Digital Circuit


This is a setup-hold time problem given in one of the digital designs book I am using. In the figure(sorry for the poor drawing), a circuit schematic is shown and we have to find out the maximum clock frequency and whether any hold time violations occur or not.

The flip flops(shown with a CLK input) have a clock to Q contamination delay of 30ps and a propagation delay of 80 ps. They have a setup time of 50ps and a hold time of 60ps. Each logic gate(rectangular boxes with operation specified) has a propagation delay of 40ps and contamination delay of 25ps.

I am having a hard time understanding and solving this problem. The book has also provided information regarding setup and hold time constrains in terms of propagation and contamination delays such that

Clock period>=clock to Q propagation delay+combinational logic propagation delay+setup time


**clock to Q contamination delay+propagation delay>=hold time**

Can anybody help me with explaining these constraints and the problem solution.


  • \$\begingroup\$ Do you know what each of these delay types mean? If you do, you can just figure out how many you need of each for you worst-case path and sum them together. I have a suspicion that they are defined in the book you are using. \$\endgroup\$
    – drxzcl
    Commented Feb 3, 2014 at 22:45

1 Answer 1


The minimum clock period is determined by the worst case propagation delay plus the setup time. In the example, this is the path from flip-flop A through 3 gates to flip-flop Y. The total propagation delay is 80ps for the flip-flop, plus 3 times 40ps for each gate, or 200ps. Adding 50ps setup time for flip-flop Y gives a minimum clock period of 250ps.

The minimum contamination delay is from flip-flop D through 1 gate to flip-flop Y. The minimum contamination delay is 30ps for the flip-flop plus 25ps for the gate or 55ps, so the input to Y may change as soon as 55ps after the clock, violating the hold time requirement of 60ps.


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