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Imagine your car's alternator spiking from 12 volts up to 15 volts every time you tap the gas pedal, but your sensitive electronics need an exact, steady 5 volts to survive.

Can a simple two-component circuit clamp this bouncing voltage into a razor-flat DC supply without burning out?

A **Zener diode** is a specialized semiconductor diode designed to operate reliably in reverse breakdown without damage.

In 1934, American physicist Clarence Zener discovered that high electric fields enable electrons to tunnel across reverse-biased p-n junctions, holding the terminal voltage nearly constant across large current variations.

In a **shunt regulator**, we place the Zener diode in parallel (shunt) with the load to drain off excess current and hold the load voltage at $V_Z$.

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; font-family: system-ui, -apple-system, sans-serif; }
    body {
      background: #f8f9fa;
      color: #1e2945;
      padding: 12px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      min-height: 100%;
      user-select: none;
    }

    .controls {
      width: 100%;
      max-width: 480px;
      display: flex;
      flex-direction: column;
      gap: 8px;
      background: #ffffff;
      padding: 10px 16px;
      border-radius: 12px;
      box-shadow: 0 2px 6px rgba(0,0,0,0.05);
    }

    .slider-row {
      display: flex;
      align-items: center;
      justify-content: space-between;
      gap: 12px;
    }

    .slider-label {
      font-size: 15px;
      font-weight: 700;
      color: #1e2945;
      min-width: 85px;
    }

    input[type=range] {
      flex: 1;
      height: 6px;
      border-radius: 3px;
      background: #e2e8f0;
      outline: none;
      accent-color: #22b7ff;
      cursor: pointer;
    }

    .btn-group {
      display: flex;
      gap: 8px;
      justify-content: center;
    }

    .preset-btn {
      flex: 1;
      padding: 6px 0;
      border: 1px solid #e2e8f0;
      border-radius: 8px;
      background: #f8f9fa;
      font-size: 13px;
      font-weight: 600;
      color: #64748b;
      cursor: pointer;
      transition: all 0.2s ease;
    }

    .preset-btn.active {
      background: #22b7ff;
      color: #ffffff;
      border-color: #22b7ff;
    }

    .circuit-container {
      width: 100%;
      max-width: 480px;
      background: #ffffff;
      border-radius: 12px;
      padding: 12px;
      margin: 8px 0;
      box-shadow: 0 2px 6px rgba(0,0,0,0.05);
    }

    svg {
      width: 100%;
      height: auto;
      display: block;
    }

    .wire { stroke: #64748b; stroke-width: 2.5; stroke-linecap: round; stroke-linejoin: round; fill: none; }
    .component { stroke: #1e2945; stroke-width: 2; fill: #ffffff; }
    .zener-symbol { fill: #1e2945; stroke: #1e2945; stroke-width: 2; }
    
    .current-flow {
      stroke-dasharray: 6, 6;
      animation: dash 1s linear infinite;
    }

    @keyframes dash {
      to { stroke-dashoffset: -12; }
    }

    .readouts {
      width: 100%;
      max-width: 480px;
      display: grid;
      grid-template-columns: 1fr 1fr;
      gap: 8px;
    }

    .badge {
      background: #ffffff;
      padding: 8px 12px;
      border-radius: 10px;
      box-shadow: 0 2px 6px rgba(0,0,0,0.05);
      display: flex;
      flex-direction: column;
      align-items: center;
      text-align: center;
    }

    .badge-title {
      font-size: 12px;
      font-weight: 600;
      color: #64748b;
    }

    .badge-val {
      font-size: 16px;
      font-weight: 800;
      margin-top: 2px;
    }

    .steady { color: #16a34a; }
    .changing { color: #0284c7; }
    .zener-drain { color: #d97706; }
  </style>
</head>
<body>

  
  <div class="controls">
    <div class="slider-row">
      <span class="slider-label" id="vinLabel">V_IN: 12.0 V</span>
      <input type="range" id="vinSlider" min="7" max="17" step="0.5" value="12">
    </div>
    <div class="btn-group">
      <button class="preset-btn" onclick="setVin(8)">Low (8V)</button>
      <button class="preset-btn active" onclick="setVin(12)">Normal (12V)</button>
      <button class="preset-btn" onclick="setVin(16)">High (16V)</button>
    </div>
  </div>

