CuCCo provides a series of MATLAB scripts that allow for calculation of 2-coil inductive link parameters, based on geometric coil definitions. Currently, wirewound solenoid coils and PCB-based spiral coils are supported. CuCCo allows seamless geometric → electrical parameter conversion to allow links to be designed without the need for FEM simulations.

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Currently an example file cochlear_example.m is provided, which shows the process for modelling an inductive link for a cochlear implant made from identical solenoid coils.

The following parameters can currently be calculated using CuCCo

• Inductance
• Resistance and Q-factor
• Parallel Capacitance and Self-resonant frequency
• Required capacitance to form a resonant tank

• Link Gain
• Link Efficiency
• Mutual Inductance/Coupling coefficient

Currently two coil objects classes are implemented SolWireCoil and PCBCoil. Each is constructed from geometric parameters, an input frequency, and a predicted source resistance. Upon construction, the electrical parameters for the coils are calculated and held as object properties. Details are summarized below.

Implements a single-layer solenoid wirewound coil.

Inputs

• n: Number of turns
• r_0: Wire cross-sectional radius
• p: Turn pitch, this can be set to zero to assume a minimum pitch (adjacent wires touching)
• r: Coil radius
• f: Drive frequency (this can be a vector)
• CP: Parallel capacitance. If this is set to zero, the constructor will attempt to predict a parallel capacitance based on geometry, this will lose accuracy for low turn counts and strange geometries.
• sourceres: Additional resistance expected to be inherent to the design. For a Tx coil this should include the source resistance, for an Rx coil this should include connecting trace resistances. This can be set to zero, but neglecting to include this resistance may produce over-optimistic Q-factor predictions.

Outputs

• l: Coil length, depends on n and p.
• L: Inductance
• Rs: Series loss resistance
• Q: Q-factor (Im(Z)/Re(Z))
• C: Tank capacitance required for the coil to resonate at the drive frequency f
• fSRF: Self-resonant frequency; either calculated from a user-supplied CP value, or predicted from geometry.
• CP: If not user supplied, this will be calculated from the predicted fSRF.
• coilZ: Total coil impedance, considering L, Rs, and CP.

Note: If f is supplied as a vector, Rs, Q, C, and coilZ will be created as vectors of the same length, with each value corresponding to the values of f in the input vector.

Implements a PCB-based spiral coil, assuming standard 1oz copper on FR4 substrate.

PCBCoil objects are generated in the same way as SolWireCoil objects, the only real difference being the input geometry parameters.

Inputs

• dout: The outer diameter of the spiral (edge to edge)
• fillfact: The 'fill factor', defining the amount of the spiral outer diameter that is filled with turns, defining the inner diameter din in the process.
• s: Spacing between turns (edge to edge)
• w: Turn track width
• f: See SolWireCoil.m f entry.
• shape: String, can be 'square','circ','hex', or 'oct'.
• sourceres: See SolWireCoil.m sourceres entry.

Outputs These are the same as for SolWireCoil.m, with din instead of l.

With coils defined, link parameters can be determined with the following functions. The simplest way to characterize a link currently is to use linkcharvsdist.m. This gives gain, efficiency, and impedance parameters for an inductive link across a range of distances. Alternatively, specific parameters can be calculated by using individual functions.

Characterizes a link at a single frequency, over a range of distances. This function will output the key performance metrics: gain, efficiency, and maximum theoretical efficiency. It will also output the link impedance and reflected impedance, as these can be of interest when designing transmitter and receiver circuits.

Inputs

• coil1, coil2: The input coil objects, can be SolWireCoil or PCBCoil
• dists: A vector containing coaxial distances between the two coil objects, e.g. linspace(1e-3,10e-3,100) for 100 distance points between 1 mm and 10 mm.
• config: can be 'SS','SP','PS', or 'PP', corresponding to each possible resonant link arrangement.
• Zout: The output load attached to the link.
• freq: Drive frequency in Hz.
• C1,C2: Resonant capacitances, these can be manually supplied to tweak the resonance to your liking. The most simple method is to use coil.C, where coil is one of your coil input objects. To improve resonance for parallel connected coils coil.C - coil.CP allows you to use the parallel capacitance of the coil as part of the resonant capacitance.

