One of the first subjects taught in engineering and physics classes is the basic operating principle of transformers. In these classes, the "ideal transformer" assumption is generally used to simplify things and teach the underlying mathematics. When you put the formulas on paper and calculate the turns ratio, everything works smoothly and perfectly. The input power is exactly equal to the output power, there is no voltage drop, and energy loss is zero.
However, when you enter a laboratory and wind a physical transformer, or when you measure a commercially bought transformer with a multimeter, you realize that the results do not perfectly match the theoretical (ideal) formula on paper. For instance, while your calculations dictate that you should get exactly 24 Volts from the secondary, your multimeter might show 22.8 Volts. So, where did this "lost" voltage go? Did you calculate the turns ratio incorrectly? In this article, we will examine in detail the fundamental differences between ideal and real (practical) transformers and why the turns ratio "deviates" in practical applications.
What is the Ideal Transformer Assumption?
An ideal transformer is a theoretical (imaginary) model created to simplify the laws of physics for educational purposes. This model is built on four main assumptions:
- Zero Resistance (Lossless Windings): The electrical resistance of the wires used in the primary and secondary windings is assumed to be zero. (I²R = 0, meaning there is no heating).
- Lossless Core: It is assumed that no energy loss occurs in the iron core carrying the transformer's magnetic field due to magnetic hysteresis (the reversal of magnetization) or eddy currents.
- Perfect Magnetic Coupling (No Leakage Flux): It is assumed that 100% of the magnetic flux generated by the primary winding is received by the secondary winding without any leakage.
- Infinite Magnetic Permeability: The core is considered to demand no additional energy (magnetizing current) to conduct the magnetic flux.
Under these assumptions, the formula Np / Ns = Vp / Vs works flawlessly.
Inevitable Losses in Practical Transformers
In the real world, no material is perfect. According to the laws of thermodynamics, during any energy conversion, a portion of the energy turns into an "unusable" form, usually heat. The main factors that differentiate a real transformer from its ideal counterpart are:
1. Copper Losses (Winding Resistance)
The coils of transformers are generally wound from copper or aluminum wires. Even though these metals are excellent conductors, they have a certain ohmic (resistance) value within themselves. When current flows through the windings, the wire heats up due to this electrical resistance.
This phenomenon, known in physics as "Joule Heating" (I²R loss), directly causes a "Voltage Drop" in the output voltage as current is drawn from the secondary winding (when it is under load). Therefore, while you expect 24V according to the turns ratio, you might read 23V under load.
2. Iron (Core) Losses
The iron core around which the windings are wrapped also consumes energy. These losses are divided into two:
- Hysteresis Loss: Alternating current (AC) changes the direction of the magnetic field 50-60 times a second (50Hz-60Hz mains). The internal friction that occurs while iron molecules try to keep up with this constant change turns into heat.
- Eddy Current Loss: The alternating magnetic field induces small, circular, and unwanted electrical currents within the conductive iron core itself. These short-circuit currents inside the core heat it up. (To prevent this, transformer cores are made of thin, insulated silicon steel laminations instead of a solid block of iron.)
3. Leakage Flux
In the ideal model, all magnetic lines created by the primary pass through the secondary. But in reality, a portion of the magnetic field "leaks" into the air or space and never reaches the secondary winding. This is called leakage flux. Leakage flux acts as if a series inductance (reactance) has been added to the transformer circuit, causing the output voltage to drop even further, especially when high currents are drawn.
How Influencing Factors Affect the Turns Ratio
When all these losses (copper resistance, iron losses, and leakage reactance) come together, that perfect equality between the turns ratio and the voltage ratio is broken.
Mathematically, our formula (a = Np / Ns = Vp / Vs) is quite close to reality for an unloaded transformer (when no device/load is connected to the secondary). However, when a device is connected to the secondary and current begins to be drawn (loaded state), the equation evolves into the following form:
Vs (Real) = Vs (Ideal) - (Internal Resistance Losses + Leakage Reactance Losses)
Manufacturers know in advance that these losses will occur when designing transformers. Because of this, they implement a correction called "Regulation." For example, a manufacturer does not wind a transformer labeled "220V In - 24V Out (At Full Load)" to give exactly 24V (the ideal ratio). Taking the efficiency loss (say 5%) into account, they wind a few "extra" turns on the secondary winding than theoretically necessary. Thus, while the transformer outputs 25-26 Volts when running unloaded, the voltage "drops" to exactly 24 Volts when the maximum current stated on the label is drawn (at full load).
This is exactly why you might see discrepancies with the voltage you measure at no-load when you physically count the windings of a transformer you have and calculate it using the theoretical formula.
Calculation and Verification Tools in Practice
Theoretical knowledge and ideal formulas are always the backbone of the work. It is impossible to calculate practical losses without first establishing this backbone. To determine your fundamental ratios during the design or repair phase, you can use our Transformatör Sarım Oranı Hesaplama tool.
This tool gives you the "ground zero" target using the Np/Ns = Vp/Vs formula based on the ideal state. Once you obtain this reference point, you can apply the engineering tolerances we discussed above. For example, if our calculator tells you the secondary winding needs to be 100 turns, you can anticipate that you should wind it as 105 turns in practical application (especially in a low-power, low-efficiency transformer) to compensate for the losses.
In conclusion, the turns ratio formula is never wrong, just "incomplete." While the ideal transformer concept allows us to understand the mathematics, comprehending real-world losses, wire resistances, and leakage fluxes is the engineering vision that enables us to transform theory into working, physical, safe devices.