  
  <div class="circuit-container">
    <svg viewBox="0 0 440 220">
      
      <path class="wire" d="M 40 180 L 400 180" />
      
      
      <path class="wire" d="M 40 40 L 100 40" />
      <circle cx="40" cy="40" r="4" fill="#0284c7" />
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      <path class="wire" d="M 100 40 L 120 40" />
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      <text x="147.5" y="44" font-size="11" font-weight="bold" fill="#1e2945" text-anchor="middle">R_S</text>
      <path class="wire" d="M 175 40 L 260 40" />
      
      
      <path id="isPath" class="current-flow" stroke="#0284c7" stroke-width="2.5" d="M 70 30 L 105 30" />
      <polygon points="107,30 101,27 101,33" fill="#0284c7" />
      <text id="isText" x="88" y="22" font-size="11" font-weight="bold" fill="#0284c7" text-anchor="middle">I_S</text>

      
      <circle cx="260" cy="40" r="3.5" fill="#1e2945" />
      <path class="wire" d="M 260 40 L 260 85" />
      
      
      
      <path d="M 246 80 L 250 85 L 270 85 L 274 90" fill="none" stroke="#d97706" stroke-width="2.5" stroke-linecap="round" />
      
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      <text id="izText" x="295" y="107" font-size="11" font-weight="bold" fill="#d97706">I_Z</text>

      
      <path class="wire" d="M 260 40 L 370 40 L 370 80" />
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      <text x="370" y="109" font-size="11" font-weight="bold" fill="#1e2945" text-anchor="middle">R_L</text>
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      <circle cx="370" cy="40" r="3.5" fill="#1e2945" />
      <circle cx="370" cy="180" r="3.5" fill="#1e2945" />

      
      <path class="current-flow" stroke="#16a34a" stroke-width="2.5" d="M 395 85 L 395 115" />
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      <text id="ilText" x="415" y="105" font-size="11" font-weight="bold" fill="#16a34a">I_L</text>

      
      <path d="M 370 40 L 400 40" stroke="#16a34a" stroke-dasharray="2,2" stroke-width="1.5" />
      <path d="M 370 180 L 400 180" stroke="#16a34a" stroke-dasharray="2,2" stroke-width="1.5" />
      <path d="M 400 40 L 400 180" stroke="#16a34a" stroke-width="1.5" marker-start="url(#dot)" marker-end="url(#dot)" />
      
      
      <text x="40" y="115" font-size="12" font-weight="bold" fill="#0284c7" text-anchor="middle">V_IN</text>
      <text x="400" y="200" font-size="11" font-weight="bold" fill="#64748b" text-anchor="end">0V (GND)</text>
      <text x="260" y="140" font-size="11" font-weight="bold" fill="#d97706" text-anchor="middle">V_Z = 5.0V</text>
    </svg>
  </div>

  
  <div class="readouts">
    <div class="badge">
      <span class="badge-title">Zener Current (Drains Excess)</span>
      <span class="badge-val zener-drain" id="izVal">I_Z = 60 mA</span>
    </div>
    <div class="badge">
      <span class="badge-title">Regulated Load Output</span>
      <span class="badge-val steady" id="voutVal">V_OUT = 5.0 V (Fixed)</span>
    </div>
  </div>

  <script>
    const slider = document.getElementById('vinSlider');
    const vinLabel = document.getElementById('vinLabel');
    const izVal = document.getElementById('izVal');
    const voutVal = document.getElementById('voutVal');
    const isText = document.getElementById('isText');
    const izText = document.getElementById('izText');
    const btns = document.querySelectorAll('.preset-btn');

    const VZ = 5.0;      // 5V Zener breakdown
    const RS = 100;     // 100 ohms
    const RL = 500;     // 500 ohms -> IL = 5V / 500 = 10mA

    function update() {
      const vin = parseFloat(slider.value);
      vinLabel.textContent = `V_IN: ${vin.toFixed(1)} V`;

      // Calculations
      const vDropRs = Math.max(0, vin - VZ);
      const isTotal = (vDropRs / RS) * 1000; // in mA
      const iLoad = (VZ / RL) * 1000;       // 10 mA
      const iZener = Math.max(0, isTotal - iLoad);

      izVal.textContent = `I_Z = ${iZener.toFixed(0)} mA`;
      voutVal.textContent = `V_OUT = 5.0 V`;
      isText.textContent = `I_S: ${isTotal.toFixed(0)}mA`;
      izText.textContent = `I_Z: ${iZener.toFixed(0)}mA`;

      // Update preset buttons active state
      btns.forEach(btn => {
        const val = parseFloat(btn.getAttribute('onclick').replace(/[^0-9.]/g, ''));
        btn.classList.toggle('active', Math.abs(val - vin) < 0.25);
      });
    }

    function setVin(val) {
      slider.value = val;
      update();
    }

    slider.addEventListener('input', update);
    update();
  </script>
</body>
</html>

What happens if the input voltage drops or the load suddenly demands more current?

