pull down resistor or something too.

If the receiver module puts out a relative signal strength on the data pin you want to use an analog input, that way you can adjust the 'threshold'
If the output is digital it doesn't matter.

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Offline CatalinaWOW

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #36 on: March 16, 2016, 09:38:21 pm »
Bandwidth is lowest frequency to highest.  Lowest used to highest used.  There are a great many details in how to evaluate bandwidth requirements, but you should wait until you have more of a grasp of the basics before you worry too much about that.  In general bandwidth requirements are determined by how fast you are trying to send data.  To a first order bandwidth requirement is a fudge factor times the data rate in bits/second.  That fudge factor is a number somewhat larger than one that depends on coding methods, error rate requirements and the like.  For an application like yours the antenna bandwidth is probably not too big an issue.  Your bandwidth requirement is likely to be only a few percent of the carrier frequency (433 Mhz).  Antenna bandwidth becomes a big issue when bandwidth is tens of percent of the carrier.

You asked if power from the antenna is transferred in currents and magnetics fields like in motors.  Technically the answer is yes, but there are big differences.  In motors the current flows in closed electrical circuits of the kind you are familiar with.  The magnetic fields are time varying, but fairly uniform over the distances of interest.  In a radiating antenna, because of the frequencies involved current (charge) can flow into and out of a conductor from just one end.  The electric and magnetic fields vary over the distance between the Tx and RX antennas as well as along the length of the antenna itself.  At the frequency involved they will go through a full cycle from high to low and back up again in a little over a half meter, and over the ranges typically used for these kinds of links may go up and down dozens of times.

Saturation of the front end means much what it sounds like.  The first stages of a radio have a lot of gain so they can detect a tiny signal.  While most have some means to adjust that gain based on the strength of the incoming signal, too much power can overwhelm them.  It is much like looking into the sun, and finding that you cannot see anything.  Since power doubles each time range halves you placed a very powerful signal on your receiver when you placed the antennas very close together.  As others have said it is not likely to have caused permanent harm.

As far as I can tell, all of the answers everyone has given you are correct.  Hopefully one or more of the slightly varying points of view can help you get a handle on this.

 

Offline chipwitchTopic starter

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #37 on: March 16, 2016, 10:35:02 pm »
Catalina, I won't deign to say I have a grasp on it, but with everyone's help I have a little better understanding of it... aspects of it at least.  That's something.

For kicks, I put the scope on the radio to see if I got a better picture.  I'm not very proficient with it, but managed to learn a little more.  The signal is pretty dirty.  Lots of artifacts.  I get a pretty good square wave at the receiver but only up to about 2 meters.  After that, I start getting little hiccups. 

I'll say this again, my arduino sketch is about as primitive as one could hope for.  I need to set up a timer interrupt on the carrier to ensure a clean signal to the Tx.  Right now, I'm simply relying on a delay() statement in the main loop to control the frequency of shift from high to low and back again.

For those unfamiliar with arduino code, it simply works by using a continuous loop.  Start loop, do the instructions one at a time, restart loop.  By using that loop, I can alternate between high and low with each iteration, creating a square wave.  With minimal instructions, I can get about 35kHz at the pin. 

while the wave looks nice and clean at the transmit pin, what I get at the receiver output is kind of echoed.  I can still see the basic square wave, but there's like a light ghosting (my term) of that wave on top of the first, more intense wave.  I played with a delay instruction at the end of the loop.  Just adding a 1 mS delay cleaned up the wave pretty good.  2mS was better.  10 to 20 mS seemed to be the best, but again, beyond 2 meters and I started getting artifacts.  That's still with the monopole antenna.  Wiring this with jumpers on a bread board isn't helping?  Maybe this isn't much help, but I added a 6" jumper wire to the ground connection on both radios to act as a dipole.  I couldn't tell that it helped.  I'll try to find some time tomorrow to do a proper antenna.
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Offline Howardlong

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #38 on: March 16, 2016, 10:49:01 pm »
FWIW, I've been meaning to do a video on how to make an FM transmitter with a $0.50 8 pin DIP PIC on a breadboard. I made a soldered up version and use it as a battery powered signal source for measuring receiver sensitivity at VHF when up towers checking coax and antenna phasing harnesses. It generates a clear 1kHz FM tone at VHF using the PIC's NCO, and I take the 13th harmonic of the NCO and filter and attenuate it appropriately to measure SINAD (a measure of sensitivity).

