A pulse train with a frequency of 1 MHz is counted using a mod-1024 ripple counter built with J-K flip-flops. For proper operation of the counter the maximum permissible propagation delay per flip-flop stage isa)100 nsb)50 nsc)20 nsd)10 nsCorrect answer is option 'A'. Can you explain this answer?

Question

Answer

Concept:

If we pass the input signal to a single T-flip flop, we will get half of the frequency at the output.

Similarly, when we pass the input signal into a divide by M bit counter, the output frequency (f_out) will be:

Calculation:

Given is a mod-1024 ripple counter which means that it can count 1024 states.

To count 1024 number of flipflop required is:

1024 = 2ⁿ

n = 10 flip-flops

t_pdff = Propagation delay of flip flops

tpdff = 10^-6 sec.

Propagation delay per flipflop =

= 10⁻⁶/10

= 100 nsec

Answer

Understanding the Problem
To determine the maximum permissible propagation delay for each flip-flop in a mod-1024 ripple counter, we must first understand the requirements of counting pulses.
Ripple Counter Basics
- A ripple counter consists of several flip-flops where the output of one flip-flop serves as the clock input for the next.
- For a mod-1024 counter, 10 flip-flops are needed since $2^{10} = 1024$.
Frequency of the Input Signal
- The input pulse train has a frequency of 1 MHz, which translates to a period ($T$) of:
$$
T = \frac{1}{f} = \frac{1}{1 \text{ MHz}} = 1 \mu s = 1000 ns
$$
Propagation Delay Considerations
- The total propagation delay ($t_{pd}$) for the ripple counter is the time taken for the output of the first flip-flop to propagate through all 10 flip-flops.
- Each flip-flop contributes a propagation delay, so for 10 flip-flops, we have:
$$
t_{pd(total)} = 10 \times t_{pd(flip-flop)}
$$
Timing Constraints
- For the ripple counter to function correctly, the total propagation delay must be less than or equal to the clock period (1000 ns):
$$
10 \times t_{pd(flip-flop)} \leq 1000 ns
$$
- Rearranging gives:
$$
t_{pd(flip-flop)} \leq \frac{1000 ns}{10} = 100 ns
$$
Conclusion
- The maximum permissible propagation delay per flip-flop stage is therefore 100 ns, making option (a) the correct answer.
- This ensures that each flip-flop can reliably toggle before the next clock pulse arrives, maintaining proper counting operation.

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