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Tuesday, May 3, 2011

"Examples Of Setup and Hold time" : Static Timing Analysis (STA) basic (Part 3c)





Static Timing analysis is divided into several parts:

Till now we have discussed a lot of theory about setup and hold time (with and without Example). Now it’s time to discuss the practical implementation of that. Means in a circuit
  • How will you calculate the setup and hold values?
  • How will you analyze setup and hold violation in a circuit?
  • If you have to improve timing of a circuit then what can you do?
There are few formulas to calculate different parameter ( Theory of those I already explained in my previous blogs). I am not going to explain those right now. First we will solve few examples which will give you an basic idea about these formulas, then in the last I will summarize all those in one place.

I saw a lot of confusion with respect to setup and hold timing calculation. Actually there are two things.
  • Timing Specification of a Block/Circuit/Library:
    • You have a block with input A and output Y. Some combinational logic is there between A and Y. Now you have to calculate following parameters for that block
      • Setup Time Value at input A
      • Hold Time value at input A.
      • Maximum operating Clock Frequency or Time Period for that block.
      • Clock To Y delay value
      • Input A to Output Y delay value.
  • Timing Violation of a circuit:
    • You have to operate a circuit at a particular clock frequency and now you have to find out whether this circuit has any setup or Hold Violation.
So in second case all the parameters are given and you have to find out whether this circuit has any violation or not and In first case you have to find out all the parameters keeping in mind that there should not be any violation.
Lets Discuss in the reverse order.
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Problem1: In the following Circuit, Find out whether there is any Setup Or Hold Violation?

  


Solution:
Hold Analysis:
When a hold check is performed, we have to consider two things-
  • Minimum Delay along the data path.
  • Maximum Delay along the clock path.
If the difference between the data path and the clock path is negative, then a timing violation has occurred. ( Note: there are few Exceptions for this- We will discuss that some other time)

Data path is: CLK->FF1/CLK ->FF1/Q ->Inverter ->FF2/D

Delay in Data path
= min(wire delay to the clock input of FF1) + min(Clk-to-Q delay of FF1) +min(cell delay of inverter) + min(2 wire delay- "Qof FF1-to-inverter" and "inverter-to-D of FF2")
=Td = 1+9+6+(1+1)=18ns

Clock path is: CLK-> buffer -> FF2/CLK

Clock path Delay
= max(wire delay from CLK to Buffer input) + max(cell delay of Buffer) + max(wire delay from Buffer output to FF2/CLK pin) + (hold time of FF2)
=Tclk = 3+9+3+2 = 17 ns

Hold Slack = Td - Tclk = 18ns -17ns = 1ns
Since Hold Slack is positive-> No hold Violation.

Note: If the hold time had been 4 ns instead of 2 ns, then there would have been a hold violation.
Td=18ns and Tclk = 3+9+3+4=19ns
So Hold Slack=Td - Tclk = 18ns - 19ns = -1ns (Violation)


Setup Analysis:
When a setup check is performed, we have to consider two things-
  • Maximum Delay along the data path.
  • Minimum Delay along the clock path.
If the difference between the clock path and the data path is negative, then a timing violation has occurred. ( Note: there are few Exceptions for this- We will discuss that some other time)

Data path is: CLK->FF1/CLK ->FF1/Q ->Inverter ->FF2/D


Delay in Data path
= max(wire delay to the clock input of FF1) + max(Clk-to-Q delay of FF1) +max(cell delay of inverter) + max(2 wire delay- "Qof FF1-to-inverter" and "inverter-to-D of FF2")
=Td = 2+11+9+(2+2) = 26ns

Note: The first part of the clock path delay (during setup calculation) is the clock period, which has been set to 15 ns. Hope You remember in last blog, I have mentioned very clearly that Setup is checked at the next clock cycle. That's the reason for clock path delay we have to include clock period also.

Clock path is: CLK-> buffer -> FF2/CLK

Clock path Delay
= (Clock period) + min(wire delay from CLK to Buffer input) + min(cell delay of Buffer) + min(wire delay from Buffer output to FF2/CLK pin) - (Setup time of FF2)
=Tclk = 15+2+5+2-4=20ns

Setup Slack = Tclk - Td = 20ns - 26ns = -6ns.
Since Setup Slack is negative -> Setup violation.

