Inductors

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

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 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.

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. 
Distrubutors that carry toroids: Amidon and Mouser also see my Disty web page.

p/n Mat O.D. in. I.D. in. Len in. 2673002402 73 0.380 0.197 0.190 2643002402 43 0.380 0.197 0.190 2643706001 43 0.140 0.033 0.097 2643000301 43 0.138 0.051 0.236

Toroid Equations

Length of a Turn

Lturn = (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.

A_L

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

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.

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 perodic 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.

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.)



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.

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
Impedance
Zo of a transmission line