Diodes

Semiconductor Devices · Diodes · Learn

Symbol and terminals

A diode has two terminals: the anode (P-side) and the cathode (N-side). Conventional forward current flows from anode to cathode — the direction the schematic triangle points.

Figure 1. Diode schematic symbol. Triangle = anode → cathode; bar = cathode.

One-way valve: forward current flows anode → cathode. Reverse is blocked.

Physical structure

A diode is a single PN junction in a package. The depletion region between the P and N sides creates the built-in barrier; everything else follows from how that barrier responds to bias.

Figure 2. PN diode cross-section. Holes (open) on the P-side, electrons (filled) on the N-side, depletion region in the middle.

Three diode models

Real diodes obey the Shockley equation, but circuit analysis usually reaches for a simpler model first. Pick the coarsest one that still answers the question.

1. Ideal model

Forward-biased = perfect short. Reverse-biased = perfect open. No threshold, no resistance.

V_D = 0,\ I_D \geq 0\ \text{(ON)}\quad\text{or}\quad I_D = 0,\ V_D \leq 0\ \text{(OFF)}

Figure 3. Ideal model: vertical line at

V_D = 0

forward, flat at

I_D = 0

reverse.

2. Piecewise-linear (constant-drop) model

Adds a fixed turn-on voltage $V_F$ (≈ 0.7 V silicon, ≈ 0.3 V germanium, ≈ 1.8 V red LED). Below the knee, no current; above it, a small forward resistance $r_{on}$ .

I_D = \begin{cases} 0 & V_D < V_F \\ (V_D - V_F)/r_{on} & V_D \geq V_F \end{cases}

Figure 4. Piecewise-linear: zero current until

V_F

, then linear conduction with slope

1/r_{on}

3. Shockley (exponential) model

The full diode equation, accurate from cutoff into moderate forward conduction:

I_D = I_S\left(e^{V_D / (n V_T)} - 1\right)

where:

$I_S$ — saturation current (≈ 1 pA for small-signal silicon).
$n$ — ideality factor, 1.0 ideal, up to 2.0 for real junctions.
$V_T = kT/q$ — thermal voltage ≈ 25.85 mV at 300 K.

Figure 5. Shockley: exponential rise once

V_D

exceeds a few

V_T

. Reverse current saturates at

-I_S

Shockley for analogue analysis. Piecewise for hand calculations. Ideal for digital and switching logic.

Reverse breakdown

Beyond a critical reverse voltage $V_{BR}$ (Zener for thin junctions, avalanche for thick ones), reverse current spikes. Zener diodes exploit this for voltage references; ordinary rectifiers must stay below their $V_{BR}$ rating.

Application: half-wave rectifier

One diode in series with a resistive load passes the positive half of an AC input and blocks the negative half — the simplest AC-to-pulsating-DC converter.

Figure 6. Half-wave rectifier circuit. The diode passes current only on positive half-cycles, so

V_{out}

across

R_L

is non-negative.

Figure 7. Half-wave rectifier waveforms: input AC (top), output across the load (bottom). Negative half-cycles are clipped.

Smoothing capacitor (filter)

A capacitor in parallel with the load charges to $V_p$ on each peak, then discharges through $R_L$ until the next one. Pulsating DC becomes a near-flat level with a sawtooth ripple.

Figure 8. Half-wave with smoothing cap. Ripple period equals the input period

T = 1/f

Peak-to-peak ripple voltage (linear-discharge approximation):

V_{r(pp)} \approx \dfrac{V_p}{f \, R_L \, C}

Average and RMS — half-wave

V_{avg} = \dfrac{V_p}{\pi}, \qquad V_{rms} = \dfrac{V_p}{2}

Application: full-wave rectifier — bridge

Four diodes in a bridge route both half-cycles to the load with the same polarity. The cap refills twice per input cycle, so ripple frequency is $2f$ and ripple amplitude halves.

Figure 9. Bridge rectifier with smoothing cap. On the positive half-cycle

D_1

and

D_2

conduct; on the negative half

D_3

and

D_4

take over.

Figure 10. Bridge output — full-wave rectified (faint) and smoothed (solid). Ripple at

2f

, half the amplitude of half-wave for the same

R_L \cdot C

Two diodes are always in the conduction path, so the load loses $2 V_F$ (≈ 1.4 V for silicon) compared to the input peak.

Average and RMS — full-wave

V_{avg} = \dfrac{2 V_p}{\pi}, \qquad V_{rms} = \dfrac{V_p}{\sqrt{2}}

V_{r(pp)} \approx \dfrac{V_p}{2 f \, R_L \, C}

Application: full-wave rectifier — center-tapped transformer

A transformer with a center-tapped secondary plus two diodes also gives full-wave rectification. Each diode conducts on alternate half-cycles, using one half of the winding at a time.

Figure 11. Center-tapped transformer + 2 diodes — full-wave with one

V_F

drop instead of two, but the secondary winding must be twice as long for the same

V_p

Bridge: 4 diodes,

2 V_F

drop, simple transformer. Center-tapped: 2 diodes,

1 V_F

drop, but needs a 2× secondary. Both give the same

V_{avg} = 2 V_p / \pi

and ripple at

2f