Note: A bigger clock period or a less maximum delay of the inverter solve this setup violations in the circuit.
E.g
If Clock period is 22ns then
   Tclk = 22+2+5+2-4=31-4=27ns   AND Td = 26ns
Setup Slack = Tclk - Td = 27-26=1ns  (No Violation)



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Problem2: In order to work correctly, what should be the Setup and Hold time at Input A in the following Circuit. Also find out the maximum operating frequency for this circuit. (Note: Ignore Wire delay). Where Tsu- Setup time; Thd-Hold Time; Tc2q- Clock-to-Q delay
Solution:
Step1: Find out the maximum Register to register Delay.


Max Register to Register Delay
= (clk-to-Q delay of U2) + (cell delay of U3) + (all wire delay) + (setup time of U1) 
= 5 + 8 + 3 = 16 ns.

Note:
  • There are 2 register to register paths
    • U2 -> U3 ->U1 (Delay=5+8+3=16ns)
    • U1 -> U4 -> U2 ( Delay=5+7+3=15ns)
  • We have to pick maximum one.

Step2: Find Out Setup Time:

A setup time = Setup time of Flipflop + Max (Data path Delay) - min(Clock path Delay)
= (Setup time of Flipflop + A2D max delay) - (Clk path min delay)
= Tsu + (Tpd U7 + Tpd U3 + wire delay) - Tpd U8
= 3 + (1+8 ) - 2 = 10 ns

Note:
  • Here we are not using the Clock period. Because we are not suppose to calculate the Setup violation. We are calculating Setup time. Please refer the part3a for the referance.
  • All the wire dealy is neglected. If Wire delay present, we have to consider those one.
  • There are 2 Data path
    • A -> U7 -> U4 -> D of U2 (Data path Delay = 1+7 =8ns )
    • A -> U7 -> U3 -> D of U1 ( Data path Delay = 1+8 =9ns )
  • Since for Setup calculation we need maximum Data path delay, we have choosen 2nd for our calculation.
Step3: Find Out Hold Time:
A hold time = Hold time of Flipflop + max(Clock path Delay) - min( Data path delay)
=( Hold time of Flipflop + Clk path max delay) - (A2D max delay)
= Thd + Tpd U8 - (Tpd U7 + Tpd U4+wire delay)
= 4 + 2 - (1+7 ) = -2 ns

Note: Same explanation as for Setup time. For hold time we need minimum data path , so we have picked first Data path.

Step4: Find out Clock to Out Time:

Clock to Out
= Cell delay of U8 + Clk-to-Q delay of FlipFlop+ Cell delay of U5+ Cell delay of U6+ (all wire delay)
= Tpd U8+ U2 Tc2q + U5 Tpd + U6 Tpd
= 2 + 5 + 9 + 6 = 22 ns

Note:
  • There are 2 Clock to Out path- one from Flip flop U1 and other from U2.
  • Since in this case the Clk-to-Q path for both Flipflop is same, we can consider any path. But in some other Circuit where the delay is different for both the paths, we should consider Max delay path.
Step5: Find Pin to Pine Combinational Delay (A to Y delay)

Pin to Pin Combinational Delay (A to Y)
= U7 Tpd + U5 Tpd + U6 Tpd
= 1 + 9 + 6 = 16 ns

Step5: Find Out Max Clock Frequency:

Max Clock Freq = 1/ Max (Reg2reg, Clk2Out, Pin2Pin)
= 1/ Max (16, 22, 16)
= 45.5 Mhz

So summery is:

Parameter
Description
Min
Max
Units
Tclk
Clock Period
22

ns
Fclk
Clock Frequency

45.5
Mhz
Atsu
A setup time
10

ns
Athd
A hold time
-2

ns
A2Y
A to Y Tpd

16
ns
Ck2Y
Clock to Y tpd

22
ns

Note: Negative hold times are typically specified as 0 ns.



