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External Leakage Field - Toroid and Solenoid Inductors

Revision History
04 November 2009. Original
18 December 2009. Added Q data and table of contents; added single turn section

Table of Contents


One bit of amateur radio lore is "a toroid inductor is self-shielding" and hence does not have an external field to interact with other inductors or with nearby conducting objects such as the enclosures.

Like many fables, there's some truth in this statement, but it's far from being 100% correct. In building a prototype notch filter recently, I ran across a case where there was not enough room to space toroid inductors to minimize unwanted coupling and hence found shields between adjacent inductor necessary. This lead me to make some simple measurements to demonstrate the difference between the external fields of a toroid and solenoid inductor.

Inductor Coupling Data

The data I collected is not the most sophisticated, but it shows the concept. The solenoid core at the left is 36 turns on a 0.5 inch diameter Delrin core, and measures approximately 7uH. The toroid core at the right is 25 turns on an T50-7 core, and measures 2.8 uH. The long object in the center is the  test coupling probe I use with a spectrum analyzer as a  "signal sniffer." It consists of a 5 turn shielded pickup loop constructed from coaxial cable, with a BNC connector at the other end of the probe handle. The two large black cores are high u ferrite cores that reduce coupling from outer shield to the sensing coil.

I connected the inductor under  test to the output port on an HP 8752B vector network analyzer and the signal sniffer coil to the VNA's receiver port, with the VNA in transmisison mode. Since these inductors are of a value and construction that would typically be used in the MF and HF range, I set the frequency range to cover 300 KHz to 30 MHz, with log sweep.

I made two pairs of measurements by positioning the sniffer coil to be coaxial with the solenoid and with the toroid core, at approximately 1 inch and at 3 inches spacing. I also made a third pair of measurements orienting sniffer coil to achieve maximum coupling at 10 MHz.

The VNA data shows the loss in dB versus frequency between the sniffer coil and the inductor under test. This loss provides a quick and dirty approximation of the external field of the two inductors and hence their propensity to couple to other inductors or the environment. If the toroid is truly self-shielding, there will be no signal pickup.

The solenoid inductor shows a worst case coupling of 37 dB at 10 MHz and even with 3 inch spacing has about 63 dB loss.

The toroid inductor—while some 10-20 dB better than the solenoid—has a far from zero external field.
The rather cluttered plot below shows all six test runs. The data shows that at lower frequencies and greater spacing the toroid has perhaps 20  to 25 dB less external field than the solenoid inductor. However, at higher frequencies and closer spacing, the external fields begin to converge.

In terms of the filter I'm working on, the photo below shows the experimental layout with shields added. The shielding material is thin tin-plate stock obtained at the local hobby shop. It's easy soldering material and can be cut with tin snips or even heavy duty scissors. Although I oriented the three large inductors to minimize coupling, given the size of the parts and the available space, there's only so much that can be done to reduce unwanted coupling by orientation and  core-to-core spacing.

Whether or not the external field of an inductor is a problem depends, of course, on the application. In many circuits, coupling between inductors down 50 or 60 dB is inconsequential. However, if you are working with a filter and wish to achieve 100 dB band stop rejection, great care must be taken to avoid unwanted coupling. In the case of the Z10020 band reject filter, careful printed circuit board layout allows very high stop band rejection to be achieved without shielding. In the case of the experimental filter pictured below, shielding is helpful in achieving target performance goals.

Single Turn Effect

Dr. Rudolf Rieder commented on my data:

When fighting against pick-up from a switching DC-DC converter I ran into a note (forgot the ref.) pointing out that although the toroid core does pretty well include the magnetic field of the coil wound around it, the coil itself forms a net 1-turn loop around the circumference of the torus. If you want a (more) "quiet" switching power supply you ought to bring the ends of the coils together by forming an external 1-turn backward-loop (or 2 1/2-turn loops), thus compensating the field (effectively a "bifilar" design). At the time this small change helped a lot.

I am therefore wondering whether a similar approach to RF-toroids wouldn't have a similarly beneficial effect, i.e. a significant reduction of stray fields and thus coupling. If you feel like it next time, please try it and repeat the measurements.  I'd be quite curious to read about it  when next visiting your page.

