Spring 2018

ECE 110

Course Notes

Learn It!

A diode is called a diode because it has two distinct electrodes (i.e. terminals), called the anode and the cathode. A diode is electrically asymmetric because current can flow freely from the anode to the cathode, but not in the other direction. In this way, it functions as a one-way valve for current. The diode's asymmetric behavior can be used to create circuits for signal processing (such as an AC to DC converter).

Figure 1

Two diodes
Fig. 1: Two diodes. In both devices shown here, the anode is on the left and the cathode is on the right. Notice that the cathode side is typically indicated by a band painted a different color.

Figure 2

The symbol for a diode
Fig. 2: The symbol for a diode. The anode is on the left and the cathode is on the right. The voltage drop $V_D$ is called the bias voltage. Note that the polarity of $V_D$ and direction of $I_D$ are labeled following the standard labeling convention. Therefore, the power absorbed by a diode is given by $P = V_D I_D$.

The I-V characteristic of a diode can be plotted on an oscilloscope in the lab. Its shape is nonlinear due to the diode's electrical asymmetry.

Figure 3

I-V characteristic of a diode
Fig. 3: I-V characteristic of a diode. When the bias voltage $V_D$ is positive and large enough, the current $I_D$ becomes positive and large too. But when $V_D$ is below the threshold voltage, then $I_D$ is close to zero.

The offset ideal model approximates the nonlinear I-V characteristic in Fig. 3 as a piecewise linear graph with a threshold voltage parameter $V_{\text{on}}$. The typical value for a silicon diode is $V_{\text{on}}=0.7\text{ V}$.

Figure 4

Offset ideal model I-V characteristic of a diode
Fig. 4: Offset ideal model I-V characteristic of a diode. If $V_D < V_{\text{on}}$, we approximate $I_D=0$. Otherwise, if $I_D > 0$, we approximate $V_D=V_{\text{on}}$. These two regions define two diode states, called OFF and ON.

Within each diode state, the diode can be replaced with a simpler linear element. If the diode is OFF, it can be replaced by an open circuit which has $I_D=0$ and can have any value of $V_D$. Otherwise, the diode is ON and it can be replaced by an element with fixed voltage drop $V_D=V_{\text{on}}$ and any value of $I_D$.

Condition State Behavior Replacement Rule
$\begin{aligned}V_D < V_{\text{on} }\end{aligned}$ OFF $\begin{aligned}I_D=0\end{aligned}$
$\begin{aligned}I_D > 0\end{aligned}$ ON $\begin{aligned}V_D=V_{\text{on} }\end{aligned}$
Table 1: Diode states and replacement rules.

The flowchart below allows you to solve for unknown voltages and currents in a circuit containing sources, resistors and one or more diodes, which are modeled by the offset ideal model.

Figure 5

Flowchart for diode circuit analysis
Fig. 5: Flowchart for diode circuit analysis.

Guess whether each diode is OFF or ON. (You should use your intuition as much as possible to make good guesses.)

Replace each diode with a linear element according to the rule in Table 1 and redraw the circuit.

In the resulting linear circuit, solve for all the voltages and currents where the diodes used to be, using KCL, KVL, Ohm's law and/or the node-voltage method.

Check whether the appropriate condition in Table 1 holds for each diode.

If any diode fails its condition, change one or more of your guesses and repeat this procedure from step 2.

Otherwise, all diodes satisfy their conditions and your guesses are correct.

Solve for the desired voltages and currents using the correct guesses for the diode states.

After some practice, you are expected to do problems involving one or two diodes quickly without explicitly redrawing the circuit in step 2.

Explore More!

A diode like the ones in Fig. 1 is made of semiconductor material (such as crystalline silicon) with impurities added in a process called doping. Different impurities are added to the anode and cathode sides to make the diode electrically asymmetric.

The semiconductor on the anode side is doped with atoms having 3 valence electrons each (such as indium, aluminum or gallium). Relative to pure silicon which has 4 valence electrons, it has a deficit of electrons and these missing electrons are called holes. A semiconductor doped in this way is called p-type, where the "p" stands for the positively-charged holes.

The semiconductor on the cathode side is doped with atoms having 5 valence electrons each (such as phosphorus or arsenic) and, thus, has an excess of electrons relative to pure silicon. This kind of doped semiconductor is called n-type because the excess electrons are negatively charged.

Figure 6

P-n junction
Fig. 6: P-n junction. A p-type semiconductor adjacent to an n-type semiconductor forms a p-n junction. Together with the terminals, the p-n junction makes a diode.

If the bias voltage $V_D>0$, we say that the p-n junction and diode are forward-biased. Note that this condition is slightly different to $V_D>V_{\text{on}}$ for the diode to be ON.

Figure 7

Forward-biased p-n junction
Fig. 7: Forward-biased p-n junction. The bias voltage $V_D > 0$ electrostatically drives the holes and electrons closer together. If $V_D > V_{\text{on}}$, these charge carriers spread freely around the semiconductor, allowing current to flow freely from anode to cathode.

If $V_D < 0$, the p-n junction and diode are said to be reverse-biased. Again, this condition is slightly different to $V_D < V_{\text{on}}$ for the diode to be OFF.

Figure 8

Reverse-biased p-n junction
Fig. 8: Reverse-biased p-n junction. The bias voltage $V_D < 0$ electrostatically separates the holes and electrons. Since these charge carriers cannot move freely throughout the semiconductor, very little current can flow through the diode.

In ECE 340: Solid State Electronic Devices, you will study these physical phenomena of p-n junctions quantitatively and derive a more realistic exponential model of a diode's I-V characteristic (shown below) than the offset ideal model.
I_D = I_S\left(\text{exp}\left(\frac{q}{kT}V_D\right)-1\right) \label{DIO-IVE}
I_S &= \text{saturation current}\\
q &= \text{charge of an electron} = 1.6 \cdot 10^{-19} \text{ C}\\
k &= \text{Boltzmann constant} = 1.38 \cdot 10^{-23} \text{ JK}^{-1}\\
T &= \text{temperature (K)}
At room temperature ($T=300$ K), equation $\eqref{DIO-IVE}$ simplifies to
I_D = I_S\left(\text{exp}\left(38.5 V_D\right)-1\right)