91 lines
4.1 KiB
Markdown
91 lines
4.1 KiB
Markdown
# ECE 240: Electronic Circuits
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## Diodes
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A **diode** is a two-terminal device that only allows current to flow in the direction of the arrow.
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<img src="https://upload.wikimedia.org/wikipedia/commons/b/b4/Diode_symbol.svg" width=300>(Source: Wikimedia Commons)</img>
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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:
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$$I=I_s\left(e^{V/V_T}-1\right)$$
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!!! tip
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- $V_T\approx\pu{25 mV}$ at 20°C
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- $V_T\approx\pu{20 mV}$ at 25°C
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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.
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<img src="https://upload.wikimedia.org/wikipedia/commons/2/2a/Diode_current_wiki.png" width=500>(Source: Wikimedia Commons)</img>
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Diodes are commonly used in **rectifier circuits** — circuits that convert AC to DC.
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By preventing negative voltage, a relatively constant positive DC voltage is obtained. The slight dip between each hill is known as **ripple** $\Delta V$.
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<img src="https://upload.wikimedia.org/wikipedia/en/8/8b/Reservoircapidealised.gif" width=500>(Source: Wikimedia Commons)</img>
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In a simple series RC circuit, across a diode, Where $R_LC>>\frac 1 \omega$, and $f=\frac{\omega}{2\pi}$:
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$$\Delta V\approx \frac{I_\text{load}}{2fC}\approx\frac{V_0}{2fR_LC}$$
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### Zener diodes
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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 $V_B$.**
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<img src="https://upload.wikimedia.org/wikipedia/commons/9/92/Zener_diode_symbol-2.svg" width=200>(Source: Wikimedia Commons)</img>
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## Voltage/current biasing
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Solving for current for each element in a series returns a negative linear line and other non-linear lines.
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- the linear line is the **load line**, which represents the possible solutions to the circuit when it is loaded
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- 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**.
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<img src="https://upload.wikimedia.org/wikipedia/commons/2/27/BJT_CE_load_line.svg" width=600>(Source: Wikimedia Commons)</img>
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- 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.
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- To bias voltage, as $R\to 0$, the slope of the load line $\to\infty$, which results in a constant voltage.
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!!! example
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<img src="https://miro.medium.com/v2/resize:fit:432/1*mijJgpHdt7DDmrPsb7tOcg.png" width=200 />
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The current across the resistor and the diode is the same:
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\begin{align*}
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i_D&=\frac{V_s}{R} \\
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i_D&\approx I_se^{V_D/V_T}
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\end{align*}
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If a diode is put in series with AC and DC voltage sources $V_d(t)$ and $V_D$:
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\begin{align*}
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i_D(t)&=I_se^{(V_D+V_d(t))/V_T} \\
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&=\underbrace{I_se^{V_D/V_T}}_\text{bias current}\ \underbrace{e^{V_d(t)/V_T}}_\text{$\approx 1+\frac{V_d}{V_T}$} \\
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&=I_D\left(1+\frac{V_d}{V_T}\right) \\
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&=\underbrace{I_D}_\text{large signal = bias = DC}+\underbrace{I_D\frac{V_d(t)}{V_T}}_\text{small signal = AC}
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\end{align*}
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Diodes may act as resistors, depending on the bias current. They may exhibit a **differential resistance**:
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$$r_d=\left(\frac{\partial i_D}{\partial v_D}\right)^{-1} = \frac{V_T}{I_D}$$
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!!! example
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Thus from the previous sequence:
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$$i_D(t)=I_D+\frac{1}{r_d}V_d(t)$$
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### Signal analysis
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1. Analyse DC signals
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- assume blocking capacitors are open circuits
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- turn off AC sources
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2. Analyse AC signals
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- assume blocking capacitors are shorts
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- turn off DC sources
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- replace diode with effective resistor (the differential resistor)
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!!! tip
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Most $R$s in the circuit can be assumed to be significantly greater than $r_d$, so $r_d$ can be removed in series or $R$ can be removed in parallel.
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!!! warning
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Oftentimes, turning off a DC source to nowhere is actually a short to ground.
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