159 lines
3.0 KiB
Markdown
159 lines
3.0 KiB
Markdown
# Ohms Law
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Solve for voltage:
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$\displaystyle V = \frac{I}{R}$
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*Solve for resistance:*
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$R = \frac{V}{I}$
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_Solve for current_
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$$
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\begin{flalign}
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I & = \frac{V}{R} &
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\end{flalign}
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$$
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# Resistors in Series
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$R = R1 + R2 + R3 ...$
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# Resistors in Parallel
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$$
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\begin{flalign}
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&\frac{1}{R} = \frac{1}{R1} + \frac{1}{R2} + \frac{1}{R3} ... &\\
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\\
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&\textit{For two resistors in parallel:} &\\
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\\
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&R = \frac{R1 * R2}{R1 + R2} &\\\
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\end{flalign}
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$$
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***Tip:***
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If resistors of the same value are in parallel the total resistance is a single resistor divided by the amount if resistors.
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## Thevenin’s Theorem
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States that it is possible to simplify any linear circuit, no matter how complex, to an equivalent circuit with just a single voltage source and series resistance connected to a load.
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# Kirchhoff's Law
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## Conservation of Charge (First Law)
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All current entering a node must also leave that node
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$$
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\begin{flalign}
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\sum{I_{IN}} = \sum{I_{OUT}}&&
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\end{flalign}
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$$
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**Example:**
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For this circuit kirchhoffs law states that:
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$\displaystyle i1 = i2 + i3 + i4$
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## Conservation of Energy (Second Law)
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All the potential differences around the loop must sum to zero.
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$\displaystyle \sum{V} = 0$
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## Capacitors in Series
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$\displaystyle \frac{1}{C_{t}} = \frac{1}{C_{1}}+\frac{1}{C_{2}}+\frac{1}{C_{3}} ...$
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### Impedance in a Circuit
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$$
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\begin{flalign}
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&Z = \sqrt{R^2 + X^2} &\\\
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\\
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&X = X_{L} - X_{C} \\
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\end{flalign}
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$$
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# Capacitive Reactance
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$\displaystyle X_{c} = \frac{1}{2 \pi fC}$
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# Inductive Reactance
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$\displaystyle X_{l} = 2\pi fL$
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# Analog Filters
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## Cutoff Frequency for RC Filters
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$\displaystyle f_{c} = \frac{1}{2\pi RC}$
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## Cutoff Frequency for RL Filters
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$\displaystyle f_{c} = \frac{R}{2\pi L}$
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## Signal Response of an RC/RL Filter
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$X_c$ = [[#Capacitive Reactance]] || [[#Inductive Reactance]]
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$\displaystyle V_{out} = V_{in}(\frac{X_{c}}{\sqrt{R^2+X_{c}^2}})$
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## Cutoff Frequency for multiple Low Pass Filters
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$\displaystyle f_{(-3db)} = f_{c}\sqrt{2^{(\frac{1}{n})}-1}$
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Where $n$ = Number if **identical** filters
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## Resonance Frequency for RLC Low Pass Filter
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$\displaystyle f_{o} = \frac{1}{2\pi \sqrt{LC}}$
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## Center Frequency with Fc and Fh
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$f_{c} = \sqrt{f_{h}*f_{l}}$
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## Filter Response for RC Filters
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$V_{out} = V_{in}(\frac{X_c}{\sqrt{R_{1}^2+X_{c}^2}})$
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## Cutoff Frequency $\pi$ Topology Filter
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When the two capacitors have the same capacitance, it can be calculated like this:
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$\displaystyle f_c = \frac{1}{4\pi\sqrt{LC}}$
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# Voltage Divider
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$V_{out} = V_{in}(\frac{R_{1}}{R_1+R_2})$
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# Angular Frequency ($\omega$)
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$\omega = 2\pi f = \frac{2\pi}{T}$ ^4ad7fc
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# RLC Series Response
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This is basically Ohms Law:
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$\displaystyle V = IZ$
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Where $Z$ is the impedance:
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$Z = \sqrt{R^2 + (X_L - X_C)^2}$
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# Current through a transistor
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$\displaystyle I_{EQ} = \frac{V_{BB}-{V_{BE}}}{\frac{R_B}{(\beta+1)}+R_E}$
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# Gain Bandwidth Product
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$GBP = A_V * f_c$
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$\displaystyle f_c = \frac{GBP}{A_V}$
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# Bandwidth of Multiple OpAmps
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Where $n$ = number of stages
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and $BW$ = Bandwidth of single op-amp
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$BW_E = BW\sqrt{2^\frac{1}{n}-1}$ |