184 lines
3.2 KiB
Markdown
184 lines
3.2 KiB
Markdown
## Ohms Law
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*Solve for voltage:*
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```latex
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\displaystyle V = I*R
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```
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*Solve for resistance:*
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```latex
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\displaystyle R = \frac{V}{I}
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```
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*Solve for current*
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```latex
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\displaystyle I = \frac{V}{R}
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```
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## Resistors in Series
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```latex
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R = R1 + R2 + R3 ...
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```
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## Resistors in Parallel
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```latex
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\frac{1}{R} = \frac{1}{R1} + \frac{1}{R2} + \frac{1}{R3} ... \\
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\textit{}\\
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\textit{For two resistors in parallel:}\\
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\textit{}\\
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R = \frac{R1 * R2}{R1 + R2}
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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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## Voltage Divider
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```latex
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V_{out} = V_{in}(\frac{R_{1}}{R_1+R_2})
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```
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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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## Conservation of Charge (First Law)
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All current entering a node must also leave that node
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```latex
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\sum{I_{IN}} = \sum{I_{OUT}}
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```
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**Example:**
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For this circuit kirchhoffs law states that:
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```latex
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\displaystyle i1 = i2 + i3 + i4
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```
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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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```latex
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\displaystyle \sum{V} = 0
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```
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## Capacitors in Series
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```latex
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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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```
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## Impedance in a Circuit
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```latex
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Z = \sqrt{R^2 + X^2} \\
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\textit{}\\
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X = X_{L} - X_{C} \\
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```
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## Capacitive Reactance
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```latex
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\displaystyle X_{c} = \frac{1}{2 \pi fC}
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```
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## Inductive Reactance
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```latex
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\displaystyle X_{l} = 2\pi fL
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```
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## Analog Filters
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## Cutoff Frequency for RC Filters
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```latex
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\displaystyle f_{c} = \frac{1}{2\pi RC}
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```
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## Cutoff Frequency for RL Filters
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```latex
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\displaystyle f_{c} = \frac{R}{2\pi L}
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```
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## Cutoff Frequency for multiple Low Pass Filters
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```latex
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\displaystyle f_{(-3db)} = f_{c}\sqrt{2^{(\frac{1}{n})}-1}
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```
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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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```latex
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\displaystyle f_{o} = \frac{1}{2\pi \sqrt{LC}}
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```
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## Center Frequency with Fc and Fh
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```latex
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f_{c} = \sqrt{f_{h}*f_{l}}
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```
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## Filter Response for RC Filters
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```latex
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V_{out} = V_{in}(\frac{X_c}{\sqrt{R_{1}^2+X_{c}^2}})
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```
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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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```latex
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\displaystyle f_c = \frac{1}{4\pi\sqrt{LC}}
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```
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## Angular Frequency ($\omega$)
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```latex
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\omega = 2\pi f = \frac{2\pi}{T}
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```
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## RLC Series Response
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This is basically Ohms Law:
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```latex
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\displaystyle V = IZ
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```
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Where $Z$ is the impedance:
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```latex
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Z = \sqrt{R^2 + (X_L - X_C)^2}
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```
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$X_L$ = Reactive Inductance
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$X_C$ = Reactive Capacativw
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## Current through a transistor
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```latex
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\displaystyle I_{EQ} = \frac{V_{BB}-{V_{BE}}}{\frac{R_B}{(\beta+1)}+R_E}
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```
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## Gain Bandwidth Product
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```latex
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GBP = A_V * f_c
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```
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```latex
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\displaystyle f_c = \frac{GBP}{A_V}
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```
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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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```latex
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BW_E = BW\sqrt{2^\frac{1}{n}-1}
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```
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## Power lost in a Resistor
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```latex
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P = IV = I^2R = \frac{V^2}{R}
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```
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