Diode Notes

Resistance Levels

• The higher the current through a diode, the lower is the DC resistance level.

• Typically, the DC resistance of a diode in the active region ranges from about 10 to 80 ohms.

AC or Dynamic Resistance

• The DC resistance of a diode is independent of the shape of the characteristic around the point of interest.

• The lower the Q-point of operation (smaller current or lower voltage), the higher is the AC resistance.

• The steeper the slope, the lower is the value of the $∆V<em>d$ for the same change in $∆I</em>d$, and the lower is the resistance.

Average AC Resistance

• Resistance determined by a straight line drawn between the two intersections established by the maximum and minimum values of input voltage.

• As with the DC and AC resistance levels, the lower the level of currents, the higher is the resistance level.

Diode Equivalent Circuits

• An equivalent circuit is a combination of elements properly chosen to best represent the actual terminal characteristics of a device or a system in a particular operating region.

Piecewise-Linear Model

• Represents the diode as a voltage source (threshold voltage) in series with a resistor (forward resistance), capturing the forward conduction region beyond the threshold.

• Below threshold voltage: diode behaves like an open circuit (no conduction).

• Above threshold: diode current increases linearly with voltage according to series resistor.

Simplified Equivalent Circuit

• Simplified equivalent circuit for the silicon semiconductor diode.

• Ideal diode

Ideal Equivalent Circuit

• Ideal diode and its characteristics.

Transition and Diffusion Capacitance

• The total capacitance in a silicon diode consists of two main components: transition capacitance $(C<em>T)$ and diffusion capacitance $(C</em>D)$.

• Transition capacitance dominates in the reverse-bias region and decreases with increasing reverse voltage due to the widening of the depletion region.

• Diffusion capacitance dominates in the forward-bias region and increases with current injection, related to minority carrier lifetime and current.

Transition and Diffusion Capacitance

• TRANSITION CAPACITANCE

• DIFFUSION CAPACITANCE

Where:

• $C_0$ is zero-bias capacitance

• $V_R$ is reverse bias voltage

• $V_K$ is a constant

• $n$ depends on manufacturing

Where:

• $\tau_T$ is minority carrier lifetime

• $I_D$ is diode current

Half-Wave Rectification

• Uses a diode to convert an AC sinusoidal input signal into a pulsating DC output by allowing current flow only during the positive half-cycle of the input.

• During the positive half-cycle (0 to T/2), the diode conducts, and the output voltage $v<em>o$ follows the input voltage $v</em>i$.

• During the negative half-cycle (T/2 to T), the diode is off, resulting in zero output voltage, effectively removing the negative half of the waveform.

Half-Wave Rectification

• Real silicon diodes have a forward voltage drop, typically around 0.7V, which must be overcome before conduction begins.

• This causes the output to be offset by $V_K$, reducing the effective output voltage by this amount.

• The output voltage $v<em>o$ is given by $v</em>o = v<em>i - V</em>K$ when vi > VK and zero otherwise, which reduces the average DC output voltage compared to the ideal case.

• The average DC voltage $V<em>{dc}$ of the half-wave rectified signal can be approximated by the formula $V</em>{dc} ≈ 0.318 V<em>m - V</em>K$ where $V<em>m$ is the peak input voltage and $V</em>K$ is the diode forward voltage drop.

• For an ideal diode with no forward drop, the average voltage is $V<em>{dc} = 0.318 V</em>m$

Full-Wave Bridge Rectifier

Full-Wave Bridge Rectifier

Center-Tapped Transformer Full-Wave Rectifier