> 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/pcb-design/mmc-bank.md). # MMC Bank

## Role The MMC (Multi-Mini Capacitor) Bank PCB contains metallized polypropylene film (MKP) capacitors, which together form the capacitor of the series LC primary resonant tank circuit. ## Schematic Overview

### Polypropylene Film Capacitor: R75TR318050H2J The `R75TR318050H2J` was chosen as the primitive MKP capacitor to form the resultant MMC bank. #### Specifications * Rated capacitance, $$C\_{mkp}$$: 0.18 $$uF$$ * $$ESR\_{mkp}$$: 6.2 $$m\Omega$$ * $$V\_{DC(mkp)}$$ rating: 1600 V * $$V\_{AC(mkp)}$$ rating: 650 $$V\_{rms}$$ * Peak current rating, $$I\_{pk(mkp)}$$: 270 $$A\_{pk}$$ * $$\frac{dV}{dt}$$ rating: 1500 $$\frac{V}{us}$$ * Thermal resistance, $$R\_{th}$$ : 28 $$\frac{^\circ{}C}{W}$$ * Max operating temperature, $$T\_{max}$$: $$125^\circ C,,(257^\circ F)$$ ### Emma Mk1 MMC Bank Parameters #### MMC Bank Equivalent Capacitance Requirement The *Emma Mk1* secondary tank resonant frequency is $$f\_{res(sec)}=264,kHz$$. To achieve the same resonant frequency within the primary tank circuit, with a primary coil inductance $$L\_{pri}=8,uH$$, the MMC capacitance, $$C\_{MMC}$$ , must be: $$ f\_{res(pri)}=\frac{1}{2\pi\sqrt{L\_{pri}C\_{MMC}}}\implies C\_{MMC}=\frac{1}{L\_{pri}(2\pi f\_{res(pri)})^2}=\frac{1}{8 \text{e-6}(2\pi \cdot 264\text{e3})^2}\approx,0.045,uF $$ #### MMC Bank Peak Voltage Rating The peak voltage seen by the MMC with capacitance $$C\_{MMC}$$ can be approximated using Ohm's law: $$ V\_{pk(MMC)} = I\_{pk(pri)}\cdot|Z\_{MMC}| $$ Where $$I\_{pk(pri)}$$ is the peak current of the primary tank circuit and $$|Z\_{MMC}|$$ is the magnitude/total impedance of the MMC bank. Assume no ESR (will be accounted for later), and thus the impedance of the MMC bank is simply the equivalent capacitive reactance, $$X\_{MMC}$$: $$ |Z\_{MMC}|=\sqrt{ESR\_{MMC}^2+X\_{MMC}^2}=\sqrt{0^2+(\frac{1}{2\pi f\_{res(pri)}C\_{MMC}})^2}=\frac{1}{2\pi f\_{res(pri)}C\_{MMC}}=\frac{1}{2\pi\cdot 264\text{e3}\cdot0.045\text{e-6}} \approx 13 ,\Omega $$ For $$I\_{pk(pri)}$$ a 20% overshoot of the maximum supported primary peak current, $$I\_{pri(max)}$$, will be assumed as a conservative safety margin, yielding the peak voltage seen by the MMC bank: $$ V\_{pk(MMC)} = (1.2\cdot300,A)\cdot13,\Omega= 4680,V $$ To satisfy this peak voltage requirement, a minimum number of MKP capacitors with a voltage rating of $$V\_{DC(mkp)}$$ in series (per parallel branch) are required. For the selected capacitor, the rated DC voltage is 1600 V. Therefore, the minimum number of MKP capacitors in series is: $$ N\_{series(min)} = ceil\Bigg(\frac{V\_{pk(MMC)}}{V\_{DC(mkp)}}\Bigg)= ceil\Bigg(\frac{4680}{1600}\Bigg) =3 $$ #### MMC Bank Peak Current Rating To ensure that the MKP capacitor peak current rating, $$I\_{pk(mkp)}$$ , is not exceeded for a given peak primary current, $$I\_{pk(pri)}$$, a minimum number of parallel branches within the MMC is needed to split the current sufficiently: $$ N\_{parallel(min)} = ceil\Bigg(\frac{I\_{pk(pri)}}{I\_{pk(mkp)}}\Bigg)= ceil\Bigg(\frac{360}{270}\Bigg) =2 $$ #### Satisfying MMC Bank Parameter Requirements The MMC bank equivalent capacitance, $$C\_{MMC}$$, resulting from a combination of $$N\_{parallel}$$ parallel branch(es), each containing $$N\_{series}$$ capacitor(s) in series, can be computed thusly: $$ C\_{MMC}= \frac{N\_{parallel}}{N\_{series}}\cdot C\_{mkp} \quad \quad \bigg( N\_{parallel} \ge N\_{parallel(min)},\text{,},N\_{series} \ge N\_{series(min)} \bigg) $$ For the *Emma Mk1,* 2 parallel branches of 8 capacitors each (for a total of 16) were used to satisfy the aforementioned requirements. Starting with the equivalent capacitance: $$ C\_{MMC} = \frac{2}{8}\cdot0.18\text{e-6}= 0.045, uF $$ The DC voltage rating of the MMC bank: $$ V\_{DC(MMC)} = N\_{series}\cdot V\_{DC(mkp)} = 8 \cdot 1600 = 12.8, kV $$ The peak current rating of the MMC bank: $$ I\_{pk(MMC)} = N\_{parallel}\cdot I\_{pk(mkp)} = 2 \cdot 270= 540, A\_{pk} $$ The ESR of the MMC bank: $$ ESR\_{MMC}= \frac{N\_{series}}{N\_{parallel}}\cdot ESR\_{mkp} = \frac{8}{2}\cdot6.2\text{e-3} \approx 25,m \Omega $$ The total impedance of the MMC bank can now be updated with the actual ESR. However, as can be seen, at the DRSSTC resonant frequency the capacitive reactance