I made another version which accepted a mic input too. It's low power of course, but it works.

Probably it'd make quite an educational vid.
 

Offline CatalinaWOW

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #39 on: March 16, 2016, 11:31:41 pm »
I suspect that your Rx/Tx pair is similar to the sparkfun devices discussed at the link below.  They expect to see an ascii byte sent serially at a low rate on the digital data pin.  With your Arduino code you are sending something which does not correspond to a valid serial data sequence (start bits, data, parity and stop bits) and thus gets lost in the shuffle.  The encoder and decoder do the best they can with what is received from the Arduino, but as you have found the results are sort of random.

The fix would be to use the Arduino serial commands to send serial data to one of the output pins, which would then be hooked to the Tx.  You could loop to send the same character continuously, particularly while you are debugging. 

https://www.sparkfun.com/datasheets/RF/KLP_Walkthrough.pdf
 

Offline chipwitchTopic starter

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #40 on: March 17, 2016, 12:06:29 am »
I suspect that your Rx/Tx pair is similar to the sparkfun devices discussed at the link below.  They expect to see an ascii byte sent serially at a low rate on the digital data pin.  With your Arduino code you are sending something which does not correspond to a valid serial data sequence (start bits, data, parity and stop bits) and thus gets lost in the shuffle.  The encoder and decoder do the best they can with what is received from the Arduino, but as you have found the results are sort of random.

The fix would be to use the Arduino serial commands to send serial data to one of the output pins, which would then be hooked to the Tx.  You could loop to send the same character continuously, particularly while you are debugging. 

https://www.sparkfun.com/datasheets/RF/KLP_Walkthrough.pdf

The circuits may be the same but they definitely look a little different than what I have.  The receiver doesn't expect to see data byte-wise... That's in the code.  The transmitter is merely sending the data bit-wise.  However, using the serial coding would possible improve the transmission, but I doubt it.  Since these are discreet tx and rx rather than transceivers, there's no way to correct errors.  Serial may have a parity check but it doesn't do much good if it can't ask for the data to be resent.

Like I said in the OP, my code is very primitive.  Serial isn't great, but I could see it may help.  If nothing else, I might attempt tweaking the trim pots if I can see the output.  Thanks for the link
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Offline borjam

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #41 on: March 17, 2016, 12:46:21 am »
Thanks for trying.  I got the first part down to just past "Second."  Then, it was like listening to someone with a heavy accent where you get every other word or so.  lol.  You made me realize one thing for sure... I've been conflating (in my mind) bandwidth with data bandwidth.  Maybe they're related?  I don't know.
Indeed they are :) Amount of information, used bandwidth and noise. It's called Information Theory, and if you want to learn more about it (without the hard mathematical aspects) there is a very good book written by John R. Pierce.

Now, let's link this relationship between amount of information, bandwidth and noise in an intuitive way :)

What happens when you are speaking to someone in a noisy place? If the place is really noisy you have to slow down or it's almost impossible to understand you. Right? Information is transmitted as a series of symbols (imagine words, phonemes...) and noise blurs the differences between them, making it more difficult to discern one symbol from another one.

Now, the bandwidth. You have noticed that voices on the phone sound dull. Generally intelligibility is not affected much, because the telephone exploits the fact that our brain evolved to rely on a relatively small bandwidth (200 Hz to 3.5 KHz) in order to understand speech. Anyway, depending on the voice of the other speaker, sometimes the telephone can make it harder to understand, especially when a weird, unusual to you accent is involved.

What happens when speaking face to face or listening to a HiFi recording of a voice? The bandwidth is much higher, say, 20 Hz to 20 KHz (although as you age you lose top end hearing. And there is indeed more information present. You understand better, you can speak much faster and still be understood, and you perceive more aspects about the voice, which, well, are also information.

