Analog circuits are the core components of modern electronic systems, and as electronic devices become increasingly complex, traditional fault diagnosis methods are no longer able to meet the demand for fault detection in modern analog circuits, especially in soft fault diagnosis, where similar signal responses make fault localization difficult. To solve this problem, a pure data-driven fault detection method based on the Koopman operator is proposed. First, the Hankel matrix is constructed through the delay embedding method, which maps the circuit output signal to a high-dimensional space and achieves system global linearization. Then, the Koopman operator is solved using dynamic mode decomposition, and the modal distribution and signal modal energy ratio are analyzed in the Koopman operator’s eigenfunction space. By extracting the Van der Monde matrix that stores the changes in the eigenvalue, the critical modes are obtained to construct a feature vector with good discriminability. Finally, it is input into a convolutional neural network to complete the fault identification. To verify the effectiveness of the method, a joint simulation model of a four-op-amp dual second-order high-pass filter circuit based on Pspice and Simulink was established, and the circuit state parameters were automatically collected using the SLPS module combined with the circuit netlist. The experimental results show that the proposed method has a high accuracy, with an average accuracy of 99.86%, which is higher than other methods.