Chapter1

Chapter2

Chapter3







Static Timing analysis is divided into several parts:
 Part1 > Timing
Paths
 Part2 > Time
Borrowing
 Part3a > Basic
Concept Of Setup and Hold
 Part3b > Basic
Concept of Setup and Hold Violation
 Part3c > Practical
Examples for Setup and Hold Time / Violation
 Part4a > Delay
 Timing Path Delay
 Part4b > Delay
 Interconnect Delay Models
 Part4c > Delay
 Wire Load Model
 Part5a > Maximum
Clock Frequency
 Part5b > Examples
to calculate the “Maximum Clock Frequency” for different circuits.
 Part 6a > How
to solve Setup and Hold Violation (basic example)
 Part 6b > Continue
of How to solve Setup and Hold Violation (Advance examples)
 Part 6c > Continue
of How to solve Setup and Hold Violation (more advance
examples)
 Part 7a > Methods
for Increase/Decrease the Delay of Circuit (Effect of Wire Length On the
Slew)
 Part 7b > Methods
for Increase/Decrease the Delay of Circuit (Effect of Size of the
Transistor On the Slew)
 Part 7c > Methods
for Increase/Decrease the Delay of Circuit (Effect of Threshold voltage On
the Slew)
 Part 8 > 10
ways to fix Setup and Hold Violation.
In the previous post we have discussed about the way tool calculate the max and min delay in a circuit. Now we will discuss other basics of the Delay and delay calculation. During your day to day work (in Semiconductor Field) or say in different Books, you come across different terminology related to the delays. There is a long list of that.
 Input Delay
 Output Delay
 Cell Delay
 Net Delay
 Wire Delay
 Slope Delay
 Intrinsic Delay
 Transition Delay
 Connect Delay
 Interconnect Delay
 Propagation Delay
 Min/Max Delay
 Rising/Falling Delay
 Gate Delay
 Stage delay
Fortunately or say luckily out of the above mention long list few are just synonym of other and few are interrelated to each other . Like Net delay also know as Wire Delay , Interconnect delay. Broadly we can divide this Long List into 2 type of delay. Net Delay (Wire delay) and Cell Delay. ( Note : Stage Delay = Net delay + Cell Delay. )
So let’s discuss these one by one. In digital design, a wire connecting pins of standard cells and blocks is referred to as a NET. A net
 Has only one driver
 Has a number of fanout cells or blocks.
 Can travel on multiple metal layers of the chip.
“Net Delay” refers to the total time needed to charge or discharge all of the parasitic (Capacitance / Resistance / Inductance) of a given Net. So we can say that Net delay is a function of
 Net Resistance
 Net Capacitance
 Net Topology
Now to calculate the Net delay, the wires are modeled in different ways and there are different way to do the calculation. Practically, when you are applying a particular delay model in a design , then you have to apply that to all cells in a particular library. You cannot mix delay models within a single library. There are few recommendations provided by experts or say experienced designer regarding the application of a particular Delay model in a design and that depends on
 Technology of design.
 At what stage you are ? Or say at what stage you want to apply a delay model.
 How accurately you want to calculate the delay.
Note : Ideally Till the physical wire is not present in you design, you cannot calculate the Net delay. Reason is ... If wire is not present , you have no idea about the Length/Width of the wires. SO YOU CANN'T CALCULATE THE ACCURATE VALUES OF PARASITIC OR SAY DELAY VALUE OF THE WIRE. But here main point is accurate value, means there is possibility of inaccurate or say approximate value of delay value before physical laying of wire in a design.
There are several delay models. Those which can provide more accurate result, takes more runtime to do the calculation and those which are fast provides less accurate value of delay. Lets discuss few of them. Most popular delay models are 
 Lumped Capacitor Model
 Lumped RC model
 Distributed RC model
 Pi RC network
 T RC network
 RLC model
 Wire Load model
 Elmore Delay model
 Transmission Line Model
Lumped Capacitor Model.
 Model assume that wire resistance is negligible.
 Source driver sees a single loading capacitance which is the sum of total capacitance of the interconnect and the total loading capacitance at the sink.
 In past (higher technology350nm and so), capacitor was dominating and that’s the reason in the model we have only capacitance.
 Older technology had wide wires,
 More cross section area implies less resistance and more capacitance.
 So Wire model only with capacitance.
 In the Fig R=0
Lumped RC (Resistance Capacitance) model:
 As the feature size decreases to the submicron dimensions, width of the wire reduced.
 Resistance of wire is no longer negligible.
 Have to incorporate the resistance in our model. And that’s the reason Lumped RC model (or say RC tree) comes into picture.
In lumped RC model the total resistance of each wire segment is lumped into one single R, combines the global capacitive into single capacitor C.
Distributed RC model:
Distributed means RC is distributed along the length of the wire. The total resistance (Rt) and capacitance (Ct) of a wire can be expressed as
Rt = Rp * L
Ct = Cp * L
Where
Cp and Rp are Capacitance and Resistance per unit length.
L is the length of the wire.
Ideally, distributing the resistance and capacitance of a wire in very small portion of the wire (say delta) give you the better performance. Now to find out the total capacitance and resistance we use the differential equation. Distributed RC model provides better accuracy over lumped RC model. But this type of model is not practically possible.
The distributed RC model can be configured by 2 ways based on the structure or say shape (pi and T). Following is the pictorial view.
T model:
 Ct is modeled as a half way of the resistive tree.
 Rt is broken into 2 sections (each being Rt/2 )
Pi Model:
 Ct is broken into 2 sections (each being Ct/2) are connected on either side of the resistance.
 Rt is in between the capacitances.
For practical purpose, wiremodels with 510 elements/nodes are used to model the wire. It will provide the more accurate result. For N element section
For T network:
 Intermediate section of resistance are equal to Rt/N.
 Intermediate section of Capacitance are modeled by Ct/N
 End section of Resistance are equal to Rt/(2N).
 This T Network is represented as TN model.
For Pi network:
 Intermediate section of resistance are equal to Rt/N.
 Intermediate section of Capacitance are modeled by Ct/N
 End section of Capacitance are equal to Ct/(2N).
 This Pi Network is represented as PiN model.
Note: Lumped Vs Distributed RC wire:
Following is the comparison between the Lumped and distributed RC network. It will help you to understand in terms of uses of the both type of network in terms of accuracy and runtime.
Following is the Step Response of Lumped Vs Distributed RC line.
Below comparison Table will give you more accurate picture.
Output Potential range

