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Passive Component Selection
As an initial caveat, the topic of selecting the proper comonents is a complex task and this page is meant to explain the logic behind our choices and guide future groups who may modify the design, but in no way is an authoritative resource, rather it should be thought of as a discussion where we convey some of the experience we have gained designing these devices.
Passive components (resistors, capacitors, and inductors)are used throughout all MPI related systems and more generally, form the foundation of analog electronics. It is no surprise then that the implications of these base-level component selections are widespread and profound. In the context of MPI there are typically two major sites where passive component selection is critical, the Tx and Rx chain.
After accepting that passives are both important and variable, the question of what makes a component well-suited for MPI arises. First, it needs to handle the appropriate power. Next, it should be linear and drift minimally, and last it ideally would be space- and cost-effective.
Under construction
Under construction
Inductors are passive components that operate by storing energy in a magnetic field, and functionally act to resist change is a circuit by inducing a voltage of the opposite polarity. While there are innumerable manuals on inductors, for now it is important to recognize that because it induced voltages proportional to the change in field, they can be potent noise sources as well as noise receivers. For this reason all inductors (besides the Tx/Rx/shift coils) are toroidal shapes. The alternative is primarily a solenoid which has the plus of being efficient with respect to paracitic effects (R and C) but produces fields which radiate strongly and are equally succeptible to noise. The toroid shaped inductor keeps the generated field inside, and due to reciprocity is only succeptible to internal noise sources (in an ideal world).
Next, the core of the toroid is important to consider. Ferrites are commonly used because they are electrically resistive and therefore even at high frequencies have very minor (effectively none for many cases) eddy currents forming unlike steel cores. Ferrites, having high magnetic succeptibility, allows for high inductances to be achieved without neccesitating large form-factors and parasitics. Unforunately, ferrite cores have the downfall of being non-linear to some degree [1]. Despite it being fairly minor non-linearity at low amplitudes, given MPI functions by detecting a non-linear response we have avoided them entirely.Thus, we have used air cores in all inductors. We have also ensured the epoxy used to stabilize the wires are also linearly magnetic.
Finally, the sizing of these air core toroidal inductors must be done as they must be matched to the frequency desired. As an example case, say we were building a resonant LC at 25kHz, as the resonant frequency is 1/(2pisqrt(L*C)), there are two degrees of freedom, L and C. Because inductor are far easier to tune to a precise value, we first pick a large capacitor value and wind an inductor to match. The large size of the capacitor enables the inductance to be smaller (large sizes become impractical with air cores). If the capacitor was chosen to be a 10uF PP metallized film (discussed above), the inductor must be 4.053uH. With 1mm wire. From there the context of the design becomes very important as factors such as "will it fit in the box" start to dominate the design decisions. For numerous in-depth discussions on optimal toroidal cores see the papers by P.N. Murgatroyd (one such example is here [2]).
[1] J. Watson, On the Nonlinearities of Inductors using Linear Ferrite Toroidal Cores, 1981
[2] P.N. Murgatroyd, The optimal form for coreless inductors, 1989