Quote
Morse code is how I think of my little carrier.  In my mind, it's the model I'm trying to use.  Transmit, don't transmit.  By varying the time of transmission against a clock at either end, time on, time off in terms of clock cycles, I could create my own comm protocol.  I'm sure there are more sophisticated ways, but this was my first endeavor. 
Morse is not very convenient for that. That's the reason why FSK was invented. It's like using two flashlights, one red, one green, for example, for bit values.

Quote
So, bandwidth is the difference between the lower and upper frequency used.  So that's FM, no?  Does AM also have bandwidth?  It doesn't seem to me that it would.  My little 433MHz transmitter doesn't have the ability to transmit AM, right?
Any alteration you make to the signal takes bandwidth. On amateur bands it's funny(*) when someone transmits in Morse with an ancient transmitter, they usually pollute half of the band with clicks because the switching is too abrupt. So, AM, FM, SSB (which is a form of AM), Morse, or any other modes, if there is any information transmitted there is a bandwidth used.

The only signal that takes no bandwidth is a continuous signal. But you can't transmit information with it. Whenever you switch it on and off you are "altering it", and using more bandwidth. It is impossible to transmit information for free :)

Quote
I might be wrong about my little transmitter now that I think about it.  There are three terminals, besides the antenna.  Vcc, Gr. and data.  Is data doing more than turning the oscillator on and off?  Is it transmitting a slightly different frequency when it's high or low?
I'm not familiar with them, but someone said  FSK.

https://en.wikipedia.org/wiki/Frequency-shift_keying

 

Offline BravoV

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #42 on: March 17, 2016, 01:20:37 am »
At $600 bucks  :o, it looks like I will have to forego ever owning a VNA.

Not sure if this helps, TI sells this sub 1Ghz RF spectrum analyzer (Link), and for sure even I don't have any clue on RF thingy, but it helps me on tinkering at 433Mhz stuffs, like orienting the antenna or finding the sweet spot.

It created buying frenzy while ago when TI "discounted" it down to $25 (incl s/h)  >:D -> Here, too bad its back to $250.
« Last Edit: March 17, 2016, 01:22:51 am by BravoV »
 

Offline chipwitchTopic starter

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #43 on: March 17, 2016, 02:12:14 am »
At $600 bucks  :o, it looks like I will have to forego ever owning a VNA.

Not sure if this helps, TI sells this sub 1Ghz RF spectrum analyzer (Link), and for sure even I don't have any clue on RF thingy, but it helps me on tinkering at 433Mhz stuffs, like orienting the antenna or finding the sweet spot.

It created buying frenzy while ago when TI "discounted" it down to $25 (incl s/h)  >:D -> Here, too bad its back to $250.

What makes them so expensive?  It's hard for me to justify even $250 bucks for something like a VNA when there are so many more essential things I should have... like a bench DMM, proper Bench PS... etc  Now, $25 I can handle!  ;)
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Offline vk6zgo

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #44 on: March 17, 2016, 03:46:09 am »
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.

In the real big,bad world where antennas live,there is no such thing as "dangling free".

We need to look at  a dipole first,as it is the easiest to explain.

A half wavelength dipole consists of two quarter wavelength wires fed from either side of the RF source.
There are reasons why feeding one with coaxial cable is not optimum,but lets ignore them & say one leg is connected to the coax braid & the other to its centre conductor.

There is capacitance between the two legs of the antenna,& inductance along the legs.
(There is capacitance between all objects,& all conductors possess inductance--the familiar coil shape is so we can get increased inductance).

Also,of course,there is real resistance in the circuit.
An antenna is,thus,an LCR circuit,& has a resonant frequency.

Radiation Resistance:-


So-called "radiation loss" occurs in all AC circuits,& efforts are made to minimise it.
Antenna designs wish to maximise radiation so they can do the job they are intended for.

At resonance,XL & Xc,cancel,leaving the antenna impedance (between the two feedpoints) as Z=Rr+Rloss.

