How Finland Transmits Electricity Through Air: Wireless Power Theory

When recent tech headlines announce that Finland transmits electricity through air, they are referring to advanced resonant inductive coupling—a method of wireless power transfer (WPT) where energy moves between two magnetically coupled coils tuned to the same resonant frequency without physical contact. In a real circuit, this eliminates galvanic (metal-to-metal) connections, replacing simple wire resistance with complex mutual inductance, coupling coefficients, and reflected impedance. People commonly confuse this near-field magnetic resonance with far-field RF radiation (like microwaves or lasers) or basic non-resonant inductive charging (like cheap electric toothbrush chargers), but resonant WPT specifically relies on high-Q LC tanks to bridge air gaps of several centimeters to meters efficiently.

The Physics of Air-Gapped Power Transfer

To understand how power crosses an air gap, you have to look at mutual inductance ($M$). When alternating current flows through a primary coil, it generates an oscillating magnetic field. If a secondary coil is placed within this field, a voltage is induced. However, in standard non-resonant systems, the coupling coefficient ($k$) drops off cubically with distance, making it useless beyond a few millimeters.

Resonant inductive coupling solves this by adding capacitors to both coils to form LC tank circuits tuned to the exact same frequency. Think of two acoustic tuning forks tuned to 440Hz: if you strike one, the sound waves will cause the other to vibrate sympathetically across the room, while forks tuned to 430Hz remain completely still. In WPT, this magnetic "sympathy" allows power to transfer efficiently even when $k$ is as low as 0.1 to 0.3.

Worked Numeric Example: Calculating Reflected Impedance

Let’s build a 5W WPT system on the bench, similar to the spatial-flexibility setups researched at Aalto University and commercialized by Nordic tech startups. We will operate at 150 kHz, a standard frequency for mid-range WPT.

• Primary Coil ($L_1$): 10 µH
• Secondary Coil ($L_2$): 10 µH
• Operating Frequency ($f$): 150 kHz
• Coupling Coefficient ($k$): 0.2 (typical for a 2 cm air gap)
• Secondary Load ($R_L$): 5 Ω

Step 1: Find Mutual Inductance ($M$)
$M = k \times \sqrt{L_1 \times L_2} = 0.2 \times \sqrt{10\mu H \times 10\mu H} = 2 \mu H$

Step 2: Find Angular Frequency ($\omega$)
$\omega = 2\pi f = 2 \times \pi \times 150,000 \approx 942,477 \text{ rad/s}$

Step 3: Calculate Reflected Impedance ($Z_{ref}$)
The formula for reflected resistance from the secondary to the primary is $Z_{ref} = \frac{(\omega M)^2}{R_L}$ (assuming secondary coil resistance is negligible for this snapshot).

• $\omega M = 942,477 \times (2 \times 10^{-6}) \approx 1.885 \Omega$
• $(\omega M)^2 \approx 3.55 \Omega^2$
• $Z_{ref} = \frac{3.55}{5} = 0.71 \Omega$

Where You Meet This in Practice

While the Wireless Power Consortium (Qi standard) governs tight-coupling phone chargers, resonant air-gap WPT is solving entirely different engineering problems:

• Rotating Machinery: Replacing carbon slip rings on motor rotors with WPT coils to eliminate friction, dust, and maintenance.
• Drone Charging Pads: Allowing UAVs to land slightly off-center on a pad and still receive 50W+ of charging current without precise pin alignment.
• Hermetic Medical Implants: Powering pacemakers or neural interfaces through the skin without risking infection pathways from physical wires.
• IoT Sensor Arrays: The specific "Finland" headline often references multi-coil transmitter arrays that track a moving receiver (like an AGV or drone) and dynamically shift the magnetic field to maintain optimal $k$ without moving parts.

Decision Path: Choosing Your WPT Topology and Components

Designing a WPT system requires matching your air-gap requirements to the correct coil geometry and driver IC. Use this decision tree to select your hardware.

The Default Pick for Bench Prototyping: If you are building a mid-range resonant WPT system to test air-gap power transfer (10-20mm), buy the Würth Elektronik 760308101107 transmitting coil. It is a 24µH Litz-wire coil optimized for 100-200 kHz operation, paired with a high-quality ferrite shield to prevent eddy current heating in nearby metal. Drive it with a standard Texas Instruments WPT controller or a basic IR2110 half-bridge driver generating a 150 kHz square wave, and tune it with a high-voltage NP0/C0G ceramic capacitor.

FAQ: Clearing Up Wireless Power Misconceptions

Is transmitting electricity through the air dangerous to humans?
In the near-field magnetic resonance systems discussed here, the magnetic field is non-ionizing and highly localized. The safety concern isn't radiation; it's thermal. If a foreign metal object (like a coin or foil) enters the magnetic field, eddy currents will heat it rapidly. Modern WPT ICs include Foreign Object Detection (FOD) by monitoring the Q-factor of the primary tank; if the Q-factor drops unexpectedly, the system shuts down in milliseconds.

Why does my WPT efficiency drop when I add a ferrite core?
Ferrite concentrates the magnetic flux, which should increase coupling ($k$). However, if your ferrite core is too small or the material grade is wrong for your frequency (e.g., using manganese-zinc instead of nickel-zinc at 150 kHz), the core will saturate or suffer high hysteresis losses. The energy is lost as heat in the ferrite rather than transferring to the secondary coil. Always check the core's complex permeability curves at your exact operating frequency.

Can I use standard electrolytic capacitors for the resonant LC tank?
Absolutely not. The resonant tank circulates massive reactive currents (often 10x to 50x higher than the actual DC load current). Standard electrolytic capacitors have high Equivalent Series Resistance (ESR) and will overheat, vent, or explode within minutes. You must use high-voltage, low-ESR film capacitors or NP0/C0G ceramic capacitors rated for the specific RMS current of your tank.