Electronics Handbook/Components/Resistor Network: Difference between revisions

Latest revision as of 14:49, 5 June 2024

Circuit	Derivation	$\frac{v_{o}}{v_{i}}$	Analysis
[[../../Circuits/Voltage Divider\|Voltage Divider]]	$\frac{V_{o}}{R_{2}} = \frac{V_{i}}{R_{1} + R_{2}}$	$\frac{v_{o}}{v_{i}} = \frac{R_{2}}{R_{2} + R_{1}}$	R₂ = 0 V_o = 0 R₂ >> R₂ V_o = 1 This configuration is ude maily to attenuate voltage
[[../../Circuits/π\|π]]	$\frac{V_{i}}{R_{1}} = \frac{V_{i} - V_{o}}{R_{2}} + \frac{V_{o}}{R_{3}}$ $V_{i} (\frac{1}{R_{1}} - \frac{1}{R_{2}}) = V_{o} (\frac{1}{R_{3}} - \frac{1}{R_{2}})$	$\frac{v_{o}}{v_{i}} = (\frac{R_{3}}{R_{1}}) (\frac{R_{2} - R_{1}}{R_{2} - R_{3}})$
[[../../Circuits/T\|T]]	$V = \frac{R_{3} - R_{1}}{R_{2}} V_{1} = \frac{R_{2} - R_{1}}{R_{2}} V_{2}$	$\frac{V_{2}}{V_{1}} = \frac{R_{1} + R_{3}}{R_{2} + R_{3}}$

Configurations	$\frac{V_{o}}{V_{i}}$
	$R_{e q} = R_{1} + R_{2} + R_{3} + . . . + R_{n}$
	$\frac{1}{R_{e q}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + . . . + \frac{1}{R_{n}}$
	$R_{E Q} = (R_{1} ‖ R_{2}) + R_{3} = \frac{R_{1} R_{2}}{R_{1} + R_{2}} + R_{3}$
	$\frac{V_{o}}{V_{i}} = \frac{R_{2}}{R_{2} + R_{1}}$
	$\frac{V_{2}}{V_{1}} = \frac{R_{2} + R_{3}}{R_{1} + R_{3}}$
	$\frac{v_{i}}{v_{o}} = (\frac{R_{3}}{R_{1}}) (\frac{R_{2} - R_{1}}{R_{2} - R_{3}})$
	$R_{1} = \frac{R_{a} R_{b}}{R_{a} + R_{b} + R_{c}}$ $R_{2} = \frac{R_{b} R_{c}}{R_{a} + R_{b} + R_{c}}$ $R_{3} = \frac{R_{c} R_{a}}{R_{a} + R_{b} + R_{c}}$ $R_{a} = \frac{R_{1} R_{2} + R_{2} R_{3} + R_{3} R_{1}}{R_{2}}$ $R_{b} = \frac{R_{1} R_{2} + R_{2} R_{3} + R_{3} R_{1}}{R_{3}}$ $R_{c} = \frac{R_{1} R_{2} + R_{2} R_{3} + R_{3} R_{1}}{R_{1}}$ </math>