Where Rr refers to Radiation Resistance & Rloss to "real" resistance,(which will dissipate RF power as heat,hence it is "lost").

In a well designed antenna Rloss is very low,compared to Rr.

So far,we are talking about a dipole,but what you want is a  single 1/4 wavelength element vertical antenna.
But what happens to the missing leg?

Many books show a quarter wave vertical as "working against ground" with one side of the feeder going to an earth stake,so the ground takes the place of the missing dipole leg.

Real "dirt" is a fairly poor conductor,so  real resistance Rloss increases,making the antenna less efficient.
This sort of design works reasonably well when the "ground" is replaced by a car body,or a tin roof.but that is not always possible.

What is usually done,is to create a "groundplane" of conductive material to connect to the "earthy"(braid) side of the feeder.
At VHF/UHF this is usually a set of four or more 1/4 wavelength "radials" mounted at the base of the antenna.

Without such a "groundplane" a 1/4 wavelength conductor,only connected to one side of the  RF feeder will be very inefficient.
http://www.rfcec.com/RFCEC/Section-3%20-%20Fundamentals%20of%20RF%20Communication-Electronics/07%20-%20ANTENNA/Antenna%20-%20Ground%20Plane%20Antenna%20(By%20Larry%20E.%20Gugle%20K4RFE).jpg

With the groundplane elements at right angle to the vertical element,the feed impedance at resonance will be
approx. 35 Ohms,but there is a sneaky trick--bending the grounplane elents down to about 45 degrees,the feed impedance is close to 50 Ohms.

http://vk6ysf.com/146mhz_ground_plane_antenna.htm

He uses more radials & a different frequency,but he gives design figures for one on 435MHz,which is close to what you want.

The frequency range over which antennas are useable varies in proportion to their centre frequency.
Hams quite often use antennas which cover most of their "70cm " Band,which is around 5MHz or so wide.

(Your 433Mhz device is actually operating in this Amateur Radio Band,but such low power devices are allowed by the Licencing Authorities)
 

Offline BravoV

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #45 on: March 17, 2016, 04:11:10 am »
What makes them so expensive?  It's hard for me to justify even $250 bucks for something like a VNA when there are so many more essential things I should have... like a bench DMM, proper Bench PS... etc  Now, $25 I can handle!  ;)

Probably the manufacturing cost ?  :-// As mine was made and assembled in Germany.  :P

Offline borjam

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #46 on: March 17, 2016, 09:47:57 am »
What makes them so expensive?  It's hard for me to justify even $250 bucks for something like a VNA when there are so many more essential things I should have... like a bench DMM, proper Bench PS... etc  Now, $25 I can handle!  ;)
Well, getting a VNA just to use it once is certainly overkill, despite being cheap. Some instruments can just be bought by a group of friends/club/hacker space and be shared.

That said, before learning of the cheap VNAs available I took some antennas to the University's microwave lab for testing. Do you know the price tag of the Agilent VNA I used there? I one on eBay right now for $29,000 ;) (Agilent E5061B)



 

Offline borjam

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #47 on: March 17, 2016, 10:52:35 am »
I forgot. There is such thing as a $25 spectrum analyzer.

Have a look at this:

http://www.rtl-sdr.com


 

Offline chipwitchTopic starter

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #48 on: March 18, 2016, 02:33:49 am »
I forgot. There is such thing as a $25 spectrum analyzer.

Have a look at this:

http://www.rtl-sdr.com

Aside from the price and being a dongle, how do they compare (or differ) to VNRs in function?  The Amazon rating is positive.  I'm inclined to buy one tomorrow.  It sounds like these are perfect for someone like me, too many hobbies, too little time and too little money.

To my untrained eye, it looks too good to be true.  .... yet it's only 25 bucks.  Anyone here have experience with them?
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Offline chipwitchTopic starter

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #49 on: March 18, 2016, 02:50:05 am »
The RTL-SDR dongles are out of stock at Amazon in the US :(  poo.  "Expecting" new shipment in a couple weeks.  Or, I can order from their China dealer (supplies low). 

