Transformers and Solenoids, What is it?

This article provides a practical introduction to how transformers and solenoids work, their key equations, parasitic effects, and typical applications for design engineers and advanced students.

What is a transformer

A transformer is a device that transfers electric energy from one alternating-current circuit to one or more other circuits, either increasing (stepping up) or reducing (stepping down) the voltage.

Ideal transformer and basic equations

For simplicity, consider first an ideal transformer with 1:1 turns ratio and an open secondary – see Figure 1.

A transformer consists of at least two windings, with the winding turns N_P on the primary side and N_S on the secondary side.

In a first step, we will look at a transformer with an open secondary winding N_S (Figure 1.).

Lets review transformer operation from an ideal model toward practical design aspects relevant for power‑electronics design engineers.

A U_P voltage pulse is created at winding N_P. Due to the inductance of the winding, this pulse generates a linearly progressive current I_P.

The primary winding has $N_{P}$ turns, the secondary winding $N_{S}$, and the turns ratio is$$a = \frac{N_{P}}{N_{S}}.$$A voltage pulse $u_{P}$ applied to the primary produces a linearly rising magnetizing current $i_{m}$ according to the inductor law$$u_{P}(t) = L_{P} \frac{\mathrm{d} i_{m}(t)}{\mathrm{d} t} \quad [1]$$where $L_{P}$ is the primary inductance.

The winding links a magnetic flux $\Phi(t)$ in the core, and the induced voltage follows Faraday’s law$$u_{P}(t) = N_{P} \frac{\mathrm{d} \Phi(t)}{\mathrm{d} t}, \qquad u_{S}(t) = N_{S} \frac{\mathrm{d} \Phi(t)}{\mathrm{d} t}. \quad$$Dividing these expressions yields the voltage transformation$$\frac{u_{P}}{u_{S}} = \frac{N_{P}}{N_{S}} = a. \quad$$With the secondary open, only magnetizing current flows and delivers no useful power to the load.

Current, power and impedance transformation

When a load resistor $R_{L}$ is connected to the secondary (see Figure 2.), the induced secondary voltage drives a current$$i_{S} = \frac{u_{S}}{R_{L}}. \quad$$In the ideal transformer, the primary current is the sum of the reflected load current and the magnetizing current$$i_{P} = i_{m} + i_{S}^{\ast} \quad$$where $i_{S}^{\ast}$ is the secondary current referred to the primary side.

Neglecting magnetizing current for a first‑order view, input and output powers are equal$$p_{P} = u_{P} i_{P} \approx u_{S} i_{S} = p_{S}.$$Combining this with the voltage ratio gives the current transformation$$\frac{i_{P}}{i_{S}} = \frac{N_{S}}{N_{P}} = \frac{1}{a}.$$Impedances referred from secondary to primary then follow$$Z_{P} = a^{2} Z_{S} = \left( \frac{N_{P}}{N_{S}} \right)^{2} Z_{S}.$$The same square law applies to resistances, inductances, capacitances and general impedances when they are referred across the transformer.

Design implication: Resistances are thus transformed with the transformation ratio squared. This also applies to inductances, capacitances and impedances. So the magnetising current is not transferred to the secondary side. It is required to generate the magnetic field. The aim of the transformer design must therefore be to keep the magnetizing current as small as possible.

Reducing magnetizing current: core and frequency

There are two possibilities here:

From a design perspective, this links core selection and operating frequency directly to copper utilization, core losses, and efficiency targets in modern switch‑mode supplies.

Parasitic effects
In reality, there are other factors that affect the behavior of transformers. The most important ones are:

• Leakage inductance
• Coupling capacitance (capacitance between windings)
• Winding capacitance (capacitance within a winding)

Leakage inductance from winding geometry

In practice, not all flux from one winding couples to the other. The uncoupled portion appears as leakage inductance in series with each winding.

For a long, single‑layer concentric solenoid coil of length $l_{W}$, cross‑sectional area $A$, and $N$ turns, the self‑inductance can be written as$$L \approx \mu_{0} \mu_{r} \frac{N^{2} A}{l_{W}}. \quad$$If a second winding is added on top, the leakage inductance depends on the effective area between the windings. For a long concentric structure the relevant area is$$A_{\text{leak}} = \text{MLT} \cdot H_{\text{ins}} \quad$$

or, more generally, a function of mean length of turn (MLT), insulation thickness $H_{\text{ins}}$, and the winding heights $H_{1}, H_{2}$.

Design implications:

• Leakage inductance is independent of core material and air gap; it is governed mainly by winding geometry.
• To reduce leakage inductance, you must either increase the effective winding length (broad windings) or decrease the distance between windings (e.g. bifilar or sandwich structures).

