2 Definitions and parameters of the impulse-technics

Transcription

1 efiniions and parameers of he impulse-echnics igial logic-circuis are driven wih signals, which only represen wo levels: he levels LOW and HIGH or he variables wih he values "" and ". These levels are for specific imes a he inpus of he logical circui. The logical circui processes he inpu levels and delivers oupu levels, ha have a funcional coherence o he inpu levels. A a digial circui he oupu values appear afer an inernal delay ime. In circuis wih memory-behavior (sequenial sysems) he previous hisory is included ino he logical combinaion. Because here are only wo saes, ideally occure square pulse signals. A many digial circuis iself he influence of inducors and capaciors canno be negleced. These energy-memories lead o falsificaions of he shape of he square pulses. A paricular circuis hese energy-memories are used for pulse shaping. This leads o pulses, ha have riangular, rapezium or exponenial shapes. In he following par-secions he parameers of impulses and he impulse-behavior of simple passive neworks are reaed. A more exac descripion of impulse echnics is given in he references.. hapes and parameers of impulses In he sandard IN 5488 he elecric impulse is described as process wih any emporal course, whose momenary value in definie areas of ime is differen from zero. An I M P L E is a process wih any course in ime of a physical quaniy, whose momenary value has wihin a definie space of ime values, which are no zero. niversiy of EFINITION OF AN IMPLE (IN 5488) IPT- An impulse consequenly is a signal wih seady saring and final value. In final imeinervals signal-aleraions beween hese values appear

2 A pulsed quaniy is a periodical process of a series of equal impulses. There are possible many courses in ime: - one sided impulses wih no change of polariy during he pulse duraion () a b c a) square pulse b) riangular pulse c) rapezium pulse niversiy of OE OF PLE AOING TO IN 5488 IPT-3 - square pulse (only wo values, ransiions from hese values in infinie shor ime) - real square-pulses in pracice are always rapezium pulses wih finie ransiion imes - if he duraion of a rapezium signal is shorened, i originaes a riangular signal, if he impulse-op vanishes and he edges ouch iself Because of processes of charging and uncharging a capaciors and inducors appear exponenial impulses. Figure IPT-4 shows his ypical impulses. quare pulse (IPT-3 a), riangular pulse (IPT-3 b), rapezium pulse (IPT-3 c), impulse wih riangle-increase and exponenial fall (IPT-4 a), square pulse wih exponenial fall (IPT-4 b) Two sided pulses have a change of polariy (alernaing pulse)

3 () a b a) unequal rising and falling pulse b) exponenial pulse niversiy of OE OF PLE AOING TO IN 5488 IPT-4 quare pulses wih exremely shor impulse-duraion are named as "needle-impulses" or "spike pulse" (IPT-7). () T niversiy of PIKE PLE IPT-7 aring from an impulse-duraion T and an impuls ampliude an impulse is defined, ha for a consan impulse-area T * a he border crossing-poin T agains zero shows an infiniely high ampliude. This impulse is called "irac-impulse"

4 An impulse is characerized by he following parameers: () % 9 % O 5 % T P T % T T F niversiy of EFINITION IPT- IPT- shows a real square-pulse wih he definiions: - rise ime T, - fall ime T F, - duraion ime T (pulse duraion, pulse widh), - pulse ampliude MAX - MIN, - pulse op MAX, - pulse boom MIN, - ramp off d / and - overshoo O O / A periodical impulses is addiionally given: - pause ime T P (pause duraion, puls pause), - periode T T T P, - repeiion frequency f / T and - duy cycle v T T / T (pulse duy facor). The definiion of he ramp off is only a he signals meaningful, ha have a nearly linear ramp off or increase of he ampliude. The rise- and fall-imes are measured beween he % and 9% values (,*( MAX - MIN ) and.9*( MAX - MIN )). The duraion-ime and he pause-duraion are measured a.5*( MAX - MIN ) or a he swiching hreshold of a logic circui (a TTL is.5 V). The values of MIN and MAX are averages of he minimum- and maximum-ampliudes, ha means, ha shor-ime appearing over- and under-shoos are no considered