By **Kirchhoff's Current Law**, the total current $I_S$ flowing through the series resistor is always the sum of the Zener current and the load current: $$I_S = I_Z + I_L$$

To keep the diode in stable breakdown, $I_Z$ must never drop below the **knee current** ($I_{ZK}$ or $I_{Z,min}$), typically a few milliamps.

The worst-case scenario for regulation failure occurs when the input voltage is at its minimum ($V_{IN,min}$) while the load pulls its maximum current ($I_{L,max}$).

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      font-family: system-ui, -apple-system, sans-serif;
      background: #f8f9fa;
      color: #1e2945;
      padding: 12px;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 12px;
    }

    /* Controls */
    .controls {
      display: flex;
      gap: 8px;
      width: 100%;
      max-width: 480px;
    }
    .btn {
      flex: 1;
      padding: 8px 4px;
      border: 1px solid #e2e8f0;
      background: #fff;
      border-radius: 8px;
      font-size: 13px;
      font-weight: 600;
      color: #64748b;
      cursor: pointer;
      text-align: center;
      transition: all 0.25s ease;
    }
    .btn.active {
      background: #22b7ff;
      color: #fff;
      border-color: #22b7ff;
      box-shadow: 0 2px 6px rgba(34, 183, 255, 0.3);
    }

    /* SVG Circuit Diagram Container */
    .circuit-box {
      width: 100%;
      max-width: 480px;
      background: #ffffff;
      border: 1px solid #e2e8f0;
      border-radius: 12px;
      padding: 10px;
      display: flex;
      flex-direction: column;
      align-items: center;
    }

    svg {
      width: 100%;
      height: auto;
      display: block;
    }

    /* Status Bar */
    .status-bar {
      display: flex;
      justify-content: space-between;
      align-items: center;
      width: 100%;
      margin-top: 6px;
      padding-top: 8px;
      border-top: 1px solid #f1f5f9;
      font-size: 13px;
      font-weight: 600;
    }
    .badge {
      padding: 3px 8px;
      border-radius: 6px;
      font-size: 12px;
      font-weight: 700;
    }
    .badge.ok { background: #dcfce7; color: #15803d; }
    .badge.warn { background: #fef3c7; color: #b45309; }
    .badge.danger { background: #fee2e2; color: #b91c1c; }

    /* Current Flow Animation */
    .flow-line {
      stroke-dasharray: 6 6;
      animation: dash 1s linear infinite;
    }
    @keyframes dash {
      to { stroke-dashoffset: -12; }
    }
  </style>
</head>
<body>

  
  <div class="controls">
    <button class="btn active" id="btnMin" onclick="setMode('min')">Worst-Case Dropout<br><span style="font-size:11px;font-weight: normal;">$V_{IN,min} \text{ & } I_{L,max}$</span></button>
    <button class="btn" id="btnMax" onclick="setMode('max')">Worst-Case Heat<br><span style="font-size:11px;font-weight: normal;">$V_{IN,max} \text{ & } I_L = 0$</span></button>
  </div>

  <div class="circuit-box">
    <svg viewBox="0 0 440 230">
      <defs>
        
        <marker id="arrow" viewBox="0 0 10 10" refX="5" refY="5" markerWidth="6" markerHeight="6" orient="auto-start-reverse">
          <path d="M 0 1.5 L 8 5 L 0 8.5 z" fill="#22b7ff" />
        </marker>
        <marker id="arrow-warn" viewBox="0 0 10 10" refX="5" refY="5" markerWidth="6" markerHeight="6" orient="auto-start-reverse">
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        </marker>
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      <circle cx="30" cy="40" r="3.5" fill="#1e2945" />
      <circle cx="30" cy="190" r="3.5" fill="#1e2945" />
      <text x="30" y="24" text-anchor="middle" font-size="13" font-weight="700" fill="#1e2945" id="vinLabel">V_IN (min)</text>
      <text x="30" y="208" text-anchor="middle" font-size="11" fill="#64748b">0V (GND)</text>

      
      <rect x="110" y="28" width="60" height="24" rx="4" fill="#f8fafc" stroke="#1e2945" stroke-width="2" />
      <text x="140" y="44" text-anchor="middle" font-size="12" font-weight="700" fill="#1e2945">R_S</text>
      <text x="140" y="20" text-anchor="middle" font-size="11" font-weight="700" fill="#22b7ff" id="isLabel">I_S (min)</text>
      
