The characteristics of classical Chua's circuit variables proposed by Leon O. Chua are the voltage on capacitor, the current in inductor and its normalized equation of state. Based on these characteristics, in this paper, three optimized and scaled circuit design methods are proposed. One is the Chua's circuit with five operational amplifiers used for limiting power amplitude for integration. The other two are Chua's function equivalent circuits with nonlinear diode for cellular neural network system integration. At the same time, an optimized cubic form of Chua's diffeomorphism circuit is given. The methods of designing these circuits are applicable to the cubic random circuits dominated by three broken lines. The universality and practical application of design method are demonstrated in the experiment on chaos secure communication.