Coupling and winding capacitances

Two main parasitic capacitances affect high‑frequency behaviour:

• Coupling capacitance between windings can be modeled as a plate capacitor whose plates are the facing copper layers. Increasing the distance or reducing overlap area reduces this capacitance, but both actions tend to increase leakage inductance.
• Winding capacitance within one winding arises from turns at different potentials separated by insulation. It increases with the number of layers and can be reduced using techniques such as Z‑winding (wire returned after each layer) or sectioned windings.

These parasitics strongly influence resonances, common‑mode noise, surge behaviour, and the achievable bandwidth of current or voltage transformers, and should therefore be included in accurate models and simulations.

Practical winding structures

Figure‑type examples often used in practice (concentric, split‑primary, sandwich, etc.) trade off leakage inductance against coupling capacitance for a given geometry. A typical improvement is a sandwich construction, where the secondary is wound between two primary halves, effectively doubling the winding length and improving coupling without shrinking creepage distances below safety requirements.

For design engineers, the recommended workflow is:

• Start from electrical requirements (turns ratio, volt‑seconds, flux density, temperature rise, insulation class).
• Choose core material and size, then iterate winding structure (concentric, split, sandwich, interleaved) to meet leakage, capacitance, and EMI constraints.
• Validate with parasitic‑aware models (e.g. physical transformer model in SPICE) and correlate with measurements.

For deep inside How Transformer Works see also video: How Transformer Works

Solenoids

Derived from two Greek words: Solen (pipe) and Eidos (coil), the solenoid is a type of an electromagnetic device that converts electrical energy into mechanical energy. It is generally made by tightly wounding wires in a helix shape around a piece of metal. Whenever an electric current passes through it, a magnetic field is created.

Working Principle

A solenoid works on electromagnetism and electromagnetic force. It consists of a round cylindrical coil that has several number of wire turns, and a metal rod inside the coil that is free to move. When an electric current is provided to the coil, a magnetic field is generated due to which the metal core or rod inside the coil gets attracted due to towards the direction where the magnetic flux is high. This electromagnetic effect in a solenoid enables any connected plunger or armature to move as per our need. 

To increase the magnetic force produced in a solenoid coil, we will have to increase the number of turns, N and the current, I.

Types Of Solenoid

AC Laminated Solenoid

It has a very high initial attracting force and very short closing time. It is made with a laminated metal or insulated thin sheets that are individually ,assembled.

DC-C Frame Solenoid

As its name states, this solenoid is constructed in such a way that it has a letter ‘C’ like frame cover around the coil. This type is widely used in gaming machines.

DC-D Frame Solenoid

As its name says, this solenoid has a coil that is covered by two ‘D’ frames on two sides. This types is generally used in AC power applications.

Linear Solenoid

This type of solenoid has a freely movable steel or iron rod called plunger inside a round cylindrical shaped coil. The iron rod is allowed to freely move in or out of the cylindrical coil depending on the current applied.

Rotary Solenoid

It is a special type of solenoid where the magnetic force is converted into a rotational force or a rotary motion. It consists of an armature core mounted on a flat disk.
When a current is provided, the armature gets attracted towards the stator and the flat disk rotates.

Applications

Solenoid Valve

The solenoid valve is a simple device in which a solenoid is used for controlling and regulating the flow of fluid. It has a coil with free movable plunger or an iron rod with a spring inside it. When we energise the coil, the plunger moves from its position due to magnetic attraction and when we cut the power to coil, the plunger comes back to its original position with the help of a spring. As soon as the plunger comes in the path of the flowing fluid, its flow stops.

Solenoid Lock

Here we use the movement of solenoid plunger for the locking and unlocking mechanism. These solenoid locks are widely used in electronic and biometric password-based locks. It consists of a strong metal plunger that can move. When the coil gets magnetised due to an electric field, the plunger moves to perform the lock and unlock mechanism.

The leakage inductance is thus independent of core material and air gap. To minimize leakage inductance you must either increase the length of the coil (broad windings) or reduce the distance between the windings (e.g. bifilar wind).

Figure 7. shows various more or less ideal winding constructions. With existing geometry the most commonly used means is a sandwich construction (Figure 7.d), in which the secondary winding is wound between the primary winding that is divided into two halves. This doubles the length of the winding.

Summary

Transformers and solenoids are key inductive components that exploit the same underlying electromagnetic principles but serve different roles in electronic systems. Transformers use magnetic coupling between windings to transfer energy between circuits, setting voltage, current, and impedance levels while their real‑world behavior is strongly influenced by magnetizing current, leakage inductance, and parasitic capacitances.

Solenoids, in contrast, convert electrical energy into controlled linear or rotary motion, with force determined mainly by current, number of turns, and mechanical construction. For design engineers, careful attention to core material, winding geometry, and parasitic effects is essential to optimize efficiency, EMC performance, and reliability in applications ranging from power supplies to actuators and valves.

Frequently Asked Questions about Transformers and Solenoids