From 34abdbc571c7eb190c91cd3c6ec6c6c807871c5c Mon Sep 17 00:00:00 2001 From: eggy Date: Wed, 1 Nov 2023 12:35:55 -0400 Subject: [PATCH] ece240: add diodes --- docs/2a/ece240.md | 73 +++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 73 insertions(+) diff --git a/docs/2a/ece240.md b/docs/2a/ece240.md index c320e86..545f065 100644 --- a/docs/2a/ece240.md +++ b/docs/2a/ece240.md @@ -1,2 +1,75 @@ # ECE 240: Electronic Circuits +## Diodes + +A **diode** is a two-terminal device that only allows current to flow in the direction of the arrow. + +(Source: Wikimedia Commons) + +The current across a diode is, where $I_s$ is a forced saturation current, $V$ is the voltage drop across it, and $V_T$ is the **thermal voltage** such that $V_T=\frac{kT}{q}$, where $T$ is the temperature, $k$ is the Boltzmann constant, and $q$ is the charge of an electron: + +$$I=I_s\left(e^{V/V_T}-1\right)$$ + +!!! tip + - $V_T\approx\pu{25 mV}$ at 20°C + - $V_T\approx\pu{20 mV}$ at 25°C + +A diode is open when current is flowing reverse the desired direction, resulting in zero current, until the voltage drop becomes so great that it reaches the **breakdown voltage** $V_B$. Otherwise, the above current formula is followed. + +(Source: Wikimedia Commons) + +Diodes are commonly used in **rectifier circuits** — circuits that convert AC to DC. + +By preventing negative voltage, a relatively constant positive DC voltage is obtained. The slight dip between each hill is known as **ripple** $\Delta V$. + +(Source: Wikimedia Commons) + +In a simple series RC circuit, across a diode, Where $R_LC>>\frac 1 \omega$, and $f=\frac{\omega}{2\pi}$: + +$$\Delta V\approx \frac{I_\text{load}}{2fC}\approx\frac{V_0}{2fR_LC}$$ + +### Zener diodes + +A Zener diode is a calibrated diode with a known breakdown voltage, $V_B$. If the voltage across the diode would be greater than $V_B$, it is **capped at $V_B$.** + +(Source: Wikimedia Commons) + +## Voltage/current biasing + +Solving for current for each element in a series returns a negative linear line and other non-linear lines. + +- the linear line is the **load line**, which represents the possible solutions to the circuit when it is loaded +- Depending on the base current $I_s$, the diode or transistor will be **biased** toward one of the curves, and the voltage and current will settle on one of the intersections, or **bias points**. + +(Source: Wikimedia Commons) + +- To bias current, as $R\to\infty$ (or, in practical terms, $R>>diode$), the slope of the load line $\to 0$, which results in a constant current. +- To bias voltage, as $R\to 0$, the slope of the load line $\to\infty$, which results in a constant voltage. + +!!! example + + + The current across the resistor and the diode is the same: + + \begin{align*} + i_D&=\frac{V_s}{R} \\ + i_D&\approx I_se^{V_D/V_T} + \end{align*} + +If a diode is put in series with AC and DC voltage sources $V_d(t)$ and $V_D$: + +\begin{align*} +i_D(t)&=I_se^{(V_D+V_d(t))/V_T} \\ +&=\underbrace{I_se^{V_D/V_T}}_\text{bias current}\ \underbrace{e^{V_d(t)/V_T}}_\text{$\approx 1+\frac{V_d}{V_T}$} \\ +&=I_D\left(1+\frac{V_d}{V_T}\right) \\ +&=\underbrace{I_D}_\text{large signal = bias = DC}+\underbrace{I_D\frac{V_d(t)}{V_T}}_\text{small signal = AC} +\end{align*} + +Diodes may act as resistors, depending on the bias current. They may exhibit a **differential resistance**: +$$r_d=\left(\frac{\partial i_D}{\partial v_D}\right)^{-1} = \frac{V_T}{I_D}$$ + +!!! example + Thus from the previous sequence: + + $$i_D(t)=I_D+\frac{1}{r_d}V_d(t)$$ +