I've been doing more work on the low frequency tuned loop antenna and
have two problems. One is that I can't find any info on how effective
the antenna will be in relation to the design parameters. That would be
the diameter of the loop, the number of turns and the spacing of the
turns. From the formulas I find for inductance, I would guess that the
spacing of the turns will want to be as small as possible, but I'm not
sure the factors that optimize self inductance are the same as what will
optimize antenna effectiveness.

What equations determine the signal strength from a low frequency tuned
loop antenna?

The other problem is finding an accurate formula for the inductance of
this design. I've found a number of equations for coil inductance, but
most are for coils with length longer than diameter. One I found
doesn't say what it's limitations are and doesn't agree with the others.
In fact, I can't find two formulas that approximate each other over
the range of interest which is 1 to 20 turns or d/l from 4 on up.

I've consulted the Radiotron Designer's Guide, Nagaoka's and Lundin's
papers on inductance of coils as well as a number of web pages. I'm
getting tired of looking... Is there a reasonable formula for
calculating the inductance of a short coil that works for a number of
turns from 1 to 20?

Rick

The National Radio Club has many publications on loop antennas, and those can answer your questions and more.



On Monday, November 26, 2012 12:10:13 PM UTC-6, rickman wrote:
I've been doing more work on the low frequency tuned loop antenna and

have two problems. One is that I can't find any info on how effective

the antenna will be in relation to the design parameters. That would be

the diameter of the loop, the number of turns and the spacing of the

turns. From the formulas I find for inductance, I would guess that the

spacing of the turns will want to be as small as possible, but I'm not

sure the factors that optimize self inductance are the same as what will

optimize antenna effectiveness.



What equations determine the signal strength from a low frequency tuned

loop antenna?



The other problem is finding an accurate formula for the inductance of

this design. I've found a number of equations for coil inductance, but

most are for coils with length longer than diameter. One I found

doesn't say what it's limitations are and doesn't agree with the others.

In fact, I can't find two formulas that approximate each other over

the range of interest which is 1 to 20 turns or d/l from 4 on up.



I've consulted the Radiotron Designer's Guide, Nagaoka's and Lundin's



papers on inductance of coils as well as a number of web pages. I'm

getting tired of looking... Is there a reasonable formula for

calculating the inductance of a short coil that works for a number of

turns from 1 to 20?



Rick

Just to give an update...

I got a response from Randy Yates in the comp.dsp group who gave me a
formula for the loop antenna signal strength which I'm including below
for reference. He said it came from the ARRL Handbook.

They dedicate an entire chapter (5) to loop antennas. Equation one
is the voltage at the loop terminals:

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

where

A = area of loop, in m^2
N = number of turns in loop
E = RF field strength in V/m
theta = angle between plane of the loop and the signal source
lambda = wavelength in meters.

Note that I know nothing about antennas - just acting as a scribe...
This is the expression for an untuned antenna. Shortly after this, they
provide the equation for a tuned antenna, which is identical except for
the addition of a Q in the numerator.
-- Randy Yates Digital Signal Labs http://www.digitalsignallabs.com

I did the calculations and at 100 uV/m with 50 foot of coax in a two
turn loop I get a bit over 1 uV, not so good. I'm going to see what I
can find about the signal level from ferrite cores. I had the
impression they would be lower, but I seem to recall better numbers than
this in the ones I've seen before.

Rick

On Mon, 26 Nov 2012 16:25:37 -0500, rickman wrote:

Just to give an update...

[...]

I did the calculations and at 100 uV/m with 50 foot of coax in a two
turn loop I get a bit over 1 uV, not so good. I'm going to see what I
can find about the signal level from ferrite cores. I had the
impression they would be lower, but I seem to recall better numbers than
this in the ones I've seen before.

Rick

When I was working with loop antennas, it became rather obvious that
optimal receiving loops too are 1 turn, with material of the largest practical
circumference. That one turn loop was coupled to one turn as the primary of a
coil / tuned transformer and on VLF / LF that concerned a potcore of the proper
material. The amount of turns for the secondary could be as much as 100 and
with a Q factor of 100 or more that meant at least 10,000 times the voltage of
the one turn loop - more than enough.

