© Brooke Clarke 2011

High Q
Energy Storage
88 mH Telephohne Loading Coil


Inductors (Wiki) are one of the basic electronic passive components along with capacitors and resistors.  A capacitor stores energy in a electric field and an inductor stores energy in a magnetic field.  The capacity of a capacitor can be incrased by using a dielectric material between its plates and an inductor can have its inductance increased by using a magnetic material as its core.


When telegraphy was getting started resistors were made by winding a specified length of wire on a bobbin.  When Tesla was working in Colorado Springs it was common to specify the inductance of a coil in meters, and the same unit was used for capacitors.  Inductors were commonly used in tube type electronic equipment and there were a large number of them available as component parts.  But they typically weigh more, take up more volume and cost more than capacitors or resistors. 

It's very difficult to include an inductor in a semiconductor type integrated circuit (IC).  Prior to ICs to make a low pass filter you would use series inductors and shunt capacitors, but now it can be done with an op amp and just resistors and capacitors.  In fact all the common filter types can be realized without using any inductors.  With the advent of Switching Mode Power Supplies (SMPS) inductors are much more popular.  These require the ability to handle the currents involved in a specific design and be small and low cost.  The efficiency of the SMPS depends in a large measure on how low a resistance the inductor exhibits and in fact the specifications for the IC depend on the quality of the inductor used. so it's common that the evaluation boards for a SMPS will use an exotic inductor.

Joseph Henry (Wiki) was the first person to make a close wound electromagnet.  He uses "Bell Wire" which was uninsulated wire that was used to mechanically ring bells, like to call a servant.  He used his wife's spinning wheel to wrap silk around the wire to form insulation.  Prior to this all the work done with electromagnetism was done with bare wire would with a large air gap between turns, or a single turn.  This led to the Telegraph and Stock Tickers which in turn led to Teletype machines that use a binary code for the characters.  My first computer used a Teletype model 33 Automatic Send Receive (ASR) for keyboard input, printing, paper tape punching and paper tape input.


Faraday's law of induction (Wiki) - The induced electromotive force (EMF) in any closed circuit is equal to the time rate of change of the magnetic flux through the circuit.
Ampère's circuital law (Wiki) - relates the integrated magnetic field around a closed loop to the electric current passing through the loop
Lenz's law (Wiki) - An induced current is always in such a direction as to oppose the motion or change causing it

High Q

To get a high Q in operation the load capacitance needs to be much higher than the self capacitance of the coil.  That's so say the coil need to be operated at a frequency that's much lower than it's self resonate frequency.  To lower the self capacity of a coil you need to pay attention to both the turn to turn capacitance AND to the voltage between those turns.  For example:

1.  In a single layer cylindrical coil with a lead at each end and let's tight would. Then you can approximate the capacitance between each turn by assuming the turns are insulated rings.  BUT, you also need to look at the voltage between the turns.  In this case the voltage between adjacent turns is Vtotal/N where N is the number of turns.

2.  In a double layer tight wound coil where the input and output wires are adjacent to each other you can use the same ring approximation for the capacitance between adjacent turns.  But now there's a huge problem because of the voltage between turn 1 and turn N.  Between these two turns the voltage is Vtotal.  That's N times higher than in the case above.  This is why using bank winding (see the Loop antenna page) is used as well as breaking the coil into sections is used to minimize the voltage between turns.

See my Q Meters web page for more.


The best reference book is Tesla's The Colorado Springs Notebook (ISBN-13: 978-9562914628).  In the early part he did not have high Q operation and showed photos of each complete setup.  Later, after adding a metal pipe vertical antenna with capacitive top loading so that the secondary coil was operating with a load capacitance much higher than it's self capacitance, he only photographed parts of the setup to keep some secrets.  He mistakenly thought he had power multiplication, rather than just the voltage multiplication that comes with high Q operation.

Note: the demonstration "Tesla Coils" that are sold for school demonstrations are not really high Q coils but rather are just RF transformers.  Their output voltage is just the input voltage stepped up by N^2.  In a true Tesla coil there would be a capacitor in parallel with the secondary and the output voltage would be Q * N^2.  Note it takes measuring the spark length between a couple of large metal spheres or a high voltage probe (these are over $1,500 used on eBay) to measure the voltage, not the gap between points.


