Lesson #15. Section BME 373 Electronics II J.Schesser

Transcription

1 Feedack and Ocillatr Len # Tranient and Frequency Repne Sectin 9.6- BME 373 Electrnic II J.Scheer 78

2 Cled-Lp Gain in the Frequency Dmain ume that th the pen-lp gain, and the eedack, β are unctin requency and we apply the Laplace tranrm cmplex variale σ: Therere, β the zer are the value which h atiy the ple are the value which atiy β BME 373 Electrnic II J.Scheer 79

3 Ple Slutin t β deine the tranient repne the ampliier Thee lutin can e either real r cmplex value Fr real value ± σ, the tranient repne will have the rm exp ± σt and will dampen ut - σ with time cntant /σ r grw σ Ple which are negative are deirale ecaue the tranient repne die ut; while ple which are pitive are undeirale ecaue will caue the ampliier t unctin uncntrllaly. BME 373 Electrnic II J.Scheer 8

4 Cmplex Plane Cmplex Numer and Phar Ntatin Im σ cmplex numer σ tan σ Phar -σ θ Re Nte that ple in the right hand plane will have pitive real part and the tranient t repne will grw expnentially BME 373 Electrnic II J.Scheer 8

5 Cmplex Plane Cmplex Cnugate Ple -σ θ Im Re a σ * σ σ tan σ * σ tan σ Cmplex cnugate yield tranient repne the rm : * ± e σt ct Bin t Ple in the right hand plane will grw while ple in the let hand plane dampen BME 373 Electrnic II J.Scheer 8

6 Tranient Slutin in the Cmplex Plane t t Mt deirale lutin ince tranient repne die ut quickly t. t t σ t t Nte: Cnugate nt hwn BME 373 Electrnic II J.Scheer 83

7 Frequency Repne Plt the magnitude netwrk unctin a a unctin Sketch the magnitude y: Calculate the magnitude r and I there are real ple, etimate the reakpint requencie a / pk and the value the magnitude the netwrk unctin I there are cmplex ple, etimate the maximum the netwrk unctin at the value Imaginary part r each ple Set the unctin t zer at the zer the netwrk unctin Fr netwrk unctin with nly real ple: The with ple urthet rm the rigin have higher 3-dB cut requencie Fr netwrk unctin with cmplex ple: gain peak will ccur at the imaginary part the ple The gain peak will e maller r the ple where the real part σ i greater than the imaginary part. BME 373 Electrnic II J.Scheer 84

8 Example # Ω h Repne Frequency in / v in v ut C L R C in LC CR in repne damped inuid tranient ±.4 4 li BME 373 Electrnic II J.Scheer 8 lim

9 Example # Cntinued Etimated 6 Calculated BME 373 Electrnic II J.Scheer 86

10 E l # R F Example # 7 Ω h Repne Frequency in / v in v ut LC CR C L R C in 4 7 LC CR in 4 lim decaying expnential repne tranient, 7.4* BME 373 Electrnic II J.Scheer 87 decaying expnential.67.4*.39

11 Example # Cntinued.67 Etimated..8 Calculated BME 373 Electrnic II J.Scheer 88

12 Example #3 h / Repne Frequency in Ω v in v ut LC CR CR C L R R in LC CR in repne damped inuid tranient ± li BME 373 Electrnic II J.Scheer 89 repne damped inuid tranient ± lim

13 Example #3 Cntinued.998 Etimated. Calculated BME 373 Electrnic II J.Scheer 9

14 Eect Feedack n Ple Lcatin Single Ple mpliier the rm : an ampliier i Let' aume that the pen - circuit gain ] [ β β π π dding eedack t the ampliier : ] [ π β π π β π, where : β β π π β β BME 373 Electrnic II J.Scheer 9

15 Example # Study the requency repne an ampliier with pen-lp mid-and gain and reak requency z r eedack β.,. and d Withut eedack : lg lg db z With β.: β. db 99.9 lg lg β. k z With β.: db β. lg β k z With β : β db BME 373 Electrnic II J.Scheer lg β M z 9

16 Example # Cntinued Gain-Bandwidth Prduct db β.... z. E6 E7 β, β β β Nte that a the eedack i increaed i.e., β increae the ple mve urther away rm the rigin. Fr ingle ple ampliier, thi al implie that the tranient time cntant decreae ince τ /π. BME 373 Electrnic II J.Scheer 93

17 Example #a Fr the Single Ple ampliier, ind the ple r the pen lp gain. Prepare a Bde Plt Find the Gain-Bandwidth Prduct v i - M Ω Rpk Ω R Ω v x v i - v Cp - x v µf v v v x v v i 3 C C p R C p 7.96x 6 p R p p v i R C 7.96x p p 3 v v v 7.96x 3 lg db db z 7.96x 3 π BME 373 Electrnic II J.Scheer v z 3 π 7.96x z Mz 94

18 Example # Uing the ampliier in in the llwing eedack circuit, calculate: β Cled-lp gain at DC Cled-lp lp andwidth k β. k 99k β β kz v i -- v v i k k -- v BME 373 Electrnic II J.Scheer 9

19 Gain and Phae Margin Staility Feedack mpliier Examine the Cled-lp gain a a unctin requency Fr a given requency, β -, then the cled-lp l gain will e ininite i.e., a ple at π Nte that withut a urce ignal, then the input ignal equal the eedack ignal and v in -β v ut When the phae β 8 i β <, the lped ignal decay in amplitude Stale i β >, the lped ignal grw in amplitude - Untale We deine Gain Margin, which i the amunt in db gain elw db when the phae β 8. The larger the gain margin the mre tale the ampliier i.e., the ple are deeper int the let hand -plane. We deine the Phae Margin, which i deined at the requency, pm, at which β pm i unity and i equal t the dierence etween the phae β pm and 8. The larger the phae margin the mre tale the ampliier. BME 373 Electrnic II J.Scheer 96

20 Staility a Feedack mpliier β db - βα φ Phae deg 36 z.e.e.e4.e6.e8.e PM 8-68 PM 76.6 kz kz π 3 β. GM -9dB GM 73 kz BME 373 Electrnic II J.Scheer 97

21 Tranient trepne Prlem: mewrk Eect Feedack n Ple Lcatin Prlem: Gain and Phae Margin Prlem: BME 373 Electrnic II J.Scheer 98