5 eal square-pulses in pracice are always rapezium impulses wih clear visible rise- and fallimes. The ransiions of MIN o MAX, i.e. of LOW o HIGH, or of HIGH o LOW are named as "posiive" respecively as "negaive edges". If he duraion of a rapezium signal is shorened, i originaes a riangular signal, if he impulse-op vanishes and he edges ouch iself. The edge-seepness a he posiive and he negaive edge are in his case consan d / d / cons. (.) Triangular impulses appear, if energy-memories are charged or uncharged. The volage a a capacior raises a a consan charging curren linear in ime. The impulse is riangular, if he capacior is uncharged again by a consan curren. Because of processes of charging and uncharging a capaciors and inducors appear exponenial impulses (see figure IPT-4). A he employmen of elecronic swiches appear because of nonlinear effecs differen charging- and uncharging processes. o follows a he charging of a capacior by a volagesource wih consan swich-resisor an exponenial increase, a he uncharging he volage sinks linear, because he swich a his ransiion shows a curren-source-behavior. There are possible all mixed forms of impulses. For he calculaion of impulse-parameers he characerisic signal-parameerss of he signaland nework-heory are used for impulses oo. I is valid (exemplary for he volage): The linear average-value as he inegral of he volage relaive on a ime-inerval: i T () d (.) T and he roo mean square ( M ): i T / M () d (.3) T T / The quoien ou of impulse-op-value MAX and he roo mean square-value M is called peak-value or cresfacor. I is valid MAX F (.4) M - 8 -

6 . Impulse-funcions () A ( - ) A () () niversiy of ELEMENTAY PLE FNTION IPT-3 For he mahemaical descripion of a square pulse he sep-funcion and he sep-funcion wih ime lag are used. These funcions are defined as für < () (.5a) A für für < ( ) (.5b) A für Through superposiion of uni-sep-funcions wih ime lag follows: () () ( ) { [ ( T )]} f (.6) The irac-impulse and he uni-irac-impulse: für () (.7a) für für () (.7b) für The ramp-funcion: für () (.8) für > - 9 -

7 .3 Impulse-behavior of passive wo-pors The wo-por, in he pas named as "quadrupole", is a circui wih wo inpu-connecions and wo oupu-connecions. The wo-pors, ha we calculae, only have resisors, capaciors and inducors. They are ime-invariable and linear. Wih he aid of he nework-heory for wo-pors he linear behavior of neworks can be calculaed. The impulse-behavior of high- and low-passes for he half-t-circui or volage divider circui wih one energy-memory is invesigaed. The high-pass wih an energy-memory can be a -circui or a L-circui. I() niversiy of () () () HIGH-PA I() () () L L () IPT- The -high-pass is driven a he ime by a volage sep wih he ampliude. Ideally exiss no rise-ime (T ) and he consan volage is valid for imes >. The mesh of he circui yields (d by d): Wih follows () () () I() (.) I () d (.) d d () (.) d - -

8 This is a differenial equaion of he firs order. In consideraion of he condiions ( ) and ( ) follows he soluion () exp (.3) and I () A (.4) () () exp () () exp (.5) wih he ime-consan (.6) The courses of he volages (), (), () and he curren I() shows figure IPT-. () () () I() niversiy of TEP-EPONE -HIGH-PA IPT- A he ime he volage () has he value.37, () has raised on,63. A he ime 4.6 () has he value, and ( ),99. The capacior is nearly charged compleely. The volage a he oupu () shows a differenial behavior. o he circui is named differeniaing circui. For he L-high-pass is valid: () () I ( ) ( ) (.7) L L L - -

9 Wih L () di L L (.8) d follows I L di L L() (.9) d nder consideraion of he condiions I L ( ) and I L ( ) / follows he soluion I L () exp (.) and A (.) () exp () L () I () exp L (.) wih he ime-consan L. (.3) Are high-passes driven by a square pulse-volage a he inpu, so appears a he falling edge a negaive oupu-volage. This can be calculaed wih he superposiion, because he squarepulse consiss ou of wo overlaid emporal posponed sep-funcions. niversiy of E () A () () A () E - square pulse HIGH-PA AN QAE PLE T / IPT-5 - -

10 For a square pulse a a high-pass i is valid: A () exp (.6) 3 K K K.! 3! Wih erminaion of he series afer he linear erm and wih T and >> T follows he approximaion T A ( T ), (.7) he decrease of he volage by he ramp off A ( T ) (.8) and T. (.9) I follows he relaive ramp off T d. (.3) A T E () has a negaive edge (sep o zero). This sep effecs a volage sep of a he resisor (he volage a a capacior never can jump!!) and one ges a negaive value of A ()