The basic unit of inductance is the Henry (Wiki) named for Joseph Henry (Wiki) who in 1828 made the first practical electromagnet (see my electronic time line page).

Any coil of wire will have some resistance and an ideal inductor would have zero resistance.

There is also capacitance between the turns of an inductor and as the frequency is swept the impedance (Wiki, my Impedance page) of the inductor goes through at least one resonance.  At a fixed frequency the ratio of the inductive reactance (Wiki) to the resistance is called the Quality or Q (Wiki) of the inductor.  When used to form a resonant circuit with an external capacitor the Q of the circuit is inversely proportional to the bandwidth of the circuit.


There are a number of ways of measuring inductance.  One way of characterizing the different methods is to look at the measurement error as a function of frequency.  This is covered in The Impedance Measurement Handbook by Agilent.  The most accurate method makes use of the 4-terminal pair connection method as used by such instruments as the HP 4274 and HP 4275 LCR Meters.

For measuring the Q specialized equipment is more accurate than using general purpose equipment.  The Boonton 160 Q meter was an early instrument that uses a 4-pin vacuum tube.  There was a motorized accessory for the HP 4284A that allowed it to measure Q.

2137787 Method and Apparatus for Electrical Measurements, H.A. Snow (Boonton Radio Corp), Nov 22, 1938, 324/654; 324/653; 338/61 - 160 Q-Meter
Class Numbers:
324 Electricity: Measuring and Testing
    653 Impedance, Admittance or other Quantities Representative of Electrical Stimulus/Response Relationship
            Lumped type parameters
                For figure of merit or Q value
    654 Impedance, Admittance or other Quantities Representative of Electrical Stimulus/Response Relationship
            Lumped type parameters
                Using inductive type measurement
338 Electrical Resistors
    61 with Inductance-Reducing

The HP 4395A can measure the impedance of a series connected component over the frequency range of 10 Hz to 500 MHz with a Resolution Band Width (RBW) as narrow as 1 Hz.

Rather than looking at the inductance and resistance at a single frequency a better method is to make a swept measurement and fit a model to the data.  This was you capture not just a 2-element model, but a more complex model.  This is the professional way to measure crystals.


June 2013 - as part of my work on the Joule Thief circuit I'm looking into ways to identify toroid cores that are unknown manufacturer and material.

Note the Tnn size designation is based on the OD in inches.
A T100 core would have an OD of approximately 1 inch,  a T 50, half inch, etc.

The first step was to make a spreadsheet listing the sizes down the left side and the materials along to top with AL values in the main body.
Note ferrite toroids are commonly named FTnn, but I've dropped the F and list them with all the other toroids.
A blank cell or "na" in a cell means no part with that material and size was found on the first try.
There were a number of sizes where there was a suffix letter like T50, T50A, T50B, T50C & T50D.
If a high letter suffix was found but no lower letters they were listed anyway.
In the case of T200A and T200B they seem to be the same?
It takes 6 letter size pages to print, so here's a photo of the AL chart.

It seems that the first step in figuring out what material you have is to measure the physical OD, ID and Height of the core.
This will eliminate the vast majority of the possible cores.
Now measuring the AL value should narrow down the possible cores.
Toroid Sizes,
              Materials and AL values

Example No. 1:
Marking: 8620  55305-A2
Color: Gray
OD: 0.909
ID: 0.5395
Ht: 0.304
The T90 is: OD 0.900, ID: 0.55, Ht: 0.3 and the T90E is OD: 0.90, ID: 0.55, Ht: 0.3
Don't have dimensions for the T90A, T90B, T90C or T90D so not sure what size this is.

Example No. 2:
Color: body: light green, one face: Blue
OD: 1.306
ID:  0.632
Ht: 0.451
The ID is slightly smaller than the T130 listed & the Ht is a little bigger.

Example No. 3
Marking: 482S  77934-A7
Color: shiny black
OD: 1.066
ID: 0.573
Ht: 0.456
This is very close to the T106 and so might be material: 60, 63, 66, 70, M125, 26, 52, 1, 2, 3, 6, 7, 12, 15, 17, 0
An AL measurement would narrow that down.  It's also not a ferrite, but rather powdered iron.

