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<header class="paper-header">
  <span class="paper-phase">Phase 1</span>
  <h1>Software-Defined Power Conversion for Cross-Ecosystem Battery Adapters: Power Electronics Design and Analysis</h1>
  <div class="paper-meta">
    <p>Matthew Long &mdash; The YonedaAI Collaboration, YonedaAI Research Collective, Chicago, IL</p>
    <p>March 2026</p>
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<main class="paper-content">

  <div class="paper-notice">
    This is the HTML summary version. <a href="../pdf/power-electronics.pdf">Download the full PDF</a> for complete formatting, equations, SPICE netlists, and simulation results.
  </div>

  <h2>Abstract</h2>
  <p>
    Modern cordless power tools are locked into proprietary battery ecosystems, each with distinct voltage platforms (18 V, 20 V<sub>MAX</sub>, 36 V, 40 V, 56 V), cell chemistries, and communication protocols. This paper presents VoltForge, a software-defined power conversion platform that enables cross-ecosystem battery interoperability through real-time switched-mode power conversion. We derive the full mathematical framework for buck, boost, and buck-boost converter topologies operating in continuous conduction mode (CCM); develop state-space models suitable for digital control; perform transient analysis of extreme load profiles (20&ndash;30 A inrush spikes, stall currents); present MOSFET switching loss models; and design protection circuitry for overcurrent, overvoltage, and reverse-polarity faults. The converter achieves a simulated efficiency of 92&ndash;95% at 15 A nominal load, voltage regulation within $\pm 0.5$ V under transient loading, and safe shutdown within $50\,\mu\text{s}$ of a fault condition.
  </p>

  <h2>1. Introduction</h2>
  <p>
    The cordless power tool market has grown to over $30 billion globally, yet consumers remain trapped within proprietary battery ecosystems. VoltForge occupies the gap between cheap passive adapters ($15&ndash;$30, no regulation, documented fire risks) and universal battery platforms that lack software-defined regulation. The adapter accepts input voltages between 14 V and 60 V, converts to any output voltage in that range, and provides overcurrent, overvoltage, reverse-polarity, and thermal protection.
  </p>

  <div class="insight-box">
    <p><strong>Key Insight:</strong> Hardware fast-path protections are non-negotiable &mdash; software alone is not sufficient for overcurrent, overtemperature, reverse polarity, or output short protection.</p>
  </div>

  <h2>2. Background</h2>

  <h3>Switched-Mode Power Conversion</h3>
  <p>
    A switched-mode power supply converts one DC voltage level to another by rapidly switching MOSFETs and filtering with inductors and capacitors. The three fundamental non-isolated topologies are buck (step-down), boost (step-up), and buck-boost (bidirectional step).
  </p>

  <h3>Continuous vs. Discontinuous Conduction Mode</h3>
  <p>
    In CCM, inductor current never reaches zero during a switching period. VoltForge operates in CCM for its primary operating range to ensure predictable, linear plant dynamics for the Phase 2 control loop.
  </p>

  <h3>Power Tool Load Characteristics</h3>
  <p>
    Power tools present uniquely challenging loads: drill/drivers draw 5&ndash;20 A with bursty spikes; circular saws sustain 10&ndash;15 A steady with 20&ndash;30 A startup spikes; angle grinders sustain 6&ndash;16 A with additional spikes. These transient profiles drive the converter design requirements.
  </p>

  <h2>3. Mathematical Framework</h2>

  <h3>State-Space Modelling</h3>
  <p>
    Each converter topology is modeled using state-space averaging, which replaces the switched circuit with a continuous time-averaged model. The state vector is $\mathbf{x} = [i_L, \; v_C]^T$ where $i_L$ is inductor current and $v_C$ is capacitor (output) voltage.
  </p>

