# Circular Coil and Field Measurement

• posted

Hi,

I am trying to measure magnetic flux density (B) in tesla using a circular loop of 0.5 inch or 0.0127 meters.

I got the followjng formula from the following two papers

Voc = 2 x pi x f x A x B x N

Where

Voc = open circuit voltage f = resonant frequency (Hz) ..............in this case 100KHz A = area of the coil ( in meters) B = magentic flux density ( in tesla ) N = number of turns of coil

The links of the papers are as follows

Paper 1:

Page 7 on Paper 2:

I build the circular loop using the following wire

I soldered the two terminals of the circular loop to one end of the BNC cable and connect the other end to the scope.

I have following confusions

1. Did I use the correct wire? I meant guage and resisatance.

1. Should I connect oscilloscope probe to directly to the loop or connect the loop to the scope using BNC cable is good?

2. I calculated the area of the coil as follows

A= pi x R x R which turned out to be 0.0127meter square. But the first paper discuss about the effective aperture which one is correct?

1. The magnetic field is resonating at 100 KHz. I am using the one turn circular loop to measure field without resonating at 100KHz. Is this a good approach. And if I want to measure the field using resonance than what will be the setup?

1. Should I use peak to peak voltage or just peak ( Voc) to calculate "B" ?

Thanks jess

• posted

El 13-02-12 23:42, Jessica Shaw escribió:

This formula is correct for calculating the open loop voltage in case of sinusoidal wave form. You may know that B = mu*H.

Are you sure that the field is uniform given the diameter of the loop?

Just connect the loop to an oscilloscope using 50 Ohms cable and 50 Ohms termination at the oscilloscope to avoid resonance effects. Wire resistance can be ignored.

Effective aperture is often used in antennas and takes resonance into account. When using a non-resonant approach, you can use A [m^2] as you did. So for 0.5" (12.7 mm) diameter it will be A = 1.27e-4 m^2.

If you can measure your field without resonance, it is the best approach. If you use resonance to get more output (or better S/N ratio on the oscilloscope), you need to measure quality factor and coupling and this may result in larger error.

As your loop is very small (assuming 1 turn), "loop reactance"

• posted

Hi,

So, if I measure 2 volts peak to peak/ Than what should I use 1 volt peak or 2 volts peak to peak or RMS. I am still confused about this. I forgot to mention in my original post that 0.5 inch is the radius of One turn coil. So the diameter of the coil is 1 inch.

Full H bridge using four NMOSFETS.

Paper 2 page 9 says something about the area of the loop and the wavelength of the sine wave. I am unable to put the concept together. The area of the loop should be less than the wavelength of the exciting signal. The wavelength of the 100KHz sine wave is 10usec. Can anyone suggest how to relate wavelength with the one turn loop?

Paper 2 is using TEM cells to calibrate the one turn coil. Is there any other inexpensive way to calibrate the coil that I am using?

Thanks jess

• posted

Doesn't matter much. That wire is fine.

Doesn't matter either.

If the field is uniform, area = aperature.

Don't try to resonate the probe coil, or the formula won't work.

