The paper proposes new accurate exponential circuits, having a multitude of practical applications in analog signal processing. The original method for obtaining the exponential function is based on the utilization of new superior-order approximation functions. The accuracy of the proposed structures is excellent and the output dynamic range is strongly extended as a result of the fourth-order approximation and of the independence of implemented function on technological errors and on temperature variations (the best original proposed architecture of the exponential generator has an output dynamic range of 70 dB for an approximation error smaller than +/- 1 dB). The exponential circuits are designed for implementing in 0.18 mu m CMOS technology, having a low-voltage operation (a minimal supply voltage of 1 V). The power consumptions of the proposed exponential circuits are smaller than 0.08 mW, for a supply voltage of I V. As application of the new exponential circuit, a dB-linear VGA circuit with high output dynamic range will be presented. The new computational structures have the possibility of generating any continuous mathematical function, presenting also an increased modularity and controllability and reduced design costs per implemented function. (C) 2013 Elsevier Ltd. All rights reserved.