Example No. 4
Color: light green body, one face blue (same as Ex No. 2 above)
OD: 2.012
ID: 1.24
Ht: 1.008
This is a T200A (same as T200B) so the material might be: 26, 52, 2, 60, 66 all powdered iron

Example No. 5
Color: light green/blue one face yellow
OD: 3.047
ID: 1.925
Ht: 1.005
This is a T300D and the material might be: 60, 63, 66 oin powdered iron

Example No. 6
Marking: -MB4- 55321-04
Color: light brown
ID: 0.869
Ht: 0.415

Example No. 7
Marking: 563S  77548-A7
Color: shiny black
OD: 1.3" (broken so a guess)
ID: 0.82 (broken so a guess)
Ht: 0.427
By comparing this one with Ex. No. 3 the marking might be decoded?

A toroid is shaped like a doughnut.  Since it has a closed magnetic path there is little magnetic leakage if the turns are a single layer wound close to the core.
Different materials behave differently with frequency and power.
These toroids were ordered for experimenting with the Joule Thief LED circuit.  These are Fair-Rite RFI suppression cores. 
  Distributorsthat carry toroids: Amidon and Mouser also see my Disty web page.
O.D. in.
I.D. in.
Len in.
2643002402 43
0.380 0.197 0.190

Fair-Rite Toroid Cores

Toroid Equations

There are different ways a toroid can be wound.
One way it to get as many turns as possible.  For these applications the "Fill Factor" becomes important.
What you're looking at is how many square mills of wire area can you fit into the hole area.  If the wire diameter was very small the fill factor will be near maximum but as the wire size increases the fill factor gets smaller.

Another way is to wind a single layer coil.  Again smaller wire sizes allows more turns than larger wire sizes, but smaller wires have more loss.

Length of a Turn

For a single turn of a single layer wound toroid:
Lturn = 2*(OD-ID) + 2*Len
Example for the first two rows of the table above, Lturn = (0.38 - 0.197) + 2 * 0.19 = 0.563
Then 10 turns would take 5.63" of wire plus a couple of 4" leads is about 10" of wire.


Each toroid has an AL value that allows the number of turns needed for a given inductance to be estimated.
N = SQRT(L/AL)   
AL = L / (N*N)
Examples with 10 turns, AL = L(10 turns) / 100
First row AL = 50uH /100 = 0.5 uH
Second row AL = 170uH / 100 = 1.7 uH


For inductors that have magnetic cores (typically without an air gap) there is a maximum limit to the amount of magnetic flux that can flow.  At some point the core saturates and no longer has magnetic properties, i.e. it's as if the core was removed and replaced by air.  At very low flux the permeability appears to be a constant value, but as the flux approaches the saturation value the permeability starts to decrease (approaches 1).

Energy Storage

The energy stored in an inductor is given by E = ½ * L * I2
But the current (I) is limited by saturation of the core material.  A way around that limitation is to insert a narrow air gap into the core.  When measuring the core current in the Joule Thief another core that was the same as the working core was used as the current transformer and the drive current was limited by the source impedance of the HP 33120 Function Generator.  A more flexible method would be to use a FET and bench power supply so that the source current would be near zero and the voltage could be higher allowing for higher currents.

The energy is stored in the non magnetic parts of the core structure, either in an air gap or in the non magnetic binder that holds the material together.

For a transformer where you want low core losses it's good to have a lot of magnetic material and not much air.  Electrical steel (Wiki) is used in thin sheets to minimize Eddy current (Wiki) losses.  This was a big improvement from solid iron bar cores, but is similar to the fine wire bundle cores.

88 mH Telephone Loading Coil (Wiki)

Oliver Heaviside (Wiki) knew that if R/G = L/C there will be minimal distortion in a transmission line.  But most phone and telegraph lines were operated such that R/G >> L/C.  In 1893 he proposed adding discrete inductors at periodic intervals along the line.  He was working for AT&T at the time and they started a patent application, but Putin beat them to it with less understanding of what was going on.

Trivia:  It's not unknown for the inventor to not understand how his device really works.  An example is the Griffin Grinding Mill (see my Gyroscope web page.)

