# Timing Analysis for Arrays

Last Edit July 22, 2001

## Worst-Case Delay Multiplication Factors

Once the sum of all the typical intrinsic and extrinsic propagation delays in a circuit or path segment is computed and adjusted for the output capacitive load, then the result must be multiplied to obtain the worst-case delay as follows:

To perform worst-case analysis, the worst-case multipliers or adjustment factors for the appropriate operating range must be used. Example bipolar array multipliers are shown below. Refer to the appropriate design manual for worst-case multipliers for a particular array series.

Many vendors specify a typical propagation delay, with or without assumed loading. Delays due to fan-out loads are also given for specific conditions. When the power supply or temperature varies from the typical specification, some derating must be applied to the typical delays. In addition, some allowances for process variations should be made.

Some vendors specify the derating required for each of these items as a separate number or curve while others provide a combined worst-case multiplier, designed to assume that everything is in the worst possible state.

There may different derating or worst-case multipliers for macros and for the interconnect nets, and there may be different multipliers for different macros.

For a given array, the designer needs to determine whether the worst-case delay multipliers apply to set-up, hold, recovery time or pulse width.

Array Series (Historical) Timing Adjustment Factors - Different Arrays

### Examples

The Raytheon design manual uses charts and shows a variation for temperature derating that spreads from 0.88 for -25C, to 1.15 for 150oC (1.10 for 130oC). The chart for the voltage derating factor varies from 0.98 at -5.72V (ECL 10K), to 1.05 at -4.68V (ECL 10K). The same range applies ECL 100K; 0.98 at -4.95V, to 1.05 at -4.05V. The chart for the process derating varies from 0.73 to 1.2. At a junction temperature of Tj = 150oC, these combine to form a worst-case derating of 1.449 max and 0.63 min.

AMCC specifies a worst-case military maximum derating factor of 1.45 for its bipolar arrays and specifies a process variation of 1.19 - 1.45 (20% variation) in combination with the temperature and voltage variations. The AMCC multipliers also account for temperature, voltage and process. The minimum operating conditions use a worst-case range of 0.70-0.89.

For interconnect delays, Raytheon provides tables to allow an estimate of fan-out delays based on fan-out load. They appear to be appear linear. (See Table 5-5.) Additional tables provide derating factors to allow adjustment for metal interconnect and metal temperature.

Table 5-5 Raytheon Adjustment Factors Factor/Variation (Historical)

 Temperature 0.88/-25oC 1.05/130oC 1.15/150oC Voltage ECL10K 0.98/-5.2V 1.05/-4.68V ECL100K 0.98/-4.95V 1.05/-4.05 Process 0.73 1.2 TOTAL 0.63 MIN 1.449 MAX

AMCC uses a non-linear equation to compute net loading and uses the macro worst-case multipliers on the interconnect delays.

For older arrays, AMCC also specified a linear relationship based only on fan-out loading (0.5ns/load for rising edge; 1.0ns/load for falling edge), also combined with the macro worst-case multipliers.

For the new BiCMOS series, the different technologies make different multipliers necessary. There is one for the bipolar interface macros and their extrinsic delays and one for the internal CMOS core macros and their extrinsic delays. The internal core macro worst-case multipliers apply to the set-up, hold, recovery time and pulse width values. An array series may have different multipliers for different arrays within the series.

### Always go back to the latest information from the array vendor.

Copyright @ 2001, 2002 Donnamaie E. White, White Enterprises
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