Blue-green toroid     What is it?
A few years ago at a hamfest I bought a handful of identical blue green toroids—I think the investment was $3 for the lot. Colored toroids are iron powder mixtures, while grey or blackish ones are ferrite toroids. However, at the time of this purchase I knew almost nothing about the different sizes, shapes, mixtures, or their physical and electronic properties. At first I imagined that the colors were a simple code that would lead to quick and easy identification of relevant electronic properties. The resistor color code (by analogy) follows the order of colors in the visible light spectrum, which makes it easy to identify a marked resistor value quickly. Iron powder toroid colors are also a code. However, toroid colors are not as straightforward to read and interpret as resistor bands are. This led to an interesting study.

    As time went on I acquired a variety of other toroids, some in radio kits, a few ordered for projects that required specific types, and some from disassembled equipment. Several came from no-longer-working Uninterruptible Power Supplies (UPS’s), by which stage the UPS’s had become IPS’s. The growing collection ranged in size from very tiny to big enough to wrap a power cord through, with the plug attached.

Outer Diameter 1.57 inches     Inches: The world is metric but for some reason, toroid classification uses inch measure. First there is an alpha prefix, ‘T’ for toroid and ‘FT’ for guess what. After that comes a number that seems mysterious, until we learn that it is the outer diameter of the annulus in hundredths of an inch. Thus the blue-green toroid in the illustration is a T157-something because first, it is an iron powder (not ferrite) toroid and second, its outer diameter is 1.57 inches. Luckily it is not necessary to be able to measure the diameter to the precision of one-hundredth of an inch, because the next smaller iron powder toroid is 1.30 inches and the next larger one is 1.84 inches—according to the mini Ring Core calculator (a useful and free utility). 

     Color specifies mix: Diameter is the easy part. Now to the nitty gritty, literally as well as figuratively speaking. To complete the identification of an unknown toroid, once the dimension has been worked out, it is necessary to ascertain the material type of the toroid, also called the ‘mix’. This term refers to the specific mixture of micro metals that are blended into the ceramic to produce desired electronic properties. This is where color code comes into play. The blue-green color of the hamfest toroid means it is mix 52.

    Mix identification based on color can be verified through measurement. The first step is to form an inductor using the toroid, by winding enough turns of suitable diameter wire to obtain a reasonably good measurement of the coil’s inductance.

Measurement and Calculation

    The test inductor pictured above consisted of 40 turns of  22 AWG solid wire. Forty was the most turns of that plastic-insulated wire that could be made to fit through the blue-green toroid hole without overlapping. The inexpensive multi-tester is reasonably accurate at an inductance range of say 50 times greater than the value displayed above, but may be presumed less accurate toward the lower end of its measurement range. Two parts of the mini Ring Core Calculator page (above right) are highlighted. At the top is the selected toroid and its color-code based mix, and at the bottom, the calculated inductance of the selected mix based on 40 turns.

    The measured inductance was 140 μH while the calculated inductance is 158 μH. That may seem a significant discrepancy, and perhaps it is; however, mix 52 from the T157 drop-down list produces the best agreement between measured and computed values of any mix in the list. The yellow bar on the extreme right shows the available mix choices for that toroid. The fact that measurement is in approximate agreement with calculation makes it an even better bet that the blue-green toroid is a T157-52 type. I should mention that equivalent calculator resources may be found on-line. For example, this page performs the same calculation as the Mini Ring Core program does for iron powder cores, and it displays the toroid colors rather more vividly than the colored object itself.

On-line calculator
Clip from on-line calculator at
Ferrite toroid     Ferrite Toroid: One of the ferrite toroids in my ‘collection’ has an unusual shape. It is fatter than most, relative to its diameter. This dimension is called ‘height’ not width. (For naming this dimension, toroids must be imagined lying flat, not in the orientation of a car wheel.)

    Obviously this second test toroid’s identifier starts with ‘FT’ rather than ‘T’. Its outside diameter as measured with a ruler is just under 7/8 inch, in other words, very close to 87/100 inch, so it must be an FT87 something. Ferrite toroids do not have a color code, so to ascertain the complete type designation will necessitate measurement. —In truth, I am not sure of this point. Do ferrite toroids have ‘50 shades of grey’? Maybe they do—I don’t know.