Outputs

• gainout: Link gain, for SP,SS units are V/V, for PS,PP units are V/A. This is a complex number, use abs(gainout) to get the absolute value.
• effout: Link efficiency.
• zlinkout: Full link impedance as viewed from the input coil.
• zreflout: Reflected impedance into the input coil from the coupled coil.
• effmax: Maximum theoretical link efficiency, given the values of Q and k.

Fundamentally the same as linkcharvsdist.m, but uses mutualLat.m to include a lateral misalignment as well as a distance variable.

Determines the mutual inductance and coupling factor of two coaxially aligned coils, separated by a distance dist. The two coil objects must currently be of the same class.

Inputs

• coil1, coil2: The input coil objects, can be SolWireCoil or PCBCoil
• dist: The coaxial distance between the two coil objects

Outputs

• M: Mutual inductance between the coils
• k: Coupling factor (M normalized to geometric mean of the two coil inductances)

Determines the mutual inductance and coupling factor of two parallel coils with a lateral displacement lat, separated by a distance dist. The two coil objects must currently be of the same class.

Inputs

• coil1, coil2: The input coil objects, can be SolWireCoil or PCBCoil
• lat: The lateral misalignment between the two coil centers.
• dist: The coaxial distance between the two coil objects

Outputs

• M: Mutual inductance between the coils
• k: Coupling factor (M normalized to geometric mean of the two coil inductances)

Determines the link impedance of two coupled coils.

Inputs

• config: can be 'SS','SP','PS', or 'PP', corresponding to each possible resonant link arrangement.
• ZL1, ZL2: impedances of coil1 and coil2 respectively.
• M: mutual inductance between the two coils.
• omega: angular drive frequency
• Zout: connected output impedance (load)
• C1, C2: resonant tank capacitors for coil1 and coil2

Outputs

• zlinkval: The impedance looking into the link, given as a cartesian complex number.

Determines the link gain of two coupled coils

Inputs

• config: can be 'SS','SP','PS', or 'PP', corresponding to each possible resonant link arrangement.
• ZL1, ZL2: impedances of coil1 and coil2 respectively.
• M: mutual inductance between the two coils.
• omega: angular drive frequency
• Zout: connected output impedance (load)
• C1, C2: resonant tank capacitors for coil1 and coil2
• Zlink: Link impedance seen at the input of the link.

Outputs

• gainval: the gain of the link, either a voltage gain or a transimpedance, depending if the input is a voltage or a current.

Determines the link efficiency for a given link arrangement, derived from the config, gain, and impedances.

Inputs

• config: can be 'SS','SP','PS', or 'PP', corresponding to each possible resonant link arrangement.
• linkgain: link gain, as produced by gain.m.
• Zlink: link impedance, as produced by zlink.m.
• Zout: connected load impedance.

Outputs

• effout: Link efficiency.

Determines the maximum theoretical efficiency of a given link.

Inputs

• k: coupling factor
• Q1, Q2: the Q-factors of the two link coils

Outputs

• max_eff: the maximum theoretical efficiency of the link with the given input parameters.

Returns peak and trough frequencies in the link impedance function of the given link. Ensure to account for changing frequency when providing the coil impedance values.

- Proper methods for efficiency calculation, currently this is manual (see cochlear_example.m).

• Currently coils are assumed to be coaxially aligned, need to add methods for lateral and angular misalignment. → Added mutualLat for lateral misalignment modelling; more complex than mutualIdeal, therefore slower
• For PCB coils, Rs prediction is sensitive to input variables. Ideally need a better approximation.
• Non-square PCB coils currently use the gap length formula for square coils; this should be updated. Non-critical, since this only affects SRF calcs.
• Improve user friendliness; implement GUI when all other functions are in place.