Donut-shaped inductors, also known as Toroidal Inductors, have gained importance in modern electrical and electronic systems. Toroidal Inductors' unique geometry and design of Toroidal ductors make them ideal for many applications needing high inductance, low loss, and minimum magnetic field leakage.

Construction of Toroidal Inductors
Toroidal inductors are made up of wire or any other conductive material that is wound around like a donut. This configuration creates a closed loop that is concentric with the axis of the donut. Compared to conventional solenoid inductors, toroids have smaller size and lower magnetic field leakage.

Principles of Operation
Toroidal Inductors work on the fundamental principle of Faraday’s law of electromagnetic induction. When an electric current passes through the wire of a toroidal inductor, Toroidal Inductors generate a magnetic field around the loop. The magnetic field produced by this kind of inductor is concentric with the axis of the donut shape and mostly restricted within itself thus minimizing magnetic field leakage.

Advantages Of Toroidal Inductors
High Inductance: Compactness together with concentricity in its magnetic fields allows toroids to achieve higher values of Toroidal Inductors than those realized using traditional solenoids.
Low Loss: Toroidal Inductors confinement area under magnetism inside limits outwardly directed fluxes hence reducing eddy current losses thereby making these types good performers at high frequencies.
Minimum Magnetic Field Leakage: Toroidal Inductors most part fluxes are contained within itself; interference with other components within system becomes negligible because they will be far away from each other due to compactness inherent characteristic feature possessed by toroidals.
Compact Design: Space saving designs enable Toroidal Inductors fit into tight electronic assemblies hence used widely for this purpose.

Applications Of Toroidal Inductors
Switch-mode power supplies commonly employ toroids as energy storage elements and filters. Audio equipment benefit from Toroidal Inductors use due to reduced sound quality degradation caused through stray magnetic fields emanating from these devices. Medical imaging diagnostic instruments which rely heavily on accurate readings can greatly benefit when shielded against the effects of strong external electromagnetic fields by toroidal inductors. 

To summarize, Toroidal Inductors have various advantages over solenoids such as compact design, high inductance, low loss and minimal magnetic field leakage. Toroidal Inductors has different working principles with unique properties that suits it for many applications demanding precision and efficiency.