Signal Integrity TUTORIAL
Time and Distance
Setup and Hold time is useful for chip designers and simulation engineers. As a PCB Designers, we need to finally measure the things in terms of the length of the trace that travel on the PCB.
The Electric signals are electromagnetic wave and their speed of propogation depends upon the dielectric constant of the material surrounding it. The Formula for the propogation speed is
v = C / √ ε_{r} |
The speed of the electromagnetic wave in the free space is 3 x 10^{8} meter per second. The dielectric constant of free space is taken as 1. Let is say, the same signal propogates in a dielectric with a dielectric constant of 4, its speed will reduce to half or 1.5 x 10^{8}. We have already learnt this in High School Physics classes. In PCB Designs we use another term propogation speed and measure it in terms of picosecond per inch. The velocity of 3 x 10^{8} meter per second is equivalent to TBD picosecond per inch.
A signal propogating in an inner layer, sandwithced between two dielectrics of dielectric constant of 4 will have a speed that is half of the free space propogatin speed. What happens if a signal propogates in an outer layer. On one side we have a free air while on the other side we have a dielectric. The speed of the propogation will be somewhere in between between. We can take the help of calculators to find the speed of propogation ( Link to calculators TBD).
As PCB designers, we will be required to match the flight time between a set of signals. We will try to match the lengths ( as required) IF the signals propogates in a sililar way in terms of the amount of length in outer and inner layers. Let us consider one signals, say CLK, propogates in outer top layer, while the other signal, say DATA, propogates inner layer. Since the DATA signal will propogate slow ( being in inner layer), we will have to reduce the length of the DATA signal to match the flight time of the CLK Signal.
The following example will explain the point.
Problem IC A is the source of a Clock and a Data Signal. The IC B is the destination of the Clock and the data signal. The Clock signal is routed all on outer signal and has a length of 12 inches. The Data signal is all routed on the inner signal. Find the length of the Data Signal to match the flight time of clock signal. Assume propogation speed on outer layer ( microstrip) as 136 ps per inch and that in the inner layer( stripline) as 170 ps per inch. Answer [Note that the propogation speed is mentioned in picosecond per inch not inch per picosecond. We usually measure speeds of the cars in sort of inch per second ....] Time taken by clock signal = Distance travelled by Clock x speed of clock signal (in ps/inch) = 12 inch x 136 ps /inch = 1632 ps Time taken by Data signal = Distance travelled by Data x speed of data signal ( in ps/inch) = Distance travelled by Data x 170 ps /inch Now, since Time taken by Data signal = Time taken by clock signal => Distance travelled by Data x 170 ps /inch = 1632 ps => Distance travelled by Data = 9.6 inch As we have seen we have to keep the distance of the Data Signal shorter. |
In normal circumstances we would like to keep the matching signals in same layers and if they are in many layers the lengths in outer and inners layers of maching signals should match. If however, we can not do that we should calculate as in above example.
In the next chapter we will see how to calculate the flight time of the signals as it propogates along the PCB.