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Problem3: In the above Circuit, Try to improve the timing by adding any "buffer" or "Register".

Solution:
Best way of doing this is “Register all Input and Output”. We are adding DFF so same specification (as U2 and U1).

Now follow all those 5 Steps onn by one.
Step1:

Max Register to Register Delay
U2 Tc2q + U5 Tpd + U9 Tsu = 5 + 9 + 3 = 17 ns

Note:
  • A lot of Register to Register path
    • U8 -> U5 -> U9 (Delay = 5+9+3=17ns)
    • U8 -> U4 -> U2 (Delay = 5+7+3=15ns)
    • U8 -> U3 -> U1 (Delay = 5+8+3=16ns)
    • U1 -> U4 -> U2 (Delay= 5+7+3=15ns)
    • U1 -> U5 -> U9 (Delay= 5+9+3=17ns)
    • U2 -> U5 -> U9 (Delay = 5+9+3=17ns)
    • U2 -> U3 -> U1 (Delay = 5+8+3=16ns)
  • Maximum delay is 17ns, Just picked anyone.
Step2:
A setup time = Tsu + A2D Tpd max - Clk Tpd min
= Tsu + (Tpd U7) - Tpd U8
= 3 + (1) - 2 = 2 ns

Note: Only One path between A and D of FF(i.e U8)

Step3:
A hold time = Thd + Clk Tpd max - A2D Tpd min
= Thd + Tpd U8 - (Tpd U7)
= 4 + 2 - ( 1) = 5 ns

Note: Only One path between A and D of FF(i.e U8)

Step4:
Clock to out:
=Tpd U8+ U9 Tc2q  + U6 Tpd
=2+5+6 = 13 ns

Step5:
No direct link between A and Y. So Not Applicable.

Step6:
Max Clock Freq = 1/ Max (Reg2reg, Clk2Out, Pin2Pin)
= 1/ Max (17, 13)
=58.8 Mhz

Parameter
Description
Min
Max
Units
Tclk
Clock Period
17

ns
Fclk
Clock Frequency

58.8
Mhz
Atsu
A setup time
2

ns
Athd
A hold time
5

ns





Ck2Y
Clock to Y tpd

13
ns



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I hope This much will help you. Now its the time to summarize all the important things and formulas.

Points to remember:
  1. Setup is checked at next clock edge.
  2. Hold is checked at same clock edge.
  3. For Hold Check ( Checking of hold Violation)
    • Minimum Delay along the data path.
    • Maximum Delay along the clock path.
  4. For SetUp Check ( Checking of Setup Violation)
    1. Maximum Delay along the data path.
    2. Minimum Delay along the clock path.







Basic 2 FlipFlop circuit.




Calculation of Setup Violation Check: Consider above circuit of 2 FF connected to each other.

Setup Slack = Required time - Arrival time (since we want data to arrive before it is required)

Where:
           Arrival time (max) = clock delay FF1 (max) +clock-to-Q delay FF1 (max) + comb. Delay( max)
           Required time = clock adjust + clock delay FF2 (min) - set up time FF2
           Clock adjust = clock period (since setup is analyzed at next edge)

Calculation of Hold Violation Check: Consider above circuit of 2 FF connected to each other.

Hold Slack = Arrival Time - Required time (since we want data to arrive after it is required)

Where:
           Arrival time (min) = clock delay FF1 (min) +clock-to-Q delay FF1 (min) + comb. Delay( min)
           Required time = clock adjust + clock delay FF2 (max) + hold time FF2
           Clock adjust = 0 (since hold is analyzed at same edge)

Calculation of Maximum Clock Frequency: 

Max Clock Freq = 1/ Max (Reg2reg delay, Clk2Out delay, Pin2Pin delay)

Where:
         Reg2Reg Delay = Clk-to-Q delay of first FF (max) + conb delay (max) + setup time of 2nd FF.
         Clk2Out Delay = Clock delay w.r.t FF (max) + clock-to-Q delay of FF1 (max) + comb. delay (max)
         Pin2Pin delay = Comb delay between input pin to output pin (max)





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