Max frequency calculation problems

Hi,

I am trying to calculate the max frequency of the following circuit. The given parameters are:

q. In the circuit shown, all the flip-flops are identical. If the set-up time is 2 ns, clock->Q delay is 3 ns and hold time is 1 ns, what is the maximum frequency of operation for the circuit.

According to me the answer should be :

max freq. = 1/ ( 3 + 3+ 2) = 125 MHz but the answer is given as 200 MHz which I don'd understand. Would someone please clarify what I am doing wrong?

Also, there is another problem wherein I am given a simple circuit(in black box form) with 2 inputs and one output. The 2nd input is just a complement of the first. The problem is to choose a function so that the output is of the same frequency as the input. I am not looking for an answer to this but if someone could throw some light on the approach required for this I can try to work it out. Thank you.

Hi rfndmw,

You don't have to consider the hold time while calculating max frequency. Hold is independent of frequency.
Hence the relation is Tcq + Tcombo = T - Tsetup
substitute values and we get T = 5ns
f= 1/T = 200 Mhz

---------- Post added at 19:32 ---------- Previous post was at 19:28 ----------

for the second problem, what is the relationship of the output to input. If frequency is only criteria you can simply pass any of the input as outputs

Hi chipmonkey,

Thanks for the reply. I do understand that the hold time need not be considered while calculating the max frequency. What I did was to take the propagation delay of the first 2 Flipflops (3ns each) and the setup time of the last flipflop i.e. 2ns. so that the calculation is :

1/(3+3+2) which does not give 200 MHz.

From what you have posted I am assuming that you are only considering the propagation delay of the last flipflop only and its setup time. But I dont understand why you have done so. Could you please clarify? thanks..

What you have done wrong is that you takes multiple cycles into account to calculate the cycle time.
The cycle time is determined by two flops that directly communicate in a cycle. The 1st flop and the 3rd flop in your circuit has no direct timing relationship because they are belonging to different cycles.

rfndmw,

While calculating max frequency for a circuit, you have to consider the path which requires the largest timeperiod. And these timing paths can be any of the below:
1) Path from input pin to D pin of a Flop
2) Path from clock pin of a flop to D pin of next flop
3) Path from clock pin of a flop to a primary output
4) Path from input to output (only combo)

So while calculating frequency, you have to analyze each of these paths and consider the path that requires largest timeperiod