A wireless power transformer transfers electrical energy between two electrically isolated coils via magnetic induction or resonance across an air gap, eliminating the need for a physical conductive connection. In a real circuit or installation, swapping a traditional wired transformer or slip ring for a wireless one replaces physical contact constraints with a coupling coefficient ($k$) constraint, allowing rotating or hermetically sealed parts to receive power while introducing alignment-sensitive losses and requiring high-frequency AC inversion. Beginners commonly confuse this near-field magnetic coupling with far-field RF energy harvesting (like passive RFID) or capacitive power transfer, but a true wireless transformer strictly relies on oscillating magnetic flux linking two discrete inductors.
How Magnetic Coupling Works Across an Air Gap
At its core, a wireless power transformer operates on the exact same Faraday’s Law principles as a standard 60Hz laminated iron-core transformer. The primary coil is driven by a high-frequency alternating current (typically 100 kHz to 6.78 MHz), generating an oscillating magnetic field. This field crosses the air gap and intersects the secondary coil, inducing an electromotive force (EMF).
The critical difference is the absence of a high-permeability iron core to confine the flux. Because air has a relative permeability of roughly 1, the magnetic circuit has high reluctance. To quantify this, engineers use the coupling coefficient ($k$), which ranges from 0 (no flux linkage) to 1 (perfect linkage). The relationship is defined by the mutual inductance ($M$) and the self-inductances of the primary ($L_1$) and secondary ($L_2$) coils:
k = M / √(L1 × L2)
At 100 kHz and above, standard solid copper wire suffers from severe skin effect, forcing current to the outer edge of the conductor and spiking AC resistance. Wireless transformer coils must be wound with Litz wire—a bundle of individually enamel-insulated thin strands woven together—to ensure uniform current distribution and keep coil Q-factor high.
Think of the primary coil as a pump creating a swirling vortex in a pool (the magnetic field), and the secondary coil as a water wheel placed in that vortex. If the wheel is perfectly centered, it catches the most water (high $k$). Move it to the edge, and it catches less (low $k$), wasting the pump's energy as turbulence (heat) in the pool. To guide this 'water' and prevent it from dissipating into surrounding metal structures, designers place high-permeability ferrite plates behind both coils.
Worked Numeric Example: 50W AGV Inductive Transfer
Let’s size and analyze a wireless power transformer for an Automated Guided Vehicle (AGV) charging station. The target is 50W of output power at 24V DC after rectification. The system operates at a switching frequency of 100 kHz.
1. Define the Coil Parameters
Assume we have two identical pancake coils, each with a self-inductance of $L_1 = L_2 = 25 \mu H$. Based on the mechanical air gap of 10mm, our magnetic simulation yields a coupling coefficient of $k = 0.6$.
2. Calculate Mutual Inductance and Induced Voltage
First, find the mutual inductance ($M$):
M = k × √(L1 × L2) = 0.6 × 25 μH = 15 μH
Next, calculate the angular frequency ($\omega$):
ω = 2π × f = 2π × 100,000 = 628,318 rad/s
If the primary inverter drives 5A RMS through the primary coil, the open-circuit RMS voltage induced in the secondary ($V_2$) is:
V2 = ω × M × I1 = 628,318 × (15 × 10^-6) × 5 = 47.1V RMS
3. Account for Leakage Inductance and Tuning
Under a real load, the secondary voltage will sag due to leakage inductance—the flux that fails to cross the air gap. The secondary leakage inductance is:
L_leak2 = L2 × (1 - k) = 25 μH × (1 - 0.6) = 10 μH
The reactance of this leakage at 100 kHz is $X_{leak} = \omega \times L_{leak2} = 6.28 \Omega$. If we draw 2A RMS to get our 50W, we lose over 12V across this leakage reactance alone, dropping our usable voltage to ~34V RMS and tanking efficiency.
The Fix: We add a series tuning capacitor ($C_2$) to the secondary coil to create an LC resonant tank that cancels the leakage reactance at exactly 100 kHz.
C2 = 1 / (ω² × L2) ≈ 101 nF.
With the capacitor installed, the reactance drops to near zero, the secondary voltage stays near 47.1V RMS, and after a full-bridge Schottky rectifier, we yield roughly 65V DC, which a downstream buck converter efficiently steps down to a stable 24V DC for the AGV battery management system (BMS).
Where You Meet Wireless Transformers in Practice
While the math remains constant, the physical implementations vary wildly based on the required air gap and alignment tolerance.
- Consumer Electronics (Qi Standard): The Wireless Power Consortium defines the Qi standard, which uses tightly coupled inductive transfer (typically $k > 0.8$) at 110-205 kHz for low-power devices, and resonant inductive transfer for higher power profiles up to 15W and beyond.
- Industrial Automation: Rotary packaging machines and robotic end-of-arm tooling use wireless transformers to replace carbon-brush slip rings. This eliminates friction, particulate dust, and maintenance downtime in high-speed environments.
- Medical Implants: Active implants like neurostimulators and artificial hearts require hermetically sealed titanium casings to prevent bodily fluid ingress and infection. A wireless transformer embedded in the casing allows transcutaneous charging without breaching the biological seal.
- Automotive EV Charging: High-power resonant systems (like the SAE J2954 standard) transfer 3.6 kW to 11 kW across a 150mm to 250mm ground-clearance air gap from a road-embedded pad to a vehicle-mounted receiver.
Frequently Asked Questions
Can a wireless power transformer work through metal walls?
No, not through standard solid metal. When oscillating magnetic flux hits a conductive metal wall (like aluminum, copper, or steel), it induces parasitic eddy currents within that metal. These eddy currents generate massive heat, create an opposing magnetic field that cancels the primary flux, and drop your coupling coefficient ($k$) to near zero. You can transfer power through non-conductive barriers like glass, plastic, wood, or ceramics. If you must pass power through a metal enclosure, the metal must be heavily slotted or machined with non-conductive gaps to break the eddy current paths.
What is the difference between inductive and resonant wireless power transfer?
Standard inductive transfer (like early Qi phone chargers) relies on tight magnetic coupling ($k > 0.8$) and requires the coils to be separated by only a few millimeters. It is highly efficient but completely intolerant of spatial misalignment. Resonant wireless power transfer adds tuning capacitors to both the primary and secondary coils, creating LC tanks matched to the driving frequency. As detailed by Texas Instruments' wireless power design guides, resonance allows the system to transfer power efficiently over much larger air gaps (up to several coil diameters) and tolerates much lower coupling coefficients ($k < 0.3$), making it ideal for EV charging and misalignment-tolerant AGV systems.
How does misalignment affect a wireless power transformer's efficiency?
Lateral (X/Y) misalignment drops the coupling coefficient drastically. For a standard single-coil pair, a 50% lateral offset can drop $k$ from 0.8 down to 0.3. This sudden drop in mutual inductance causes the primary inverter to see a highly reactive load. To maintain the same output power, the primary controller must push significantly higher RMS current, which squares the $I^2R$ copper losses and usually trips the system's thermal or overcurrent shutdown. Modern high-end systems solve this by using multi-coil arrays (like 3-coil or 5-coil transmitter pads) and electronically multiplexing the drive to the coil closest to the receiver.