Time Elapsed
 
Distributed RC Network

Lumped RC network
 
0 to 90%

1.0RC

2.3RC

10% to 90% (rise time)

0.9RC

2.2RC

0 to 63%

0.5RC

1.0RC

0 to 50%

0.4RC

0.7RC

0 to 10%

0.1RC

0.1RC

RLC model
In the past since the design frequency was low so the impedance (wL) was dominated by Resistance (wL << R). So we are not caring “L”. However if you are operating at higher frequency and use the wider wire that reduce the resistivity then we have to take account the inductance into our modeling.
Distributed RLC Model 
nice explanation.
ReplyDeleteI have a question though, when we calculate the total delay of the path we addup cell delay + interconnect delay and cell delay is calculated by taking into account the interconnect loading effect.So, isn't this wrong as we are taking the interconnect effect twice in our delay calculation
Hi Shubham,
ReplyDeleteIts not like that .. we take care about the every reasons/cause of the delay with in a particular path. But we never do anything twice.If you can wait for sometime .. you will see in my few next blog, how we usually calculate the cell delay. Just give me some more time. If its urgent .. please drop me a mail.. I will try to explain you there..
excellent work for who are looking for detailed and well explained STA especially freshers
ReplyDeleteDear sir,
ReplyDeleteplease explain about wire load model also.
Hi,
DeleteIts Done. Please Check the next blog.
Dear Sir,
ReplyDeletePlease explain the need of interconnect delay model.