What a Transformer Transforms: Voltage, Current, and Impedance Explained

A transformer transforms alternating current (AC) electrical energy from one voltage and current level to another through electromagnetic induction, while conserving overall power and frequency. It is the fundamental component that makes modern power distribution, bench electronics, and industrial motor control possible. By manipulating the ratio of wire turns between two isolated coils, we can step voltage up for efficient transmission or step it down for safe utilization, all without a direct electrical connection between the primary and secondary circuits.

The Core Math: What a Transformer Transforms (and What It Doesn't)

To understand how a transformer transforms energy, you have to look at the turns ratio ($N_p/N_s$), which is the physical ratio of primary winding turns to secondary winding turns. This single physical dimension dictates three electrical transformations:

• Voltage: Transforms directly with the turns ratio ($V_p/V_s = N_p/N_s$). A 10:1 ratio steps 120V down to 12V.
• Current: Transforms inversely with the turns ratio ($I_p/I_s = N_s/N_p$). If voltage drops by a factor of 10, available current increases by a factor of 10.
• Impedance: Transforms by the square of the turns ratio ($Z_p/Z_s = (N_p/N_s)^2$). This is critical in audio and RF design for matching source and load impedances to maximize power transfer.

Think of it like a hydraulic system: a step-down transformer acts like a pressure-reducing valve that trades high water pressure (voltage) for a higher volume of water flow (current) to deliver the same total hydraulic power.

Crucially, a transformer does not transform frequency (60Hz in remains 60Hz out) and it does not create power. In an ideal transformer, $V_p \times I_p = V_s \times I_s$. In the real world, core losses (eddy currents and hysteresis) and copper losses ($I^2R$ heating) mean the secondary delivers about 95% to 98% of the primary power in large units, and perhaps 85% in small PCB-mounted units.

Worked Example: Sizing a Step-Down Control Transformer

Theory is clean, but jobsite reality introduces inrush currents and voltage sag. Let's size a 240V to 24V control transformer for an industrial HVAC panel powering three heavy-duty contactor coils.

Step 1: Calculate Holding VA
At steady state, the secondary load is $24V \times 1.5A = 36 \text{ VA}$. A standard 40VA transformer seems sufficient on paper.

Step 2: Account for Inrush Current
When a contactor coil is first energized, the air gap in the magnetic core is open, causing it to draw roughly 10 times its holding current for the first 50 milliseconds. The inrush current here is $1.5A \times 10 = 15A$. The inrush VA demand is $24V \times 15A = 360 \text{ VA}$.

Step 3: Check Voltage Sag
If we use a 40VA transformer, it cannot supply 360VA without massive internal impedance causing the secondary voltage to collapse. Contactors typically require at least 85% of nominal voltage (20.4V) to pull in reliably. A 40VA transformer will sag well below this threshold, resulting in a chattering contactor and burnt coil. According to Fluke's electrical troubleshooting guidelines, control transformers must be sized to handle inrush VA while maintaining secondary voltage. We must upsized to a 150VA transformer to ensure the voltage stays above 20.4V during the 50ms inrush spike.

Step 4: Calculate Reflected Impedance and Primary Current
Using the 150VA transformer (Turns ratio = 10:1):
Secondary impedance at holding: $Z_s = 24V / 1.5A = 16\Omega$.
Reflected primary impedance: $Z_p = Z_s \times (N_p/N_s)^2 = 16\Omega \times (10)^2 = 1,600\Omega$.
Primary holding current: $I_p = 36 \text{ VA} / 240V = 0.15A$. This means the primary side only needs a 1A fuse, while the secondary side requires a 5A slow-blow fuse to survive the inrush without nuisance tripping.

Where You Meet Transformer Transforms in Practice

You interact with transformer transformations constantly, whether you are wiring a house or debugging a bench circuit.

• Grid Distribution: Power plants use massive step-up transformers to push voltage to 345kV. Because $P = V \times I$, raising the voltage drastically reduces the current, which minimizes $I^2R$ heating losses in the transmission lines. Neighborhood pole transformers then step this down to 120/240V split-phase for residential use. The U.S. Department of Energy notes that these large power transformers operate at efficiencies exceeding 99%, making them some of the most efficient machines ever built.
• Microwave Ovens: The high-voltage transformer inside a microwave steps 120V line voltage up to roughly 2,000V AC. This high voltage is then rectified and fed into the magnetron to generate 2.4GHz microwaves. If this transformer fails, the microwave will run but produce zero heat.
• Audio Amplifiers (Impedance Matching): In vacuum tube amplifiers, the output tubes operate at high voltage and low current (high impedance, e.g., 5,000$\Omega$), but speakers require low voltage and high current (low impedance, e.g., 8$\Omega$). An output transformer transforms the impedance by the square of its turns ratio, allowing maximum power transfer to the speaker without melting the voice coil.
• Current Transformers (CTs): Used in metering, a CT transforms high primary current (e.g., 200A busbar current) down to a safe, measurable 5A or 333mV secondary signal. The primary "winding" is often just the single busbar passing through the toroidal core.

Common Confusions: Transformers vs. Power Supplies and DC

When diagnosing circuits or ordering parts, people frequently mix up what a transformer actually does versus what a complete power system does.

Confusion 1: "A transformer is a power supply."
A transformer only transforms AC voltage. A "power supply" (like a wall wart or bench supply) includes a transformer, but also adds a rectifier (diodes to convert AC to DC), filter capacitors (to smooth the ripple), and a voltage regulator (to hold the DC output steady under varying loads). If you need 12V DC for an Arduino, buying a "12V transformer" will leave you with 12V AC, which will instantly destroy your microcontroller.

Confusion 2: "Watts and VA are the same thing."
Transformers are rated in Volt-Amps (VA), not Watts. Watts measure real power (work done), while VA measures apparent power. Because transformers must supply current to reactive loads (like motors and coils) where current and voltage are out of phase, the windings must be sized for the total current flow (VA), regardless of whether that current is doing real work or just building magnetic fields.

Confusion 3: "Autotransformers provide isolation."
Standard transformers have physically separate primary and secondary windings, providing galvanic isolation (you can touch one secondary wire and not get shocked to ground). Autotransformers (like Variacs) use a single tapped winding. They transform voltage efficiently and cheaply, but they do not provide isolation. The output is still referenced to the primary mains ground.