A seasoned amplifier designer encountering an unexplained rise in the noise floor, or a persistent intermodulation product that survives every shielding attempt, will eventually arrive at a conclusion that surprises: the board itself has grown a transformer. Nobody designed it. It assembled itself from the output inductor on one side of the PCB and the sensitive input traces on the other. Every ampere pushed through the output coil was quietly radiating a magnetic field, threading itself through the loops formed by the input circuitry. What was designed as a stability network became an aggressor. What was designed as a signal path became a victim.
Understanding how this happens, and why the cure is geometric rather than electronic, requires tracing the physics from the wire all the way to the measured distortion figure.
What the Boucherot Cell Contains and Why the Inductor Is the Problem
A Boucherot cell typically consists of a resistor and capacitor in series, usually placed across a load for stability. It is commonly seen in analog power amplifiers at the output of the driver stage, just before the output inductor. The speaker coil inductance of a loudspeaker generates a rising impedance, which is worsened by the output inductor generally found in analog power amplifiers; the cell is used to limit this impedance.
The full output network therefore contains two inductive elements working in tandem: the series output inductor in the signal path, and the speaker's own voice coil inductance at the load. Without a defined HF load, the output stage can form a resonant circuit with the parasitic and load capacitance, resulting in oscillations. The RC Boucherot cell damps this resonance.
The series output inductor is the electromagnetic aggressor of interest here. Unlike the capacitor and resistor in the Boucherot cell, the inductor does not confine its energy to the circuit traces. High-current inductors can generate magnetic fields that interfere with nearby traces or ICs. In a power amplifier delivering tens of watts into an 8-ohm load, the current through the output inductor swings several amperes with every audio cycle. Each change in that current is precisely the kind of time-varying field that Faraday's law converts into an induced electromotive force in any nearby conductor loop.
The resonant frequency of the output network interacting with cable capacitance and load establishes the frequency at which that field is most energetic. For the series LC formed by the output inductor L_out and the effective shunt capacitance C_load, this corner sits at f₀ = 1 / (2π · √(L_out · C_load)). A typical value of L_out = 1 µH combined with cable capacitance of 10 nF places f₀ near 50 kHz, within the band where audio feedback is still active and where an induced signal can enter the loop unattenuated. The Boucherot cell damps the Q of this resonance by inserting a series resistance R_B, targeting a damping factor ζ = R_B / (2 · √(L_out / C_load)) close to unity.
How Ampere's Law Turns the Input Trace into a Crosstalk Victim
Magnetic field coupling occurs when energy is coupled from one circuit to another through a magnetic field. Since currents are the sources of magnetic fields, this is most likely to happen when the impedance of the source circuit is low. Coupling between circuits occurs when the magnetic field lines from one circuit pass through the loop formed by the other. Schematically, this is represented as a mutual inductance between the two signal wires.
Every input trace on the PCB, together with its return path through the ground plane, forms exactly such a loop. The area of that loop and its orientation relative to the output inductor's field determine how much flux threads through it and how much voltage is consequently induced. Faraday's law states this precisely: the induced EMF is ε = −dΦ/dt, where Φ = B · A · cos θ is the magnetic flux threading through the loop area A at angle θ to the field B. When expressed in terms of mutual inductance M between aggressor and victim circuits, the induced voltage simplifies to V_induced = −M · (dI/dt), where I is the current in the output inductor. This formulation makes the two levers of control immediately visible: reduce M by changing geometry or orientation, or reduce dI/dt by limiting the rate of current change, which in audio practice means controlling slew rate.
The induced voltage is not random noise. It is a faithful, if attenuated, replica of the signal driving the output stage, including all of its harmonic and intermodulation content. When this appears at the input of the preamplifier or feedback network, it is indistinguishable from a legitimate input signal. The amplifier processes it and delivers it to the output alongside the original program material. What the designer hears is a rise in THD at frequencies where output current is highest, or elevated intermodulation between test tones at different levels. The distortion is real. Its source is not in any active component. It lives in the geometry of the board.
Both inductive and capacitive coupling are proportional to frequency for the weak coupling case with resistive loads. Reducing mutual inductance reduces crosstalk proportionally. Moving wires farther apart helps, as does bringing them closer to the ground plane. In practice, amplifier boards are compact, and distance alone is frequently insufficient.
The Coupling Coefficient and Its Dependence on Angle
Mutual inductance between two coils depends on distance, geometry, and the angular relationship between their magnetic axes. The general expression is M = k · √(L₁ · L₂), where L₁ and L₂ are the self-inductances of the two coils and k is the dimensionless coupling coefficient ranging from zero to unity. For two coaxial air-core solenoids this coefficient is highest; for two solenoids whose axes are at an angle θ to each other, the effective mutual inductance scales as M(θ) = M₀ · cos θ, where M₀ is the mutual inductance at θ = 0. The coupling coefficient k is equal to the ratio of the flux cutting one coil to the flux originating in the other.
What determines k in free space, apart from distance? The flux density produced by a solenoid is strongest along its axis and falls to zero in the plane perpendicular to that axis. A second coil placed so that its axis lies at 90 degrees to the first sits in the plane where the first coil's axial field vanishes. The net flux threading through the second coil is zero. At θ = 90°, cos θ = 0, so M(90°) = 0 exactly. Mutual inductance can be positive or negative based on the relative orientation of magnetic fields in coupled circuits, but at the orthogonal condition the coupling collapses to its theoretical minimum regardless of sign.