      <line id="isArrow" x1="75" y1="32" x2="102" y2="32" stroke="#22b7ff" stroke-width="2.5" marker-end="url(#arrow)" />

      
      <circle cx="250" cy="40" r="3.5" fill="#1e2945" />

      
      <line x1="250" y1="40" x2="250" y2="90" stroke="#94a3b8" stroke-width="2" />
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      <path d="M 234 108 L 236 102 L 264 102 L 266 96" fill="none" stroke="#1e2945" stroke-width="2" stroke-linecap="round" />
      
      <line id="izArrow" x1="236" y1="60" x2="236" y2="85" stroke="#22b7ff" stroke-width="1.5" marker-end="url(#arrow)" />
      <text id="izText" x="230" y="75" text-anchor="end" font-size="11" font-weight="700" fill="#22b7ff">I_Z,min</text>
      <text x="268" y="118" font-size="11" font-weight="600" fill="#64748b">D_Z (V_Z)</text>

      
      <line x1="370" y1="40" x2="370" y2="85" stroke="#94a3b8" stroke-width="2" />
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      <text id="rlText" x="370" y="120" text-anchor="middle" font-size="12" font-weight="700" fill="#1e2945">R_L</text>
      
      <line id="ilArrow" x1="392" y1="60" x2="392" y2="85" stroke="#22b7ff" stroke-width="3" marker-end="url(#arrow)" />
      <text id="ilText" x="398" y="75" font-size="11" font-weight="700" fill="#22b7ff">I_L,max</text>

      
      <circle cx="410" cy="40" r="3.5" fill="#1e2945" />
      <circle cx="410" cy="190" r="3.5" fill="#1e2945" />
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      <text x="424" y="118" font-size="11" font-weight="700" fill="#1e2945">V_OUT</text>
    </svg>

    
    <div class="status-bar">
      <span id="formula" style="font-family: monospace;">I_S = I_Z(min) + I_L(max)</span>
      <span id="statusBadge" class="badge ok">✓ Regulated</span>
    </div>
  </div>

  <script>
    function setMode(mode) {
      const btnMin = document.getElementById('btnMin');
      const btnMax = document.getElementById('btnMax');
      const vin = document.getElementById('vinLabel');
      const isL = document.getElementById('isLabel');
      const izT = document.getElementById('izText');
      const ilT = document.getElementById('ilText');
      const izArr = document.getElementById('izArrow');
      const ilArr = document.getElementById('ilArrow');
      const rlBox = document.getElementById('rlBox');
      const rlText = document.getElementById('rlText');
      const formula = document.getElementById('formula');
      const badge = document.getElementById('statusBadge');

      if (mode === 'min') {
        btnMin.classList.add('active');
        btnMax.classList.remove('active');

        vin.textContent = 'V_IN (min)';
        isL.textContent = 'I_S (min)';
        izT.textContent = 'I_Z,min';
        izT.setAttribute('fill', '#22b7ff');
        izArr.setAttribute('stroke-width', '1.5');
        izArr.setAttribute('marker-end', 'url(#arrow)');

        ilT.textContent = 'I_L,max';
        ilT.setAttribute('fill', '#22b7ff');
        ilArr.setAttribute('stroke-width', '3.5');
        ilArr.setAttribute('marker-end', 'url(#arrow)');
        ilArr.style.opacity = '1';
        rlBox.style.opacity = '1';
        rlText.style.opacity = '1';

        formula.textContent = 'I_S(min) = I_Z,min + I_L,max';
        badge.textContent = '✓ Must keep I_Z ≥ I_Z,min';
        badge.className = 'badge ok';
      } else {
        btnMax.classList.add('active');
        btnMin.classList.remove('active');

        vin.textContent = 'V_IN (max)';
        isL.textContent = 'I_S (max)';
        izT.textContent = 'I_Z,max (ALL)';
        izT.setAttribute('fill', '#d97706');
        izArr.setAttribute('stroke-width', '4');
        izArr.setAttribute('marker-end', 'url(#arrow-warn)');

        ilT.textContent = 'I_L = 0';
        ilT.setAttribute('fill', '#94a3b8');
        ilArr.style.opacity = '0';
        rlBox.style.opacity = '0.2';
        rlText.style.opacity = '0.2';

        formula.textContent = 'I_S(max) = I_Z,max';
        badge.textContent = '⚠️ Max Zener Power (P_Z)';
        badge.className = 'badge warn';
      }
    }
  </script>
</body>
</html>

How do we derive an exact formula to guarantee the resistor $R_S$ satisfies both boundary conditions?

