📑 Electric Transformers ​

1.How Transformers are Constructed

The scientists Joseph Henry and Michael Faraday, each independently, discovered that a continuous change in the current of one inductor (coil) inevitably leads to the induction and generation of an electric current in a neighboring inductor. The credit for the discovery of this physical phenomenon, known as "mutual induction," is attributed to the scientist Michael Faraday.

Modern transformers are made by winding two independent coils of copper wire; either side by side or one on top of the other, on a common magnetic core made of either soft iron or ferrite. The soft iron concentrates the magnetic flux lines and confines them within the structure of the transformer, preventing their dispersion and significantly increasing the overall operational efficiency of the system.​

🔄How Transformers Work

When an electric current flows through an inductor (the primary coil), a magnetic field is created around the coil. If we place a second inductor (the secondary coil) within this magnetic field, we will encounter two cases depending on the type of current:

• In the case of direct current (DC): the magnetic field is constant and stationary (no relative motion and no change in the lines), and therefore nothing will happen at all, and no voltage will be transferred to the secondary coil.
• In the case of alternating current (AC): the current changes continuously, causing the magnetic field to expand and contract periodically. As the current rises, the magnetic field expands beyond the turns of the secondary coil to induce a current in a specific direction. When the current decreases and reverses, the magnetic field contracts beyond the turns in the opposite direction to induce another alternating current in the secondary coil.

Despite the absence of any direct mechanical or electrical connection between the two coils, the alternating current in the primary coil succeeded in transferring energy and inducing an equivalent alternating current in the secondary coil through the medium of the changing magnetic field.

🧮 Turns Ratio Law

The output voltage of the transformer is primarily determined by the turns ratio between the two coils.

For example, if the first coil (primary) consists of 1,000 turns, and the second coil (secondary) consists of 100 turns, the induced voltage in the secondary coil will necessarily be $1/10$ of the primary coil's voltage. If the primary voltage is 120 volts, the secondary voltage will be 12 volts. The relationship is mathematically expressed as follows:

$$\frac{V_p}{V_s} = \frac{N_p}{N_s}$$

Whereas:

• $V_p$ and $V_s$: The voltage of the primary and secondary coils, respectively.
• $N_p$ and $N_s$: the number of turns of the primary and secondary coils, respectively.

⚡ Voltage and current exchange and the volt-ampere (VA) rule

The transformer that produces a secondary voltage lower than the primary voltage is called a "step-down transformer." This drop in voltage does not imply a loss or waste of energy; as the voltage decreases, the current increases proportionally and by the same ratio (law of conservation of energy):

• Example calculation: If we have a transformer with a turns ratio of $10:1$, and the secondary voltage is 12 volts connected to a load with a resistance of 100 ohms, then the secondary current will register 120 milliamps ($12\text{ V} / 100\ \Omega$). In contrast, due to the turns ratio, the primary winding will only draw 12 milliamps from the power supply.

If you increase the voltage, the current decreases, and if you decrease the voltage, the current increases.

$$\frac{V_p}{V_s} = \frac{I_s}{I_p} = \frac{N_p}{N_s}$$

Note that the load consumes a real power of 1.44 watts ($12\text{ V} \times 0.12\text{ A}$). The product of voltage and current in the primary also equals 1.44. However, it is scientifically and practically incorrect to use the unit "watts" to express power within the transformer windings themselves; because the transformer does not produce or consume real power (except for minor losses). Therefore, we technically use the unit "volt-ampere" (Volt-Ampere - VA) to describe the apparent power of transformers; watts are reserved only for the actual consumed loads ($P = I^2 R$).

🔁 Current Feedback

The effect of voltage transfers from the primary to the secondary based on the turns ratio, but the effect of current is reversed to flow from the secondary to the primary; the primary current is fully determined by the amount of current drawn by the load in the secondary:

1. In the previous example (the load is 100 ohms), the secondary current was $120\text{ mA}$ and the primary current was $12\text{ mA}$.
2. If we change the load to 200 ohms, the secondary current will drop to $60\text{ mA}$, which forces the primary current to immediately drop to $6\text{ mA}$ (maintaining a ratio of $10:1$).
3. If we completely disconnect the load (open circuit in the secondary), the secondary current becomes zero, and as a result, the primary current collapses to nearly zero (except for a very slight magnetizing current).

How does this complex process occur?

