This paper presents an analysis of noise adding radiometers that includes the effects of flicker, or 1/f, noise which often limits radiometer performance. The 1/f noise processes within the detector are affected by the modulation of the detector voltage as a result of the injected noise power and cause the overall 1/f noise to increase. The functional dependence of the 1/f noise parameters on degree of source modulation is determined experimentally. The primary result of this paper is a concise mathematical formula for the noise equivalent temperature difference of a noise adding radiometer explicitly showing the dependences on the radiometer parameters, as well as detector voltages when the source is on and off. From this formula, we derive the optimum on and off voltage ratio that maximizes sensitivity.