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Thursday, August 4, 2011

"Delay - Timing path Delay" : Static Timing Analysis (STA) basic (Part 4a)






Static Timing analysis is divided into several parts:



This particular post is inspired by a question asked by Lalit. And Frankly speaking I am not able to resist myself to write a blog on this. I was thinking to capture all this since long but every time because of work  I have to drop my thoughts.. But today after reading his question.. I am not able to control myself. :)

So the Question is: (original question)

I have a doubt regarding how delay is calculated along a path.i think there are two ways
1) to calculate max delay and min delay, we keep adding max delays and min delays of all cells(buffer/inverter/mux) from start point to end point respectively.
2)in other way, we calculate path delay for rising edge and falling edge separately. we apply a rise edge at start point and keep adding cell delay. cell delay depends upon input transition and output fanout. so now we have two path delay values for rise edge and falling edge. greater one is considered as Max delay and smaller one is min delay.
which one is correct ?

Short Ans is .. both are correct and you have to use both. May be you all become confuse, so let me give you few details.

As I have mention that for Setup and Hold calculation , you have to calculate the Delay of the Timing path (capture path or launch path). Now in a circuit there are 2 major type of Delay.
  1. CELL DELAY
    • Timing Delay between an input pin and an output pin of a cell.
    • Cell delay information is contained in the library of the cell. e.g- .lef file
  2. NET DELAY.
    • Interconnect delay between a driver pin and a load pin.
    • To calculate the NET delay generally you require 3 most important information.
      • Characteristics of the Driver cell (which is driving the particular net)
      • Load characteristic of the receiver cell. (which is driven by the net)
      • RC (resistance capacitance) value of the net. (It depends on several factor- which we will discuss later)
Both the delay can be calculated by multiple ways. It depends at what stage you require this information with in the design. e.g During pre layout or Post layout or during Signoff timing. As per the stage you are using this, you can use different ways to calculate these Delay. Sometime you require accurate numbers and sometime approximate numbers are also sufficient.

Now lets discuss this with previous background and then we will discuss few new concepts.


Now in the above fig- If I will ask you to calculate the delay of the circuit, then the delay will be

Delay=0.5+0.04+0.62+0.21+0.83+0.15+1.01+0.12+0.57=4.05ns (if all the delay in ns)

Now lets add few more value in this. As we know that every gate and net has max and min value, so in that case we can find out the max delay and min delay. (on what basis these max delay and min delay we are calculating .. we will discuss after that)


So in the above example, first value is max value and 2nd value is min value. So

Delay(max)= 0.5+0.04+0.62+0.21+0.83+0.15+1.01+0.12+0.57=4.05ns
Delay(min)= 0.4+0.03+0.6+0.18+0.8+0.1+0.8+0.1+0.5=3.51ns

Till now every one know the concept. Now lets see what's the meaning of min and max delay.

The delay of a cell or net depends on various parameters. Few of them are listed below.
  • Library setup time
  • Library delay model
  • External delay
  • Cell load characteristic
  • Cell drive characteristic
  • Operating condition (PVT)
  • Wire load model
  • Effective Cell output load
  • Input skew
  • Back annotated Delay
If any of these parameter vary , the delay vary accordingly. Few of them are mutually exclusive. and In that case we have to consider the effect of only one parameter at a time. If that's the case , then for STA, we calculated the delay in both the condition and then categorize them in worst (max delay) condition or the best condition (min delay). E.g- if a cell has different delay for rise edge and fall edge. Then we are sure that in delay calculation we have to use only one value. So as per their value , we can categorize fall and rise delay of all the cell in the max and min bucket. And finally we come up with max Delay and min delay.


Information used in Cell and net delay calculation (Picture Source - Synopsys)
The way delay is calculated also depends which tool are you using for STA or delay calculation. Cadence may have different algorithm from Synopsys and same is the case of other vendor tools like mentor,magma and all. But in general the basic or say concepts always remain same.
I will explain about all these parameter in detail in next of few blogs, but right now just one example which can help you to understand the situation when you have a lot of information about the circuit and you want to calculate the delay.

In the above diagram, you have 2 paths between UFF1 and UFF3. So when ever you are doing setup and hold analysis, these path will be the part of launch path (arrival time). So lets assume you want to calculate the max and min value of delay between UFF1 and UFF2.

Information1:

UOR4
UNAND6
UNAND0
UBUF2
UOR2
DELAY(ns)
5
6
6
2
5


Calculation:
Delay in Path1 : 5+6=11ns,           
Delay in Path2:  6+2+5+6=19ns,    
So
Max Delay = 19ns - Path2 - Longest Path - Worst Path
Min Delay = 11ns - Path1 - Smallest Path - Best Path

Information2:

UOR4
UNAND6
UNAND0
UBUF2
UOR2
Rise Delay (ns)
5
6
4
1
1
Fall Delay (ns)
6
7
3
1
1


Calculation:
Delay in Path1 :        Rise Delay : 5+6=11ns,              Fall Delay: 6+7=13ns
Delay in Path2:         Rise Delay : 4+1+1+6=12ns,      Fall Delay: 3+1+1+7=12ns
So
Max Delay = 13ns -Path1 (Fall Delay)
Min Delay = 11ns - Path1 (Rise Delay)

Note: here there are lot of more concepts which can impact the delay calculation sequence, like unate. We are not considering all those right now. I will explain later.

Information3:
Library
Delay
UOR4
UNAND6
UNAND0
UBUF2
UOR2
Min
Rise Delay (ns)
5
6
4
1
1
Fall Delay (ns)
6
7
3
1
1
Max
Rise Delay (ns)
5.5
6.5
4.5
1.5
1.5
Fall Delay (ns)
5.5
6.5
2.5
0.5
0.5


Calculation:
For Min Library:
Delay in Path1 :        Rise Delay : 5+6=11ns,              Fall Delay: 6+7=13ns
Delay in Path2:         Rise Delay : 4+1+1+6=12ns,      Fall Delay: 3+1+1+7=12ns
For Max Library:
Delay in Path1 :        Rise Delay : 5.5+6.5=12ns,              Fall Delay: 5.5+6.5=14ns
Delay in Path2:         Rise Delay : 4.5+1.5+1.5+6.5=14ns,      Fall Delay: 2.5+0.5+0.5+6.5=10ns
So
Max Delay = 14ns- Path1(Fall Delay)/Path2(Rise Delay)
Min Delay = 10ns - Path2(Fall Delay)

As we have calculated above, STA tool also uses similar approach for finding the Max delay and Min Delay. Once Max and Min delay is calculated then during setup and hold calculation, we use corresponding value.

Once again I am mentioning that all these values are picked randomly. So it may be possible that practically the type/amount of variation in value is not possible.

In next part we will discuss these parameter in detail one by one.




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