Unveiling Diodes: A Comprehensive Guide to Diode Theory

SECTION 01

Demonstrative Video

Lecture Recording

SECTION 02

Need for a Diode — Initial Thoughts

Charger Circuit Operation

Signal Conversion Chain

\[\xrightarrow[\text{110 V}]{\text{ac voltage}} \xrightarrow[\text{4 V}]{\text{Transformer}} \xrightarrow[\text{3.5 V}]{\text{dc voltage using LPF}}\]

Battery charger circuit block diagram showing AC mains, step-down transformer, diode rectifier and low-pass filter producing DC output — Fig. 2.1 — Battery charger circuit block diagram

Why a Diode is Needed

Output of the transformer using a black box exhibits a zero dc content — the negative and positive half-cycles enclose equal areas, leading to a zero average value.
A diode eliminates the negative half-cycle to produce a non-zero average (DC) output.

AC waveform showing positive and negative half cycles; negative half-cycle eliminated by the diode to yield pulsating DC — Fig. 2.2 — Negative half-cycle elimination by the diode

Switch analogy of a diode: closed switch (short circuit) in forward bias, open switch in reverse bias — Fig. 2.3 — Diode as a switch: ON (forward bias) and OFF (reverse bias)

SECTION 03

DIODE — Basic Ideas

Linear vs Nonlinear Device

Resistor \(\rightarrow\) linear device \(\rightarrow\) current vs voltage is a straight line.
Diode \(\rightarrow\) nonlinear device \(\rightarrow\) \(I\) vs \(V\) is not a straight line.
The reason is the barrier potential.

Energy band diagram of a p-n junction showing the contact potential (barrier potential Vb) at the depletion region — Fig. 3.1 — Barrier potential \(V_b\) at the p–n junction depletion region

\[\boxed{V_d < V_b \;\rightarrow\; I_d\downarrow} \qquad \boxed{V_d > V_b \;\rightarrow\; I_d\uparrow}\]

Diode Symbol and Circuit

Standard IEEE diode schematic symbol with anode (A) and cathode (K) terminals labelled — Fig. 3.2 — Diode schematic symbol: anode (A), cathode (K)

Simple series circuit with DC voltage source, resistor and diode showing voltage and current direction — Fig. 3.3 — Series diode circuit for I–V analysis

Typical I-V characteristic of a semiconductor diode showing forward conduction knee and reverse breakdown — Fig. 3.4 — Typical diode \(I\)–\(V\) characteristic

Annotated diode I-V curve labelling the cut-in voltage, forward conduction, reverse saturation and breakdown regions — Fig. 3.5 — Annotated \(I\)–\(V\) curve with operating regions

Ideal Diode

Definition

Ideal Diode: acts like a perfect conductor (zero resistance) when forward biased and like a perfect insulator (\(\infty\) resistance) when reverse biased.

Ideal diode I-V characteristic: step function — short circuit for positive voltage, open circuit for negative voltage — Fig. 3.6 — Ideal diode \(I\)–\(V\) characteristic (first approximation)

Offset-voltage diode model I-V curve showing forward knee at barrier potential (0.7 V for Si, 0.3 V for Ge) — Fig. 3.7 — Offset-voltage model (second approximation)

SECTION 04

Diode Characteristic Curve

Forward Biased p–n Junction

\[\begin{aligned} & V_{\text{anode}} > V_{\text{cathode}} \leftarrow \text{on} \\ & V_{\text{anode}} < V_{\text{cathode}} \leftarrow \text{off} \\ & V_{\text{anode}} - V_{\text{cathode}} = V_D \end{aligned}\]

I–V Characteristic Curves

Real Diode

Real semiconductor diode I-V curve: gradual exponential forward conduction knee, small reverse saturation current — Fig. 4.2 — Real diode \(I\)–\(V\) characteristic

Ideal Diode

Si vs Ge

Comparison of Silicon (knee ~0.7 V) and Germanium (knee ~0.3 V) diode I-V curves — Fig. 4.4 — Silicon vs Germanium: cut-in voltages \(\approx 0.7\) V and \(\approx 0.3\) V respectively

Above the knee voltage, the diode current increases rapidly.
A small increase in the diode voltage causes large increases in diode current.