    After identifying the toroid number, based on outer diameter, I discovered that the FT87 comes in two different heights. Plain FT87 is 1/4 inch, while FT87A is 1/2 inch in height.  The one pictured is an FT87A.  The ‘A’ stands for ‘fAt’ (not). Without having color as a pointer to the mix, the remainder of the identification process proceeded smoothly nevertheless, in part because coils wound on ferrite cores produce a higher range of inductance.

Ferrite Toroid type by inductance

    Millihenrys is a better range for the multi-tester than microhenrys. A 50-turns inductor measures 10.10 mH on the multi-tester. (The turns are rather messy, I know.) According to the calculator (above right), the inductance should be 9.06 mH if the material is type F, and as it happens 9.06 mH is closest to the 10.10 mH measured value, from among any mix listed for this toroid type. Trial and error (iteratively computing inductance for listed mixes) demonstrates that mix ‘F’ is the only one to produce a computed inductance that is near the measured value. The same finding may be reproduced using the on-line calculator at this page, which performs the reverse calculation (e.g., 52 turns for 10.1 mH). Thus, this ferrite toroid can be confidently identified as type FT87A-F. But not so fast! Supplementary measurement produced a different result. See the section labeled ‘Anomalous measurement’ near bottom of page.

Yellow-white iron powder toroid     One more: I will present one more example, partly because the toroid is pretty, but also because, for this one, two mix types yield very similar calculated inductance values; thus correct classification depends on its color code.

    The underside is white, so it is a yellow-white iron powder toroid. The outside diameter is approximately 17/16 inch. That makes it a T106 something. The test coil had 23 turns—more would have been better, but that was the length of the wire scrap.

    The multi-tester displayed 50 μH (0.05 mH below), once again toward the low-end of the instrument’s measurement range. The corresponding calculated value was 49.197 μH for mix 26 and 50.255 μH for type 52 material. The problem in this case is that there is not much difference in the calculated inductance for the two closest mixes, or between either of them and the measurement. Other computed parameters of the 26 and 52 materials are also similar (e.g. frequency range and AL).

    While measurement of this test toroid yields a difficult-to-interpret or ambiguous result, it is not necessary to guess whether the mix is type 26 or 52, because type 26 is yellow and white, while type 52 is blue and green (as in the first example on this page). Therefore this particular toroid is a T106-26 type.

Measurement and calculation of yellow-white toroid


     Measuring Inductance: The preceding paragraphs allude to my lack of confidence in measurement at the low end of the multi-meter’s inductance range. Part of the problem is that the microhenrys 10’s digit is the right-most of the multi-meter’s display, which reads in mH. Inductance can be measured in ways
other than relying on the inexpensive multi-meter. However, the accuracy of measurement depends on the precision with which other component values of the measurement circuit are known.

    Frequency, capacitance and inductance are the 3 variables in a tank circuit. Frequency can generally be measured quite precisely. Thus the accuracy of an inductance determination that is based on resonant frequency depends on how accurately the LC circuit’s capacitance is known.

    Many common capacitors, such as small ceramic disks, have a precision of 20% or worse. Evidently it is possible to purchase capacitors of 1% precision, but I do not have any. On the other hand, I do have a number of identical Mylar capacitors marked 1 nF at 10%. Testing a few of these with the JYE capacitance meter (also uncalibrated) yielded a range of 997 pF to just over 1 nF in measured values. I selected one that read exactly 1 nF on the meter. Of course, its true capacitance remains unknown. Using this capacitor and the first of the iron powder toroids described above (the one with 40 turns reading 0.14 mH on the multi-meter), I constructed this simple measurement circuit on a small breadboard.

Tank Circuit
Measurement Setup

    Lx refers to the coil whose inductance is to be determined. The subscript ‘x’ indicates that the inductance is unknown, notwithstanding that it was previously measured with the multi-meter. The function generator produces a 1-volt P-P sine wave that can be varied in frequency at the same time as the output of the tank circuit i
s observed on the oscilloscope. In this way the resonant frequency can be quickly and easily determined. It is the frequency at which the output amplitude reaches its maximum value. With a 1 volt signal, the maximum is determined to the nearest KHz only, due to limitations inherent in vertical scaling.