dominates: $$ |Z\_{MMC}|=\sqrt{ESR\_{MMC}^2+X\_{MMC}^2} = \sqrt{25\text{e-3}^2+13^2} \approx 13,\Omega $$ Therefore, the original approximation of the peak voltage seen by the MMC bank, $$V\_{pk(MMC)} = 4680,V$$, still holds. The RMS current of the primary tank circuit during operation, and therefore the RMS current seen by the MMC bank, can be approximated using the following equation (see here for [derivation](/mujoseph-docs/emma-mk1-drsstc/hardware-overview/electrical-design/pcb-design/mmc-bank/mmc-rms-current-approximation.md)): $$ I\_{RMS(MMC)}=I\_{sd}\sqrt{f\_b\bigg(\frac{t\_a}{6}+\frac{1-e^{-2\alpha t\_r}}{4\alpha}\bigg)} $$ Using the parameters below yields an MMC RMS current of: $$I\_{RMS(MMS)}\approx,32, \text{A}$$ | Parameter | Value | Unit | | ------------ | ----- | -------------- | | $$f\_b$$ | 200 | Hz | | $$t\_{cmd}$$ | 400 | $$\mu s$$ | | $$I\_{OCD}$$ | 300 | A | | $$\phi$$ | 0 | $$\text{rad}$$ | The RMS current seen by each parallel branch of the MMC bank is: $$ I\_{RMS(branch)} = \frac{I\_{RMS(MMC)}}{N\_{parallel}}=\frac{32}{2} = 16,\text{A} $$ The power dissipated by each capacitor in the bank can be computed as follows: $$ P\_{dis(cap)}=I\_{RMS(branch)}^2\cdot ESR\_{mkp} $$ Where $$ESR\_{(mkp)}$$ is the ESR of the MKP capacitor: $$6.2, m\Omega$$. Therefore the power dissipated is: $$P\_{dis(cap)}=16^2\cdot 6.2\text{e-3}=1.59 ,\text{W}$$ The temperature rise per capacitor, $$\Delta T\_{cap}$$, for a given MMC Bank RMS current can be expressed as: $$ \Delta T\_{cap}=R\_{th}\cdot P\_{dis(cap)} $$ Where $$R\_{th}$$ is the thermal resistance of the MKP capacitor, which is $$28 ,\frac{C^\circ}{W}$$ for the `R75TR318050H2J` . Therefore, each capacitor will increase by $$\Delta T\_{cap}=28\cdot 1.59\approx45^\circ C,(113^\circ F)$$ above ambient. Assuming the ambient temperature is $$22^\circ C,(72^\circ F)$$, each capacitor will theoretically see a temperature of $$67^\circ C,(185^\circ F)$$ for the given MMC bank RMS current, $$I\_{RMS(MMC)}$$. Note that the max rated temperature, $$T\_{max}$$, for the `R75TR318050H2J` is $$125^\circ C,(257^\circ F)$$, which allows plenty of margin given the projected temperature rise. Regardless, the *MMC Bank* PCB is [actively cooled](/mujoseph-docs/emma-mk1-drsstc/hardware-overview/mechanical-design/ebox-assembly.md#active-cooling) to help mitigate excessive temperature rise during operation and extend capacitor operating life. ## PCB Design The nets connecting each of the MKP capacitors are mirrored on both the top and bottom layers (see image below) to increase transmission line capacitance and minimize parasitic inductance. The paralleled copper planes also reduce the overall ESR of the net, and the via stitching between layers increases thermal conductivity and hopefully helps balance the current passing through the PCB between the top and bottom layers. Each MKP capacitor has a PCB cutout directly underneath as well as a minimum clearance of 0.320" (8.128 mm) between each neighbor to ensure adequate airflow for active cooling. The *MMC Bank PCB* mates with the [Bus Bar Pericope](/mujoseph-docs/emma-mk1-drsstc/hardware-overview/electrical-design/busbar-periscope.md) (and ultimately to one side of the [primary coil](/mujoseph-docs/emma-mk1-drsstc/hardware-overview/electrical-design/primary-coil.md)) and one of the [*Half-Bridge PCB*](/mujoseph-docs/emma-mk1-drsstc/hardware-overview/electrical-design/pcb-design/half-bridge.md)*s* via the [board-to-board interface](/mujoseph-docs/emma-mk1-drsstc/hardware-overview/electrical-design/pcb-design.md#board-to-board-interface).

*MMC Bank* Rev B PCB top layer (top), bottom layer (bottom)

Primary Capacitor PCB - 4x5 array
by Eastern Voltage Research. Form factor used
as a reference for MMC Bank Rev B.

### PCB Manufacturing Specifications * Fabrication: [JLCPCB](https://jlcpcb.com/) * Layers: 2 * Copper weight: 4.5 oz * Material: FR-4 (TG135) * Plating: ENIG * Board thickness: 62 mil (1.6 mm) * Assembly: By hand ## Gallery

Measuring total capacitance of fully assembled
*MMC Bank* Rev B PCB: 0.045\,\mu F\, (ESR:\,4.25 \Omega)

## Additional Resources * [Kaizer Power Electronics-MMC / resonant tank capacitor design for Tesla coils and inverters](https://kaizerpowerelectronics.dk/tesla-coils/drsstc-design-guide/mmc-tank-capacitor/)