When 100kHz and 32.768kHz square waveforms are applied to the inputs of Centraflow's 4017 sequencing circuit then the following depicts how the width of half of the output pulses grows as these two unsynchronized signals beat against each other with creeping phases. (later on, the pulses shrink).
Nothing except the AND or NOR gate's performance limits how narrow these green pulses can get.
Note that the green pulses mostly come in pairs ( actually in
groups of 2 and rarely 3 pulses ):
With square CP0=100kHz and CP1=32.768kHz, the probabilities of occurrences are as follows:
94.82% : 1 complete 5µs pulse and 1 partial pulse (or vice versa),
2.59% : 2 complete 5µs pulses,
2.59% : 3 pulses (partial+complete+partial), ...occurring 848 times per second.
This happens because 100kHz / 32.768kHz ≈ 3.05 which means that a little more than 3 cycles of the 100kHz signal fit in 1 cycle of the 32.768kHz signal ...but since it is a square wave then only half of that cycle is spent at the high level, thus only a little more than 1.5 cycles of the 100kHz signal fit inside the high level period of the 32.768kHz signal where the AND or NOR gate lets them pass though.
Thus you always see 1 complete cycle of the 100kHz signal in the group (which contains 1 complete 5µs high pulse of that cycle) and a fraction of one or two other cycles which can contain a second complete 5µs high pulse (rare) or fractional pulse/s. It is also possible that the 15.26µs pulse symmetrically straddles 1.5 cycles of the 100kHz square waveform which results in 3 pulses per group (1 fractional pulse + 1 complete 5µs pulse + 1 fractional pulse), this case is illustrated below:
A rare situation with 3 pulses per group ( probability: 2.59% ).This rare situation does not happen for square CP1 waveforms having frequencies 3x the CP0 frequency (or higher, e.g.: CP0=100kHz and CP1=34kHz ), or when the length of the CP1's active state is equal or less than 3x the length of CP0's active state. The lack of these triple pulses prevents periodic
mode switching of the
A,B,C,B sequencing circuit, e.g.: based on the
74HC175 / 40175 chip, or on the
74HC174 / 40174 chip, or on the
4017 chip.
Mode switching is a weird feature of these sequencing circuits where in one mode the pulses at the B output are wider than the pulses at the A & C outputs and a second mode in which the pulses at the B output are narrower than the pulses at the A & C outputs. These modes
do not switch as long as the number of CP pulses per group evenly divides the number of states of the sequencing circuit (4), i.e.: 2 CP pulses per group.
Mode Switch. Note the widths of the B pulses wrt A & C pulses before and after the triple CP pulse (circled in red)These mode switches cause inversions of the duty cycle. This affects the DC-level and low-frequency components of the A,B,C waveforms.
Below is a long-term plot of the B signal averaged by a simple
RC integrator that illustrates this phenomenon. Note that sometimes 2 phase wraparounds between the CP0 and CP1 signals occur before a mode switch. All in all, this creates a low frequency
analog signal.
Low frequency components of the B signal caused by the inversions of the duty cycle and phase wraparounds (cycles at 424Hz)Finally, during the low level part of the 32.768kHz square waveform (also 15.26µs long), the AND or NOR gate always blocks the transmission of the 100kHz waveform so we see a gap in the CP signal without any edges, which causes the sequencing circuit to pause and elongate its current output pulse.
P.S.
If my pet hypothesis is correct, then the second pulse in each group should always be longer than the first pulse.
This circuit generates such pulse sequences ...but not all the time (less than half of the time, in fact). This happens because the two frequencies beat against each other with creeping phases. On the encouraging side, this sequencing circuit generates many pulse width ratios randomly. Maybe some of these ratios are magic... In spin echo experiments some pulse width ratios and spacings definitely are special.
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Topic: What is Known about the TPU (Read 589066 times)