Before I pull the trigger, I did a quick google search and found other brands (some for even less money!).  Since I don't know what I'm looking at to compare them, could someone advise me?  Connectors, protocols, resolution... etc.  What should I be most concerned with.  I think they all use the same chip.  Maybe there's a better one in the same price range?
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Offline vk6zgo

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #50 on: March 18, 2016, 07:15:56 am »
I forgot. There is such thing as a $25 spectrum analyzer.

Have a look at this:

http://www.rtl-sdr.com

Aside from the price and being a dongle, how do they compare (or differ) to VNRs in function?  The Amazon rating is positive.  I'm inclined to buy one tomorrow.  It sounds like these are perfect for someone like me, too many hobbies, too little time and too little money.

To my untrained eye, it looks too good to be true.  .... yet it's only 25 bucks.  Anyone here have experience with them?

The SDR is a Receiver,which with a bit of fiddling can  substitute for a Spectrum Analyser.
What it doesn't have,that a VNA does,is a swept signal which is applied to your antenna,nor does it have any way of looking at the matching of that antenna,much less,a way of displaying the Resistive & Reactive components of  antenna Impedance.

Clever people have worked out ways to provide these functions,& you can probably find websites describing this,but the device linked to is just a receiver,which can be used as a Spectrum Analyser,in a pinch.
 

Offline Towger

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #51 on: March 18, 2016, 07:19:02 am »
Is a Grid Dip meter still a good poor man's alternative to a VNA?  I used to lust after them in the back of the radio mags when I were a lad. In those days I drove the neighbours mad building CB antennas in the back garden.
 

Offline borjam

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #52 on: March 18, 2016, 08:15:05 am »
The RTL-SDR dongles are out of stock at Amazon in the US :(  poo.  "Expecting" new shipment in a couple weeks.  Or, I can order from their China dealer (supplies low). 

Before I pull the trigger, I did a quick google search and found other brands (some for even less money!).  Since I don't know what I'm looking at to compare them, could someone advise me?  Connectors, protocols, resolution... etc.  What should I be most concerned with.  I think they all use the same chip.  Maybe there's a better one in the same price range?
It's not the same as a VNA, I commented it because someone mentioned a small spectrum analyzer that was on sale some time ago.

That said, it's a simple way to at least do a rough comparation between antennas. And, in the first placem it allows you to verify wether you are actually transmitting or not, very useful to debug problems.

 

Online nfmax

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #53 on: March 18, 2016, 09:11:29 am »
Here is something that might help you understand the design and properties of aerials:

Circuit theory is only an approximation, a trick to avoid having to solve Maxwell's equations, that works in many common situations but not everywhere. The operation of aerials is one of the situations where it doesn't work.

To describe the propagation of radio waves in free space (no conductors or dielectrics around) Maxwell's equations describe the electric and magnetic fields and the relations between them, and give solutions which are waves that travel at the speed of light. Inside a circuit, where just about everything is a conductor or a dielectric, Maxwell's equations are too complicated to solve and we use the circuit laws: Kirchhoff's laws, Ohm's law etc. These can in principle be derived from Maxwell's equations, but in practice we ignore that and work directly with 'circuit' properties such as current, voltage, resistance, capacitance, inductance & the rest.

An aerial is a strange beast: one side of it interacts with the electric and magnetic fields of the radio waves propagating around it (the world of solving Maxwell's equations), while the other side lives in the world of circuits. At one end of it circuit theory doesn't work, and at the other end Maxwell's equations become too difficult to solve directly. Tricky!

For this reason, once you beyond the realm of cookbook recipes, which have been developed over the years and found to work well, you enter the realm of domain experts, and the specialised (and very expensive) tools they use.

I hope this helps

Maxwell (no relation)
 

Offline CatalinaWOW

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #54 on: March 18, 2016, 07:05:32 pm »
The SDR could be useful, but is also likely to add to your list of hobbies that require time and effort to understand and put to use.