Jan

On 11/27/2012 11:01 PM, Arid ace wrote:
On Mon, 26 Nov 2012 16:25:37 -0500, wrote:

Just to give an update...

[...]

I did the calculations and at 100 uV/m with 50 foot of coax in a two
turn loop I get a bit over 1 uV, not so good. I'm going to see what I
can find about the signal level from ferrite cores. I had the
impression they would be lower, but I seem to recall better numbers than
this in the ones I've seen before.

Rick

When I was working with loop antennas, it became rather obvious that
optimal receiving loops too are 1 turn, with material of the largest practical
circumference. That one turn loop was coupled to one turn as the primary of a
coil / tuned transformer and on VLF / LF that concerned a potcore of the proper
material. The amount of turns for the secondary could be as much as 100 and
with a Q factor of 100 or more that meant at least 10,000 times the voltage of
the one turn loop - more than enough.

Jan

I have come to a similar conclusion, but not about using a single loop.
The single loop is the best antenna if your constraint is the total
length of cable. But if your limitation is the size of the loop, it
will be improved by more turns at the same diameter.

When I wrote the message you replied to I had left the Q factor out of
the equation. I calculated the Q factor at slightly over 100
considering just the resistance of the center conductor. I am also
aware of the idea of coupling using a ferrite core. I don't know
anything about ferrite cores (I suppose I'll need to learn that soon)
and I don't know what the optimal turns ratio would be. I assume that
the resistance of the load reflects back into the antenna as a parallel
resistance? Using your numbers that would mean a 1 Mohm input impedance
would result in a 10 kohm load. At the frequency of 60 kHz and with an
antenna inductance of about 90 uH that gives a reactance of 34 ohms. So
10 kohms shouldn't be a problem. But I read one reference that
indicated the Q needs to be factored in as well which means it would be
100 ohms vs. 33 ohms, and so 1 Mohm might not be high enough.

The input impedance of the device I am using is not characterized. I'll
have to measure it, but I expect it will be rather high, easily 10 Mohm
which should be good enough (30x).

I'm also not sure if there will be a loss of Q due to capacitance of the
cable. I haven't found a clear reference on this. Some say
inter-winding capacitance will reduce the Q, but I don't think this will
be subject to inter-winding capacitance because of the shield. So the
question is will the distributed capacitance to ground create any sort
of problem? This cable has 16.2 pF per foot and I plan to use 50 feet.
I expect this will simply appear as part of the resonating capacitance.

Rick

On Thu, 29 Nov 2012 14:43:33 -0500, rickman wrote:

On 11/27/2012 11:01 PM, Arid ace wrote:
On Mon, 26 Nov 2012 16:25:37 -0500, wrote:

Just to give an update...

[...]

I did the calculations and at 100 uV/m with 50 foot of coax in a two
turn loop I get a bit over 1 uV, not so good. I'm going to see what I
can find about the signal level from ferrite cores. I had the
impression they would be lower, but I seem to recall better numbers than
this in the ones I've seen before.

Rick

When I was working with loop antennas, it became rather obvious that
optimal receiving loops too are 1 turn, with material of the largest practical
circumference. That one turn loop was coupled to one turn as the primary of a
coil / tuned transformer and on VLF / LF that concerned a potcore of the proper
material. The amount of turns for the secondary could be as much as 100 and
with a Q factor of 100 or more that meant at least 10,000 times the voltage of
the one turn loop - more than enough.

Jan

I have come to a similar conclusion, but not about using a single loop.
The single loop is the best antenna if your constraint is the total
length of cable. But if your limitation is the size of the loop, it
will be improved by more turns at the same diameter.

I used Al strip, bent in a circle, for the loop (used from 0.1 to 30 MHz). It
was cheap and easy but making a multi-turn loop would have been quite a task.

