The theory for frequency modulation given by Karplus has been extended to include Doppler broadening and arbitrarily large modulation depths. It is shown that the detection limit for second harmonic detection is of the same order as for first harmonic detection: the modulation depth must be approximately the full linewidth of the line profile. Procedures are discussed for extracting from experimental data the linewidth and center frequency of an absorption line with a Voigt profile. At zero detuning information about collisional line broadening can be obtained from the dependence of the second harmonic signal upon the modulation depth. Some experimental examples in the microwave region are presented as a test of the theory. Measurements on the rotational transition J = 2 ¿ 3 (v2 = 1) of OCS yield collisional self-shift and self-broadening parameters of -0.14 (±0.01) and 5.97 (±0.01) MHz/Torr, respectively; these values are in accordance with literature but are more accurate. For the line center at zero pressure a much more accurate value of 36 571 422.0 ± 0.7 kHz has been found, which is in agreement with recent theoretical calculations.