Analog Circuits and Systems

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Avis Houston
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1 Analog Circuit and Sytem Prof. K Radhakrihna Rao Lecture 39: Summing up Analog Sytem Deign

2 Macro Modeling It refer to modeling a given ytem to the level of detail of concern to the application onhand It alo refer to the implet model of the ytem adequate to undertand it function.

3 Macro Modeling (contd.,) It could be linear or nonlinear, zeroth, firt, econd or higher order model In mot Op Amp application it i ufficient to ue a imple model of VCVS with a voltage gain of A (000 to 0000) 3

4 Macro Modeling (contd.,) If one need to bring in next important parameter GB (gain-bandwidth product) the Op Amp need to be modeled a a firt-order ytem If aturation of the ignal i of importance then the Op Amp will have to be modeled a a non-linear ytem. 4

5 Macro Modeling (contd.,) Slew rate effect can only be conidered uing a non-linear model of the Op Amp 5

6 Analog Sytem a Second Order Sytem All analog ignal proceing ytem can be deigned uing active econd-order analog/digital ub-ytem a building block A econd-order analog ubytem i realized uing Op Amp a active device, reitor and two independent capacitor 6

7 Analog Sytem a Second Order Sytem (contd.,) A digital ub-ytem i made up of an ADC, DSP and DAC. When large delay or lag demand large value of paive component in analog ubytem, digital ub-ytem have to be ued 7

8 Analog Sytem a Second Order Sytem (contd.,) Any analog ytem i functionally a filter A econd order ytem can be repreented by a tranfer function with a econd order polynomial in a the denominator, and a numerator that can be a contant, an -term, one plu -term, one plu term or a econd order polynomial in. 8

9 Second Order Filter H Q H Q H Q - Low Pa Filter - High Pa Filter - Band Pa Filter 9

10 Second Order Filter (contd.,) H Q + Q + + Q - Band Stop Filter All Pa Filter 0

11 Higher Order Analog Sytem Higher order analog ytem do require the determination of parameter value accurately, ometime up to everal decimal place. It i not poible to achieve thee accuracie with the paive component available in dicrete form or integrated circuit form.

12 Higher Order Analog Sytem (contd.,) Mot of the analog ubytem need to be tuned in practice. Preent day practice i to ue digital tuning of analog ubytem When ytem have to be finally tuned, the initial deign need not be accurate, and approximate deign would be adequate.

13 Higher Order Analog Sytem (contd.,) Paive component in highfrequency analog ytem can be in the range of the paraitic aociated with the active component, and that make their exact determination of ytem parameter i very difficult. A the parameter drift with temperature and time tuning mechanim need to be integrated into analog ytem. 3

14 Negative Feedback Negative feedback make the performance of ytem le enitive to variation in value of parameter aociated with forward path In output-feedback ytem the performance of the analog ytem i inenitive to variation in value of all parameter Output-feedback ytem are preferred in the preent day analog IC (voltage, current, frequency, phae etc. follower) 4

15 Output follow the input 5

16 Negative Feedback Higher order (> ) feedback ytem have alway the iue of intability to be taken care of. All higher-order analog ytem are deigned through cacading econd order ytem. 6

17 Negative Feedback (contd.,) Deigning of high peed (RF and microwave) ytem alway require avoidance of feedback 7

18 Low-Pa Filter Firt-Order filter = ( + CR) + BW Second-Order filter where + + Q 0 0 = andq = 0 LC CR 0 8

19 Interconnect Interconnect i any connection between two point (node) in an electronic ytem An interconnect can be modeled at high frequencie a a low pa filter 9

20 Elmore Delay When everal node are involved the net tranfer function t i known a Elmore delay The coefficient of i the Elmore delay e τ = ( τ) + τ ! The tranfer function of the internet may approximated by + τ 0

21 Multiple Interconnect Elmore delay of thee the interconnect i the coefficient of of the combined tranfer function ( ) ( ) τ= CR + C R + R + C R + R + R 3 3

22 Multiple Interconnect If there are n-node ( ) ( ) ( ) τ= CR + C R + R + C R + R + R +...C R + R + R +...R 3 3 n 3 n All higher-order ytem are approximated a above

23 Band-Pa Filter 0 Q + + Q 0 0 where = andq = LC 0 0 CR 3

24 Band-Stop Filter Q 0 0 where = andq = 0 LC CR 0 4

25 High-Pa Filter Q 0 0 where = andq = 0 LC CR 0 5

26 Amplifier with Negative Feedback R + R + + Q 0 0 where βgb Q = ; = βgb 0 6

27 Compenated Amplifier R α + + R GB α 3 Q 0 0 α + + 7

28 Filter HN() Q 0 0 where = 0 RC 8

29 Ocillator Q = and = = 0 RC 9

30 PLL + + Q 0 0 where g = K K K ; = L0 pd VCO A LP RC g = g andq = 0 LP L0 L0 LP 30

31 Second Order Linear Sytem Paive filter, amplifier, active filter, ocillator, all other negative feedback ytem like DC regulator, AGC/AVC, amplitude tabilized ocillator, PLL and FLL are deigned a econd order linear ytem 3

32 Comparator Comparator are ued a interface component between analog and digital ytem Poitive regenerative feedback i ued in comparator to bring about hyterei 3

33 Comparator (contd.,) Comparator i a -bit; A to D converter An integrator with a comparator can form a function generator loop. Thi i a mixed-mode ytem. It form the bai of S-d modulator ued in data converter. Such ytem can only be modeled in time domain 33

34 Comparator (contd.,) Comparator are alo ued in Pule Width Modulator, Duty Cycle Generator, DC-DC converter, Cla D Power Amplifier and Switched Mode Power Supplie 34

35 Where do we go after thi coure? Analog IC Deign Power Electronic RF Electronic Microwave Circuit 35

36 Concluion 36

Mixed Method of Model Reduction for Uncertain Systems

SERBIAN JOURNAL OF ELECTRICAL ENGINEERING Vol 4 No June Mixed Method of Model Reduction for Uncertain Sytem N Selvaganean Abtract: A mixed method for reducing a higher order uncertain ytem to a table reduced