IC Design Interview 6: Op-amp Circuits

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 = -(R₂/R₁)V_in

V_in/R₁ = -V_out/R₂
-(R₂/R₁)V_in = V_out

Non-Inverting Op-Amp (Buffer)

V_out = V_in(1+R₁/R₂) = V_in((R₂+R₁)/R₂)

V- = V_out R₂/(R₂+R₁)  [Voltage Divider]
Assume V- = V_in
V_in = V_out R₂/(R₂+R₁)
(R₂+R₁)/R₂ V_in = V_out
The special case of R₂ being open (infinite resistance) creates a Unity Gain Buffer

Difference Amplifier

V_out = R₂/R₁ (V_B-V_A)

Assume V- = V+
V+ = V_B R₂/(R₁+R₂)   [Voltage Divider]
Since I₁=I₂                 [Kirchoff's Current Law]
(V_out-V-)/R₂ = (V--V_A)/R₁
Solve for V-
R₁V_out+R₂V_A = V-
      R₂+R₁
Which is the same as V+, so
R₁V_out+R₂V_A = V_B R₂
      R₂+R₁             R₁+R₂
Which can be solved for V_out
                                                                                         V_out = R₂/R₁ (V_B-V_A)