By Ohm's law, the voltage drop across the series resistor is $V_{IN} - V_Z$, meaning its resistance is given by: $$R_S = \frac{V_{IN} - V_Z}{I_S} = \frac{V_{IN} - V_Z}{I_Z + I_L}$$

To guarantee that $I_Z \ge I_{ZK}$ under the weakest supply and heaviest load, we calculate the **maximum allowable resistance**: $$R_{S,max} = \frac{V_{IN,min} - V_Z}{I_{ZK} + I_{L,max}}$$

Choosing any resistor value larger than $R_{S,max}$ will starve the diode of current, causing it to fall out of reverse breakdown and lose regulation.

Let's put this into practice with a complete engineering design calculation.

Suppose we want to regulate a fluctuating input of $12\text{ V}$ to $16\text{ V}$ down to a stable $5.1\text{ V}$ using a Zener with $I_{ZK} = 5\text{ mA}$ and power rating $P_{Z,max} = 1\text{ W}$. The load current $I_L$ varies between $10\text{ mA}$ and $40\text{ mA}$.

First, calculate $R_{S,max}$ at minimum input ($12\text{ V}$) and maximum load current ($40\text{ mA}$): $$R_{S,max} = \frac{12\text{ V} - 5.1\text{ V}}{0.005\text{ A} + 0.040\text{ A}} = \frac{6.9\text{ V}}{0.045\text{ A}} \approx 153.3\text{ }\Omega$$

We select the nearest standard E24 resistor value below this limit, choosing $R_S = 150\text{ }\Omega$ to guarantee sufficient current.

<!DOCTYPE html>
<html lang="en">
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    .schematic-zener { stroke: #2563eb; stroke-width: 2.5; fill: #dbeafe; }
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    .badge-vin { background: #f1f5f9; color: #334155; border-color: #cbd5e1; }
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<body>

  
  <div class="circuit-box">
    <svg viewBox="0 0 540 210">
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      <line x1="50" y1="40" x2="130" y2="40" class="schematic-wire" />
      
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      <text x="170" y="44" font-size="11" font-weight="700" fill="#713f12" text-anchor="middle" dominant-baseline="middle">R_S = 150 Ω</text>
      
      
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      <line x1="50" y1="180" x2="480" y2="180" class="schematic-wire" />

      
      <circle cx="50" cy="40" r="4" fill="#334155" />
      <circle cx="50" cy="180" r="4" fill="#334155" />
      <text x="48" y="24" font-size="12" font-weight="700" fill="#334155" text-anchor="middle">V_IN</text>

      
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      <text id="lblIs" x="95" y="18" font-size="11" font-weight="700" fill="#0284c7" text-anchor="middle">I_S</text>

      
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      <text id="lblIz" x="348" y="68" font-size="11" font-weight="700" fill="#dc2626" text-anchor="start">I_Z</text>

      
      
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      <text x="310" y="125" font-size="11" font-weight="700" fill="#2563eb" text-anchor="middle">V_Z = 5.1 V</text>

      
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      <text id="lblIl" x="492" y="68" font-size="11" font-weight="700" fill="#16a34a" text-anchor="start">I_L</text>

      
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      <text x="470" y="107" font-size="11" font-weight="700" fill="#475569" text-anchor="middle">LOAD</text>
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  </div>

  
  <div class="stats-row">
    <div>I_S = <span id="valIs" class="badge badge-is">72.7 mA</span></div>
    <div>I_Z = <span id="valIz" class="badge badge-iz">62.7 mA</span></div>
    <div>I_L = <span id="valIl" class="badge badge-il">10.0 mA</span></div>
    <div>P_Z = <span id="valPz" class="badge badge-pz">320 mW</span></div>
  </div>

  
  <div class="presets">
    <button class="btn active" id="btnWorst">Worst-Case Max Stress (16V, 10mA)</button>
    <button class="btn" id="btnNominal">Nominal (12V, 25mA)</button>
    <button class="btn" id="btnMin">Min Input (8V, 10mA)</button>
  </div>

  
  <div class="controls-grid">
    <div class="ctrl-card">
      <div class="ctrl-head">
        <span>Input Voltage (V_IN)</span>
        <span id="dispVin" class="badge badge-vin">16.0 V</span>
      </div>
      <input type="range" id="sliderVin" min="8" max="16" step="0.1" value="16">
    </div>

