Determine the output frequency of the given circuit if the input CLK frequency is 1 MHz.

Concept:

T flip-flop

The truth table of the T flip-flop is given by:

The characteristic table of the T flip-flop is:

The characteristic equation of the T flip-flop is:

Q(t + 1) = T ⊕ Q(t)

Analysis:

From the given circuit two flip-flops are present and the Q₁’ output is connected to the input of the second flip-flop.

T₂ = Q₁’

Given circuit is an example of the Down counter.

The below figure represents the waveforms for the respective clock edges.

The flip-flop2 will trigger only when the Q₁’ is going from 0 to 1, i.e., positive triggering of the Q₁’.

In the output is Q₁ the total time period is 4 times that of the clock (4T).

Conclusion:

As the time period is 4 times then the frequency will be divided by four times.

\({f_{out}} = \frac{f}{4} = \frac{{1MHz}}{4}\)

f_out = 0.25 MHz = 250 kHz