Antenna Simulation in LTspice

Is this a current transformer or a voltage transformer? .--------. .--------. | | | | | C||C > VAC C||C > Load | C||C > | | | | `--------' `--------'

--

Rick

It may sound like hyperbole, but it's mathematically sound. The midpoint theorem, for example, guarantees that, between two points, you must've hit some point inbetween, somewhere, as long as the function is continuous. More usefully, functions arising in electronics are often one-to-one, so it's not only true that you are guaranteed midpoints, but you'll find them in order, too.

If you aren't looking at the extreme cases, you aren't doing your job. Whatever's left inbetween can simply be interpolated!

The point here being, an antenna which doesn't couple into free space obviously has a crappy SNR. The signal level can be anything, it doesn't matter. The signal need not be small, because internal losses generate thermal noise. With sufficient Q, you can push that thermal noise up to your receiver threshold (which you said is an ADC) and detect signal. It'll be bandlimited, ~60kHz noise, a useless signal, but present nonetheless.

In general, antennas which do couple strongly to free space have low Qs. A 1/2 wave resonant dipole has a Q of only 1 or 2, so bothering to call it resonant is actually kind of weak. This is similarly true for a large loop, which of course would be highly impractical here. So there must be some middle case where SNR is reasonably unaffected, which will be the best choice antenna.

Since atmospheric noise dominates, the antenna can stand to be pretty small.

You hadn't mentioned that before...

Any ESR? Example, the ATmega series 10 bit ADC specifies, I think, around

10pF + 10k ESR (somewhat depending on how many mux switches it's going through to get there).

I could write a book on the subject to explore it in detail, but there are many available already, and there are too many holes in my knowledge to really be worth it, plus this is Usenet, you get what you pay for. I was hoping you'd Google in the blanks.

There's yet another theorem in networks that has to do with matching.

A resonant tank's impedance varies wildly with frequency. But it will always be resistive at resonance. If you connect this to another network, which has a resistive input impedance at the same frequency, you don't care what the L and C are, it will simply work -- old fashioned resistor divider action!

You *do* have to worry about L and C and reactance and bandwidth to solve for the frequency response and stuff, but you can at least approximate that with Q factor (i.e., how much loss is draining power out of the system).

So if your ADC input is exactly 10p + 10M, you could resonate it with 0.7H (well...), which has a resonant impedance of 264k, and thus a reasonable Q of 38. (The real world typically bitchslaps the theorist at this point, as 0.7H chokes with 38 at 60kHz don't exist.) If the capacitance's ESR is less than 6.9kohms (i.e., 264k / 38), it won't have significant effect.

You can couple to this tank via parallel or series. If you did series, the input impedance would be 264k / 38, or 6.9k, not horrible; going from the 0.78 ohm loop to this in a single transformer requires a 1:100 CT, which works fine at 60kHz. (This CT would require high inductance, so as to avoid skewing results, but that's typical of a CT. An amorphous core CT would probably suffice. So at least that part is physically realizable.) Note the irony of coupling a current loop to a current loop, where in both cases, the CT looks like a small impedance relative to the loop it's within. That's simply how huge the impedance at the ADC is.

Since all these resistances are matched, the power transfer theorem holds, and you're pushing as much voltage and power into the ADC as possible. The bandwidth is about 1.6kHz, so the thermal noise floor is around 5uV at the ADC. A received power of 1nW will generate 0.1V, which is probably a reasonable figure. The SNR of the receiver is limited by quantization noise for 14 bits. A 16 bit converter wouldn't be too expensive at this sample rate (note it's the analog sample-and-hold speed which limits direct conversion performance; a sigma-delta, running at 100Hz, with no S&H, won't see jack).

Considering theoretical 0.7H chokes aren't commercially available, you might swamp it with more C, which stabilizes the value, and requires less L to resonate. Rub: resonant impedance is lower, so the Q of the components must be higher in order to achieve the same performance. Even with a Q of 200, you still need over 0.25H, which is just as unlikely a combination. Well, if you really wanted to try, maybe a gapped ferrite-cored inductor could be made. Still, the only practical choice seems to be lower signal level.

So ultimately, the question is, how little signal can you tolerate before you need an amplifier? How many bits of conversion, how much sample rate can you afford before a linear amplifier becomes cheaper on the power budget?