11 Is a high-pass driven by a periodical square pulse one ges in he seady sae he following exreme-values of he oupu-volage in: E () A () A T T P A niversiy of HIGH-PA AN QAE PLE PEIO IPT-6 and TP exp AMAX (.4) T exp T exp AMIN (.5) T exp wih and T T T. P The calculaion of hese values: (for he seady sae is valid ) Firs inerval ( < T ): ( dash) A ' ' ( ) AMAX exp - 4 -

12 A T : T ( T ) exp A AMAX AMIN econd inerval (T < T T P ): A A T T P : A ( ' ) AMIN exp ' T P ( T T ) exp P AMIN T AMAX These are wo equaions wih wo unknown values. o one can calculae he exreme-values

13 A low-pass is as - or L-circui: I() niversiy of () () () LOW-PA I() L () L () () IPT- One ges for he volages and he curren a a -low-pass: () exp A (), (.3) () () exp, (.3) I () () exp (.33) and he ime-consan For a L-low-pass is valid: wih he ime-consan. (.34) A (.35) () exp () L. (.36) - 6 -

14 In he echnology of digial circuis one ofen finds wo-pors wih only one ime-consan. A hese circuis one can ake direcly he general soluion of he differenial-equaion of. order for deermine he course of he exponenial funcion. If one knows he sar-value ( ), he final value ( ) and he ime-consan he following soluion is valid: E () Z Z () A niversiy of () E () E - sep-funcion IIT WITH IMPEANE IPT-5 ( ) ( ) [ ( ) ( ) ] exp. (.39) or in oher forms () ( ) ( exp ) wih ( ) ( ) () ( ) exp. Pus one for T*, so one ges for his ime a definie volage ( T*). In his case one can calculae by knowledge (e.g. hrough measuremen) of ( T*) he belonging ime T*. Ou of (.39) follows ( ) ( ) * ( ) ( ) T ln. (.4) * T For he deerminaion of any ime-inervals T T - T a an exponenial course (wihou inermission and only wih one ime-consan) i is valid, if he volage has changed in he ime T abou (T ) - (T ): - 7 -

15 ( ) ( ) T ln. (.4) T For he deerminaion of he rise-ime and fall-ime one ses,9 -,,8. Then follows T T T,. The overview-figure IPT-5 shows all combinaions wih sep-answers of simple circuis, ha can be realized by he volage divider circui. The sar- and final-values of he sep-answers and he ime-consans are in he able. Z Z a b c d e f g h i j k l m n () niversiy of -IIT WITH ONE TIME ONTANT IPT-5-8 -

16 - 9 - a: b: c: d: ) ( e: f: g: h: ) ( i: j: k: more han one ime consan ) ( ) ( l: m: n: more han one ime consan ) ( ) (

17 .4 ircuis for producing impulses.4. omparaors The comparaor-funcion can be realized by an operaional amplifier, if he invering inpu is conneced wih a reference-volage and he noninvering is he inpu of he circui. OMP niversiy of OMPAATO EBE-36 The ransfer-characerisic shows figure EBE-36: niversiy of TANFE HAATEITI OF A OMPAATO EBE-36 The levels can be adaped o he level-range of a circui-family (e.g. TTL). - -

18 .4. chmi-trigger A level-conrolled rigger-circui wih wo differen hreshold-volages is called chmirigger. The difference of he swich-on-hreshold IE and he swich-off-hreshold IA is he hyseresis H. Figure T-4 shows he symbol and he ransfer-characerisic of a chmi-rigger. niversiy of I Q Q QY YMBOL AN HAATE- ITI OF THE HMITT- TIGGE QX IA IE I T-4 The mode of operaion shows figure T-4. I niversiy of IE IA Q QY MOE OF OPEATION OF THE HMITT- TIGGE QX T-4 - -

19 One can see, ha a disurbed inpu-signal is regeneraed by a chmi-rigger. Forbidden levels do no lead o a swiching of he oupu of he chmi-rigger. o his circui can be used as signal-regeneraor..4.3 Timer Asable and monosable circuis wih logic-circuis (NAN or NO) show deviaions ino he emporal course, because of unsable hreshold-volage and because of deviaions of he inpuand oupu-resisors. To he avoidance of hese disadvanages inegraed imer-circuis were developped, ha include a precision chmi-rigger and a -flipflop. An in he ONcondiion very low resisive swiching-ransisor serves for a fas discharging of a imecapacior. By exernal resisors and he ime-capacior is generaed he required impulsewidh. The figure T-6 shows he srucure of he precision-chmi-rigger. OMP G A IA > Q I K A I OMP > I IB K B G B Q I B I A I niversiy of PEIION HMITT TIGGE T-6 The hreshold-volages are derived from reference-volages, ha are a he inpus of wo comparaors K A and K B. A -flipflop is cleared (Q L), if he inpu-volage I crosses he level IA, and se, if I falls under he level IB. I IB :, : se IB I IA :, : sore (hold) IA I :, : rese (clear) IB I IA :, : sore (hold) I IB :, : se This circui is used a he "sandard" imer 555 and 7555 (in TTL- respecively MOechnology). The simplified circui of he imer wih he applicaion as asable rigger-circui (mulivibraor) shows figure T-6: - -

