Semiconductor Diodes & Power Rectification: Rapid-Review Notes

Ideal Diode
  • Two-terminal, switch-like device: conducts one way, open the other.
  • Forward region ⇒ short-circuit (R<em>F≈0R<em>F \approx 0) ; reverse region ⇒ open-circuit (R</em>R→∞R</em>R \to \infty).
  • PIV/PRV: max reverse V before Zener/avalanche.
Semiconductor Basics
  • Intrinsic Si/Ge: conductivity between conductors & insulators, resistivity ρ\rho in Ω⋅cm\Omega\cdot\text{cm}.
  • Extrinsic doping:
    • n-type (donor, 5 valence e⁻) – electrons majority.
    • p-type (acceptor, 3 valence) – holes majority.
  • Energy gap EgE_g: Si 1.1 eV1.1\,\text{eV}, Ge 0.67 eV0.67\,\text{eV}.
p-n Junction & Shockley Equation
  • Depletion region forms at junction; width ↑ with reverse bias.
  • Diode I–V (T in kelvin): I<em>D=I</em>S (eV<em>D/ηV</em>T−1)I<em>D = I</em>S\,(e^{V<em>D/\eta V</em>T}-1) where VT=kTq≈26 mV @ 300 KV_T= \frac{kT}{q} \approx 26\,\text{mV @ 300 K}, η=1\eta=1(Ge) or 2(Si low I).
  • Temperature: ISI_S doubles ≈ every 10∘C10^{\circ}\text{C} rise.
Resistance Definitions
  • DC/static: R<em>D=V</em>D/IDR<em>D=V</em>D/I_D (point value).
  • AC/dynamic: r<em>d=ΔV/ΔI≈ηV</em>TI<em>D+r</em>Br<em>d=\Delta V/\Delta I \approx \frac{\eta V</em>T}{I<em>D}+r</em>B (vertical-rise region).
  • Average ac (large swing): r<em>av=ΔVΔI∣</em>end ptsr<em>{av}=\frac{\Delta V}{\Delta I}\big|</em>{\text{end pts}}.
Diode Equivalent (Models)
  1. Ideal: arrow + open; VF=0V_F=0.
  2. Simplified: ideal + VT (0.7 Si,0.3 Ge)V_T\,(0.7\,\text{Si},0.3\,\text{Ge}).
  3. Piecewise-linear: simplified + ravr_{av}.
Key Datasheet Parameters
  • V<em>FV<em>F @ I</em>FI</em>F; I<em>FmaxI<em>F^{\text{max}}; I</em>RI</em>R @ V<em>RV<em>R; PIV; P</em>DP</em>D; C<em>TC<em>T, t</em>rrt</em>{rr}; TopT_{op}.
Capacitances & Switching
  • Transition/depletion: C<em>T=εA/WC<em>T=\varepsilon A/W, ↓ as ∣V</em>R∣|V</em>R| ↑.
  • Diffusion/storage C<em>D∝I</em>FC<em>D \propto I</em>F (forward).
  • Reverse recovery time t<em>rr=t</em>s+ttt<em>{rr}=t</em>s+t_t (few ns → µs).
Zener Diode
  • Sharp breakdown at VZV_Z (avalanche/Zener).
  • Regulator models: ideal V source V<em>ZV<em>Z + small r</em>Zr</em>Z.
  • Design limits: I<em>Z,minI<em>{Z,min} for regulation, I</em>Z,max=P<em>ZM/V</em>ZI</em>{Z,max}=P<em>{ZM}/V</em>Z.
  • Turn-on with R<em>L≥R</em>L,min=RV<em>ZV</em>i−V<em>ZR<em>L\ge R</em>{L,min}=\frac{R V<em>Z}{V</em>i-V<em>Z} ; V</em>i,max=R(I<em>ZM+I</em>L)+VZV</em>{i,max}=R(I<em>{ZM}+I</em>L)+V_Z.
Light-Emitting Diode (LED)
  • Materials: GaAsP, GaP,… ; light via electroluminescence.
  • V<em>F≈1.7!–!3.3 VV<em>F\approx1.7!–!3.3\,\text{V} ; I</em>F≈5!–!30 mAI</em>F\approx5!–!30\,\text{mA}.
Rectifiers
  • Half-wave (HW): uses 1 diode.
    • V<em>DC=0.318 V</em>mV<em>{DC}=0.318\,V</em>m ; g<em>HW=1.21g<em>{HW}=1.21 ; η</em>HW=40.6%\eta</em>{HW}=40.6\% ; TUF=0.287\text{TUF}=0.287.
  • Full-wave (FW, CT or bridge):
    • V<em>DC=0.636 V</em>mV<em>{DC}=0.636\,V</em>m ; g<em>FW=0.48g<em>{FW}=0.48 ; η</em>FW=81.2%\eta</em>{FW}=81.2\% ; TUFbridge=0.693\text{TUF}_{bridge}=0.693.
  • PIV: HW =V<em>m=V<em>m; FW-CT =2V</em>m=2V</em>m; Bridge =Vm=V_m.
Filters (Ripple Reduction)
  • Inductor (L): g=1.13 RLωLg=\frac{1.13\,R_L}{\omega L} → best at high I.
  • Capacitor (C): HW g=123fCR<em>Lg=\frac{1}{2\sqrt{3}fCR<em>L}; FW g=143fCR</em>Lg=\frac{1}{4\sqrt{3}fCR</em>L} → best at low I.
  • LC (choke-input): g=1.19ω2LCg=\frac{1.19}{\omega^2LC} independent of R<em>LR<em>L ; critical L ≥0.471 R</em>L/f\ge0.471\,R</em>L/f.
  • π\pi (CLC/CRC) cascades: further reduce gg (multiply individual factors).
Power-Supply Metrics
  • Line regulation: %ΔV<em>OV<em>O per %ΔV</em>inV</em>{in}.
  • Load regulation: %ΔVOV_O from no-load to full-load.
  • Ripple factor g=V<em>ac/V</em>dcg = V<em>{ac}/V</em>{dc}.
  • Efficiency η=P<em>dc/P</em>ac\eta=P<em>{dc}/P</em>{ac}.
Essential Equations (quick list)
  • Shockley: I<em>D=I</em>S(eV<em>D/ηV</em>T−1)I<em>D=I</em>S\left(e^{V<em>D/\eta V</em>T}-1\right)
  • Dynamic r: r<em>d≈ηV</em>T/IDr<em>d\approx\eta V</em>T/I_D
  • HW V<em>DC=0.318V</em>mV<em>{DC}=0.318V</em>m ; FW V<em>DC=0.636V</em>mV<em>{DC}=0.636V</em>m
  • Ripple (C filter, FW): g=143fCRLg=\frac{1}{4\sqrt3 f C R_L}
  • Zener design: R=V<em>in−V</em>ZI<em>L+I</em>ZR=\frac{V<em>{in}-V</em>Z}{I<em>L+I</em>Z} (choose IZI_Z within limits).