  <h4>Buck Converter State-Space Model</h4>
  <p>The state-space averaged model:</p>
  $$\dot{\mathbf{x}} = \mathbf{A}\mathbf{x} + \mathbf{B}u$$
  <p>where:</p>
  $$\mathbf{A} = \begin{bmatrix} -\frac{R_L + (1-D)R_{\text{DS(on)}}}{L} & -\frac{1}{L} \\ \frac{1}{C} & -\frac{1}{RC} \end{bmatrix}, \quad \mathbf{B} = \begin{bmatrix} \frac{D}{L} \\ 0 \end{bmatrix}$$

  <h4>Buck Converter Transfer Function</h4>
  <p>The control-to-output transfer function:</p>
  $$G_{vd}(s) = V_{\text{in}} \cdot \frac{1}{LC} \cdot \frac{1 + sR_C C}{s^2 + s\left(\frac{1}{RC} + \frac{R_L}{L}\right) + \frac{1}{LC}}$$

  <h4>Boost Converter</h4>
  <p>The boost converter exhibits a right-half-plane (RHP) zero that fundamentally limits achievable control bandwidth:</p>
  $$\omega_z = \frac{(1-D)^2 R}{L}$$

  <h3>Voltage Regulation</h3>
  <p>For a buck converter, the ideal voltage conversion ratio is $V_{\text{out}} = D \cdot V_{\text{in}}$ where $D$ is the duty cycle. For a boost converter, $V_{\text{out}} = \frac{V_{\text{in}}}{1-D}$.</p>

  <h3>Inductor Ripple Current</h3>
  $$\Delta i_L = \frac{V_{\text{in}} - V_{\text{out}}}{L} \cdot D \cdot T_s$$

  <h3>Output Voltage Ripple</h3>
  $$\Delta v_{\text{out}} = \frac{\Delta i_L}{8 f_s C}$$

  <h2>4. Transient Analysis</h2>

  <h3>Startup Inrush Current</h3>
  <p>
    Tool motors exhibit large inrush currents at startup. A circular saw can draw 25&ndash;30 A for 50&ndash;200 ms during blade spinup. The converter must handle these transients without tripping overcurrent protection prematurely.
  </p>

  <h3>Load Step Response</h3>
  <p>
    Drill profile: bursty 5&ndash;20 A spikes with near-zero idle. Circular saw profile: steady 10&ndash;15 A with spikes to 30 A during blade binding. The second-order transient response of the output voltage is characterized by natural frequency $\omega_n$ and damping ratio $\zeta$.
  </p>

  <h2>5. MOSFET Switching Analysis</h2>

  <h3>Conduction Losses</h3>
  $$P_{\text{cond}} = I_{\text{rms}}^2 \cdot R_{\text{DS(on)}}$$
  <p>At 15 A with $R_{\text{DS(on)}} = 3.2\,\text{m}\Omega$: $P_{\text{cond}} = 0.72\,\text{W}$.</p>

  <h3>Switching Losses</h3>
  $$P_{\text{sw}} = \frac{1}{2} V_{\text{DS}} \cdot I_D \cdot (t_r + t_f) \cdot f_s$$

  <h3>Total MOSFET Losses</h3>
  $$P_{\text{total}} = P_{\text{cond}} + P_{\text{sw}} + P_{\text{gate}} + P_{\text{rr}}$$

  <h2>6. Simulation Methodology</h2>
  <p>
    The design is validated through LTspice circuit simulation with detailed MOSFET models. A companion Rust <code>no_std</code> simulation library mirrors the firmware to be deployed on the STM32 target in Phase 4. Simulation covers steady-state regulation, load transient response, startup sequencing, and fault protection.
  </p>

  <h2>7. Component Selection</h2>

  <h3>MOSFET Selection</h3>
  <p>
    Primary selection: 80 V, $3.2\,\text{m}\Omega$ $R_{\text{DS(on)}}$ silicon MOSFETs for the high-side and low-side switches. GaN devices considered for future efficiency improvements. Key criteria: breakdown voltage, on-resistance, thermal performance, gate charge.
  </p>