Resonant Frequency Measurement

    The input-output composite illustration above shows the measured resonant frequency of the LC circuit for the T157-52 with 40 turns, where C was taken to be 1 nF. The familiar formula for resonant frequency is shown below. This formula
can be solved for either capacitance or inductance, given frequency and the other tank circuit component value. Thus, an unknown inductance can be computed using the right-hand version of this formula.

Resonant frequency of a tank circuit

Calculator display    Units are Hertz, Farads, and Henrys, so there are several 10-something terms in the calculation. Being careful with the decimal point and using 423 KHz as the resonant frequency (the measured value), and 1 nF (10-9 F) for capacitance (its marked and weakly measured value), yields a calculated inductance of 141.5 μH. This value compares favorably with the multi-tester 0.14 mH result.

    The same measurement procedure and calculation, when applied to the 23-turn T106-26 test inductor, also obtains an inductance value that agrees with the multi-tester result (0.05 mH) to within the tester’s precision. When that test coil is placed in the tank circuit, the frequency of maximum amplitude is 725 KHz. Substituting 725,000 for Fres in the formula for Lx leads to a calculated inductance of 48.2 μH.   

     Anomalous measurement: At this point my luck ran out. A few days after posting the preceding addendum I bought an inexpensive ($40) handheld LC meter (Goupchn), and exercised it by testing the three toroids featured on this page.

Goupchn LC Meter Readings

Measurements were proceeding merrily until I came to the ferrite toroid—the one where the mix was previously deduced to be type ‘F’. Instead of displaying a value in the neighborhood of 10 mH, the Goupchn meter read approximately 1.4 mH. In a flash I realized that I had not double-checked the multi-meter result for this toroid by the resonant frequency method.

F = 130 KHz    There were three possibilities for the anticipated outcome of the resonant frequency test: 1) confirm the original multi-meter result, 2) confirm the Goupchn meter reading, or 3) ‘none of the above’. Using the same 1 nF capacitor (same tank circuit) as before, the resonant frequency was found to be 130 KHz. From this measurement the calculated inductance is 1.5 mH, which confirms (approximately) the Goupchn reading.

    Bafflement leads to strange hypotheses. The next thought was that the coil had changed. A wire had broken or shorted or something. So I plugged the toroid back into the multi-tester and once again that meter displayed approximately 10 mH for the inductance. Nothing had changed in the inductor. The multi-meter was simply wrong.  Thus the classification of the mix as type ‘F’ must surely also be wrong. The problem is that NO choice of mix, among those selectable from the mini Ring Core Calculator drop-down list, yields an inductance that is close to the revised measured value. According to this on-line calculator, just 20 turns are needed to produce 1.5 mH with mix ‘F’ and no mix that has a smaller μ is available.

    What would the relative permeability need to be, in order to produce 1.5 mH inductance in a 50 turn winding on that FT87A? Another on-line calculator computes inductance from toroid dimensions, number of turns, and μr. For the present problem, the dimensions and number of turns are constant. Once these are entered it is possible to play with the relative permeability number while observing the calculated inductance.

Inductance versus relative permeability

    As the clip reproduced above shows, the round number 500 for relative permeability yields the approximate inductance measured (1449 μH ≈ 1.4 to 1.5 mH). For a definition of relative permeability see this page.

    Digression: Measurement often depends on comparing an observed value to an established reference value—a standard or known value. This comparison is implicit when the measuring instrument has been calibrated for a range that includes the observed value. However, when making a measurement, it is not always possible to rely on a calibrated instrument, or for that matter, a precisely known comparison value. This was the context that led me to think about the meaning of component tolerance.

    Tolerance: If a resistor is marked 100 ohms / 10% (brown, black, brown / silver) then, by definition, 99.7% of similarly marked resistors will fall within 90 ohms and 110 ohms, in other words 100 ohms 10% of 100 ohms. In general, percent tolerance means that the 3σ proportion of component values (99.7%) will fall within the stipulated percent of the marked value.