Key Diode Datasheet Parameters

Bulk Resistance:

\[R_B = R_p + R_n\]

\(R_B\) is less than 1 Ω and depends on the size of the p and n regions and how heavily doped they are.
Maximum DC Forward Current: If the current in a diode is too large, the excessive heat can destroy the diode. The \(I_{F(\max)}\) is one of the maximum ratings given on a datasheet.
Power Dissipation:

\[\begin{aligned} P_D &= V_D \cdot I_D \\ P_{\max} &= V_{\max} \cdot I_{\max} \end{aligned}\]

The power rating is the maximum power the diode can safely dissipate without shortening its life or degrading its properties.

Three diode approximation models: (a) ideal switch, (b) offset-voltage, (c) piecewise-linear with bulk resistance R_B — Fig. 4.5 — Diode approximation models: ideal switch, offset-voltage, piecewise-linear with \(R_B\)

SECTION 05

Diode Current Equation

Shockley Diode Equation

The diode current equation relating the voltage and current:

\[I = I_o\left[\mathrm{e}^{\left(V / \eta V_T\right)} - 1\right]\]

\[\begin{aligned} I &= \text{diode current} \\ I_o &= \text{diode reverse saturation current at room temperature} \\ V &= \text{external voltage applied to the diode} \\ \eta &= \text{a constant: 1 for germanium, 2 for silicon} \\ V_T &= kT/q = T/11600 \quad\text{(thermal voltage)} \\ k &= \text{Boltzmann's constant} = 1.38066\times10^{-23}~\mathrm{J/K} \\ q &= \text{charge of the electron} = 1.60219\times10^{-19}~\mathrm{C} \\ T &= \text{temperature of the diode junction (K)} = \bigl({}^\circ\mathrm{C} + 273^\circ\bigr) \end{aligned}\]

Reverse Bias and Saturation Current

Key Result

\[\boxed{I = I_o\left[\mathrm{e}^{\left(V / \eta V_T\right)} - 1\right]}\]

When the diode is reverse biased, its current equation may be obtained by changing the sign of the applied voltage \(V\).
Thus, the diode current with reverse bias is:
\[I = I_o\left[\mathrm{e}^{\left(-V / \eta V_T\right)} - 1\right]\]
If \(V \gg V_T\), then the term \(\mathrm{e}^{(-V/\eta V_T)} \ll 1\), therefore \(I \approx -I_o\) — termed as reverse saturation current, which is valid as long as the external voltage is below the breakdown value.

SECTION 06

Effect of Temperature

Temperature Effects on Diode Characteristics

Family of diode I-V curves at increasing temperatures T1, T2, T3 showing the characteristic shifts left as temperature rises — Fig. 6.1 — Effect of temperature on the diode \(I\)–\(V\) characteristic

\(T\uparrow \;\Rightarrow\;\) generation of electron–hole pairs increases, which increases the conductivities.
If \(T\uparrow\) at fixed \(V \;\Rightarrow\; I\) increases.
To bring \(I\) to normal \(\;\Rightarrow\; V\downarrow\).

SECTION 07

Load Lines

Load Line Equation

Load Line (KVL)

\[I_D = \frac{V_S - V_D}{R_s}\]

Load line: a straight line on the \(I_D\)–\(V_D\) plane whose intersection with the diode characteristic defines the Q-point.

Load line drawn on the diode I-V plane: y-intercept at Vs/Rs and x-intercept at Vs — Fig. 7.1 — Load line on the diode \(I_D\)–\(V_D\) characteristic plane

Q-Point Determination

If \(V_s = 2~\mathrm{V}\), \(R = 100~\Omega\)
\(V_D = 0 \;\Rightarrow\; I_D = 20~\mathrm{mA}\)
\(I_D = 0 \;\Rightarrow\; V_D = V_s = 2~\mathrm{V}\)
The straight line is called the load line.
\(Q\) is an abbreviation for quiescent, which means "at rest."