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<!DOCTYPE html>
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<header class="paper-header">
<span class="paper-phase">Phase 3</span>
<h1>Thermal Modeling and Management for High-Current Software-Defined Power Tool Battery Adapters</h1>
<div class="paper-meta">
<p>Matthew Long — The YonedaAI Collaboration, YonedaAI Research Collective, Chicago, IL</p>
<p>March 2026</p>
</div>
</header>
<main class="paper-content">
<div class="paper-notice">
This is the HTML summary version. <a href="../pdf/thermal-management.pdf">Download the full PDF</a> for complete thermal circuit models, simulation data, and case studies.
</div>
<h2>Abstract</h2>
<p>
Software-defined battery adapters must manage substantial thermal loads at currents exceeding 30 A in ambient temperatures reaching 40°C on construction sites. This paper presents a comprehensive thermal management framework: heat source analysis for MOSFETs, inductors, PCB traces, and connectors; lumped-parameter thermal circuit modeling; enclosure thermal design for passive cooling; and a multi-threshold protection strategy with warning (70°C), derating (75°C), and shutdown (85°C) thresholds with hysteresis. The adapter sustains 20 A continuous at 40°C ambient while maintaining junction temperatures below 85°C.
</p>
<h2>1. Introduction</h2>
<p>Thermal management is critical for three reasons:</p>
<ul>
<li><strong>Safety:</strong> Uncontrolled heating risks thermal runaway, MOSFET failure, and fire hazard</li>
<li><strong>Reliability:</strong> Every 10°C increase in junction temperature approximately halves semiconductor lifetime (Arrhenius model)</li>
<li><strong>Performance:</strong> $R_{\text{DS(on)}}$ has a positive temperature coefficient (+0.4% to +0.8%/°C), creating a thermal positive feedback loop</li>
</ul>
<h2>2. Background: Heat Transfer Fundamentals</h2>
<h3>Conduction</h3>
<p>Fourier's law for steady-state conduction through a slab:</p>
$$R_{\theta,\text{cond}} = \frac{L}{kA} \quad \left[\frac{{}^{\circ}\text{C}}{\text{W}}\right]$$
<h3>Convection</h3>
$$R_{\theta,\text{conv}} = \frac{1}{hA_s}$$
<p>For the VoltForge enclosure (~80 x 50 x 30 mm, surface area ~0.013 m$^2$):</p>
$$R_{\theta,\text{enc-amb}} = \frac{1}{10 \times 0.013} \approx 7.7\;{}^{\circ}\text{C/W}$$
<div class="insight-box">
<p><strong>Key constraint:</strong> Every watt dissipated raises enclosure temperature by approximately 7.7°C above ambient — a substantial constraint at 40°C ambient.</p>
</div>
<h3>Radiation</h3>
$$q_{\text{rad}} = \varepsilon \sigma A_s (T_s^4 - T_\infty^4)$$
<p>Radiation contributes 20–30% of total heat dissipation from a dark-colored enclosure at operating temperatures.</p>
<h3>Electrical-Thermal Analogy</h3>
<table>
<thead><tr><th>Thermal Domain</th><th>Electrical Domain</th></tr></thead>
<tbody>
<tr><td>Temperature $T$ (°C)</td><td>Voltage $V$ (V)</td></tr>
<tr><td>Heat flow $Q$ (W)</td><td>Current $I$ (A)</td></tr>
<tr><td>Thermal resistance $R_\theta$ (°C/W)</td><td>Resistance $R$ (Ω)</td></tr>
<tr><td>Thermal capacitance $C_\theta$ (J/°C)</td><td>Capacitance $C$ (F)</td></tr>
</tbody>
</table>
<h2>3. Heat Source Analysis</h2>
<h3>MOSFET Conduction Losses</h3>
$$P_{\text{cond}} = I_{\text{rms}}^2 \cdot R_{\text{DS(on)}}(T_j)$$
<p>With temperature-dependent $R_{\text{DS(on)}}$: $R_{\text{DS(on)}}(T_j) = R_{\text{DS(on),25}} \cdot \left(\frac{T_j + 273}{298}\right)^{2.3}$</p>
<h3>MOSFET Switching Losses</h3>
$$P_{\text{sw}} = \frac{1}{2}V_{\text{DS}} I_D (t_r + t_f) f_s + Q_{rr} V_{\text{DS}} f_s$$
<h3>Inductor Losses</h3>
<p>Core losses (Steinmetz equation): $P_{\text{core}} = k f^a B^b \cdot V_e$</p>
<p>Copper losses: $P_{\text{cu}} = I_{\text{rms}}^2 \cdot R_{\text{DCR}}$</p>
<h3>PCB Trace and Connector Losses</h3>
<p>At 30 A peak, trace resistance and connector contact resistance contribute non-trivial heating, especially in compact enclosures.</p>
<h3>Loss Summary at 15 A, 18 V Output</h3>
<table>
<thead><tr><th>Source</th><th>Power (W)</th></tr></thead>
<tbody>
<tr><td>MOSFET conduction (x2)</td><td>1.44</td></tr>
<tr><td>MOSFET switching</td><td>0.94</td></tr>
<tr><td>Inductor core</td><td>0.48</td></tr>
<tr><td>Inductor DCR</td><td>0.34</td></tr>
<tr><td>PCB traces</td><td>0.15</td></tr>
<tr><td>Connectors</td><td>0.30</td></tr>
<tr><td><strong>Total</strong></td><td><strong>3.65</strong></td></tr>
</tbody>
</table>
<h2>4. Thermal Circuit Modeling</h2>
<h3>Junction-to-Ambient Thermal Resistance Chain</h3>
$$T_j = T_a + P_{\text{diss}} \cdot (R_{\theta,jc} + R_{\theta,cs} + R_{\theta,sa})$$
<p>Junction-to-case, case-to-sink, sink-to-ambient resistances form the complete thermal path.</p>
<h3>Multi-Node Thermal Network</h3>
<p>
A multi-node RC network captures thermal interactions between MOSFETs, inductor, PCB, and enclosure. Each node has thermal capacitance (mass x specific heat) and is connected by thermal resistances.
