3.0 KiB
Ohms Law
Solve for voltage:
\displaystyle V = \frac{I}{R}
Solve for resistance:
R = \frac{V}{I}
Solve for current
\begin{flalign}
I & = \frac{V}{R} &
\end{flalign}
Resistors in Series
R = R1 + R2 + R3 ...
Resistors in Parallel
\begin{flalign}
&\frac{1}{R} = \frac{1}{R1} + \frac{1}{R2} + \frac{1}{R3} ... &\\
\\
&\textit{For two resistors in parallel:} &\\
\\
&R = \frac{R1 * R2}{R1 + R2} &\\\
\end{flalign}
Tip: If resistors of the same value are in parallel the total resistance is a single resistor divided by the amount if resistors.
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.
Kirchhoff's Law
Conservation of Charge (First Law)
All current entering a node must also leave that node
\begin{flalign}
\sum{I_{IN}} = \sum{I_{OUT}}&&
\end{flalign}
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
\begin{flalign}
&Z = \sqrt{R^2 + X^2} &\\\
\\
&X = X_{L} - X_{C} \\
\end{flalign}
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}
Signal Response of an RC/RL Filter
X_c = #Capacitive Reactance || #Inductive Reactance
\displaystyle V_{out} = V_{in}(\frac{X_{c}}{\sqrt{R^2+X_{c}^2}})
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}}
Voltage Divider
V_{out} = V_{in}(\frac{R_{1}}{R_1+R_2})
Angular Frequency (\omega)
\omega = 2\pi f = \frac{2\pi}{T} ^4ad7fc
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}
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}