Question

Calculate the maximum clock frequency at which a 4-bit asynchronous counter can work reliably. Assume the propagation delay of each flip-flop to be 40 ns and the width of the strobe pulse to be 20 ns.
1. 12.5 MHz
2. 6.25 MHz
3. 5.56 MHz
4. 16.67 MHz

Answer 1

Correct Answer - Option 3 : 5.56 MHz

Concept:

Lockout free condition: If a counter from an unused state enters one of the used states then the counter is called lock-out free. While taking any unused state as the initial state if the next state comes out to be a used state, the counter is said to be lockout free.

Synchronous counter: A counter in which all the flip-flops are triggered with the same clock pulse. In such counters, if the propagation delay of one flip-flop is tf, then the propagation delay for the whole counter will also be tf

Asynchronous counter: A counter in which all the flip flops are not triggered by the same clock pulse. In such counters, total propagation delay will be equal to the sum of propagation delay for all flip flops.

Calculation:

Given that, propagation delay of each flip-flop = 40 ns

Width of the strobe pulse = 20 ns

Total propagation delay = 40 × 4 + 20 = 180 ns

Maximum clock frequency \({f_{max}} = \frac{1}{T} = \frac{1}{{180 \times {{10}^{ - 9}}}} = 5.56\;MHz\)