Came in two different colored wire (red and green).  A single winding has a DC resistance of 4 Ohms. 

In the telephone application these were used to "load the line".  There are two key ideas: 1) If the signal could be transformed to a higher impedance the line resistance would cause lower loss.  This is the method used to deliver AC mains power by means of transformers.  Transformers are not a viable option in telephone circuits, but the line impedance can be raised using series inductors.  There is a decrease in line loss of about 1.4 dB per mile (1.6 dB/mi to 0.2 dB/mi.   It's best if a 500 or 2500 telephone is used that compensates for the distance between the phone and the central office.   Older phones will not work as well.  2) A low pass filter can be formed where the inductance is that of the line plus the added loading inductor and the capactance is that of the line.  For 88 mH coils the typical distance between coils is 6,000 feet.  At the start and end of the line the distance is 3000 feet.  Testing should be done within that range and is typically done at 1 kHz for audio signals.  The first test at 10 kHz was too high.

Also see my web page on line impedance when operating below the critical frequency.  Details on the use of loading coils can be found in BC Burden's 1948 Handbook for Telephone Managers and Engineers.

Note:  Loadins should only be done between the central office and a single phone.  If a party line phone is connected somewhere in the middle of the line the loading will not work properly and the loss may (probably will) increase.  A party line could be implemented by having home run circuits from the CO to each subscriber and bridging them in the CO using bridge lifters (Saturable inductors that present a high impedance at voice frequencies to the line(s) that are not in use to prevent them from imposing a shunt capacitance across the line circuit, which would degrade transmission on the pair that is in use. The DC current through the inductor connected into the active line saturates it, causing its impedance to drop to a negligible value.)

Telephone Line
            Loading Coil Schematic from Wiki

Wiki: Primary line constants: Loaded Line

Some vacuum tube power supplys included a "swinging choke" whose inductance changed with the current flowing, i.e. very similar to the telephone saturable inductor.

As received the same color coils were connected together by adhesive tape.  Some care was used when seperating each coil
88 mH
                    Telephohne Loading Coils
There are four leads since this is a dual coil, or transformer. Just as the schematic symbol has one of the wires for each winding marked with a dot this has one wire marked with yellow sleeving.

When testing a winding (one yellow & one non yellow found by experiment) it measures about 22 mH and a Q of about 150

But when connected as shown (in series) the inductance is 87 mH with a Q of about 200.  Note doubling the number of turns should multiply the inductance by 4 since inductance in proportional to (# turns)^2.
88 mH Telephohne
                    Loading Coil (Red)

It's my understanding that when used in phone service the individual coils would be connected in series with the tip and ring wire pair.  Some type of test would need to be done (you can tell from the mechanical layout of the coil) to be sure tip went to tip, i.e. that the wires were not reversed.  They are connected so the yellow sleeve points the same way for the DC current, i.e. one pointing to the CO and one pointing to the subscriber.

519346 Apparatus for Telegraphic or Telephonic Transmission, M.I. Pupin, May 8 1894, 381/98; 307/102; 379/41 -
652231 Art of Reducing Attenuation of Electrical Waves, M.I. Pupin, June 19 1900, 178/45 - - has info on various model numbers and sizes.
Also see my Telephone Poles web page.



SR 715 LCR
HP 427x LCR
88 mH (connected) Telephone Loading Coil (Red)
88 mH
                    Telephohne Loading Coil (Red)
4 + 4
87 mH
200 (10 kHz)
65 (1 kHz)

88 mH (connected) Telephone Loading Coil (Green)
88 mH Telephohne
                    Loading Coil (Green)

4 + 4
6.3 (10 kHz)
65 (1 kHz)

Note 1: the Fly Back (Ring Tester) LEDs are codes as 1R, 2R, 3R, 4R, 1G, 2G, 3G, 4G with 1Red being the poorest result and 4G being the best result.


HP 4260A Universal Bridge
HP 4274A & HP 4275A LCR Meters
HP 4332 LCR Meter
HP 4395A in Impedance Analyzer mode
Marconi TF-2700 Universal Bridge
Stanford Research 715 LCR Meter
ZM-11 Impedance Bridge
Crystal Radios
Zo of a transmission line


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