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A 3 bit ripple counter uses j k flip flops.if the propagation delay of each flipflop is 50 nsec,then the maximum clock frequency that can be used in megahertz... please explain the soln

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$T_{propagation-delay} = n*T_{flipflops} + T_{combinational}$  // In case of ripple counters

And $T_{clock}$  $\geq$  $T_{propagtion-delay}$

$\frac{1}{Freq_{clock}} \geq 3*50ns  + 0$

$Freq_{clock} \leq \frac{1000*10^{6}}{150}$

$Freq_{clock} \leq 6.667MHz$
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max clock frequency=1/3*50*10^-9 clock frequncy=1/t (for asychronous  tt= n*propogation delay)

                                 =6.67 MHz
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First flip flop i.e. lsb changes every clock cycle. Since 3 flip flops are in cascade, it requires minimum 3*Tpd for all the 3 bits i.e state to be stable.... If at any time<3 times Tpd, again clock is applied..... Lsb again toggle and the counter will still work but will not act as an up counter or a down counter, since there is no stable state... We only get undesired values as states...... Therefore for proper working as an up counter or a down counter, Tclk should be greater than Or equal to 3*Tpd.....

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