EMC 122 – Diodes Comprehensive Notes

Course Road-Map Context

• Sequence of topics in EMC 122:
  • Basic Electrical Theory → DC Circuits → Transient Circuits → AC Circuits → Semiconductors (Diodes & Transistors) → Operational Amplifiers → Electronics.
• Placement of today’s topic (Diodes) after AC analysis underscores the need to understand time-varying signals before discussing semiconductor rectification.
• Conceptual bridge: Diodes will later underpin transistor operation and op-amp input protection.

Diodes – Fundamental Definition & Uses

• Two-terminal semiconductor device that behaves like an electrical one-way valve.
• Exhibits:
  • Very low dynamic resistance when forward-biased (anode more positive than cathode).
  • Very high resistance when reverse-biased.
• Practical applications:
  • Rectification (AC → DC) in power supplies.
  • Over-voltage and reverse-polarity protection.
  • Voltage reference / regulation (Zener diodes).
  • Signal demodulation, logic clamping, etc.
• Symbol & polarity conventions:
  • Arrow of conventional current enters the anode (A) and exits the cathode (K).

Voltage–Current (V–I) Characteristics

• Forward region (right half of graph):
  • Begins at the “knee” or “turn-on” threshold: ≈ $0.3\,\text{V}$ for Germanium, ≈ $0.7\,\text{V}$ for Silicon.
  • After the knee, $i<em>D$ rises exponentially with $v</em>D$.
• Reverse region (left half):
  • Small leakage current (micro-ampere level). Typical: <$20\,\mu\text{A}$ (Si), <$50\,\mu\text{A}$ (Ge).
  • At sufficiently large negative voltage, diode enters breakdown (Zener/avalanche) where current increases sharply while voltage remains nearly constant.
• Key points marked:
  • Knee voltage, reverse breakdown voltage, leakage.
• Mathematical idealization often replaced with piecewise-linear or step approximation.

Semiconductor Physics Snapshot

• p-n junction forms a depletion region devoid of free carriers.
• Forward bias:
  • External voltage reduces junction potential; depletion width narrows; majority carriers cross easily → current flows.
  • Turn-on voltage $\approx 0.7\,\text{V}$ (Si) arises when external field cancels built-in potential.
• Reverse bias:
  • Depletion region widens; only a tiny reverse leakage flows.
  • At high reverse voltage, avalanche or Zener breakdown occurs; current surges while junction voltage clamps.

Ideal-Diode Approximation (1st Approx.)

• Model rules:
  • ON (conducting): $v_D = 0\,\text{V}$, current positive.
  • OFF (blocking): $i_D = 0$, voltage can be any value < 0.
• Truth table perspective resembles a perfect switch directed by junction polarity.
• Circuit diagrams often replace ON diode with short circuit, OFF diode with open circuit.

Strategy for Circuits Containing Ideal Diodes

1. Assume a conduction state for each diode.
2. Replace each diode with its model counterpart (short or open).
3. Solve circuit for unknown node voltages & branch currents.
4. Verify assumption:
   • If assumed ON ⇒ check i_D > 0.
   • If assumed OFF ⇒ check v_D < 0.
5. If contradiction arises, flip the assumed state and resolve.

• Comment: This logical approach mirrors nodal-analysis with inequality constraints and foreshadows MOSFET piecewise linear analysis.

Worked Example 1 (Ideal Diodes)

• Original network (page 8): three equal $4\,\text{k}\Omega$ resistors, one $6\,\text{k}\Omega$, dual DC sources (10 V, 3 V), diodes $D<em>1, D</em>2$.
• Two hypotheses tested:
  1. $D<em>1$ OFF, $D</em>2$ ON → calculated $v<em>{D1} = +7\,\text{V}$ (positive while OFF) ⇒ violates vD < 0 rule ⇒ invalid.
  2. $D<em>1$ ON, $D</em>2$ OFF → obtained $i<em>{D1} = 0.5\,\text{mA} > 0$ and v{D2} < 0 while OFF ⇒ consistent ⇒ correct operating point.
• Outcome: instructs importance of iteration and logical checking rather than blind substitution.

Simple Piecewise-Linear Approximation (2nd Approx.)

• Improves realism by introducing finite forward voltage $V_f$ rather than 0 V.
• Model:
  • ON: $v<em>D = V</em>f$ (constant), $i_D$ unrestricted positive.
  • OFF: open circuit (same as ideal).
• Typical $V_f$ values: $0.7\,\text{V}$ for Si, $0.3\,\text{V}$ for Ge, higher for power diodes.
• Graph: horizontal step at $V_f$ followed by vertical line (current axis), simplifying exponential curve into 2 straight segments.

Solving Strategy with Piecewise-Linear Diode

• Similar assumption/verification loop but inequalities adjust:
  • ON assumed ⇒ set $v<em>D = V</em>f$, solve, require i_D > 0.
  • OFF assumed ⇒ set $i<em>D = 0$, solve, require vD < V_f.

Classic Application – Half-Wave Rectifier with Capacitor & Load

• Circuit elements: AC source $v<em>s(t)$, ideal diode, smoothing capacitor $C$, resistive load $R</em>L$.
• Operation over a cycle:
  1. Positive half-cycle: diode ON, capacitor charges to near peak $V_{m}$ minus one diode drop.
  2. Negative half-cycle: diode OFF, capacitor discharges through $R<em>L$ producing load current $i</em>L(t)$.
• Waveform features:
  • Output $V<em>L(t)$ exhibits ripple $V</em>r$; desired $V<em>r$ minimized by large $C$ or larger $R</em>L$.
  • Input current $i_D(t)$ is pulsating, limited to conduction intervals.
• Practical implications:
  • Filter design involves trade-off between ripple, size, cost.
  • Diode’s reverse recovery and forward drop affect efficiency & heat dissipation.

Connections & Broader Significance

• Builds on DC source analysis; prepares for full-wave bridges, Zener regulators, and later transistor biasing.
• Ethical/Practical: Proper diode selection (voltage rating, current capacity) critical to avoid catastrophic failure in consumer electronics.
• Real-world examples: Phone chargers, solar panel bypass diodes, automotive alternator rectifiers.

Numerical / Algebraic References

• Ideal diode constraints:
  • $v_D = 0 \text{ (ON)}$
  • $i_D = 0 \text{ (OFF)}$
• Piecewise-linear ON voltage:
  • $v<em>D = V</em>f$ (e.g. $0.7\,\text{V}$).
• Example current: $i_D = \frac{10\,\text{V} - 3\,\text{V}}{(4 + 6)\,\text{k}\Omega} = 0.5\,\text{mA}$.

Q & A / Clarifications Raised

• Why prefer Silicon over Germanium today? → Higher temperature stability, lower leakage, easier fabrication.
• What happens if reverse breakdown is exceeded? → Unless diode is rated as Zener, thermal runaway and permanent damage.
• Forward drop variation with current? → In real devices $v<em>D$ increases logarithmically with $i</em>D$ (Shockley equation), captured by more sophisticated models.

Study Reminders

• Always state your diode assumption explicitly in homework/test solutions.
• Sketch expected current direction before writing KVL/KCL.
• Memorize typical Si turn-on $0.7\,\text{V}$ but note temperature coefficient ≈ −2 mV/°C.