| One of the main challenges in the development of Radio Frequency (RF) and analog circuits is the non-linearity of the circuits resulting in the limited dynamic range, inter-modulation, and harmonic distortion of the signals. This problem has been addressed by Harmonic Balance and the Shooting methods, however, these numerical methods have their limitations including resolution, convergence issue. In this work, two novel algorithms are developed to address these issues. The first method is a non-iterative nonlinear system solver termed "Inverse Self-Convolution Equations (ISCE) solver" which overcomes the convergence issue. The second algorithm is a frequency domain technique termed "Cross-Referenced Coordinates" (CRC) that uses multi-dimensional pass-band to base-band mapping of the signal and the inter-modulations products resulting in an increase in the simulation efficiency and higher accuracy compared to the other methods. The proposed algorithms are then combined resulting in a highly accurate and numerically time efficient method for the analysis of nonlinear circuits. In contrast with the existing solutions, CRC/ISCE analysis does not require time domain simulation. A complete method for the analysis and simulation of nonlinear blocks has been developed using the CRC/ISCE algorithms. It is shown that for digitally modulated signals, the CRC/ISCE simulator is highly accurate and offers better time efficiency. The actual nonlinear measurements for a Low Noise Amplifier (LNA), a mixer, and a Power Amplifier (PA) are used to validate the accuracy of the CRC/ISCE method. Accuracy and performance of the proposed technique along with Harmonic Balance and Shooting methods are demonstrated and compared for a number of benchmark RF circuits. |
