Tech Talk
Loudspeaker Crossover Air Core Inductors: A Look Inside
George E. Short III | Senior Principal Acoustic Engineer
Inductors are one of the three key elements in a loudspeaker passive crossover network (the others being the capacitor and the resistor). The function of an inductor is to pass low frequencies and attenuate high frequencies, exactly the opposite of the Capacitor, as discussed in Tech Talk November 2023. In almost all passive crossovers, at least one inductor can be found in series with the woofer.
Electrical current – which is simply electrons flowing through a wire – creates a magnetic field encircling the wire. A constant current will create a constant magnetic field. Rolling the wire into a coil concentrates the magnetic field in the central core of the coil through the principle of superposition. To make the magnetic field stronger, add more windings to the coil, more electrical current, or both.
Magnetic Field Lines of a loosely wound coil
Image: The Mirror Universe
This is precisely how an electromagnet works, and they can be made incredibly strong. Here is an example of an electromagnet lifting a car:
Chris, you should have parked in the North Lot like the rest of us!
But a strange thing happens to coils of wire with variable current flowing through them in a circuit: changes in the current creates changes in the magnetic field, and the changing magnetic field induces an electromotive force on the electrons within the wire in the opposite direction of the current flow; that is, the coil pushes back against the electrons flowing within itself. Even more strangely, the push back strength is proportional to the rate of change of the magnetic field, which is precisely the frequency of the variable current flowing through the wire.
This induced opposing force impedes the free-flowing, variable electron current, which is why loudspeaker crossover coils are largely referred to as inductors, and their nature is to impede electron current flow as its variability rate (hence its frequency) increases. At right is the electrical impedance of an inductor, plotted with increasing frequency.
Inductor Electrical Impedance with Frequency
An inductor’s inductance – that is, a measure of how hard it impedes current flow with increasing frequency – is mostly proportional to the square of the number of windings. All other things being equal, a coil with more turns has more inductance, so less high frequencies get through it. This is why in loudspeaker crossovers, one generally finds large inductors with lots of turns in series with the woofer, medium sized coils in series with the midrange, and no coils in series with the tweeter.
In a perfect world, that is all anyone would ever need to know about air core inductors……
Digging Deeper
…but of course, there’s more...
Wire Gauge, Resistance and Skin Effect
Copper wire comes in many diameters, with thinner wire exhibiting much higher electrical resistance per unit length than thicker wire. Resistance converts electrical energy into heat, which is how toasters and electric space heaters work. At right is a toaster.
Resistance adds up proportionately with wire length, and resistance particularly in an inductor in series with a woofer is bad because it wastes amplifier energy (by converting it to heat) within the inductor wire, instead of converting it to cone motion through the woofer motor. A large woofer coil can require several hundred turns to induce a large enough back-electromotive-force to reach the required inductance for a low crossover frequency, therefore several hundred feet of wire.
For inductors wound with optimum geometry (see below), a thicker wire always results in a larger, heavier, costlier inductor but with a lower resistance, therefore less energy inefficiently wasted in the crossover and more being transformed into sound by the woofer. Simply put, larger gauges have cleaner bass.
Then there is Skin Effect, a phenomenon where: as frequency increases, electrons are pushed to the outermost surface of the conductor. Essentially, because no current flows through the middle of the conductor, the wire effective cross sectional area decreases at higher frequencies withing the audio range. Thus, the conductor’s resistance increases with increasing frequency. Solutions include making a woven “Litz” master wire from several thinner individually insulated wires, to maximize surface area for equivalent gauge, or to manufacture the inductor with copper foil and insulating film rather than insulated copper wire. While Skin Effect is easy to measure and fun to talk about, it is only a factor in very large gauge inductors and as these are used to cross out woofers at a low frequency. Even more strangely, subjective tests indicate skin effect when audible is actually considered beneficial in woofer crossover networks.
Current Density as a function of frequency
Engineering requires we seek a balance, and the general rule is that the inductor intrinsic resistance is 10% or less of the woofer’s DC resistance, or less than 0.5dB of woofer output being lost.
Winding Geometry
Winding geometry – the number of coil turns per layer, the number of layers, and the dimension of the empty core at the coil center – can have a significant impact on the amount of wire required and therefore the inductors’ intrinsic resistance and losses. Even though geometry can be easily optimized for minimum wire of each gauge to reach a target inductance, the space limitations inside a loudspeaker cabinet, the precise size of available wire widths, and in some cases for small volumes the manufacturer’s reliance on existing core sizes, means that sometimes the “perfect” sized coil just can’t be made or simply will not fit. In the old days, this forced designers to accept the second best solution, but today with computer optimization and Solid-Works wizardry, we are able to fine-tune the cabinet internals and winding geometry to reach both our resistance requirement and space restrictions pre-production and without accepting a geometric compromise.
Winding Stability
Electrons are trapped within the wire, so the forces they experience get transferred to the wire. In the case of loosely wound inductors (called “scramble-wound’), if the windings are not rigidly bonded they can actually vibrate, once again dissipating electrical energy as heat with no benefit to the sound. That said, scramble-wound inductors actually exhibit lower self-capacitance than hex-laid inductors, which some people feel is beneficial.
Likewise, there is a lot of energy trapped inside a loudspeaker cabinet, and anything that can buzz will. Inductor windings that are not stabilized will join the party.
The solutions lie in the manufacturing processes: wet-winding, where a very thin bonding layer is applied to the coil continuously as it is wound; and/or vacuum-dipping the inductor into bonding fluid after it is wound, so any trapped air percolates out and is replaced with bonding fluid, permanently stabilizing the windings.
Eddy Currents
Oh, all these terrible things that happen to inductors never seem to end! And now, its Eddy Currents!
Eddy currents are induced by the coils’ magnetic field into any conductor the field can reach. This means that for an inductor mounted on a PC Board, if mounted near the solid electrically conducting ground plane, localized currents are induced and swirl within the plane. This affects the inductors’ magnetic field and represents another form of energy loss, and additionally the eddy currents can energize other elements on the PCB.
An inductors’ magnetic field is concentrated through the core, weakening with the square of the distance from the egresses, so inductors mounted flat on PCBs will usually have a blanked area aligned below their cores. Alternatively, they will be mounted on “golf tee” standoffs elevating the inductor away from the board.
Lastly, they can be mounted on edge, so only a section of the weakest part of the magnetic field interacts with the PCB.
Induced Eddy Currents in Ground Plane
Image by BrainCart
Mutual Inductance
Mutual Inductance occurs when the magnetic field created by one inductor interacts with the windings of another. Because Back Electromotive Force experienced by electrons can be caused from any magnetic field, current flowing in one inductor can induce current flow in another. This effect is actually the fundamental operating principal of electrical transformers, but in crossover world it is a liability.
To visualize mutual inductance, envision an arrow being shot through the core of one inductor, following a circular path and flying though the core of a second inductor. The magnetic field will follow the same path as the arrow.
Mutual inductance – induced distortion turns out to be the most audible crossover component artifact distortion. In complex crossovers where several inductors are closely spaced, mutual inductance becomes a serious problem.
The solution is to align the inductors in quadrature, where the inductor cores are mounted perpendicular to each other, and maximizing the physical separation between inductors, and in some cases to magnetically shield one inductor from another.
Inductors in Quadrature
What we do
Here at HARMAN Luxury Audio, we routinely specify inductors manufactured to the highest mechanical standards and optimized dimensions and develop single or multiple crossover circuit PCBs to eliminate opportunity for secondary distortions. Paying attention to the smallest details always leads to better results.