Modeling Signal Integrity in High-Frequency and Radio Frequency Circuits: A Comparison of Ohm's Law Variants
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Abstract
High-frequency circuit performance is significantly impacted by impedance variations, particularly within the low-resistance regime. Traditional Ohm's Law-based modeling approaches often fail to accurately predict circuit behavior in these conditions, leading to design inaccuracies and potential system failures. The Standard Ohm's Law-based model's prediction of infinite current as resistance approaches zero is unrealistic and hinders its application in practical scenarios. Despite recognizing these limitations, existing models have not comprehensively addressed the complex impedance behavior observed in high-frequency circuits. This paper introduces a modified version of the Ohm's Law incorporating an exponential correction term to overcome these challenges. The accuracy of the Modified Ohm's Law was evaluated through simulated experiments across a wide frequency range (1kHz to 1GHz) using various electronic components. The findings demonstrate the superior performance of the modified model in predicting currents under low-resistance and high-current conditions compared to the Standard Ohm's Law model. By providing finite and accurate current values, the proposed model effectively mitigates the unrealistic infinite current predictions of the standard approach. The enhanced predictive capabilities of the Modified Ohm's Law hold significant implications for high-frequency circuit design and analysis. Its application can improve performance and reliability in power electronics, telecommunications, and other high-frequency systems. By incorporating non-linear impedance behavior, the model offers a more accurate representation of real-world circuit conditions. Future research should focus on refining the exponential term's parameters to optimize the model's accuracy across a broader range of applications. Additionally, real-time implementation and hardware validation are essential to assess the model's practical utility in complex circuit environments.
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