 

Offline borjam

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #55 on: March 18, 2016, 08:15:47 pm »
The SDR could be useful, but is also likely to add to your list of hobbies that require time and effort to understand and put to use.
If you are developing something that must transmit wireless signals, a spectrum analyzer is a great time saver.

Spectrum analyzers are very expensive, but a SDR can be a very useful substitute. That's why we are mentioning them  :)
 

Offline CatalinaWOW

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #56 on: March 18, 2016, 11:48:44 pm »
I don't disagree with the usefulness of a spectrum analyzer.  If you have the knowledge, background and time, a SDR is a cheap way to a modest performance spectrum analyzer.

The OP is a beginner with limited understanding.  Remember the purpose is to get a data link going, which if it had gone well would not have sidetracked into antenna design.  Further sidetracking into getting (or heaven forbid writing) appropriate software for the SDR, learning the foibles of its USB interface and antenna connection, and then interpreting spectrum information may be a fascinating further rabbit hole to enter, or it may be a barrier to the original goal. 

My only point was to warn the OP to stop and think about this before proceeding.  It all depends on what kind of learning OP is primarily interested in.  It might have to do with the things on both ends of the data link instead of the data link itself. 
 

Offline vk6zgo

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #57 on: March 19, 2016, 01:59:50 am »
Although a Vector Network Analyser is the best tool for characterising the Impedance of an Antenna or other RF load,it is not essential-----after all,we don't carry a torque wrench around with us for changing a car's spare wheel.
Often,we can get close enough,using,(as in the spare wheel simile),much simpler tools.

Let's recap:-

The OP wrote in the first posting:- "I've attached 17mm copper wires to the antenna hole"
In the ensuing pages we have pointed out the reasons for the classic forms of antenna construction.

We have all assumed that the antenna will be fed from some form of coaxial feeder,so it is an external device,capable of being tested using a VNA,Scalar Network Analyser or whatever.

My suggestion is that chipwitch produce two groundplane antennas as per a "recipe".
If they work satisfactorily as is,no more needs to be done.

A messy,but possible way to "tweak" the antennas is to trim one at a time for maximum signal strength,using your existing transmitter & receiver.

Here,an SDR would be useful.
Replace the receiver with your SDR,set to give a spectrum display,find your carrier,set it a less than maximum level,& trim your receive antenna,watching the signal strength on the display.
Repeat for your Transmit antenna.

There are other ways,such as an RF sweep,used with a directional coupler,either in the form of a sweeper & calibrated detector,a Spectrum Analyser with a Tracking Generator,a standalone Scalar Network Analyser,or various homebrew SWR meters,return loss bridges,etc.---not to leave out the Grid Dip meter.
Some of the latter start to "run out of grunt" at 400 -odd MHz,though.



 

Offline Howardlong

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Re: Quantity chickens sacrificed for 433MHz antenna?
« Reply #58 on: March 19, 2016, 08:56:10 am »
It's absolutely corect that you don't need a VNA to tune an antenna. However I would say that without one (or as pointed out a scalar network analyser, or an SA with tracking generator with a return loss bridge) it is signficantly harder and time consuming, frequently with a lot more guesswork.

The reason I originally mentioned the USB VNA is that in real terms it's astonishing value for what it does, and not only is it a measuring tool it will allow you to understand the concepts so much more easily. It comes down to how much you value your time. If, like I did, you spend years with an SWR meter fruitlessly trying to match antennas and trying to dovetail the theory with the practice with little correlation, you'll find a VNA an absolute godsend.

Those 3GHz miniVNAs even have a $20 calibration kit. You _have_ to have a cal kit if you want to properly use a VNA.

If you're into understanding and building antennas, a VNA or SA with TG & RLB has more value than an SA on its own, but those minVNAs are cheaper than an SA+TG+RLB. In fact an SA or SDR on its own has little value when designing antennas other than to tell you your antenna is working or not at all: how well it is working needs antenna ranges and/or anechoic chambers, and calibrated antennas and signal sources.

If you're into debugging RF circuits as opposed to antennas, then an SA or SDR plus signal generator or TG is of far more value than a VNA, in fact a VNA has almost no value in this scenario.
 


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