A family of detuning insensitive algorithms with an odd number of points and a maximum of seven is developed here following a simple algebraic approach. Detuning insensitive algorithms are quite useful because the phase error due to any possible phase shifter miscalibration can be substantially reduced. A method to evaluate the second order detuning error, that is, the frequency range over which the insensitivity to detuning remains valid, is given, so that the best algorithm can be selected. A few of the most interesting algorithms from this point of view are described. This method, if desired can be extended to any number of points.
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