  <h3>Inductor Selection</h3>
  <p>
    Target inductance: $10\,\mu\text{H}$ for the buck converter at 100 kHz switching. Saturation current rating must exceed 30 A peak. Core material: powdered iron or ferrite for acceptable core losses.
  </p>

  <h3>Capacitor Selection</h3>
  <p>
    Output capacitance: $200\,\mu\text{F}$ ceramic (MLCC) plus electrolytic for bulk energy storage. Low ESR required for acceptable ripple and transient response.
  </p>

  <h2>8. Efficiency Analysis</h2>
  <p>
    Total loss breakdown at 15 A, 18 V output: MOSFET conduction (0.72 W), switching (0.94 W), inductor core (0.48 W), inductor DCR (0.34 W), gate drive (0.08 W). Total: approximately 2.56 W, yielding 92&ndash;95% efficiency depending on operating point.
  </p>

  <h2>9. Safety Design</h2>
  <ul>
    <li><strong>Overcurrent Protection (OCP):</strong> Hardware comparator with $50\,\mu\text{s}$ response time, cycle-by-cycle current limiting</li>
    <li><strong>Overvoltage Protection (OVP):</strong> TVS diode clamping plus firmware detection</li>
    <li><strong>Reverse Polarity Protection:</strong> P-channel MOSFET in high-side path</li>
    <li><strong>Soft-Start:</strong> Gradual duty cycle ramp over 10 ms to limit inrush</li>
    <li><strong>Undervoltage Lockout (UVLO):</strong> Prevents operation below safe battery voltage</li>
    <li><strong>Battery Discharge Protection:</strong> Configurable low-voltage cutoff per chemistry</li>
  </ul>

  <h2>10. Battery Ecosystem Analysis</h2>
  <table>
    <thead>
      <tr><th>Brand</th><th>System</th><th>Voltage</th><th>Notes</th></tr>
    </thead>
    <tbody>
      <tr><td>DeWalt</td><td>20V MAX</td><td>20 V max, 18 V nominal</td><td>5S Li-Ion</td></tr>
      <tr><td>Milwaukee</td><td>M18</td><td>18 V nominal</td><td>5S Li-Ion</td></tr>
      <tr><td>Makita</td><td>18V LXT</td><td>18 V nominal</td><td>5S Li-Ion</td></tr>
      <tr><td>Ryobi</td><td>ONE+</td><td>18 V nominal</td><td>Consumer-grade</td></tr>
      <tr><td>Bosch</td><td>18V</td><td>18 V nominal</td><td>Professional</td></tr>
    </tbody>
  </table>

  <h2>11. PCB Layout Considerations</h2>
  <p>
    Power loop minimization, copper weight and trace sizing for 30 A peak, thermal via arrays under MOSFETs, and current sense resistor placement for accurate measurement. Four-layer PCB recommended with dedicated power and ground planes.
  </p>

  <h2>12. Digital Implementation Considerations</h2>
  <p>
    ADC sampling quantization, PWM resolution at 100 kHz, computational delay compensation, dead-time generation for half-bridge, and interrupt-driven control architecture. These considerations feed directly into Phase 4 firmware design.
  </p>

  <h2>13. Results and Discussion</h2>
  <ul>
    <li>Simulated efficiency: 92&ndash;95% at 15 A nominal</li>
    <li>Voltage regulation: $\pm 0.5$ V under transient loading</li>
    <li>Safe shutdown: within $50\,\mu\text{s}$ of fault condition</li>
    <li>Load transient recovery: sub-millisecond</li>
  </ul>

  <h2>14. Conclusion</h2>
  <p>
    This paper established the power electronics foundation for VoltForge. The validated plant model &mdash; state-space matrices, transfer functions, and transient characterization &mdash; feeds directly into Phase 2 (PID and state-space control loop design) as the controlled system.
  </p>

  <div class="insight-box">
    <p><strong>Phase 2 Interface:</strong> The converter plant model $G_{vd}(s)$ and $G_{id}(s)$ derived here become the controlled system for the cascaded PID controller designed in Phase 2.</p>
  </div>

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