It's getting closer, but with adjustments (to the transformer inductance) to make the resonances line up (same frequencies). Plus whatever compromise you need to make on gain.

Tim

--
Deep Friar: a very philosophical monk. 
Website: http://seventransistorlabs.com

Voltage. How about this?

Tim

--
Deep Friar: a very philosophical monk. 
Website: http://seventransistorlabs.com

I was warned a long time ago to be wary of people speaking in "glittering generalities". You seem to insist on using terms without giving a mathematical basis. How about if we use some math?

V = (2 * pi * A * N * E * cos(theta)) / lambda

V is the voltage on the antenna, A is the loop area, N is the number of turns, E is the field strength, theta is the rotation angle of the antenna and the transmitter (just consider this term to be 1, lamba is the wavelength (c/f)

This is multiplied by the Q factor when resonated by a capacitor. So higher Q, higher signal.

Where in here do you think I am having a problem?

You are making assumptions that don't hold true in my design.

You didn't ask.

FET input resistance. I will double check that though.

I thought I was doing well, but you seem to be telling me I am making mistakes, but I can't figure out what they might be.

We are still having communications difficulties. You keep talking in terms I can't relate to. I don't need you to write a book, but I do need you to communicate clearly.

I am using a 1 bit ADC. Don't assume that I am doing what you have done in the past.

--

Rick

I have to say I don't follow the distinction. It is a transformer, no?

--

Rick

I built a passive 60KHz bandpass filters out of a collection of ferrite cores from an old modem front end. I left it at a previous consulting job, but can resurrect the design if necessary. Incidentally, during my limited testing at home, I found that the biggest determent to decent reception was all the switching power supply noise found around the house. I finally ended up using a battery power oscilloscope a gel cell for powering the RF amp, and turning off the main power to the house. Then, I could sorta see a signal.

Very random. Compare the above graph with Santa Clara which looks less random:

On the east coast, besides a weak signal, you also have the potential for 60KHz interference from the UK:

I had a 100KHz LORAN antenna on the roof of a former employer. The signal was just fine, until someone turned on the mercury vapor arc parking lot lamps at night. They were changed to low pressure sodium, which made testing possible at night.

Incidentally, got any clue as to the vertical scale? My guess(tm) is

20 uv/meter signal strength per division, but I'm not sure.

It's now 17dB drop at the beginning of each UTC second. The change came in about 2008.

The BPSK signal is much better at rejecting interference and digging the signal out of the noise. I don't know exactly how much, but I'm sure it's in a NIST publication somewhere.

It's delta-sigma.

Not exactly. Small loopsticks receive a proportional amount of noise. The ratio of signal to atmospheric noise remains roughly the same within a fixed bandwidth for any antenna. That's why tiny little loopsticks, inside "atomic time" wristwatches work. The small loopsticks also use the magnetic field instead of the electric field, which is why they can be made so small.

Ok, I made a bad guess(tm). Even at 5Hz BW, the maximum Q of 60KHz / 5Hz = 12,000 is not going to happen in a loop or loopstick antenna.

Agreed.

--
Jeff Liebermann     jeffl@cruzio.com 
150 Felker St #D    http://www.LearnByDestroying.com 
Santa Cruz CA 95060 http://802.11junk.com 
Skype: JeffLiebermann     AE6KS    831-336-2558

Holy crap! That's a lot of trouble to see a signal. By "see" I assume you mean on the scope. How large was the signal?

The place where I am working currently is not very close to much and there isn't much in the house. I'm told the fridge is the biggest source of noise. We'll see how the CFL lamps do.

Funny, last night my two RCC's both updated like they should. One is an analog clock and runs at 8x speed to get the hour ahead. In the fall it does this to go 11 hours ahead. Quite a sight! They both did the job, but my PC didn't update until it had been on for awhile, without being connected to the I'net.

Loop antennas have a null that can be steered toward the source of interference. I expect that will solve that problem...

That's for an ideal receiver. I have my limitations and I have no idea how that will impact the reception.

Actually I always say that with a smiley as it can be either.

In my case I am not worried that the SNR isn't better, I just need a strong enough signal to drive the LVDS input. I will be providing feedback to eliminate any DC bias, but even that will only be so good. The input is claimed to have no hysteresis, but even a tiny amount can ruin this design. I will only know if this will work when I try it.

--

Rick

The second one is a current transformer. They both consist of coils around a magnetic core driving some kind of load. The difference is the source of power and that causes them to behave very differently as well as being constructed differently.

