The solution of the Bloch differential equations is given for the case of sideband modulation. The discussion of the results indicates possibilities for control systems for the automatic balancing of the nuclear resonance spectrometer for detection of dispersion or absorption signals, with optimum adjustment of the high frequency part. Experimental realizations are reported and some spectra are presented to illustrate performance. The solution of the Bloch differential equations furthermore allows an assessment of the optimum modulation index and a calibration of the effective high frequency field.