A Design of Sine-wave Oscillator Based on an Improved OP-amp Differentiator Zinan Zhou

Transcription

1 6th International onference on Mechatronic Material Biotechnology and Environment (IMMBE 6) A Deign of Sine-wave Ocillator Baed on an Imroved OP-am Differentiator Zinan Zhou Deartment of Jiangu Union echnical Intitute Jiangning branch Nanjing hina @qq.com Keyword: O-am differentiator; o-am amlitude-frequency characteritic; ine-wave ocillator; harmonic ditortion Abtract. By analyzing of tyical o-am differentiator circuit conidered the o-am amlitude-frequency characteritic we give out a deign of ine-wave ocillator baed on an imroved o-am differentiator. hi ocillator i not only the outut ine wave harmonic ditortion very low but alo eay to deign and eay to trimming to fine. Introduction At reent the active R ine-wave ocillator include Wien bridge ocillator [] and R hae hift ocillator. he frequency electing circuit of Wien bridge ocillator i two-order band-a circuit and it quality factor i /3. he frequency electing circuit of R advanced hae hift ocillator i three order high a circuit. he frequency electing circuit of R delayed [] hae hift ocillator i three-order low a circuit. heir frequency characteritic are oor o they outut large harmonic comonent. hi aer ue modified active R differential circuit for frequency electing circuit. By uing the R hae hift circuit the hae condition of the ocillator i atified [3]. With variable gain amlifier the amlitude condition and tability condition of the ocillator are alo atified. he frequency of outut ine-wave frequency of the circuit i cloe to the center frequency of the frequency electing circuit. he quality factor of the frequency electing circuit i uually greater than o the outut harmonic ditortion of ine-wave i very low. he range of ocillation frequency i at leat (.~.). i o-am gain bandwidth roduct. he baic active R differential circuit Figure i the baic active R differential circuit [4]. If the amlifier i the ideal o-am it tranfer function i hown a below: H ( ) = R Uing EWB a imulation oftware firt-order o-am model i tye of LF353. With imulation of the circuit in Figure we get the amlitude frequency characteritic of the tranfer function a hown in Figure. It i the ame a the amlitude frequency characteritic of the two band a filter. ( f=99.79khzq=39.4am=63db) Figure Figure he tranfer function of the baic active R differential circuit i derived a follow with 6. he author - Publihed by Atlanti Pre 55

2 firt-order o-am model. k A () = + () i the amlifier oen-loo gain / i one ole. Lit current and loo voltage equation: v v v v / I N O N + R = v O an be olved: H() = = Av () N k ( k + ) + ( + ) + R R = Am Q + + Q (3) (4) In the above formula the reonance angle frequency (et k>>) the quality k k k Q = Am = = = f factor + k the gain of the reonant frequency + k = = π R f.if et R=5.9 =4nFLF353( =4MHzk=.5 5) we can calculate anwer from the 4th formula: =.5kHzQ=39.76Am=64.3dB.he imulation reult in Figure are in agreement with the theoretical reult. If take (.~.).k Q = f =. f +.k max{ Q} = Q f 5 f = = = k Q k = 5 = + f. f k 4 8 k hu we can ee that the active differential circuit can be regarded a the two order frequency electing circuit with a high Q value. Imroved active R differential circuit he requirement of ocillator vibration hae condition are hift or an integer multile of. In other word feedback hould be a oitive feedback. From the 4th formula circuit outut and inut of Figure have an invere relationhi. In order to get oitive feedback it need to be added a 8 degree hae hift circuit. he imrovement of the baic active R differential circuit i hown in Figure 3. he amlitude frequency characteritic of the tranfer function are hown in Figure 4. 56

3 Figure 3 ( f =99.87kHzQ=39.8A max =3.96dB ) Figure 4 Lit current and loo voltage equation: vi vn vo vn / + R = (5) vo = ( vi vn) A () an be olved: k R H() = A m ( k + ) = (6) + ( + ) R R Q hi i the tranfer function of the high Q two-order low a frequency electing circuit. In the above formula the reonance angle frequency (et k>>) the quality factor k Q = + k gain at zero frequency A k = = = AQ f = = π f A = m gain at the reonant frequency max m R.If et R=5.9 =4nFLF353 ( =4MHzk =.5 5 ) we can calculate anwer from the 4th formula: =.5kHz Q=39.76 Amax=3.99dB.he imulation reult in Figure 4 are in agreement with the theoretical reult. hu it can be een that the imroved active R differential circuit i a two-order high Q low a circuit. omared with the baic active R differential circuit the reonant frequency and the quality factor have not been changed and the gain at the reonant frequency ha been changed. he hae hift of the circuit at the reonant frequency i -9 degree. Sine-wave ocillator baed on imroved active R differential circuit Sine-wave ocillator baed on imroved active R differential circuit i hown in figure 5. Figure 5 In order to make the hae hift of the whole circuit degree a hae lead circuit i required 57

