This paper presents a novel method for generating Linear Frequency Modulation (LFM) waveforms. Conventional Look-Up Table (LUT)-based method require large storage resources, especially in high-resolution, multi-mode radar systems. To address this issue, we propose a ROM-free, real-time LFM waveform generator. It uses the fourth-order Runge-Kutta (RK-4) method to solve differential equations for the in-phase and quadrature components. The proposed approach dynamically generates LFM waveforms using only parameters such as pulse width, bandwidth, and sampling rate, eliminating the need for pre-calculated waveforms and LUTs. This method completely removes storage requirements, enabling faster synthesis times and achieving minimal latency. The generator’s performance is validated through simulation and FPGA implementation using a full hardware description language. Results confirm its effectiveness, making it a strong candidate for advanced radar systems that demand high performance with limited hardware resources.