Electronics Handbook/Components/Resistor Network

Circuit	Configuration	Derivation	${\frac {v_{o}}{v_{i}}}$	Analysis
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 Vo = 0 R2 >> R2 Vo = 1 This configuration is ude maily to attenuate voltage
π		${\frac {V_{i}}{R_{1}}}={\frac {V_{i}-V_{o}}{R_{2}}}+{\frac {V_{o}}{R_{3}}}$ $V_{i}({\frac {1}{R_{1}}}-{\frac {1}{R_{2}}})=V_{o}({\frac {1}{R_{3}}}-{\frac {1}{R_{2}}})$	${\frac {v_{o}}{v_{i}}}=({\frac {R_{3}}{R_{1}}})({\frac {R_{2}-R_{1}}{R_{2}-R_{3}}})$
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	${\frac {V_{o}}{V_{i}}}$
	$R_{eq}=R_{1}+R_{2}+R_{3}+...+R_{n}\,$
	${\frac {1}{R_{eq}}}={\frac {1}{R_{1}}}+{\frac {1}{R_{2}}}+...+{\frac {1}{R_{n}}}\,$
	$R_{EQ}=(R_{1}\|R_{2})+R_{3}={R_{1}R_{2} \over R_{1}+R_{2}}+R_{3}$
	${\frac {V_{o}}{V_{i}}}={\frac {R_{2}}{R_{2}+R_{1}}}$
	${\frac {V_{2}}{V_{1}}}={\frac {R_{2}+R_{3}}{R_{1}+R_{3}}}$
	${\frac {v_{i}}{v_{o}}}=({\frac {R_{3}}{R_{1}}})({\frac {R_{2}-R_{1}}{R_{2}-R_{3}}})$
	$R_{1}={\frac {R_{\mathrm {a} }R_{\mathrm {b} }}{R_{\mathrm {a} }+R_{\mathrm {b} }+R_{\mathrm {c} }}}$ $R_{2}={\frac {R_{\mathrm {b} }R_{\mathrm {c} }}{R_{\mathrm {a} }+R_{\mathrm {b} }+R_{\mathrm {c} }}}$ $R_{3}={\frac {R_{\mathrm {c} }R_{\mathrm {a} }}{R_{\mathrm {a} }+R_{\mathrm {b} }+R_{\mathrm {c} }}}$ $R_{\mathrm {a} }={\frac {R_{1}R_{2}+R_{2}R_{3}+R_{3}R_{1}}{R_{2}}}$ $R_{\mathrm {b} }={\frac {R_{1}R_{2}+R_{2}R_{3}+R_{3}R_{1}}{R_{3}}}$ $R_{\mathrm {c} }={\frac {R_{1}R_{2}+R_{2}R_{3}+R_{3}R_{1}}{R_{1}}}$</math>