Editing Wien bridge oscillator (section)

===Analyzed from loop gain===
According to Schilling,<ref name="Schilling"/> the loop gain of the Wien bridge oscillator, under the condition that R<sub>1</sub>=R<sub>2</sub>=R and C<sub>1</sub>=C<sub>2</sub>=C, is given by

:<math>T = \left( \frac { R C s  } {R^2 C^2 s^2 + 3RCs +1 } - \frac {R_b} {R_b + R_f } \right) A_0  \,</math>
where <math> A_0   \,</math> is the frequency-dependent gain of the op-amp (note, the component names in Schilling have been replaced with the component names in the first figure).

Schilling further says that the condition of oscillation is T=1 which, is satisfied by

:<math>  \omega = \frac {1} {R C} \rightarrow f = \frac {1} {2 \pi R C}\,</math>

and

<!-- Note, if A_0 has any phase shift then R_f/R_b would have a phase shift.  It is mathematically correct but impractical.  R_f and R_b are purely real -->
<!-- What Actually must happen is that the oscillation frequency shifts so that the positive feedback arm provides a necessary phase shift to make net phase shift as zero-->
<!-- If A_0 does have phase shift, there is still a solution for T=1, but it is non-trivial to find. -->
:<math>  \frac {R_f} {R_b}  =   \frac  {2 A_0 + 3} {A_0 - 3} \,</math>  with <math>\lim_{A_0\rightarrow \infin} \frac {R_f} {R_b} = 2 \, </math>

Another analysis, with particular reference to frequency stability and selectivity, is in {{Harvtxt|Strauss|1970|p=671}} and {{Harvtxt|Hamilton|2003|p=449}}.