3.2 KiB
Ohms Law
Solve for voltage:
\displaystyle V = I*R
Solve for resistance:
\displaystyle R = \frac{V}{I}
Solve for current
\displaystyle I = \frac{V}{R}
Resistors in Series
R = R1 + R2 + R3 ...
Resistors in Parallel
\frac{1}{R} = \frac{1}{R1} + \frac{1}{R2} + \frac{1}{R3} ... \\
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\textit{For two resistors in parallel:}\\
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R = \frac{R1 * R2}{R1 + R2}
Tip: If resistors of the same value are in parallel the total resistance is a single resistor divided by the amount if resistors.
Voltage Divider
V_{out} = V_{in}(\frac{R_{1}}{R_1+R_2})
Thevenin’s Theorem
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.
Conservation of Charge (First Law)
All current entering a node must also leave that node
\sum{I_{IN}} = \sum{I_{OUT}}
Example:
For this circuit kirchhoffs law states that:
\displaystyle i1 = i2 + i3 + i4
Conservation of Energy (Second Law)
All the potential differences around the loop must sum to zero.
\displaystyle \sum{V} = 0
Capacitors in Series
\displaystyle \frac{1}{C_{t}} = \frac{1}{C_{1}}+\frac{1}{C_{2}}+\frac{1}{C_{3}} ...
Impedance in a Circuit
Z = \sqrt{R^2 + X^2} \\
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X = X_{L} - X_{C} \\
Capacitive Reactance
\displaystyle X_{c} = \frac{1}{2 \pi fC}
Inductive Reactance
\displaystyle X_{l} = 2\pi fL
Analog Filters
Cutoff Frequency for RC Filters
\displaystyle f_{c} = \frac{1}{2\pi RC}
Cutoff Frequency for RL Filters
\displaystyle f_{c} = \frac{R}{2\pi L}
Cutoff Frequency for multiple Low Pass Filters
\displaystyle f_{(-3db)} = f_{c}\sqrt{2^{(\frac{1}{n})}-1}
Where n = Number if identical filters
Resonance Frequency for RLC Low Pass Filter
\displaystyle f_{o} = \frac{1}{2\pi \sqrt{LC}}
Center Frequency with Fc and Fh
f_{c} = \sqrt{f_{h}*f_{l}}
Filter Response for RC Filters
V_{out} = V_{in}(\frac{X_c}{\sqrt{R_{1}^2+X_{c}^2}})
Cutoff Frequency \pi Topology Filter
When the two capacitors have the same capacitance, it can be calculated like this:
\displaystyle f_c = \frac{1}{4\pi\sqrt{LC}}
Angular Frequency (\omega)
\omega = 2\pi f = \frac{2\pi}{T}
RLC Series Response
This is basically Ohms Law:
\displaystyle V = IZ
Where Z is the impedance:
Z = \sqrt{R^2 + (X_L - X_C)^2}
X_L = Reactive Inductance
X_C = Reactive Capacativw
Current through a transistor
\displaystyle I_{EQ} = \frac{V_{BB}-{V_{BE}}}{\frac{R_B}{(\beta+1)}+R_E}
Gain Bandwidth Product
GBP = A_V * f_c
\displaystyle f_c = \frac{GBP}{A_V}
Bandwidth of Multiple OpAmps
Where n = number of stages
and BW = Bandwidth of single op-amp
BW_E = BW\sqrt{2^\frac{1}{n}-1}
Power lost in a Resistor
P = IV = I^2R = \frac{V^2}{R}