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This page is obsolete. If you are a student of this Section, here is Lab VI


This page contains discussion of previous Lab VI passive circuit

Passive circuits

Consider this circuit as shown on the side. It is best to solve with the phasor method. However, to avoid the typing of imaginary symbol i, we will let expression iω be s instead (Laplace transform variable).
Then, we can use the node voltage method to solve the circuit. Obviously, it has only one essential node, but because we are interested in B node, not A node, we still keep it as a two-node problem so that we can get B voltage directly.

So, here is the NVM equation:
which can be solved:

  =>

This gives the result:

and

Phasor plot on the complex plane



Phasor and Bode plots



Active circuit - high pass
For the circuit on the side figure, we have similar approach with the NVM:



and:

which leads to:


where we define tau coupled (tau cp) as R2 (C1 C2)/(C1+C2)
Go to the bandpass figure at the end for app link


Active circuit - low pass
Using the NVM again:




Solve for it:

and the final results:

where we define tau coupled (tau cp) as C3 (R3 R4)/(R3+R4) 
Go to the bandpass figure at the end for app link

Active circuit - band pass


The transfer function for the above bandpass filter is simply the product of each part of the circuit. It is customary to assume that the output impedance (Thevenin) of the first op amp is small and negligible to the input impedance of the second circuit.