The inductor inherently resists changes in current; and since AC is constantly changing, the high self-inductance of the primary coil prevents and restrains the flow of current through it like a barrier as long as the secondary is open.

However, as soon as the secondary circuit is closed and a load is connected, the secondary current begins to flow; the passage of this current through the secondary windings generates a reverse magnetic field that has a polarity completely opposite to that of the original magnetic field of the primary. The secondary field cancels and weakens part of the magnetic field of the primary, which directly leads to a reduction in the self-inductance resistance of the primary coil, allowing the primary coil to draw a higher current from the power source that precisely matches what the secondary requested. In professional transformers, the primary current in the no-load condition is nearly zero.

🗂️ 2. Types of Electrical Transformers

A. Step-up and Step-down Transformers

In a step-up transformer, the secondary voltage is higher than the primary voltage, while in a step-down transformer, the secondary voltage is lower. These transformers are characterized by their ability to be reversed; for example, if you take the aforementioned step-down transformer ($10:1$) and apply 12 volts AC to its secondary winding, you will get 120 volts AC at the terminals of its primary winding. (However, transformers are designed and made ideal in factories to perform a specific function with maximum efficiency).

B. Isolation Transformers

Isolation transformers have a transformation ratio of $1:1$; that is, the secondary voltage exactly matches the primary voltage, and they are used for vital purposes:

• Blocking DC: If you have a signal that oscillates periodically between 10 volts and 20 volts (a varying signal that does not reverse its direction), it is essentially a composite signal consisting of 15 volts of direct current (DC) mixed with 10 volts peak-to-peak of alternating current (AC). When this signal is passed through an isolation transformer, only the variation will pass (the magnetic field breathes up and down through the secondary windings), and the signal will exit the secondary oscillating purely between $-5$ and $+5$ volts (oscillation of 10 volts $V_{pp}$), while the 15 volts of direct current is completely blocked and held in the primary.
• System and user protection: It is used to isolate sensitive equipment from the traps of the public electricity network and to limit short-circuit currents. Imagine a small isolation transformer connected to a 120-volt outlet and designed with an internal output resistance of 100 ohms. If we create a dead short directly at the wall outlet, a terrifying current of up to 20 amps will surge, causing sparks, smoke, and tripping the protective breakers; however, if we create the same short at the output of this isolation transformer, the current will not exceed 1.2 amps only ($120\text{ V} / 100\ \Omega$), thus protecting the control board and preventing the destruction of the building's power supply network.

🚨 Professional Maintenance Alert: Do not confuse the isolation transformer with the Variac® (variable transformer); the Variac is an autotransformer that consists of only one winding and does not provide any protective isolation from the public electricity network!

c. Impedance-matching transformers

It is used in advanced electronic circuits and amplifiers to match the impedance between two different stages; this ensures maximum possible power transfer without signal reflection.

D-Tapped Transformers

They are transformers that contain additional connection and tap points located at various places along the winding:

• Center-Tapped: It divides the secondary winding into two equal halves to provide two identical voltages, each equal to half of the total voltage (and is widely used in full-wave rectifier circuits with two diodes).
• Primary windings: They are designed to cope with fluctuations in power network standards; the 120-volt voltage can practically range between 114 and 126 volts depending on local distribution efficiency, allowing us to select the appropriate winding to match the actual voltage.

E. Multiple Winding Transformers

These transformers contain two completely separate primary or secondary windings or more; they are commonly used to make electronic equipment universally compatible with different power standards (the American standard of 120 volts and the European/Moroccan standard of 240 volts):

• For operation on the European system (240V): the two primary coils are connected in series; thus, the high voltage is evenly distributed between them (120 volts per coil).
• For operation on the American system (120V): The two primary windings are connected in parallel; so that both windings are exposed to the same low source voltage and ensure the full capacity of the transformer.

🚨 Critical security warning during connection (Polarity Lock): When connecting multiple coils, it is essential to consider polarity and direction (Polarity) based on the written markings (such as $+$ and $-$ signs, or angular readings of 0 and 120, or wire color codes).

• When connecting in parallel: the positive must be connected to the positive and the negative to the negative.
• When connecting in series: the positive of the first coil must be connected to the negative of the second coil. If you make a mistake and connect the coils in reverse, the resulting magnetic fields will completely consume and cancel each other out, and the transformer will not output any voltage; instead, it will draw a massive thermal current that will cause the transformer coils to char and burn immediately.​

F. The self-converter

It is an economical transformer consisting exclusively of a single shared wire coil; where the primary coil and the secondary coil form separate parts of the same coil through mechanical branches.