Let's assume ideal components (a good place to start when learning a new concept). The voltage transformer is driven by a source that provides a constant voltage, no matter what the load. The transformer takes this voltage and converts it to some other voltage depending on the turns ratio; Vout = Vin * Ts / Tp. For example, if the primary has 100 turns and the secondary has 20 turns and the primary is supplied with 50 volts, the secondary will provide 10 volts. As the secondary load changes, this voltage remains the same but the current changes. If the secondary is open-circuited, the voltage still stays the same. If the secondary is short-circuited, the current becomes infinite; that's why real voltage transformers are protected by fuses or similar devices.

Now for the current transformer, it is driven by a source that provides a constant current no matter what the load. The transformer takes this current and converts it to some other current depending on the turns ratio; Iout = Iin * Tp / Ts (note the inversion of the turns ratio). For example, if the primary has 1 turn (a common number for real transformers) and the secondary has 5 turns and the primary is supplied with 5 amps, the secondary will provide 1 amp. As the secondary load changes, this current remains the same but the voltage changes. If the secondary is short-circuited, the current still stays the same. If the secondary is open-circuited, the voltage becomes infinite; that's why real portable current transformers have a shorting switch on the secondary that the operator must close before disconnecting the load.

Also, note the difference in the number of turns, voltage transformers have a lot of turns and current transformers have few turns.

For a loop antenna with an external resonating capacitor, a voltage transformer would be connected in parallel with the loop and capacitor; all three in a parallel circuit. A current transformer would be connected in series with the antenna and capacitor so that the three form a series circuit. If the loop itself is used as the primary of the transformer and another winding is used as the secondary, the distinction between the two types is blurred. Also, a real antenna is neither a voltage source nor a current source but something in between.

--
Jim Mueller wrongname@nospam.com 

To get my real email address, replace wrongname with dadoheadman. 
Then replace nospam with fastmail.  Lastly, replace com with us.

Turning off the house was easier than finding the multiple sources of noise at 60KHz. What drove me nuts for about an hour was that much of the noise was coming from my bench oscilloscope. Argh.

This is typical. WWVH through an active preamp showing the effect of power line noise (probably from attached switching power supplies). and after adding some better line filtering: Main page:

I didn't log the setup or take pictures. So, let's do the math and guesswork. I plugged in some guesses and recollections as to what the antenna (Q=30) and amp (+20dB gain) were doing and got:

-15.8dBm or about 36mv into 50 ohms. I amplified this about 20dB with two or three U310 JFET's (I forgot what I did) to about 3V rms on the scope. I didn't bother with the 50 ohm to scope input Z conversion. Most of what I saw was noise, noise, and more noise. However, if I was patient, I could see the data fade in an out. As I vaguely recall, it was less than 1 division or about 0.1v change.

Sigh. Most of what I found at 60KHz was coming from lightning storms over Florida. The local sources were all switching power supplies, including those in my test equipment. I didn't have an CFL or LED room lights at the time. I've recently found them to be a rather nasty noise source. Also, the switching power supply wall warts were rather awful. My standard test is to fire up my antique IC-735 HF xceiver, attach a long length of RG-58c/u to the antenna with a resonant loop at the end, tune it to 100KHz (as low as it will go), and sniff around the house.

What you'll see on a spectrum analyzer. If you're thinking of removing all that junk with a 5Hz wide digital filter in software, please note that you'll need to have the input A/D handle the total power of almost all that junk. Also, the amplifier that you're trying to avoid between the antenna and A/D will also need to be rather linear, and therefore rather high power, in order to avoid producing more spurious junk via intermodulation products.

So that's how they change daylight savings time. If I had known, I would have stayed and watched. Thanks for the tip.

The depth of the notch seems to be less as the antenna shrinks in size. I'm not sure about this as I haven't attempted to recently model a 60KHz magnetic loop with 4NEC2, but that's what my tinkering shows. If there were a deep notch, most of the home "atomic clock" receivers would be orientation sensitive and I would expect warnings in the docs.

Well, you have to start somewhere, and an ideal receiver is a good place to start. The advantage is that reality only makes everything worse, never better. You should be able to build the BPSK demodulator, and then use a PC to decode the data. I've seen several such programs that do not require I/Q outputs. Here's one based on FreeBSD intended to sync the system clock to WWV/WWVH: I'm sure there are others.