    Similarly, if a capacitor is selected from a batch of 20% capacitors all marked 1 nF, then 3σ or 99.7% of capacitors from that batch will fall between 800 pF and 1.2 nF (i.e., 1 nF 20%). Actual component values are assumed to be normally distributed about the marked (mean) value. This assumption is based on the fact that multiple independent sources of error contribute to variation in component values. Thus, it means the same thing to say that the probability is 0.997 that the actual value of a selected capacitor from that batch will fall between 800 pF and 1.8 nF.

Identical capacitors in series-parallel

Same-valued capacitors in series-parallel     Playing the odds: Suppose that four capacitors are randomly selected from a batch marked 1 nF at 10%, and are connected in series-parallel to make a circuit having the same 1 nF capacitance, as illustrated above. What would be the appropriate tolerance designation for the 4-capacitor circuit? If the individual capacitors are all 1 nF then the circuit capacitance is also 1 nF, but the σ value for a hypothetical batch of 4-capacitor circuits will be the standard error of the mean, denoted σm. To compute this statistic, divide σ by √N. In this case N is 4 and √4 is 2 so σm = σ/2. As previously noted, tolerance corresponds to 3σ (i.e., tolerance is proportional to σ), which means that the tolerance of the 4-capacitor circuit is the constituent capacitor tolerance divided by 2, which in the example would be 5%. It is possible to iterate the idea, so that 16 capacitors similarly configured would make a circuit with 2.5% tolerance, and so forth, but that would be silly—better to spend a dollar for a 1% capacitor.

Function Generator Output   Measurement torture: While mildly interesting as a path to improving the precision of a measurement, the preceding was of no use in figuring out the unyielding FT87A mix problem. Frequency measurements were the same to 2 or 3 significant digits, whether a single-capacitor was used for the tank circuit, or four. While in the midst of this perseverative exercise, I recalled another method of determining inductance, the half-voltage frequency method, for which I had made a convenience calculator. This recollection caused me to think about one of the assumptions of the method, namely that the function generator’s output impedance is 50 ohms. The Siglent generator that I was using has the requisite output impedance (photo left), but I wasn't sure of the attached cable, which had been changed from the manufacturer-supplied cable at some point in the past, so I replaced the output cable with a known 50-ohm impedance lead.

   Fresh start: In one sense starting over is just another kind of perseveration, but I was curious if the FT87A might have an inconspicuous marking on it, maybe in the middle somewhere (obscured by the coil). Also the 50-turn test coil was poorly wound, loose, unevenly spaced. I should make a better test coil. The most disturbing part of the classification problem was not the failure of identifying the mix, but rather the inconsistent results of measurements. Different methods of measuring the same thing, whether the thing being measured is length or weight or inductance, should yield the same approximate answer.     

Bare ferrite toroid 20 turns of plastic insulated wire    Stripped of its first test coil, the ferrite toroid had no hidden inscription on either outside or inside, and was just one shade of grey! The chance of its having an identifying mark was a long shot, of course. For the next suite of tests with this toroid I wound 20 turns of plastic insulated wire, somewhat more neatly than the enamel-insulated wire coil had been wound. The plan was to measure the new coil’s inductance in four different ways, while recording details at each step. Snapping a cellphone photo at each step is one way to temper haste.

    The four measurement procedures can be summarized as 1) Goupchn L/C meter direct measurement, 2) Multi-meter measurement, 3) Tank circuit resonant frequency determination, and 4) Half-voltage frequency measurement. The following is a picture story.

Four Measurements of Inductance

Measurement 1 - L/C Meter

Multi-meter Inductance

Inductance by Resonant Frequency

Half-voltage Frequency Method

    Clearly, this replication produced more consistent results than studies with the 50-turn coil did. Three of the 4 measurements were quite close and the multi-meter result was not extremely far off. To summarize, the four independently derived inductance measures were 243 μH (L/C meter), 380 μH (multi-meter), 258 μH (resonant frequency) and 231μH (half-voltage frequency). Changing the function generator cable had negligible effect. Neither resonant frequency nor half-voltage frequency changed for this inductor when the lead was replaced. In general I exercised greater care with this second series of measurements, but cannot point to a specific difference, other than the test coil itself. Discarding the multi-meter outlier, the average of the 3 similar readings is 244 μH. I am inclined to accept this number as the approximate true inductance, which leaves identification of the FT87A mix unresolved. That’s the best I can do for now.

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