• The Variac® device is considered a commercial model of a variable output autotransformer, and the ignition coil in cars (Ignition Coil / bobbin) is a direct application of self-wound transformers. (It is characterized by its small size and low cost, but it is flawed by the lack of electrical insulation between the input and output).

G. Tesla Coil

It is a very special and advanced type of self-transformer with an open structure, driven and powered by a high-frequency resonant oscillator. Tesla coils can generate high voltages and extremely high currents, creating arcs and electrical discharges in the air.

📉 3. Analysis of Losses and Wastage in Transformers (Transformer Efficiency)​

Although transformers are among the most efficient electrical machines (approaching 95–98%), they still suffer from two types of thermal losses:

A.Core Losses

It is the energy consumed and lost within the iron core metal itself, resulting from two phenomena:

1. Magnetic Hysteresis Phenomenon (Hysteresis): It is the internal molecular resistance of the metal when attempting to reverse its magnetic polarity. With each oscillation of the AC current, the fine magnetic particles of the core are forced to flip and rotate by an angle of 180 ∘ , producing molecular friction that dissipates as heat within the iron
   
   2..Eddy Currents Phenomenon: Since the core is made of soft iron, and iron is a good conductor placed within a varying magnetic field, closed circular currents are generated inside the iron metal. These currents serve no purpose other than producing excessive heat. To reduce them, transformer cores are manufactured in factories as thin laminated plates, each insulated from the other with a layer of varnish/enamel. This interrupts the path of the eddy currents and suppresses them.
2. التيارات الدوامية (Eddy Currents): بما أن القلب مصنوع من الحديد المطاوع، والحديد موصل جيد للكهرباء ومتموضع داخل مجال مغناطيسي متغير، تتولد داخل معدن الحديد تيارات كهربائية دائرية مغلقة لا فائدة منها سوى توليد حرارة عالية. للحد من هذه التيارات، تُصنع قلوب المحولات في المصانع على هيئة صفائح رقيقة معزولة عن بعضها البعض بطبقة من الطلاء/المينا (Laminated plates)؛ مما يقطع مسار هذه التيارات الدوامية ويخنقها.

B. Copper Losses

They result directly from the pure ohmic resistance ( 𝑅 ) of the copper wires forming the windings, according to the thermal loss law ( 𝐼² 𝑅 ).

To reduce copper losses and ensure the transmission of high currents, factories must increase the diameter and thickness of the copper wire. With the increase in wire thickness, the designer is mechanically compelled to enlarge and reinforce the iron core to accommodate the bulky windings.

To reduce copper losses and ensure the transmission of high currents, factories must increase the diameter and thickness of the copper wire. With the increase in wire thickness, the designer is mechanically compelled to enlarge and reinforce the iron core to accommodate the bulky windings.

📋 4. Commercial and Technical Specifications of Transformers (Specifications)

In academic theory, we always focus on the “turns ratio” for calculations. However, in the market, when you want to purchase a replacement transformer, the turns ratio is never mentioned in the specifications list. Instead, the transformer is defined by its input voltage, output voltage, and maximum apparent power (or secondary current).

Here are two completely equivalent ways to write the specifications of the same transformer in the market:

What is the difference between the two formats?

There is actually no difference; the VA is simply the product of the secondary voltage and the maximum secondary current. Example:12  V × 2  A = 24  VA

• ⚡ Tip for checking and calculating the primary current: If you need to know the maximum current that the primary winding will draw from the public power grid (to determine the appropriate fuse rating for protection), divide the transformer’s total VA by the primary voltage: 
   𝐼 𝑝 𝑟 𝑖 𝑚 𝑎 𝑟 𝑦 = 𝑆 /𝑉 𝑝 𝑟 𝑖 𝑚 𝑎 𝑟 𝑦
  ​$$I_{primary} = \frac{\text{Maximum Load } (VA)}{V_{primary}} = \frac{24\text{ VA}}{117\text{ V}} \approx 205\text{ mA}$$
  ⚠️ Warning: During your measurements and testing, be very careful not to mix up the voltage and current values between the primary and secondary sides; this could destroy measuring instruments or put you at risk.