Gain at 60KHz is very cheap. Watch out for overload issues. If you design it to work at full scale with whatever you get at 50uV/m, and the signal climbs to 100uV/m, your input A/D isn't going to be very happy. AGC will help, but I don't think it will be needed if you calculate your signal levels so that the A/D input amp isn't clipping.

Out of service for a day. It seems that about 30 years of chemistry experiments has finally destroyed much of the kitchen sink plumbing. I hate plumbing.

--
Jeff Liebermann     jeffl@cruzio.com 
150 Felker St #D    http://www.LearnByDestroying.com 
Santa Cruz CA 95060 http://802.11junk.com 
Skype: JeffLiebermann     AE6KS    831-336-2558

What you are describing is a difference in the source NOT a difference in the transformer!

The transformer behaves exactly the same in both cases, the inversion is merely down to ohms law.

A transformer is a transformer. The only time it gets tricky is when the core and saturation etc etc comes into play.

Jeff

In Europe we have DCF-77 which is at 77.5 kHz. The trouble receiving it is similar to WWVB. I have several clocks in the house but some of them have only very weak sync. Also, to save battery they only sync once every 12 hours or so. At DST change, they may display the wrong time for a couple of days, especially the one in the kitchen. I need to relocate it to a place where I know there is better signal.

The problem is (harmonics of) switching power supplies here as well. Once I had a big open-frame SMPS that I used to power my radio equipment and that switched around 25 kHz. Under the right circumstances, the

3rd harmonic wiped away all DCF-77 receiving within 5 meters or so. Old CRT computer monitors also were problematic.

I presume you have some specific needs, low power being among them, to stay focussed on WWVB for your clock sync. Most computer users would use GPS now, or simply sync via the internet. GPS has a different receiving conditions problem, but at least it isn't so much affected by prominently present local interference.

Of course a GPS receiver requires a lot more power than a WWVB receiver, although this has come down over the years. Using some sort of on/off switching (syncing with the received time and then having it run free for some time) may help a bit, the battery powered radio clocks do that as well.

I can't say I understand the distinction.

This is ok so far.

I don't follow how any of this has to do with a difference in the transformers. Bth transformers obey both equations you have presented. Both transformers change the voltage as well as the current, no?

I don't see how this follows from what you have written. What is there about these two transformers that define the number of turns? The current transformers I am interested in using use 100 or 300 turns. Is that a lot or just a few?

What I have gotten from this is that Tim's original usage of the terms implies how the transformer is connected to the antenna. As you say, a voltage transformer will be connected across the coil in parallel with the capacitor and a current transformer will be connected in series with the antenna and capacitor.

I was planning to use the antenna wire itself in the middle of the antenna loop as the primary of the transformer. So I guess that will be a current transformer. I may try a simulation to see just what happens with a parallel connection.

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Rick

Yes, like I said, not much in this house and there is not much near it. I have a laptop and my roommate (when he is here) uses one along with an iPhone. I suppose they might generate some noise, but he turns off his laptop at night I'm sure. Otherwise, there just isn't much in the house that isn't 10 or 15 years old. I have a car radio on a linear regulator and an electric shaver that sits charging (part of the time). Otherwise it should be pretty quiet electrically here.

I'm not sure why you used 1900 meters for the distance. I also don't get why you used 5 ohms for the receiver input impedance.

There's just not much of that in this house.

What A/D? Oh, you mean the LVDS input. How do you saturate a 1 bit ADC?

I wouldn't say the *depth* of the null depends on the size of the loop. I think it is a null with a Q, much like a resonance peak, but a null of course. The smaller the loop, the sharper the null like a high Q resonance, so the orientation becomes very critical. In theory at least, the null is perfect, 0 signal.

PC?!!! We don't need no stinking PCs! The demodulator is simple. The signal is beat with a quadrature reference which will bring it down to 0 Hz. This gives two values, a sin and a cos signal. Take the ratio and do an arcTan. This is a simple table lookup made simpler by some convenient math relations. For example, the table only needs to cover

0° to 45° since the ratio can be swapped for 45° to 90° and the other three quadrants distinguished by the sign bits.

Some folks would like you to think this has to be done like a high fidelity receiver, but it only has to pull the signal out of the noise.

If this is *signal* strength then it won't matter. If this is noise you are talking about, I'm not sure it will be a problem, the signal will still be able to be dug out with enough processing gain.

