> For the complete documentation index, see [llms.txt](https://mujoseph.gitbook.io/mujoseph-docs/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://mujoseph.gitbook.io/mujoseph-docs/emma-mk1-drsstc/hardware-overview/electrical-design/primary-coil.md). # Primary Coil ## Design Considerations

The primary coil is a planar circular spiral inductor. To satisfy the primary resonant frequency $$f\_{res(pri)}=264,\text{kHz}$$ with an MMC bank capacitance of $$C\_{MMC}=0.045,\mu F$$, the primary coil inductance must be $$L\_{pri}=8,\mu H$$. The minimum inner diameter, $$d\_{in(min)}$$, of the primary coil was constrained by the secondary coil assembly (see below); it must be large enough to accommodate it and provide enough clearance to help mitigate arc formation between the primary and secondary coils during stressful drive conditions. Once the inner diameter was known, a conductor width, `w`, and spacing, `s`, was chosen to yield a satisfactory ESR and fill ratio, respectively.

Primary coil and secondary coil assembly.

## Physical Properties With the inner diameter, conductor width, and conductor spacing set, the number of turns, `n`, needed to satisfy the target inductance of $$8,\mu H$$ was computed using the `computePlanarSpiralInductance` function within the [DRSSTCToolbox](/mujoseph-docs/emma-mk1-drsstc/drsstctoolbox/drsstc-drc/computing-planar-spiral-inductor-inductance.md):

`computePlanarSpiralInductance` output with d_{in},s, \text{and}\, w held constant and sweeping
the number of turns, n.

As illustrated, 5 turns achieve a target inductance of $$8, \mu H$$. Measuring the inductance with an LCR meter (*`Extech 380193`)* confirms the accuracy of the approximation (see image below).

Measuring the primary coil inductance with an LCR meter. The measured
inductance of 8.3\,\mu H agrees closely with the expected \approx 8\,\mu H (at 5 turns) from
the aforementioned approximation.

The ESR of the primary coil: $$ ESR=\rho\_{cu}\frac{l}{A}=\rho\_{cu}\frac{l}{w\cdot t} $$ Where: * $$\rho\_{cu}=1.68 \times10^{-8}$$ is the resistivity of copper \[$$\Omega\cdot m$$] * $$l$$ is the length of primary coil \[$$\text{m}$$] * $$w$$ is the width of the primary coil conductor \[$$\text{m}$$] * $$t$$ is the thickness of the primary coil conductor \[$$\text{m}$$] Substituting the primary coil parameters below: $$ ESR=2.23 ,m\Omega $$ ### Primary Coil Parameters

| Parameter | Description | Value | | ------------ | ---------------------------- | ------------------ | | $$d\_{out}$$ | outer diameter | 539.65 mm (21.25") | | $$d\_{in}$$ | inner diameter | 145.95 mm (5.75") | | $$w$$ | conductor width | 25.40 mm (1.00") | | $$s$$ | conductor spacing | 12.70 mm (0.50") | | $$t$$ | conductor thickness | 1.6 mm (0.063") | | $$l$$ | conductor length | 5.39 m (212.20") | | $$n$$ | number of turns | 5 | | ESR | equivalent series resistance | $$2.23, m\Omega$$ | ## Primary Coil Construction **Material:** 63 mil (1.6 mm) copper sheet **Fabrication:** [SendCutSend](https://sendcutsend.com/) sheet cutting service ## Primary Coil Coupler Assembly Refer to the image below, *Emma Mk1 Primary Coil Coupler Assembly (render)*: The primary coil is connected to the switch node of the [*Half-Bridge* PCB 2](/mujoseph-docs/emma-mk1-drsstc/hardware-overview/mechanical-design/pcb-rack-assembly.md#d-half-bridge-pcb-2) via a 6 AWG stranded copper cable (`E`) terminated on both ends with an M5 ring terminal (`B`). The ring terminal is fastened to the [board-to-board interface](/mujoseph-docs/emma-mk1-drsstc/hardware-overview/electrical-design/pcb-design.md#board-to-board-interface) of the [*Half-Bridge*](/mujoseph-docs/emma-mk1-drsstc/hardware-overview/electrical-design/pcb-design/half-bridge.md) PCB with an M5 screw, lock washer, and nut. The primary coil coupler assembly consists of two components, the top (`A`) and bottom (`C`) jaws. The hole slot (`D`) in the bottom jaw allows for vertical adjustment, ensuring the coupler assembly makes good electrical contact with the top and bottom of the primary coil winding. Once the jaws are firmly seated, the connection (along with the copper cable ring terminal) is secured with an M5 screw, lock washer, and nut.

*Emma Mk1* Primary Coil Coupler Assembly (render)

The image below shows the primary coil coupler assembly clamped onto the final turn of the primary coil and secured with M5 hardware within the *Emma Mk1*:

*Emma Mk1* Primary Coil Coupler Assembly (actual)

### Coupler Assembly Construction To ensure good planar contact between the coupler jaw faces and the primary coil itself, the bottom jaw of the coupler was bent at 85 degrees (see image below) to add a small amount of preload to the copper bend as it pushed into the underside of the primary coil.

Primary coil coupler bottom jaw (source: SendCutSend fabrication order portal)

**Material:** 40 mil (1.02 mm) copper sheet **Fabrication:** [SendCutSend](https://sendcutsend.com/) sheet cutting and bending services