When I wrote the message you replied to I had left the Q factor out of
the equation. I calculated the Q factor at slightly over 100
considering just the resistance of the center conductor. I am also
aware of the idea of coupling using a ferrite core. I don't know
anything about ferrite cores (I suppose I'll need to learn that soon)
and I don't know what the optimal turns ratio would be. I assume that
the resistance of the load reflects back into the antenna as a parallel
resistance? Using your numbers that would mean a 1 Mohm input impedance
would result in a 10 kohm load. At the frequency of 60 kHz and with an
antenna inductance of about 90 uH that gives a reactance of 34 ohms. So
10 kohms shouldn't be a problem. But I read one reference that
indicated the Q needs to be factored in as well which means it would be
100 ohms vs. 33 ohms, and so 1 Mohm might not be high enough.

The antique booklet I have on potcores (Soft Ferrites, October 1973) lists the Q
realized with a core of certain dimensions as a function of ue of the material.
At 60 KHz, a P 11/7 core with material FXC 3B7/3H1 and ue=68 has the lowest Q,
220. The use of material with ue=220 delivers a Q of 420. This might serve as an
estimate of what could be expected: the 11/7 is the smallest potcore and the
bigger ones result in higher maximum Q, to well over 1,000.

When using a FET device as input, at 60 KHz the input impedance can be
neglected.

The input impedance of the device I am using is not characterized. I'll
have to measure it, but I expect it will be rather high, easily 10 Mohm
which should be good enough (30x).

The impedance of a source-follower will be much higher than 10 M - at 60 KHz.

I'm also not sure if there will be a loss of Q due to capacitance of the
cable. I haven't found a clear reference on this. Some say
inter-winding capacitance will reduce the Q, but I don't think this will
be subject to inter-winding capacitance because of the shield. So the
question is will the distributed capacitance to ground create any sort
of problem? This cable has 16.2 pF per foot and I plan to use 50 feet.
I expect this will simply appear as part of the resonating capacitance.

Rick

With a one turn loop coupled to the one turn primary of an RF transformer,
there's no need for a shield. It's fairly easy to provide the piece of wire used
for the primary with a center tap that will be grounded so the loop is
symmetrical. That also obviates the need for a differential amplifier. A 50 feet
loop is huge. I once (in Europe) designed a frequency standard synchronized to
DCF77 and reception was OK at distances over 2,000 Km with just a ferrite rod of
12 cm length and 1 cm diameter. In order to keep it easy for constructors, the
coil had just 140 turns with 2n2 to resonate the LC. I don't think the approach
for WWVB at 60 KHz could be much different (apart from the modulation format).
I had designed the ferrite antenna amp as a small device that could be fed via
coax, so one could install it in a place with the lowest noise.

Jan

On Thu, 29 Nov 2012, Arid ace wrote:


With a one turn loop coupled to the one turn primary of an RF
transformer, there's no need for a shield. It's fairly easy to provide
the piece of wire used for the primary with a center tap that will be
grounded so the loop is symmetrical. That also obviates the need for a
differential amplifier. A 50 feet loop is huge. I once (in Europe)
designed a frequency standard synchronized to DCF77 and reception was OK
at distances over 2,000 Km with just a ferrite rod of 12 cm length and 1
cm diameter. In order to keep it easy for constructors, the coil had
just 140 turns with 2n2 to resonate the LC. I don't think the approach
for WWVB at 60 KHz could be much different (apart from the modulation
format). I had designed the ferrite antenna amp as a small device that
could be fed via coax, so one could install it in a place with the
lowest noise.

Some of the issue may be habit. Over the decades, various WWVB receivers
were described, and I remember them all as using some sort of larger loop.
It may have nothing to do with design so much as habit, once an idea is
planted, others continue it.

In the early days of "amateur radio", everything was so low in frequency,
big loops and 60KHz probably weren't that foreign. So the collective
memory may retain that, a long time after hams were relegated to those
"uselss" shortwave frequencies.

The fact that all those WWVB clocks have relatively small loops is an
indicator that not much is needed. I don't know how complicated the
receivers have become, if at all. I can get WWVB here in Montreal on my
Casio Waveceptor watch, and whatever that uses has to be way smaller than
the loops in the small WWVB clocks.

