Diode models

YOU WILL BE ABLE TO

State the Shockley equation and interpret its terms.
Apply the ideal, constant-voltage-drop, and piecewise-linear models.
Choose an appropriate model for a given analysis.
Solve a simple diode circuit with the constant-drop model.

The junction's physics gives an exact current-voltage law, the Shockley equation. It is honest and it is exponential — and an exponential inside a circuit equation means no closed-form solution by the methods of CA-3. So the working engineer keeps a ladder of models and climbs only as high as the question demands.

i_D = I_S\left(e^{v_D / V_T} - 1\right)

the Shockley equation

$I_S$ is the saturation current, a device constant in the nanoamp range or below; $V_T$ is the thermal voltage, $kT/q$ , about $26$ mV at room temperature. Two consequences of that exponential are worth internalising. Forward: current rises so steeply that a change of about $60$ mV multiplies it by ten — which is why "the diode drop" behaves like a nearly fixed voltage over decades of current. Reverse: with $v_D$ negative and a few $V_T$ in magnitude, the exponential vanishes and $i_D \approx -I_S$ — the leakage of Lesson 1.

The forward characteristic: nothing much, then a knee near 0.7 V, then a nearly vertical rise.

WORKED EXAMPLE

A diode in series with a resistor

A silicon diode and a $1$ kΩ resistor in series across $5$ V, diode forward-biased.
Constant-drop model: the diode takes $0.7$ V, leaving $5 - 0.7 = 4.3$ V for the resistor.
$i = 4.3/1000 = 4.3$ mA — and the same current flows through the diode, since they are in series.
Check the model's honesty: at $4.3$ mA a real silicon diode drops perhaps $0.68$ V, so the current error is under 1%. The model earns its keep.

i = 4.3

WORKED EXAMPLE

Assume, solve, verify

With multiple diodes, you cannot always tell which are conducting. The method: ASSUME a state for each, solve, then CHECK the assumption.
A diode assumed ON must come out with positive current; a diode assumed OFF must come out with a reverse voltage across it.
If any check fails, flip that assumption and re-solve. With $n$ diodes there are $2^n$ combinations, but physical reasoning usually finds the answer on the first or second try.
This assume-solve-verify loop is the whole technique for diode circuits — and it reappears for every nonlinear device in this track.

State assumptions explicitly, then let the arithmetic judge them.

PRACTICE

A silicon diode in series with $470$ Ω sits across $3.3$ V, forward biased. Find the current using the constant-drop model.

Using the rule that roughly $60$ mV multiplies diode current by ten: a diode carries $1$ mA at $0.65$ V. Estimate its voltage at $10$ mA and at $0.1$ mA.

A diode's cathode is at $2$ V and its anode at $0$ V, in a circuit with a $10$ kΩ series resistor. Which model applies, and what current flows?

When would the constant-drop model mislead you badly enough to need something better? Name two situations.