Chapter 2: Logical levels, timing and delay

Transcription

1 haper 2: Logical levels, iming and delay Dr.-ng. Sefan Werner Winersemeser 216/17 Table of conen haper 1: Swiching lgebra haper 2: Logical Levels, Timing & Delays haper 3: Karnaugh-Veich-Maps 2.1 Logical levels haper 4: Number Sysems 2.2 Timing diagrams 2.3 Propagaion delays haper 5: inary rihmeic 2.4 Hazards haper 6: inary odes haper 7: ombinaional ircui Design haper 8: Laches and Flip Flops haper 9: Finie Sae Machines haper 1: asic Sequenial ircuis Winersemeser 216 2of 2 1

2 Ranges for logical values in posiive logic in posiive logic low: signal mus be smaller hen he upper bound of he range high: signal mus be a leas equal o he lower border of he range hese wo areas are separaed by a hird area (hus U L,max U H,min ) so ha a corruped logical signal migh be recognized U H,max Range for logical l1 U H,min Logic values undefined U L,max U L,min Range for logical Winersemeser 216 3of 2 Typical volage ranges for logic gaes Logical Logical TTL circuis 7V V MOS circuis -.5 V 3 15 V Keep in mind: here is sill he difference beween posiive logic and negaive logic Umax U max Umin logical logical 1 U min logical logical 1 Winersemeser 216 4of 2 2

3 Example: iming diagram for he conjuncion = Winersemeser 216 5of 2 Example: iming diagram for he disjuncion =+ Winersemeser 216 6of 2 3

4 Example: propagaion delays for an inverer U in U ou change of npu signal PLH oupu response o inpus change change of npu signal Oupu goes from low -> high Keep in mind: i is he oupu ha rules PHL oupu response o inpus change Oupu goes from high -> low Winersemeser 216 7of 2 Example: propagaion delays for an inverer U in U ou PLH <!!! PHL Winersemeser 216 8of 2 4

5 Rise ime and fall ime U in U ou Signals need ime o fall => fall ime F Signals need ime o rise => rise ime R Winersemeser 216 9of 2 How o calculae R and F? U ou 9% 1% R F To calculae R and F measure he acual imes for he signal having 1% and 9% of he acual volage. R =(U=.9 U max ) (U=1U (U=.1 U max ) F =(U=.1 U max ) (U=.9 U max ) Keep in mind: no neccessarily F = R Winersemeser of 2 5

6 Propagaion delays and signal flanks U inpu 9% 5% 1% U ou Now: several possibiliies o measure delays, e.g.:?? npu sars changing o oupu sars changing?? npu sars changing o oupu ends changing?? ec... 9% 5% 1% Winersemeser of 2 Propagaion delays and signal flanks U inpu 9% 5% 1% U ou PLH PHL Propagaion delays are measured as he ime beween he inpu signal being 5% of he maximum volage and he oupu volage being 5% of he maximum volage 9% 5% 1% Winersemeser of 2 6

7 Example: Propagaion delays of combinaional circuis D D E=D ++ K=++ Theoreical resul for four differen inpu saes D mplemenaion of x=(++) D =E K ll gaes have he same propagaion delays: PLH = PHL = PL =1ns ssign: E=D K=++ =E K Winersemeser of 2 Timing diagram D E K P P T= 2 P P T= 2 P P The circui is called a regular wo layer circui, as any inpu signal has o pass exacly wo elemens wih a fixed ransiion ime for all possible inpu combinaions of T =2 P. Winersemeser of 2 7

8 Timing diagram for a differen implemenaion Z D W Differen implemenaion of f = (++) D D Z ++ he oal propagaion delay for his inpu sae is p =3 ns. Winersemeser of 2 Example for gliches and hazards onsider he following implemenaion of a funcion =(+) and he given inpu sequence Obviously he oupu of a circui implemening his funcion should remain for he given inpu sequence. Now: onsider he given implemenaion propagaion delays of 1 ns Draw he iming diagram Winersemeser of 2 8

9 Example for gliches and hazards onsider he following implemenaion of a funcion =(+) and he given inpu sequence he informaion abou going up reaches he las gae by P earlier han he informaion abou going down. Winersemeser of 2 Example for gliches and hazards onsider he following implemenaion of a funcion =(+) and he given inpu sequence ns 1 ns hazards and he resuling gliches migh rigger unwaned saes in he circui somewhere else, so hey mus no be ignored Winersemeser of 2 9

10 Using hazards 1 ns circui generaes (heoreically ) a permanen 1 circui is obviously a hazard. p Noice: when jumps from ->1, he circui generaes a glich glich has pulse widh of Pulswidh = P. circui can be seen as a pulse generaor (raising-flank-o-pulse converer); i generaes a pulse whenever a raising flank occurs a. Using an (odd) number of n inverers i is possible o generae pulses of Pulswidh =n P wih his echnique. Winersemeser of 2 Flank-o-pulse converer wih riple pulse widh 3 p Winersemeser of 2 1