We could equally use jw in place of s if we wanted to get an idea of the phase effects of a circuit and this will be done later.
Boldly going forth with the above supposition, a Wien bridge oscillator can now be analyzed.
The performance of modern components is such that in most cases, the above assumptions are perfectly acceptable and very little performance degradation occurs as we move away from the ideal.
Long before the op amp was invented, Kirchoff's law stated that the current flowing into any node of an electrical circuit is equal to the current flowing out of it.
This only happens at one frequency (when w = 1/CR).
At this frequency the real terms of the numerator cancel and the phase shift represented by the imaginary terms in both numerator and denominator cancel (essentially, if you have no j terms in either numerator or denominator, there is no phase shift). Using Kirchoff's law, the currents flowing into and out of the nodes around the op amp can be translated into equations and from this the transfer function can be derived.This approach, although quick, does not always mean the designer has a fundamental understanding of the theory of the circuit operation.This application note explains how the transfer function of most op amp circuits can be derived by a simple process of nodal analysis.The technique of nodal analysis can be used to analyze circuits with reactive components.In the same way we considered the conductances of resistors, with reactive components the equations are made easier by considering their admittances. Note that the Laplace nomenclature is used, since again it makes the equations look easier and the psychological effects of this are considerable.From this equation two conclusions can be drawn, both of which are well known conditions for oscillation of the Wien bridge oscillator.First, for oscillation to occur, there must be zero phase shift from the input to the output.Abstract: The creation of the op amp introduced a new fundamental component and marked a change in thinking for analog designers.Since it is so widely used, pretty much any op amp circuit that an engineer needs to implement has already been designed and the engineer can merely tailor the component values.Figure 3 shows the generic configuration of this circuit.Again, to keep the equations simple most engineers keep the resistor values equal and the capacitor values equal.