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A design methodology for tuning a circuit by analyzing its sensitivity to various design parameters is presented. This analysis helps in comprehending the critical design parameters so that they can be tuned for obtaining the most optimal desired circuit behavior. The methodology is exemplified through the design of a 2.3 GHz radio-frequency Low Noise Amplifier(LNA) for Worldwide Interoperability for Microwave Access (WIMAX) applications using 0.35 um technology. The circuit designed is an inductively loaded amplifier along with inductive source degeneration. The effect of various design circuit parameters on gain, input resistance and noise figure is analyzed. The simulated Noise figure for the optimized LNA is 1.102dB and the voltage gain is 15.11dB at 2.3 GHz. The LNA is designed to match an input impedance of 50Ω and an output impedance of 50Ω. The circuit has an input return loss of -19.23dB and an output return loss of -10.97dB. The 1-dB compression point is 8.69dBm and Input Third-order Intercept Point (IIP3 ) of the LNA is 6.537dBm. The Rollet's Stability factor (K factor) of the circuit is greater than 1 which shows that the circuit is unconditionally stable. The designed LNA consumes a power of 1.656mW at a supply voltage of 3.3 V. The LNA developed in the present work achieves a high gain along with a high linear range while consuming less power.