Peak volts corresponds to peak field strength.

```--
John Larkin, President       Highland Technology Inc
www.highlandtechnology.com   jlarkin at highlandtechnology dot com   ```
• posted

You can use free PC Tools to verify this, but when measuring a magnetic field created by a magnetic dipole and you want at least 1% accuracy, you need to be a minimum distance away, at least 3 diameters of the largest coil dimension. What this means is that for a sensing coil 1 inch diameter you can NEVER be closer than 3 inches, and if the field generator is 1 foot in diameter, you shouldn't be closer than 3 feet. In other words, the distance away should be three times the largest dimension.

Also at that distance, you're not going to interact much with the field. So if the source is resonant, you won't detune it much.

Wavelength? at 100kHz the wavelength is LONG!! ignore.

Calibrate? you can calibrate by very carefully constructing a Helmhotz coil, large enough so that your construction tolerances keep your accuracy. But even then you have to be careful exactly where you place the sensing coil and route your connections to the sensing coil. From memory, one tenth dimension in the center of the Helmholtz coil [a pretty small volume] will yield 1% accuracy, but check using a free PC tool, like femm 4.2

Don't forget a scope is usually a 3% measuring tool not a lot of absolute accuracy, good relative accuracy. You'd be surprised how difficult it is to accurately measure with a scope. Today, scopes have improved; check manufacturer's spec, and of course whether the calibration tag is up to date.

Also, you can accurately measure, I MEAN accurately measure, the dimensions of your sensing coil, put that into the femm 4.2 for analysis and CALCULATE the voltage you will measure. With very accurate dimensions and using a very small mesh you will not need to 'calibrate', only verify your sensing coil's accuracy.

• posted

First off, to the best of my knowledge, Mister Science makes no statement about resonance and nothing concerning RMS or peak readings. It is all symplifyed generic mumble; drawings when included amazingle disclose AIR core windings. So, for any real-life measurements to be reasonable and meaningful, you need the following conditions: Frequency of generator / power source driving "winding" or loop (any shape you want, but KISS and make it circular and solenoidal (not pancake) to be well below resonance of coil/loop. Test loop, if used to also have resonance frequency well above that of generator. All out in "free space"; not close to any magnetic material or conductive blocks (cars, steel buildings,etc). What you then have is the magnetic equivalent of short antennas in that space. Remember, all power transformers (to be more eXplicit, transformers used for power transmission) are run far below "resonance".

Measurements: take your pick but be CONSISTENT; RMA, average, peak but make dern sure the reading gives the correct value. For example, take the probe loop and use a simple diode feeding a capacitor and a hi-Z meter is across the meter; peak reading, eh? Well, more or less yes IF the reading is a fair number of volts - but NO if in the 0.1-0.7V range. Know your measuring equipment!

Hmm..do not remember anything said about aperture, but a little common sense may be of help. Take a "large" driven loop (the "unknown" or "primary"). If the test loop is "small" (as Einstein said, it is all relative - aunts, uncles etc) then the field at any "point" could be measured and one can plot the divergence that some texts elegantly show. As a motivated novice experimenter, this can be of great value. If the test loop is made the same size and placed close to the driven antenna (oops--meant to say loop) then the full radiated field is "captured". Nominally speaking, if the test loop is large WRT the driven loop, that should give the same reading.

• posted

Simple math can be the way to calculate the produced field. A one-turn coil is one of the better means of generation; the other way is to use a straight wire, where the turn-around is far away. Generator lead to test wire is straight line, test wire say is ten feet long, then curve wire to return line spaced say ten feet away. Measurements and calculations based on a few inches away from and in the center of the test length gets one close to the ASS-u-ME-ption of "infinite" length and one wire.

You can use DC..take a pair of wires and lay them side-by-side for a foot or so,short them together at one end and for a brief period of time,drive this "collapsed" loop with a car battery - the wires will JUMP!! Experiment some with wire separation (an inch or two), keeping them parallel. Correlate amount of jump and direction with separation, and compare that with what a crude calculation would show. Refine if you choose by using current limiting resistor (better consistency as poor battery does not get unduly stressed) and a current meter in constant state. Use scale to measure the force between the wires at a given separation. Theory and practice will meet fairly well and the B-field calculated under the same conditions could be used as a "standard"

• posted

El 14-02-12 2:23, Jessica Shaw escribió:

So A = 507e-6 m^2. If you read 2 Vpp from the oscilloscope, this will convert to 1 Vp and

0.707 Vrms (only valid for sinusoidal wave form).

The "calibration" is the formula, given that "loop size"

• posted

From the transmisison loops perspective, barely. At 100 KHz the wavelength is 3Km, until the dimensions of the setup reach some moderate fraction of this the transmission will be almost totally near field, and the relationship between drive current and surrounding B is pretty well independent of frequency. In fact, for higher frequency excitation, the 'sensitivity' (tbd) will reduce because the loop reactance is higher, resulting in less current for the same driving voltage and lower B in the surrounding field.

Of course, at the receive end, higher frequencies will result in higher induced voltages due to the higher dv/dt.

• posted

El 14-02-12 12:03, Bruce Varley escribió:

We are discussing small receive/measuring loops here, this may only add confusion.

Sensitivity is Vpk/Bpk. As Jess has a small loop (some hundreds of nH, that will be around j0.2 Ohms at 100 kHz), up to several MHz the loading due to 50 Ohms is negligible. So V/B will be proportional to frequency up to several MHz (as indicated by the formula).

