E6D10 (A) |

What is a primary advantage of using a toroidal core instead of a solenoidal core in an inductor? |

A. Toroidal cores confine most of the magnetic field within the core material |

B. Toroidal cores make it easier to couple the magnetic energy into other components |

C. Toroidal cores exhibit greater hysteresis |

D. Toroidal cores have lower Q characteristics |

**E6D - Toroidal and solenoidal Inductors: permeability, core material, selecting, winding; transformers; piezoelectric devices**

Solenoidal and toroidal inductors are both used in amateur radio equipment. A solenoidal inductor is a coil of wire wound around a cylindrical core, while a toroidal inductor is a coil of wire wound around a

circular or toroidal core. Solenoidal inductors often have just an air core, while toroidal inductors are wound around a ferrite or powdered-iron core.

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) 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)

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 **. (E6D05) **Ferrite beads **are commonly used as VHF and UHF parasitic suppressors at the input and output terminals of transistorized HF amplifiers. (E6D09)

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 × √(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 millihenries/1000 turns. (E6D11)

N = 1000 × √(1/523) = 1000 × .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 × √(L/AL)

Using that equation, **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 microhenries/100 turns. (E6D01)

N = 1000 × √(5/40) = 100 × .353 = 35.3 turns

When designing circuits with ferrite-core inductors, you have to be careful not to saturate the core. The definition of saturation in a ferrite core inductor is that **the ability of the inductor’s core to store magnetic energy has been exceeded**. (E6D12)

One problem that may occur in a circuit with inductors is self-resonance. The primary cause of inductor self-resonance is **inter-turn capacitance**. (E6D13) At some frequency, also called the “selfresonant frequency,” this capacitance forms a parallel resonant circuit with the inductor.

Variable inductors are made by inserting a slug into an air-core inductor. By varying the position of the slug, you vary the inductance. **Ferrite and brass **are materials commonly used as a slug core in a variable inductor. (E6D04) **Brass **is the type of slug material decreases inductance when inserted into a coil. (E6D14)

*Transformers*

A transformer consists of two inductors that are closely coupled. Connecting an AC voltage across one of the inductors, called the primary winding, causes a current to flow in the primary, which then generates a magnetic field. As the lines of this field cross the turns of the secondary winding, it induces a current to flow in the secondary, and the voltage across the secondary is equal to the voltage across the primary winding times the number of turns in the secondary winding divided by the number of turns in the primary winding. The current in the primary winding of a transformer is called the **magnetizing current **if no load is attached to the secondary. (E6D15)

Transformers are often used to match the output impedance of one circuit to the input impedance of another. In this application, it's important not to saturate the core of the transformer. The core saturation of a conventional impedance matching transformer should be avoided because **harmonics and distortion could result**. (E6D17)

In some applications, a transformer's secondary winding may be subjected to voltage spikes. In these applications, the designer may connect a capacitor to absorb the energy in that voltage spike to prevent damage to the transformer. The common name for a capacitor connected across a transformer secondary that is used to absorb transient voltage spikes is **snubber capacitor**. (E6D16)

*Piezoelectric devices*

Piezoelectric crystals are used in several amateur radio applications. They are called piezoelectric crystals because they rely on the piezoelectric effect, which is the **physical deformation of a crystal by the application of a voltage**. (E6D03) The equivalent circuit of a quartz crystal is a **motional capacitance, motional inductance, and loss resistance in series, all in parallel with a shunt capacitor representing electrode and stray capacitance**. (E6D02)

Thanks to KB6NU DAN ROMANCHIK