Extra Class question of the day: Toroids

Toroidal inductors are very popular these days. A primary advantage of using a toroidal core instead of a solenoidal core in an inductor is that toroidal cores confine most of the magnetic field within the core material. (E6D10)

Another reason for their popularity is the frequency range over which you can use them. The usable frequency range of inductors that use toroidal cores, assuming a correct selection of core material for the frequency being used is from less than 20 Hz to approximately 300 MHz. (E6D07) Ferrite beads are commonly used as VHF and UHF parasitic suppressors at the input and output terminals of transistorized HF amplifiers. (E6D09)

An important characteristic of a toroid core is its permeability. Permeability is the core material property that determines the inductance of a toroidal inductor. (E6D06)

One important reason for using powdered-iron toroids rather than ferrite toroids in an inductor is that powdered-iron toroids generally maintain their characteristics at higher currents. (E6D08) One reason for using ferrite toroids rather than powdered-iron toroids in an inductor is that ferrite toroids generally require fewer turns to produce a given inductance value. (E6D16)

To calculate the inductance of a ferrite-core toroid, we need the inductance index of the core material. The formula that we use to calculate the inductance of a ferrite-core toroid inductor is:

L = AL×N2/1,000,000

where L = inductance in microhenries, AL = inductance index in µH per 1000 turns, and N = number of turns

We can solve for N to get the following formula:

N = 1000 x sqrt (L/AL)

Using that equation, we see that 43 turns will be required to produce a 1-mH inductor using a ferrite toroidal core that has an inductance index (A L) value of 523 millihenrys/1000 turns. (E6D11)

N = 1000 x sqrt (1/523) = 1000 x .0437 = 43.7 turns

The formula for calculating the inductance of a powdered-iron core toroid inductor is:

L = AL×N2/10,000

where L = inductance in microhenries, AL = inductance index in µH per 1000 turns, and N = number of turns

We can solve for N to get the following formula:

N = 100 x sqrt (L/AL)

Using that equation, we calculate that 35 turns turns will be required to produce a 5-microhenry inductor using a powdered-iron toroidal core that has an inductance index (A L) value of 40 microhenrys/100 turns. (E6D12)

N = 1000 x sqrt (5/40) = 100 x .353 = 35.3 turns