</p>
<h3>Transient Thermal Impedance</h3>
$$Z_{\theta}(t) = R_{\theta} \left(1 - e^{-t/\tau}\right), \quad \tau = R_\theta C_\theta$$
<h2>5. Enclosure Thermal Design</h2>
<p>
Natural convection analysis, thermal interface materials (1–5 W/m·K), heat spreading through copper planes, and worst-case ambient temperature design (40°C on summer job sites). FR-4 thermal conductivity (0.25 W/m·K) is 1500x lower than copper, so heat must be channeled through copper planes and thermal vias.
</p>
<h2>6. Thermal Protection Strategy</h2>
<h3>NTC Thermistor Sensing</h3>
<p>Steinhart-Hart equation for temperature calculation:</p>
$$\frac{1}{T} = A + B \ln(R) + C (\ln R)^3$$
<h3>Multi-Threshold Protection</h3>
<table>
<thead><tr><th>Threshold</th><th>Temperature</th><th>Action</th></tr></thead>
<tbody>
<tr><td>Warning</td><td>70°C</td><td>Log event, increase monitoring frequency</td></tr>
<tr><td>Derating</td><td>75°C</td><td>Linearly reduce max current</td></tr>
<tr><td>Shutdown</td><td>85°C</td><td>Disable output, enter safe state</td></tr>
</tbody>
</table>
<h3>Hysteresis Design</h3>
<p>
Each threshold includes 5°C hysteresis to prevent oscillation near boundary conditions. Shutdown at 85°C, re-enable at 80°C.
</p>
<h3>Thermal Derating Curves</h3>
<p>Linear derating between 75°C and 85°C:</p>
$$I_{\max}(T_j) = I_{\max,\text{rated}} \cdot \frac{T_{\text{shutdown}} - T_j}{T_{\text{shutdown}} - T_{\text{derate}}}$$
<h2>7. Simulation Methodology</h2>
<p>
Lumped-parameter thermal simulation using Forward-Euler time integration. FEA simulation approach for enclosure design validation. Model fidelity rated as "Medium" — approximate thermal behavior sufficient for design decisions, validated against analytical solutions.
</p>
<h2>8. Case Studies</h2>
<h3>Case 1: Worst Case — 30 A Saw Load at 40°C Ambient</h3>
<p>
Total dissipation ~8.5 W. Junction temperature reaches 85°C shutdown threshold in approximately 45 seconds. Requires thermal derating to sustain continuous operation. Heatsink mandatory.
</p>
<h3>Case 2: Typical — 10 A Drill Intermittent at 25°C</h3>
<p>
Total dissipation ~1.6 W. Junction temperature stabilizes at 52°C — well within safe margins. Intermittent nature of drill use provides natural cooling periods.
</p>
<h3>Case 3: Cold Start at -10°C</h3>
<p>
$R_{\text{DS(on)}}$ is lower at cold temperatures (better efficiency), but battery internal resistance increases. Thermal performance is actually improved in cold conditions.
</p>
<h2>9. Embedded Rust Implementation</h2>
<p>
The thermal management subsystem is implemented in <code>no_std</code> Rust with NTC thermistor ADC interface, Steinhart-Hart temperature calculation, multi-threshold state machine, and derating curve computation.
</p>
<h2>10. Conclusion</h2>
<p>
With proper heatsinking and copper area allocation, the adapter sustains 20 A continuous at 40°C ambient while maintaining junction temperatures below 85°C. The thermal thresholds and derating curves feed directly into Phase 4 firmware shutdown logic.
</p>
<div class="insight-box">
<p><strong>Phase 4 Interface:</strong> Thermal thresholds (70/75/85°C), derating curves, and hysteresis parameters are compiled into the Phase 4 firmware as <code>const</code> configuration values enforced by the safety supervisor.</p>
</div>
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