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20-80 Percent to 10-90 Percent Rise Time Conversion Factor Derivation kgsmith Revised 13SEP10 Initiated 10SEP10 What is a good way to estimate 10% - 90% rise and fall times from 20% - 80% rise and fall times? Silicon Labs generally specifies the rise times and fall times of its timing products using 20%-80% threshold levels. This is the convention used by modern standards such as PCI Express. The question arises as to how to convert from 20% - 80% rise and fall times to their 10% - 90% counterparts. Depending on the assumptions made regarding the waveform, the conversion factors in the literature range from about 1.3x to 1.6x. Cable and connector vendors for example often use a factor of 1.5x. The largest practical conversion factor is for a single-pole response such as an LVCMOS buffer driving a lumped capacitive load. As derived in this attachment, this ratio can be shown to be roughly tr10-90/tr20-80 = 1.59 or ~1.6. So for example, if a CMOS output buffer is specified to have a nominal 20% - 80% rise time of 1ns, it can be estimated to have a nominal 10% - 90% rise time of 1.6 ns. Note: If trying to calculate a worst case tr10-90 number based solely on an existing tr20-80 spec or data set, we would suggest adding margin by increasing the conversion factor to 1.7 just to be conservative. Derivation For a single-pole system we can write: V (t ) VFINAL 1 e t / V (t ) 1 e t / VFINAL e t / 1 V (t ) VFINAL V (t ) t / ln 1 V FINAL 1 t ln V (t ) 1 VFINAL Let V1 V (t 1 ) 1 t 1 ln V1 1 VFINAL Similarly we can write 1 t 2 ln V2 1 VFINAL For V2 V1 and t 2 t 1 tr t2 t1 1 1 t r ln ln V2 V1 1 1 VFINAL VFINAL 1 1 t r ln ln V2 V1 1 1 V VFINAL FINAL Let V1 and V2 be percentages. 1 1 ln t r ln 1 V1 1 V2 100 100 100 100 ln t r ln 100 V 100 V 2 1 t r ln100 ln100 V2 ln100 ln100 V1 t r ln100 V1 ln100 V2 100 V1 t r ln 100 V2 This last formula, repeated below, is very useful. Just keep in mind that it is written for V1 and V2 expressed as percentages. 100 V1 t r ln 100 V2 Let’s check for the well known case that 5 time constants means the voltage should have reached 99.3% of the final value. 100 0 100 100 tr099.3 ln ln ln ln142.9 5.0 100 99.3 0.7 0.7 That checks out so now let’s apply it to the standard threshold rise times. 100 10 90 t r 10 90 ln ln ln9 100 90 10 t r 10 90 2.2 100 20 80 t r 20 80 ln ln ln4 100 80 20 t r 20 80 1.4 t r 1090 ln9 2.2 t r 2080 ln4 1.4 t r 1090 1.6 t r 2080 //