I have to square wave signals with the same frequency where one is delayed compared to the other. Put two signals to the input of a NAND gate (two inputs). Is there way (math, or some kinds of proofs) to see that the output signal of NAND gate also has the same frequency as the input signal?
If you draw the two inputs (A,B) and output (C) with their relative timings you should be able to get an idea of what is happening.
Suppose T is the period of the square wave and dT is the delay. As dT changes the output waveform maintains its frequency but alters the mark/space ratio.
If dT = T/2 (exactly 180 out of phase) the output goes HIGH (inputs are either 1,0 or 0,1 so output is 1) with no clock output!
What happens to the output in the interval T/2 < dT <= T?