This is correct. The typical toroid inductor can be considered to be two inductors. One is the traditional "circular solenoid" where the magnetic flux follows the core and the second is the one-turn loop mentioned by Dr. Rieder. Thus, even if 100% of the flux of the "circular solenoid" is confined to the magnet core, the one-turn loop is certainly not so confined.

I'll look at the one-turn effect in more detail in the future.


Effect of Nearby Shielding on Q

One consequence of flux leakage is that the inductor loss—and hence Q—is influenced by nearby metallic objects. The leakage flux induces current in nearby conductors and since the energy lost in the conductors is provided by the inductor, the inductor's total loss increases. Q is inversely proportional to loss, so increased loss translates to lower Q.

This effect can be visualized in several ways. Perhaps the simplest is to think of it as a transformer, with the inductor as the primary and nearby conductors as multiple secondary windings.  The secondary windings have resistance and hence loss. The induced current and hence the level of loss depends, in transformer terms, upon the coupling coefficient, which relates primary flux and secondary flux. In a good transformer, primary and secondary flux is tightly coupled, with a coupling coefficient very near 1.00. In the case of a toroid inductor's field inducing currents into a nearby conductor such as a shield, the coupling coefficient will be nearly, but not quite, zero.

A common example of induced field loss is seen when a toroid is near a shield. This may be an intentional shield to reduce inter-stage coupling, or it may be an inadvertent shield such as an aluminum enclosure wall. Or, the toroid may be mounted horizontally on a printed circuit board with a ground plane.

In order to demonstrate the effect of shielding on inductor Q, I made a simple test using a small piece of thin aluminum and a 2.8 uH inductor wound on a T50-2 powdered iron core, as in the earlier leakage  test. The aluminum sheet is approximately 2" (50mm) x 4" (100mm) and is 0.050" (1.25mm) thick.

The toroid is held in place with an axial screw, and spaced from the aluminum sheet with nylon washers, 0.1" (2.5mm) thick. I made measurements with the inductor touching the shield, with 0.1" and 0.2 (5mm) spacing, with a plastic (nylon) axial screw and a stainless steel screw. Finally, I made measurements with an intentionally poor mounting method, one that forms a shorted turn.

I measured Q and inductance with an HP 4342A Q-meter at 7.9 MHz. The "free space reference" is the measured Q without the aluminum plate.


The plot shows a rather small change in Q when nylon mounting hardware is used. Indeed, even with the core touching the aluminum plate, the measured Q dropped by 10 points, from 246 to 236. A small gap of 0.1" (2.5mm) reduces the Q by 5 points and increasing the gap to 0.2" (5mm) reduces Q by 4 points.

In contrast, using a stainless steel mounting screw results in a much greater Q loss. (The screw did not form a shorted turn; rather it was just a single vertical element with a stainless steel washer on the top.

Shorted Turn Mounting

It's common knowledge—and if it's not, it should be—that a toroid should not be mounted with conducting hardware that forms a "shorted turn," i.e., a continuous conductor making a loop through the toroid hole. The reason is that this configuration makes a rather efficient transformer and couples energy from the inductor into the unintentional one-turn shorted secondary winding formed by the mounting hardware.

To demonstrate this effect, I made a quick shorted turn mounting, illustrated to the right. This is perhaps not a very good mount, but the better the mount, the greater the loss and the lower the Q. A pair of aluminum stand-offs, for example, one through the core and one adjacent to the core edge, with a thick aluminum bar joining the two will have a greater Q reducing effect than the long mounting strap I used.

The shorted turn mount  reduced the measured Q from a free space value of 246 to 152. It also reduced the measured inductance from 2.8 uH to 1.69 uH. The reason for the inductance reduction is that the secondary inductance appears in parallel with the primary (the 2.8uH free space measured inductance).

I expected the inductance to be considerably lower than 1.69uH and the resulting Q to be worse than the 40% reduction.


Mounting Conclusions

With small cores such as the T50 series, only minimal loss of Q results so long as the core is at least 0.1 inch from the nearest conducting surface, where non-conducting hardware is used. Conducting hardware should not be used under normal circumstances and if conducting hardware is used, it should not be allowed to form a shorted turn.