20 K A G A OMP > Q Y OMP > KB G B T niversiy of MLTIVIBATO WITH TIME 555 T-6 By he volage-divider consising ou of he hree same resisors from he supply-volage are derived he reference-volages A and B. Through he high relaive accuracy of he resisors wih deviaions of maximum % (yp. 5%) a he 555 and maximum 6% (yp. %) a he 7555 only a low ime-error appears. The hresholds B and A are / 3 and / 3. A he asable circui he -flipflop is cleared if he volage a he capacior is higher han he upper hreshold A, i.e. he oupu Y has LOW-level. The oupu of he flipflop has HIGH-level, he ransisor T is conducing and he capacior is discharged over he resisor, unil he lower hreshold B is reached. Then he oupu of comparaor K B has HIGHlevel, ses he -flipflop and closes he ransisor T. Over he resisors of and he capacior is charged again. o he capacior-volage in he seady sae changes wih exponenial course beween A and B. Inerval T : Inerval T P : /3,, ( ) * /3,, * The impulse-duraion follows o T ( ) * * ln[( B ) / ( A )] T ( ) * * ln and he impulse-pause o T P * * ln[ A / B ] T P * * ln - 3 -

21 niversiy of 3 3 Y T T P IMPLE- IAGAM OF THE MLTI- VIBATO WITH TIME 555 T-6 I follows he frequency f / (T T P ),44 / [(! ) * ] A symmerical recangle-vibraion wih a pulse-duy-facor v T,5 (T T P ) can be generaed, if parallel o he resisor a diode is swiched, whose caode is conneced wih he capacior. The resisors and mus have he same value. A he charging of he capacior hrough he conducing-resisor F of he diode is bridged. For >> F one ges approximaely he same ime-consans for charging and discharging. I is possible o change he values for he hreshold-volages by changing he volage-divider or he supply-volage. The change of he supply-volage enables he employmen of he imer as a volage conrolled oscillaor (VO) or as frequency-modulaor. Wih a simple circui-aleraion he imer operaes as monosable rigger-circui (T-6). Ino he sable sae he capacior is shorened consanly by he conducing ransisor T. A LOW-acive rigger-impulse a he comparaor K B ses he -flipflop and he ransisor T is blocked. The capacior is charged over he resisor from nearly V unil A / 3. The -FF is cleared, he oupu has he LOW-level. Now he capacior is discharged over he ransisor T in a very shor ime (T-6). Inerval T : V,, * The impulse-duraion follows o T * * ln[( V) / ( A )] T * * ln 3-4 -

22 K A OMP G A > Q Y OMP > X K B G B T niversiy of MONOFLOP WITH TIME 555 T-6 X niversiy of 3 T IMPLE- IAGAM OF THE MONOFLOP WITH TIME 555 Y T-6 Wih help of an exernal ransisor T* he monoflop can be expanded as a reriggerable monosable rigger-circui. The circui and he courses of he impulses are shown in he figures T-65 and T-66. The rigger-impulse discharges in his HIGH-phase he capacior and ses he oupu Y o HIGH. If he rigger-impulse reaches he LOW-level he exernal ransisor T* is blocked, and could be charged over he resisor. If during his phase a new rigger-impulse appears, he capacior is discharged over T*. The oupu Y remains all he ime on HIGH, unil he - 5 -

23 capacior-volage reaches he hreshold A. The pulse-duraion T is beween he falling edge of he las rigger-impulse and he falling edge of he oupu-signal Y. This circui can be used for deecing missing-pulses, e. g. clock-impulses of a microprocessor (wachdog). K A OMP G A > Q Y T * OMP > I K B G B T niversiy of ETIGGEABLE MONOFLOP WITH TIME 555 T-65 I niversiy of 3 T IMPLE- IAGAM OF THE MONOFLOP WITH TIME 555 Y T