```--
Wim
PA3DJS```
• posted

A while back, I made a FEMM model using your stated dimensions for your Helmholz pair, with a few assumptions about dimensions you didn't state, and came up with this:

Using the current that my Spice model of your driving circuit predicts, along the center line:

Inches Tesla

0.00000000e+00 1.30583733e-04 5.36912752e-02 1.30850685e-04 1.07382550e-01 1.31139773e-04 1.61073826e-01 1.31446743e-04 2.14765101e-01 1.31761796e-04 2.68456376e-01 1.32014215e-04 3.22147651e-01 1.32231648e-04 3.75838926e-01 1.32406949e-04 4.29530201e-01 1.32569725e-04 4.83221477e-01 1.32735154e-04 5.36912752e-01 1.32911050e-04 5.90604027e-01 1.33046444e-04 6.44295302e-01 1.33142564e-04 6.97986577e-01 1.33229981e-04 7.51677852e-01 1.33284040e-04 8.05369128e-01 1.33322538e-04 8.59060403e-01 1.33347711e-04 9.12751678e-01 1.33345975e-04 9.66442953e-01 1.33333547e-04 1.02013423e+00 1.33302946e-04 1.07382550e+00 1.33251592e-04 1.12751678e+00 1.33183973e-04 1.18120805e+00 1.33110426e-04 1.23489933e+00 1.33025326e-04 1.28859060e+00 1.32899908e-04 1.34228188e+00 1.32774662e-04 1.39597315e+00 1.32622677e-04 1.44966443e+00 1.32465277e-04 1.50335570e+00 1.32306744e-04 1.55704698e+00 1.32148922e-04 1.61073826e+00 1.31963374e-04 1.66442953e+00 1.31777429e-04 1.71812081e+00 1.31569142e-04 1.77181208e+00 1.31358985e-04 1.82550336e+00 1.31135027e-04 1.87919463e+00 1.30907034e-04 1.93288591e+00 1.30694807e-04 1.98657718e+00 1.30482471e-04 2.04026846e+00 1.30231365e-04 2.09395973e+00 1.29992725e-04 2.14765101e+00 1.29738618e-04 2.20134228e+00 1.29502711e-04 2.25503356e+00 1.29262583e-04 2.30872483e+00 1.28996282e-04 2.36241611e+00 1.28750476e-04 2.41610738e+00 1.28504786e-04 2.46979866e+00 1.28274547e-04 2.52348993e+00 1.28040490e-04 2.57718121e+00 1.27808243e-04 2.63087248e+00 1.27606736e-04 2.68456376e+00 1.27401720e-04 2.73825503e+00 1.27148315e-04 2.79194631e+00 1.26908757e-04 2.84563758e+00 1.26679297e-04 2.89932886e+00 1.26480478e-04 2.95302013e+00 1.26299284e-04 3.00671141e+00 1.26117038e-04 3.06040268e+00 1.25937682e-04 3.11409396e+00 1.25756772e-04 3.16778523e+00 1.25582758e-04 3.22147651e+00 1.25411621e-04 3.27516779e+00 1.25251493e-04 3.32885906e+00 1.25104538e-04 3.38255034e+00 1.24984490e-04 3.43624161e+00 1.24867806e-04 3.48993289e+00 1.24758849e-04 3.54362416e+00 1.24654574e-04 3.59731544e+00 1.24567204e-04 3.65100671e+00 1.24481288e-04 3.70469799e+00 1.24417464e-04 3.75838926e+00 1.24356030e-04 3.81208054e+00 1.24315458e-04 3.86577181e+00 1.24278792e-04 3.91946309e+00 1.24262897e-04 3.97315436e+00 1.24246774e-04 4.02684564e+00 1.24248172e-04 4.08053691e+00 1.24256858e-04 4.13422819e+00 1.24277183e-04 4.18791946e+00 1.24312229e-04 4.24161074e+00 1.24365623e-04 4.29530201e+00 1.24410118e-04 4.34899329e+00 1.24481702e-04 4.40268456e+00 1.24559675e-04 4.45637584e+00 1.24654528e-04 4.51006711e+00 1.24752604e-04 4.56375839e+00 1.24865146e-04 4.61744966e+00 1.24984828e-04 4.67114094e+00 1.25120250e-04 4.72483221e+00 1.25269382e-04 4.77852349e+00 1.25430150e-04 4.83221477e+00 1.25576955e-04 4.88590604e+00 1.25726794e-04 4.93959732e+00 1.25891911e-04 4.99328859e+00 1.26078993e-04 5.04697987e+00 1.26289533e-04 5.10067114e+00 1.26485834e-04 5.15436242e+00 1.26692724e-04 5.20805369e+00 1.26904842e-04 5.26174497e+00 1.27124541e-04 5.31543624e+00 1.27341151e-04 5.36912752e+00 1.27570472e-04 5.42281879e+00 1.27800685e-04 5.47651007e+00 1.28048645e-04 5.53020134e+00 1.28283580e-04 5.58389262e+00 1.28504853e-04 5.63758389e+00 1.28728854e-04 5.69127517e+00 1.28964545e-04 5.74496644e+00 1.29204117e-04 5.79865772e+00 1.29489374e-04 5.85234899e+00 1.29740435e-04 5.90604027e+00 1.30009410e-04 5.95973154e+00 1.30242644e-04 6.01342282e+00 1.30472529e-04 6.06711409e+00 1.30672808e-04 6.12080537e+00 1.30904356e-04 6.17449664e+00 1.31138649e-04 6.22818792e+00 1.31370889e-04 6.28187919e+00 1.31588021e-04 6.33557047e+00 1.31789381e-04 6.38926174e+00 1.31963798e-04 6.44295302e+00 1.32134092e-04 6.49664430e+00 1.32304648e-04 6.55033557e+00 1.32467343e-04 6.60402685e+00 1.32618578e-04 6.65771812e+00 1.32757224e-04 6.71140940e+00 1.32896603e-04 6.76510067e+00 1.32995577e-04 6.81879195e+00 1.33095782e-04 6.87248322e+00 1.33172271e-04 6.92617450e+00 1.33237728e-04 6.97986577e+00 1.33295395e-04 7.03355705e+00 1.33330247e-04 7.08724832e+00 1.33348907e-04 7.14093960e+00 1.33339450e-04 7.19463087e+00 1.33327429e-04 7.24832215e+00 1.33285033e-04 7.30201342e+00 1.33220894e-04 7.35570470e+00 1.33141473e-04 7.40939597e+00 1.33038658e-04 7.46308725e+00 1.32925816e-04 7.51677852e+00 1.32780082e-04 7.57046980e+00 1.32618985e-04 7.62416107e+00 1.32442710e-04 7.67785235e+00 1.32215476e-04 7.73154362e+00 1.31967666e-04 7.78523490e+00 1.31727378e-04 7.83892617e+00 1.31448866e-04 7.89261745e+00 1.31126217e-04 7.94630872e+00 1.30817657e-04 8.00000000e+00 1.30510441e-04