4 before an imroved active R differential circuit. he circuit i required to rovide an advanced hae hift of aroximately 9 degree in order to atify hae condition of the ocillator. he circuit i comoed of R and. he characteritic frequency = hould be much larger than the outut frequency of the ocillator. In thi way the whole circuit can be rovided with a lightly le than 9 degree hae hift. Becaue the hae hift of the circuit i lightly le than 9 degree the imroved differential circuit will be more than -9 degree below the reonance frequency of the ignal. Ignoring the hae hift of the voltage follower and the hae amlifier he abolute value of the extended lag circuit rovide advanced hae hift and imroved differential hae hift circuit generate the abolute value i equal. herefore the actual ine-wave frequency of the ocillator will be lightly lower than the theoretical value. he inut reitance i very mall in the vicinity of the reonant frequency of the active differential circuit o a voltage follower i added between the hae lead circuit and the imroved active R differential circuit [5]. hi circuit i comoed of AR. Obviouly adding voltage follower not only imrove the erformance of the circuit but alo make the circuit analyi and deign imle and eay to adjut [6]. he circuit alo need to be able to automatically adjut the gain of the in-hae amlifier which i comoed of AR3 R R3 D and D. It caue the whole circuit to meet the amlitude AF condition of the ocillator. At the time of the ocillation the gain i > and the gain can be AF adjuted automatically to = after the ocillation. In thi circuit F = F =. An examle-- deign of a ine-wave ocillator baed on an imroved active R differential circuit A ine-wave ocillator with a frequency of khz and an amlitude of V i required. he circuit i hown in figure 5. he amlifier i LF353. Set =4MHzk=.5 5. From (4) formula characteritic frequency can be calculated by the imroved differential circuit : f f = =.5kHz f (7) onidering the load caacity of the o-am We take the nominal value : R= 6kΩ = 3.9nF. he hae hift of the imroved differential circuit i - 9 degree. hen etimate the quality factor: k Q k (8) Becaue of f >> f take the characteritic frequency of the hae lead circuit a follow: f f = 8 f = 8MHz (9) It rovide the lead hae can be etimated to be: f ϕ = 9 tg 89.3 o f () After the circuit i table the gain of the amlifier i A3 =. he gain of the imroved differential circuit at the reonant frequency A i about 39.8 A= AAA 3 F = AF =.Becaue of the gain Aof the hae lead circuit i about /8.onidering the caacitance i not too mall we et R =.After etimation π f 8R 99nF () At the time of hae amlifier tart ocillation A 3 = 3 AF = AAA 3 =.5 > meet the vibration condition [7];When table A 3 = AF = A AA 3 = meet the tability condition. At thi oint reitance caacitance element can et nominal value : R= 6kΩ = 3.9nF 58

5 R = Ω = nf R = R = kω 3 R = kω Bia voltage= ± V. After connecting the circuit adjuting the R the outut ine-wave frequency i khz. By meauring we obtain R= 6.kΩ = 3.94nF R =. When Ω the amlitude of the outut ine-wave i about.35v. R = 4.kΩ When the amlitude of the outut ine-wave i about V. When R = k Ω the amlitude i about 5.8V. When the outut amlitude i.5v een from Figure 6 harmonic ditortion i meaured with the digital ocillocoe. It can be een that hardly detected harmonic ditortion in the Figure 6 on the right. Figure 6 oncluion hi aer ue modified active R differential circuit for frequency electing circuit. By uing the R hae hift circuit the hae condition of the ocillator i atified. With variable gain amlifier the amlitude condition and tability condition of the ocillator are alo atified. he frequency of outut ine-wave frequency of the circuit i cloe to the center frequency of the frequency electing circuit. he quality factor of the frequency electing circuit i uually greater than o the outut harmonic ditortion of ine-wave i very mall. he ocillation frequency range i at leat (.~.). he circuit i imle and eay to deign and adjut. he circuit i alo uitable to be made into a ine-wave ocillator chi. It i exected to make a chea high-erformance ine-wave ocillator chi. Reference [] HUIJSING J H. Oerational amlifier-theory and deign [M]. tinghua univerity re [] LANGEN K D. HUIJSINGJH. omact low-voltage ower-efficient oerational amlifier cell for VLSI [J].IEEE Journal of Solid-State ircuit998 33() : [3] GRAY P R HUES P Jet al. Analyi and deign of analog integrated circuit[m]. 4th ed. tinghua univerity re [4] SALIMI K KRUMMENAHER F DEHOLLAIN et al. wo-tage high wing fully integrated tunable quadrature ine ocillator[j] IEE Electronic Letter. (8) : [5] SHANERBERGER MAWAD S S. he imlementation of a digital ine-wave ocillator uing the MS35: ditortion reduction and alication [J]. IEEE ranaction on Intruction and Meaurement 9 39() : [6] DOMINGUEZ M A AUSIN J L DUQUEARILLO J FORELLI G. A high-quality 59

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