**You must know your op-amp circuits to do analog circuit design!**During an interview, you even have to derive the operation equations. Each of these derivations starts with the result in bold (because you must just know that) followed by the derivation.

Inverting Op-Amp |

**V**

_{out }= -(R_{2}/R_{1})V_{in}**V**

_{ }_{in}/R

_{1}= -V

_{out}/R

_{2}

-(R

_{2}/R

_{1})V

_{in}= V

_{out}

Non-Inverting Op-Amp (Buffer) |

**V**

_{out }= V_{in}(1+R_{1}/R_{2}) = V_{in}((R_{2}+R_{1})/R_{2})V- = V

_{out}R

_{2}/(R

_{2}+R

_{1}) [Voltage Divider]

Assume V- = V

_{in}

V

_{in}= V

_{out}R

_{2}/(R

_{2}+R

_{1})

(R

_{2}+R

_{1})/R

_{2 }V

_{in }= V

_{out}

The special case of R

_{2}being open (infinite resistance) creates a Unity Gain Buffer

Difference Amplifier |

**V**

_{out}= R_{2}/R_{1}(V_{B}-V_{A})**Assume V- = V+**

V+ = V

_{B}R

_{2}/(R

_{1}+R

_{2}) [Voltage Divider]

Since I

_{1}=I

_{2 }[Kirchoff's Current Law]

(V

_{out}-V-)/R

_{2}= (V--V

_{A)}/R

_{1}

Solve for V-

__R__= V-

_{1}V_{out}+R_{2}V_{A}R

_{2}+R

_{1}

Which is the same as V+, so

__R__=

_{1}V_{out}+R_{2}V_{A}__V__

_{B}R_{2}R

_{2}+R

_{1 }R

_{1}+R

_{2}

Which can be solved for V

_{out}

V

_{out}= R

_{2}/R

_{1}(V

_{B}-V

_{A})