I could post a pretty picture of the field to a.b.s.e. ,but you're on Google, so you wouldn't see it.

```--
"For a successful technology, reality must take precedence
over public relations, for nature cannot be fooled."```
• posted

```--
"For a successful technology, reality must take precedence
over public relations, for nature cannot be fooled."```
• posted

Hi,

1. How did you calculate the wavelength of the 100KHz sine wave to be
3Km?

1. How can I measure the BNC connector is 50 Ohms?

2. Paper 2 is suggesting to use TEM cell ( Transverse Electromagnetic cell ) or Crawford cell. Is the author comparing the measurment done in between TEM cell and helmholtz coils. If yes, than I have two options

1. to use TEM cell by myself.

1. replace the TEM cell option with something inexpensive option.

I am not familiar with FEMM, Quick field and MATLab software options yet.

jess

• posted

Jessica Shaw Inscribed thus:

f/C

The connector will be but the circuit that its in may not be. Scopes are often 1Mohm.

```--
Best Regards:
Baron.```
• posted

femm is an incredibly useful FREE Finite Element Analysis tool written by Dr. David Meeker. if you're using Windows, download a copy of femm42bin.exe and jointhe users group to ask questions QuikField is another finite element analysis program. I believe out of Russia, also have a free version, but extremely small total number of nodes limitation, rendering mainly educational, rather than useful. Matlab costs money and is a high level form of analyses software, like a high form of Excel ;) but requires to buy it. octave is a FREE clone version, extremely powerful ANother FREE option is to download python, which has its own unique advantages.

Using femm 4.2; you can analyze your sensing coil. Construction defines your performance, so there is no real need to 'calibrate', just verify.

Again, dowload a copy of octave and oin the users group to ask questions.

• posted

• The BNC connector size (length) and configuration (50 ohm, 75 ohm) is not relevant at these DC frequencies.

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