Abstract: A digitally synthesized frequency back-up circuit which, after removal or failure of applied A.C. power, will reproduce signals precisely indicative of each zero transition point of the A.C. waveform. A high frequency binary counter continually counts internally generated pulses and at the end of each A.C. period, stores one-half the count, representing 180.degree. , in a storage buffer. When the A.C. fails, the inverted value of the buffer count is loaded into the counter which is incremented by the internally generated pulses to count only up to the value stored in the buffer, at which point the circuit generates an output pulse. As long as the A.C. frequency remains off, the counter will continue to reload from the buffer and count the value representing this 180.degree. period. An additional and separate buffer section in the circuit stores the binary count representing the 90.degree. point in each A.C. cycle and continuously generates 90.degree.