The better the loop, of course, the more selectivity it provides. I don't
have any of those WWVB receiver articles handy, but again I remember them
as being relatively simple amplifiers, fairly depending on the loop for
selectivity. The larger the loop, the more directional it can be, which
presumably helps with all the local junk generated that can cause issues.

The analog part (or what most people were interested in until recent
times), wsa the antenna and selectivity and a good amplifier. Simple and
complicated at the same time. And it's a spectrum area often "unkonwn",
not many receivers to tune down there, so one wonders if the signal is
there, or it's the equipment, until the equipment becomes right enough for
the signal to appear. if I'm building a WWV receiver, it's easy to check
for the signal since I have a few receivers that cover the frequency
range.

It's not a new field. There was one guy, I can't remember his name, who
wrote a number of articles in QST about WWVB and WWVL reception, and high
stability frequency standards, I can picture on in the summer of 1971.

Don Lancaster did an article about WWVB, more an introduction, and he has
it on his webpage at www.tinaja.com, titled something like "Experiments in
WWVB Reception".

Ken Cornell spent a lot of time writing about low frequency work, he had a
"cookbook" out at one point, initially self-published but a later edition
published by Ham Radio Magazine. But he died, and access to the book
other than used died with him.

Ralph Burhan, who was a ham, wrote a lot about low frequencies. Using
Loran as a frequency standard (or was it time?), all kinds of articles in
various hobby magazines about low frequency antennas (sometimes loops, but
often short whips, directly coupled to a very high impedance buffer). I'm
not sure any of that is online, but it might be worth a search.

There have been quite a few WWVB receiver articles in the ham magazines,
though I have no dates. I think one wsa in September 1971 "73". The ones
I saw all predate WWVB's more recent visibility as a feed to all those
"atomic clocks". Most were interested in the station as a frequency
standard, though as early as that seventies Don Lancaster article, people
were thinking about decoders to get the time.

I think there are groups and pages devoted to this sort of thing, but I
don't follow it so anyone's search is as good as mine would be.

The interest may be picking up, talk of a low frequency ham band (or is it
already in place? I forget). And of coruse, there is the 160-190KHz
"license free band" that some have put a lot of effort into, "lowfers",
searching for that sort of thing might turn up useful information, albeit
needind scaling down to 60KHz.

Michael VE2BVW

On Thu, 29 Nov 2012 22:21:15 -0500, Arid ace wrote:

I used Al strip, bent in a circle, for the loop (used from 0.1 to 30 MHz). It
was cheap and easy but making a multi-turn loop would have been quite a task.

I remember years ago someone suggested the following to make a 'simple'
multi-turn loop:

Get a length of 'flat computer cable' -- e.g., like the IDE cables for
PC HD's. Such cable can be found in 'surplus' outlets -- sometimes as
an 'end piece' on a cable reel.

Form your loop -- cutting the flat cable to the length you desire.
Connect every-other cable wire to every-other-other (HI!HI!) cable wire.
Your ends, then, are the two outside wires on either side of the
cross-over connection zone.

Such cable can be re-'sized' to just the loop count you want by
un-zipping unwanted runs of the cable.

Depending on how neatly you mount your loop, you should have no problems
with wires shifting position with relation to one another and de-tuning
the resultant lash-up.

Attribution unknown...

HTH,
Jonesy W3DHJ http://jonz.net/W3DHJ

On 11/29/2012 10:21 PM, Arid ace wrote:
On Thu, 29 Nov 2012 14:43:33 -0500, wrote:

I have come to a similar conclusion, but not about using a single loop.
The single loop is the best antenna if your constraint is the total
length of cable. But if your limitation is the size of the loop, it
will be improved by more turns at the same diameter.

I used Al strip, bent in a circle, for the loop (used from 0.1 to 30 MHz). It
was cheap and easy but making a multi-turn loop would have been quite a task.

I am making a shielded loop so I'm using coax to make the construction
simple. Multiturn won't be a problem.


