first-order circuit Complete response can be regarded as the superposition of zero-input response and zero-state response.

Transcription

1 Experimen 4:he Sdies of ransiional processes of 1. Prpose firs-order circi a) Use he oscilloscope o observe he ransiional processes of firs-order circi. b) Use he oscilloscope o measre he ime consan of firs-order circi. c) Know he conceps of differenial circi and inegral circi. d) Observe he characerisics of he sep response and he sqare-wave response of firs-order circi. 2. Principal and Illsraion A. Firs-order circi and is ransiional processes he circi conaining energy-sorage elemens is called dynamic circi. When he characerisics of he dynamic circi can be described by firs-order differenial eqaion, he dynamic circi is called firs-order circi. When he dynamic circi is on is seady sae, as is srcre or parameers change, he ransiional process emerges. he ransiional process of a circi conains zero-inp response, zero-sae response and complee response. As shown in Figre 3-5-1(a), if he response is capacior volage c in he firs-order circi, is complee response can be represened by ( ) = U m [ ( ) U m ] e (3-5-1) where c ( ) is he iniial capacior volage, U m is direc crren volage exciaion, which is added ino he circi and = is he ime consan. omplee response can be regarded as he sperposiion of zero-inp response and zero-sae response. (1) When c ( )= or he iniial energy-sorage capacior is zero, we have ( ) = U ( 1 e ) m (3-5-2) his is he zero-sae response, prodced by he volage exciaion. (2) When s =, we have ( ) = ( ) e (3-5-3)

2 his is he zero-inp response, prodced by he iniial energy-sorage capacior. When he exciaion is sep signal, zero-sae response is called sep response in he circi. he response of a firs-order circi o sqare-wave plse seqence signal can be regarded as he sperposiion of several sep responses. he ransiional process of dynamic circi is one-ime changing process wihin a very shor ime. For he circi wih relaively large ime consan, we can se lra-low freqency oscilloscope o observe is ransiional process. However, if we se common inermediae freqency oscilloscope o observe is ransiional process and measre relaed parameers, we need o make sre ha he one-ime changing process appear repeaedly. herefore, we se he signal generaor o generae sqare-wave signal o simlae sep exciaion signal in he experimen. In oher words, we regarded he rising edge of he sqare-wave op as posiive sep exciaion signal of zero-sae response, and he falling edge of sqare-wave as negaive sep exciaion signal. As long as we choose he periodic of he sqare-wave ha is mch larger han he ime consan of he circi, i can be considered ha, when some edge of he principal wave is coming, he ransiional process ha he former edge prodces has already disappeared. he ransiional process excied by he sqare-wave seqence plse signal is almos he same as he ransiional process cased by rning on and off D power. B. ime consan and is measremen When we ge he waveform of response shown on he oscilloscope, we can esimae ime consan of he circi by he waveform. When he amplide of capacior volage rises o 63.2% of final vale in he zero-sae response of firs-order circi, he corresponding ime is, as shown in Figre 3-5-1(b). When he amplide of capacior volage declines o 36.8% of saring vale in he waveform of zero-inp response, he corresponding ime is, as shown in Figre 3-5-1(c). 1 S Um.632Um Um.368Um (a) Firs-order circi. (b) he waveform of zero-sae response. (c) he waveform of zero-inp response Figre circi and he measremen of is ime consan

3 . Differenial circi and inegral circi Differenial circi and inegral circi have specific reqiremens of he circi elemen parameers and he period of inp signal, and hese wo circis are raher ypical ones in one-order circis. If he op of firs-order circi is from he volage across a resisance, namely o =, as shown in Figre 3-5-2, where s is he sqare plse seqence wih periodic. When i is saisfied = << 2, we have <<, S o = d = d d d where he op volage o of he circi is direcly proporional o he differenial of he inp volage s, and hs he circi is called differenial circi. When i is saisfied = >>, we have 2 << o = = id = d d where he op volage o of he circi is direcly proporional o he inegral of he inp volage s, and hs he circi is called inegral circi. o o Figre differenial circi. Figre inegral circi. he relaionship beween differenial circi and inegral circi is shown in Figre and Figre he waveforms of he inp s and he corresponding op o are shown in Figre for he differenial circi. he waveforms of he inp s and he corresponding op o are shown in Figre for he inegral circi.

4 US US /2 /2 Figre he waveforms of inp s and op of differenial circi Figre he waveforms of inp s and op c of inegral circi 3. onens and Seps he experimen ses firs-order circi elemen board shown in Figre Figre Firs-order circi elemen board A. Observe elecro-charge and elecro-discharge processes and he measremen of ime consan in inegral circi onnec he wires, as shown in Figre According o he wo grops of vales given in able 3-5-1, respecively, choose and elemen properly in he elemen board (Figre 3-5-6). he exciaion s is sqare volage signal, whose amplide is U m = 3V and freqency is f=1khz. he exciaion s and he response c are conneced o wo inp channels H1 and H2 of he oscilloscope, respecively.

5 H1 H2 Signal generaor We can observe he change of exciaion s and response c in he screen of oscilloscope. omplee he following experimen. (1) Observe he consan from he screen of oscilloscope and record he daa ino able (2) Observe he waveforms of exciaion s and response c in he oscilloscope and plo he graph proporionally in he able respecively (please se graphic paper, bogh from he shop, o plo he graph and he proporion is 1:1). (3) Seadily increase he vale of, observe is inflence on c qaliaively and record he daa. able he elecro-charge and elecro-discharge processes of differen parameers in he inegral circi. Figre inegral circi Parameers = 1kΩ, = 33pf = 1kΩ, =.1µf ime consan (µs) heoreical vale Observed vale O Observed waveforms

6 B. Observe he waveforms of differenial circi onnec he wires as shown in Figre According o he wo grops of vales given in able 3-5-3, respecively, choose and elemen properly in he elemen board (Figre 3-5-5). he exciaion S is sqare volage signal, whose amplide is U m = 3V and freqency is f=1 khz. (1) Observe he waveforms of exciaion s and response in he oscilloscope and plo he waveforms of response in he able respecively (please se graphic paper, bogh from he shop, o plo he graph and he proporion is 1:1). (2) Seadily increase he vale of, observe is inflence on he response qaliaively and record daa. (3) When increases o 1 MΩ, observe he essenial difference beween inp and op waveforms and record daa. Signal Generaor H1 H2 Figre differenial circi able he elecro-charge and elecro-discharge processes of differen parameers in he differenial circi. Parameers =.1µf, = 1kΩ =.1µf, = 1kΩ Observed waveforms O 4. Qesions (1) Wha elecrical signals can be regarded as he exciaion signal of zero-inp response, zero-sae response and complee response in he one-order circi?

7 (2) Sppose =1kΩ and =.1µF, ry o calclae he ime consan, and according o physical meaning of, ry o figre o how o measre pracically. (3) Wha are inegral circi and differenial circi? Wha condiions shold hey possess? Given he exciaion of sqare wave seqence plse, how do heir op signal waveforms change? (4) In he circi, when or varies, wha s he inflence on he response of he circi? 5. Wriing Yor epor (1) omplee he calclaion of able (2) According o yor experimenal resl, plo he crves of elecric-charge and elecric-discharge, differenial circi and inegral circi of firs-order circi in yor graphic paper. (3) According o he crve of elecric-charge and elecric-discharge of firs-order circi, esimae he ime consan. (4) Answer he qesions in he 4 h secion.