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Inaccuracies of insertion loss measurements caused by deviation of a square law detector from square law set a practical upper limit on the r.f. power which can be applied to a bolometer. The detection of the audio modulation after extraction from the carrier by a bolometer is limited by the behaviour of the second detector in the presence of noise and sets a lower limit. Since square law and synchronous detectors are superior to linear detectors at a low ``signal to noise ratio'', their behaviour is studied in more detail. It is shown that the bandwidth of the amplifier ahead of the second detector is not the controlling factor for the accuracy of the measurement. The concept of ``ratio of amplifier bandwidth to indicator bandwidth'' is introduced. Graphs are given for the indicator fluctuations as a function of this concept and of the ``signal to noise ratio'' at the amplifier output for both synchronous and square law detectors. A graph is furnished showing the range of insertion loss measurement as a function of the accuracy desired based upon the accuracy limitations at the high end low power end.