Correction of traditional incorrect oscillation formula for the Wien‐Bridge Oscillator

Abstract

Abstract An incorrect mistake that the DC bias resistance cannot change the oscillation frequency exists for the traditional formula of the Wien‐Bridge oscillator. From the rigorous hardware experiments and theoretical proofs in this study, the proposed new formula exploits the fact that the oscillation frequency of the Wien‐Bridge oscillator is indeed determined by the DC bias resistance. The feedback theory and Barkhausen criterion are often utilised to address the oscillating formula of the Wien‐Bridge oscillator for traditional approaches. However, the steps of the feedback theory are complicated, and its severe shortcoming is the utilisation of Kirchhoff's law. The traditional Barkhausen formula is only necessary but not sufficient for the Wien‐Bridge oscillator. Hence, the oscillator with a feedback device, which fulfils the Barkhausen criterion does not necessarily oscillate at a frequency and then this fact will make the Barkhausen criterion impractical. This study applies our series research Chen's Electric Unifying Approach to overcome the serious shortcomings of the traditional Barkhausen method and yields a necessary and sufficient oscillation formula for the Wien‐Bridge oscillator. Another important feature of our proposed method is that the oscillation condition is effective for a range value, and it can solve the impact caused by the change in environmental factors.

Keywords

• Barkhausen criterion
• feedback theory
• Routh‐Hurwitz stability theorem
• Wien‐Bridge oscillator