    <div class="ctrl-card">
      <div class="ctrl-head">
        <span>Load Current (I_L)</span>
        <span id="dispIl" class="badge badge-il">10.0 mA</span>
      </div>
      <input type="range" id="sliderIl" min="5" max="50" step="1" value="10">
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    const RS = 150;
    const VZ = 5.1;

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    const dispVin = document.getElementById('dispVin');
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    const valIz = document.getElementById('valIz');
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    const btnNominal = document.getElementById('btnNominal');
    const btnMin = document.getElementById('btnMin');

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      const vin = parseFloat(sliderVin.value);
      const il_mA = parseFloat(sliderIl.value);

      dispVin.textContent = vin.toFixed(1) + ' V';
      dispIl.textContent = il_mA.toFixed(1) + ' mA';

      // Calculation
      const is_A = Math.max(0, (vin - VZ) / RS);
      const is_mA = is_A * 1000;
      const iz_mA = Math.max(0, is_mA - il_mA);
      const pz_mW = VZ * iz_mA;

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      valIz.textContent = iz_mA.toFixed(1) + ' mA';
      valIl.textContent = il_mA.toFixed(1) + ' mA';
      valPz.textContent = Math.round(pz_mW) + ' mW';

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      lblIz.textContent = `I_Z = ${iz_mA.toFixed(1)} mA`;
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      btnNominal.classList.toggle('active', vin === 12 && il_mA === 25);
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    btnNominal.addEventListener('click', () => {
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      sliderIl.value = 25;
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    btnMin.addEventListener('click', () => {
      sliderVin.value = 8;
      sliderIl.value = 10;
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    update();
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</body>
</html>

Now verify the worst-case thermal stress on the Zener at maximum input ($16\text{ V}$) and minimum load ($10\text{ mA}$): $$I_{S,max} = \frac{16\text{ V} - 5.1\text{ V}}{150\text{ }\Omega} = 72.7\text{ mA}$$

The Zener current is $I_Z = 72.7\text{ mA} - 10\text{ mA} = 62.7\text{ mA}$, producing a dissipation of $P_Z = 5.1\text{ V} \times 62.7\text{ mA} = 0.32\text{ W}$, comfortably below our $1\text{ W}$ maximum limit.

A frequent mistake is sizing $R_S$ using the **nominal averages** (like $14\text{ V}$ input and $25\text{ mA}$ load) rather than the simultaneous worst-case extremes.

If you calculate $R_S$ using average values, your circuit may work on the test bench but immediately drop out of regulation during real-world brownouts or heavy load pulses.

Always remember to size the resistor's physical **power rating** as well: here, $P_{RS} = I_{S,max}^2 R_S = (0.0727)^2 \times 150 \approx 0.79\text{ W}$, meaning a standard $0.25\text{ W}$ resistor would quickly burn out, so a $1\text{ W}$ or $2\text{ W}$ rated part is required.

electronics

Simple Zener Diode Shunt Voltage Regulators. Calculate the series current-limiting resistor value to maintain Zener breakdown conduction under variable input voltage and load current.

Zener Diode as a Voltage Regulator and Series Resistor Design

Zener Diodes - Voltage Regulator Circuit Analysis and Loading Characteristics

A-Level Electronics: Power Supplies, Zener Regulation and Load Line Analysis

Teaching sequence starts with reviewing the reverse I-V characteristic curve of PN diodes versus Zener diodes, establishing the concept of an operating 'window' bounded by $I_{ZK}$ (knee) and $I_{ZM}$ (thermal maximum). Use a 2x2 boundary matrix ($V_{\text{in(min)}} / V_{\text{in(max)}}$ vs $I_{L(\text{min})} / I_{L(\text{max})}$) so students systematically identify why $R_S$ is sized at $(V_{\text{in(min)}} - V_Z) / (I_{Z(\text{min})} + I_{L(\text{max})})$ to prevent drop-out, and why power ratings are checked at $(V_{\text{in(max)}} - V_Z)^2 / R_S$ and $V_Z \cdot I_{Z(\text{max})}$ to prevent thermal runaway. Reinforce learning with an interactive circuit simulator (e.g., Falstad or Multisim) allowing real-time sweeping of load resistance to observe the transition from regulation to potential divider drop-out.

Simple Zener Diode Shunt Voltage Regulators

The Zener Shunt Clamp

Current Balance and the Worst Case