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The IEEE 802.16e-2005 standard, also denoted as mobile WIMAX, was introduced as one of the first real efforts towards the deployment of fourth generation communication systems providing fixed and mobile broadband wireless access. In this paper, we present the studying and sizing of the multi-mode sigma delta analog digital converter intended for use in the WiMAX band from 3.4GHz to 3.6GHz in 5MHz, 7MHz and 10MHz channel bandwidth. We use the pole placement method, linearization technique of loop sigma delta, to calculate and analyze the noise shaping transfer function of sigma delta analog digital converter according to the loop gain variation. This method aims to calculate the coefficients of continuous-time filter to achieve the desired noise shaping. For such specifications, a multi-mode fourth-order continuous-time sigma delta ADC, with mono-bit quantizer, is presented and its simulation results are shown by using Matlab Simulink.