When I wrote the message you replied to I had left the Q factor out of
the equation. I calculated the Q factor at slightly over 100
considering just the resistance of the center conductor. I am also
aware of the idea of coupling using a ferrite core. I don't know
anything about ferrite cores (I suppose I'll need to learn that soon)
and I don't know what the optimal turns ratio would be. I assume that
the resistance of the load reflects back into the antenna as a parallel
resistance? Using your numbers that would mean a 1 Mohm input impedance
would result in a 10 kohm load. At the frequency of 60 kHz and with an
antenna inductance of about 90 uH that gives a reactance of 34 ohms. So
10 kohms shouldn't be a problem. But I read one reference that
indicated the Q needs to be factored in as well which means it would be
100 ohms vs. 33 ohms, and so 1 Mohm might not be high enough.

The antique booklet I have on potcores (Soft Ferrites, October 1973) lists the Q
realized with a core of certain dimensions as a function of ue of the material.
At 60 KHz, a P 11/7 core with material FXC 3B7/3H1 and ue=68 has the lowest Q,
220. The use of material with ue=220 delivers a Q of 420. This might serve as an
estimate of what could be expected: the 11/7 is the smallest potcore and the
bigger ones result in higher maximum Q, to well over 1,000.

I'm not sure I understand. This sounds more like a ferrite core antenna
where the ferrite is an integral part of the antenna itself. I was
asking about the type of ferrite for a ferrite loop to use as the core
of a transformer to couple the output using multiple turns to boost the
voltage.


When using a FET device as input, at 60 KHz the input impedance can be
neglected.

This will be driving an input on an IC so I don't have much info on it.
I expect it is very high impedance just like the FET.


The input impedance of the device I am using is not characterized. I'll
have to measure it, but I expect it will be rather high, easily 10 Mohm
which should be good enough (30x).

The impedance of a source-follower will be much higher than 10 M - at 60 KHz.

I'm also not sure if there will be a loss of Q due to capacitance of the
cable. I haven't found a clear reference on this. Some say
inter-winding capacitance will reduce the Q, but I don't think this will
be subject to inter-winding capacitance because of the shield. So the
question is will the distributed capacitance to ground create any sort
of problem? This cable has 16.2 pF per foot and I plan to use 50 feet.
I expect this will simply appear as part of the resonating capacitance.

Rick

With a one turn loop coupled to the one turn primary of an RF transformer,
there's no need for a shield. It's fairly easy to provide the piece of wire used
for the primary with a center tap that will be grounded so the loop is
symmetrical. That also obviates the need for a differential amplifier. A 50 feet
loop is huge.

The loop won't be 50 foot in diameter, it is 50 feet of coax wound in
some 8 turns give or take. At 8 turns that is 2 foot diameter or 300 mm
radius.

As to the shield, I'm told the shield will be a big help in eliminating
local interference from E-field sources. I read that household
appliances are a major source of electrical noise and I know from
experience that my radio controlled clocks seem to have trouble working
near my computers.


I once (in Europe) designed a frequency standard synchronized to
DCF77 and reception was OK at distances over 2,000 Km with just a ferrite rod of
12 cm length and 1 cm diameter. In order to keep it easy for constructors, the
coil had just 140 turns with 2n2 to resonate the LC. I don't think the approach
for WWVB at 60 KHz could be much different (apart from the modulation format).
I had designed the ferrite antenna amp as a small device that could be fed via
coax, so one could install it in a place with the lowest noise.

Yes, if I can get away with it, I'll use a ferrite rod. But I want to
eliminate the front end amp and will be driving the input directly from
the antenna. The inductance of this coil will be much lower than a
ferrite core and will need a lot more capacitance to resonate. The coax
coil is what I'm starting with and can always back off to a ferrite
antenna if needed.

Thanks for the input.

Rick

Thanks for that, Michael! For several months I had been trying to pump
my feeble brain to recall
that brilliant author/engineer, Don Lancaster. I was so bummed out when they
booted him off
the last of the great magazines published by the ??????? group. Now, darn
it, even forgot the
name of the old time publishing outfit that had the good stuff.
Thanks again, Michael!

Old Chief Lynn, W7LTQ since 1948