Not much fun, but then what it if you have to work on your knees and get dirty? I don't enjoy working on my car anymore either.

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Rick

Yes, noise can be a problem I understand. I am hoping to get the bandwidth down much more than most receivers so the noise won't be so big a factor. With a signal bandwidth of a handful of Hz, it should be possible.

Yes, this is actually a demo to illustrate how low power an FPGA can be. An FPGA will run both the clock and the receiver and use power from the environment rather than batteries.

Yes, the receiver itself only has to run part of the time, >10% perhaps. The clock has to run 100% obviously. Interesting enough, the FPGA has a base power consumption (0 Hz) of nearly 50% of the power budget and I am confident it will still make the goal.

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Rick

(Quick reply... still working on my expanding plumbing problem).

The 1900 meters is because I screwed up. It should be about 1900Km from San Francisco to Denver. However, any distance greater than zero will suffice for this calculation. The controlling numbers are the

100uV/m field strength, the -3dB antenna gain, and the receiver bandwidth (5Hz). All of the other numbers can change without having any effect on the recovered power. The 5 ohms rx input Z was because the original antenna that I used, was a base loaded 100ft "whip" antenna with a rather impedance. I couldn't decide if the field strength to receive power form wanted the antenna impedance before the 50 ohm matching network, or if it treated the matching as part of the antenna. I flipped a coin and chose 5 ohms. I guess for a loop, 100-200 ohms would be more appropriate. Again, the value makes no difference in the calculations.

(Back to plumbing and fixing the 48" farm jack that my neighbor borrowed and returned looking like a pretzel).

--
Jeff Liebermann     jeffl@cruzio.com 
150 Felker St #D    http://www.LearnByDestroying.com 
Santa Cruz CA 95060 http://802.11junk.com 
Skype: JeffLiebermann     AE6KS    831-336-2558

It sounds like your neighbor doesn't know jacks. ;-)

But this is all relative. My first "atomic clock" ran on the same set of AA batteries for five or six year, and the second set is now four years old. The Centrios "atomic" wall clock (digital) uses one AA battery, I'm not sure how long that's been in. My watch is a Casio Waveceptor, 3 or 4 years old, which has a solar cell to refresh the battery and it's never been less than fully charged.

Fice or six years seems almost as good as 'shelf life" and while I had a small LCD clock (not "atomic") that seemed to run a long time on an AA cell, I'm not sure it was all that lower current than the 'atomic clock".

I'm more impressed by the clock running off 1.5v than that the batteries last reasonably long.

These things are amazing, considering the effort people used to put into making WWVB receivers, admittedly the "atomic clock" craze has very much benefitted from the power increase at the station.

I do orient them, but here in Montreal it's the rare night that they don't sync up, and I don't think since I've had more than one that they all miss the sync.

Michael

Very true. A transformer is a transformer and all obey the same equations. But that doesn't prevent real transformers from being called voltage or current transformers. And it doesn't prevent them from being constructed differently or their outputs behaving differently.

Part of the problem is that real-world AC current sources are rather rare. So current transformers are seldom connected as shown in the example that was given. They are usually connected in series between a voltage source and some other load, frequently for the purpose of measuring the current. This is what gives rise to the different constructions.

Voltage transformers have to withstand the source voltage across their primaries so they have to have enough turns to prevent the core from saturating. The actual number of turns depends on the voltage, frequency, and core size and material.

Current transformers are generally constructed to have minimum primary voltage drop so they have few turns on the primary, frequently only one. Considerations of frequency, core size and material still apply, of course. The differences in the name and construction are determined by the intended use. Many current transformers consist of a secondary winding on a toroidal core. The primary is supplied by the user by passing a wire through the hole in the core; thus, one turn.

For a loop antenna with a secondary, there is voltage across the antenna winding and current through it. Which is the secondary responding to? The current, since this is what produces the magnetic field. But, since this current is flowing through some number of turns and developing a voltage, it could also be considered a voltage transformer, which is why I said the distinction is blurred.

--
Jim Mueller wrongname@nospam.com 

To get my real email address, replace wrongname with dadoheadman. 
Then replace nospam with fastmail.  Lastly, replace com with us.

Since you can't have a current thorough the antenna without a voltage the answer is both, It is a chicken and an egg situation tied together by Ohm's Law.

Jeff