The magnitude of coil 2's emf depends not only on distance from coil 1 but also on the physical orientation of coil 2 to the direction of coil 1's magnetic flux. Although putting sufficient space between the coils will certainly minimize crosstalk, there exists a far better solution, particularly where space is at a premium.
This is the theoretical foundation of orthogonal inductor placement: not a rule of thumb, but a direct consequence of the vector nature of magnetic flux. Two coils with perpendicular axes have theoretically zero mutual inductance regardless of separation. In practice, real inductors are not perfect solenoids, their fringe fields extend laterally, and assembly tolerances introduce angular error. Even so, perpendicular placement reduces the coupling coefficient by an order of magnitude compared to parallel alignment, and this reduction translates directly into a proportional reduction in induced voltage and in the distortion contribution of the magnetic crosstalk mechanism.
Why Toroidal Cores Change the Calculation
Not all output inductors are air-core solenoids. Many production amplifiers use toroidal or ferrite-core inductors for their higher inductance per unit volume and smaller footprint. A toroidal inductor confines most of its magnetic flux within the core material, so the stray field outside a well-wound toroid is substantially lower than that of an equivalent air-core solenoid.
However, "substantially lower" is not zero. Imperfect winding distribution, gaps, and asymmetries allow some flux to escape. Inductors that use magnetic cores suffer from hysteresis and saturation distortions. At high output current levels, partial saturation of a ferrite core disrupts the toroidal field distribution, increasing stray radiation precisely when low distortion matters most.
For a ferrite-core inductor, reduced stray field means orthogonal placement matters less in absolute magnitude, but the relative gain from correct orientation remains similar. For air-core inductors, which are common in high-performance discrete amplifiers precisely because they avoid hysteresis and saturation, orthogonality is not optional. The stray field of an air-core coil extends far and falls off slowly, and only the geometric null at 90 degrees provides reliable attenuation at short distances.
Why the Input Stage Suffers Most When Small Signals Meet Large Magnetic Fields
The severity of the problem scales with the ratio of the induced voltage to the legitimate signal at the input. In a high-gain preamplifier stage operating at input levels of a few millivolts, even a few microvolts of magnetically induced signal represents a meaningful fraction of the input amplitude. More significantly, if the induced signal is correlated with the output, which it always is when the inductor carries the amplified version of the input signal, it creates a feedback path that bypasses the intentional feedback network entirely. This phantom loop contributes phase shift and amplitude variation that the designer has not modeled and cannot compensate through conventional loop correction.
The frequency dependence of the problem is built directly into the induction mechanism. Since V_induced = −M · (dI/dt), and for a sinusoidal output current I(t) = I_peak · sin(2πft) the derivative is dI/dt = 2πf · I_peak · cos(2πft), the induced voltage amplitude scales as V_induced(peak) = M · 2πf · I_peak = ω · M · I_peak. Every doubling of frequency doubles the induced interference voltage, which means the effective magnetic crosstalk rises at 20 dB per decade across the audio band. In a Class AB amplifier, the reactive current through the output inductor also grows with frequency as the speaker's voice coil inductance presents a rising impedance, compounding this slope further. The result is a distortion signature that worsens toward the top of the audio band, appearing as elevated high-frequency THD or increased intermodulation between widely spaced test tones, neither of which points obviously back to a layout problem.
Layout Practices That Follow Directly from the Physics
Several layout practices emerge directly from this analysis:
- The output inductor should be positioned as far as practical from the input stage and input traces, since mutual inductance falls with distance.
- Where distance is constrained, the output inductor's axis should be oriented perpendicular to the plane containing the nearest sensitive signal loop, driving the cosine projection of the field through that loop toward zero.
- In stereo amplifiers, the output inductors of the two channels should be oriented orthogonally to each other to minimize interchannel magnetic crosstalk that would otherwise degrade stereo separation at high output levels.
- The area of input signal loops should be minimized, since induced voltage is proportional to the flux threading through the loop area.
- A solid ground plane constrains the return current path close beneath each signal trace, shrinking the effective loop area and reducing magnetic pickup across the entire audio band.
Air-core output inductors should be wound on forms with a known axis, and that axis must be documented in the assembly drawing. This requirement belongs in the formal layout specification, not in verbal folklore passed between engineers. When treated as a constraint, it survives design revisions, component substitutions, and board respins. When it lives only in memory, it disappears at the first pressure to reduce board area.
The Geometry Is the Circuit
There is a seductive tidiness to placing all components in the same orientation on a PCB. Automated assembly favors consistent rotation, and visual inspection is easier when every inductor faces the same way. These are legitimate considerations, and all of them push toward parallel inductor placement. They are outweighed by the magnetic coupling argument precisely when inductors carry large, signal-correlated currents near sensitive circuitry, which is the exact condition in an audio power amplifier with an output filter network adjacent to an input buffer or preamplifier stage.
The output LR coil does not need to be far away, behind a metal shield, or wound on a special low-radiation core to stop coupling into the input traces. It needs to be turned 90 degrees. The physics has been understood since Faraday. What prevents the fix is not ignorance of the mechanism but a failure to recognize that the board's physical geometry is a circuit element in its own right, one that generates mutual inductance values, coupling coefficients, and induced voltages as precisely as any component in the schematic.
Orthogonal placement of inductors in amplifier output networks is the application of a physical law. It is the one geometric operation that drives the coupling coefficient toward zero without adding components, increasing board area, or degrading any electrical parameter of the circuit. Its absence generates distortion that no amount of feedback can fully correct, because the feedback loop itself is the intended signal path and the magnetic coupling routes its interference around it.
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