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Function generators are vital tools for many industrial applications. Sinusoidal oscillators are the essential units of function generators and investigating their performance is therefore necessary. The Barkhausen criterion is widely applied in designing sinusoidal oscillators because of its simplicity. The authors exploit a crucial necessary and sufficient oscillation criterion for Wien Bridge and Colpitts oscillators based on Simple Chen's Electric Unifying Approach. Their approach resolves the shortcoming of the traditional Barkhausen criterion, namely that it entails only a necessary condition. They propose a simple oscillation determining criterion that uses a stable sine-wave oscillator with an adjustable oscillation frequency. The derived oscillation criterion establishes a precise condition for the existence of oscillatory behaviour and does not require the fixed value used in the traditional Barkhausen criterion. To demonstrate its applicability, the proposed approach for the Wien Bridge and Colpitts oscillators is applied to implement a function generator.