Designing Circuits Synthesis - Lego

Transcription

1 Deigning Circuit Synthei Lego Port a pair of terminal to a cct Oneport cct; meaure I and at ame port I Drivingpoint impedance input impedance equiv impedance Twoport Tranfer function; meaure input at one port, output at another I MAE4 Linear Circuit I I L C Input Output 88

2 Tranfer function Tranfer function; meaure input at one port, output at another I I Input Output Tranfer function zero tate repone tranform input ignal tranform I.e., what the circuit doe to your input MAE4 Linear Circuit 89

3 Example, T&, 6th ed Tranfer function? Input impedance? T C C I C MAE4 Linear Circuit 9

4 Cacade Connection We want to apply a chain rule of proceing When can we do thi by cacade connection of OpAmp cct? Cacade mean output of cct i i input of cct i Thi make the deign and analyi much eaier Thi rule work if tage i doe not load tage i oltage i not changed becaue of next tage Either Or T T T T 3... Tk Output impedance of ource tage i zero Input impedance of load tage i infinite Work well if out,ource << in,load MAE4 Linear Circuit 9

5 MAE4 Linear Circuit 9 Cacade Connection I chain rule valid? _ C C 3 Meh analyi T total? T T C C C C C C C C I I! " # $ % &! " # $ % & I C I I I C! " # $ % &!!!! " # $ $ $ $ % &! " # $ % & C C I I 3 C C C C C C I C C C C C C C C I No! Why?

6 Cacade Connection OpAmp cct OpAmp can be ued to achieve the chain rule property for cacade connection The input to the next tage need to be driven by the OpAmp output Conider tandard configuration Noninverting amplifier No current drawn from no load I MAE4 Linear Circuit Inverting amplifier Current provided by I Need to make ure that tage i driven by OpAmp output to avoid loading 93

7 MAE4 Linear Circuit 94 OpAmp Cct and tranfer function Node B: Node B: _ A B C T B B B _ A B C T B B B

8 Example 4, T&, 5th ed, p5 Find the tranfer function from to C C C C C C C C T C C C MAE4 Linear Circuit 95

9 Circuit a Signal Proceor Deign a circuit with tranfer function I j 48 j L C T C C C3 LC C 3 3 C L 3 O Ω, C C µf, C 3 µf, L7mH, 3 Ω MAE4 Linear Circuit 96

10 Tranfer Function Deign OpAmp Stage Firt order tage α Κγ Κ Serie L deign α Κ Kγ T K γ α Serie C deign MAE4 Linear Circuit 97

11 Kγ Firtorder tage α K Parallel L deign Kγ α T K γ α Κ Parallel C deign MAE4 Linear Circuit 98

12 Deign Example, T&, 5th ed, p 54 Deign two cct to realize Ω Ω T Ω 3 3Ω 4 µf 5µF Stage Stage T ' $ % 3 " % " %& 3 " # [ ] T [ ][ 4 ] Unrealitic component value caling needed MAE4 Linear Circuit 99

13 Deign Example 9, T&, 5th ed, p 539 Noninverting amplifier deign T 3 4 Ω 5µF µf Ω Ω Ω Stage oltage Divider Stage OpAmp Stage 3 oltage Divider Le OpAmp but more difficult deign Three tage: lat tage not driven Unrealitic component value till caling needed MAE4 Linear Circuit

14 Scaled Deign Example, T&, 5th ed, p 544 More realitic value for component ΚΩ ΚΩ ΚΩ 3ΚΩ nf 5nF Need to play game with element to cale The ratio formula for T help permit thi caling It certainly i poible to demand a deign T which i unrealizable with enible component value Like a pole at 3 Hz MAE4 Linear Circuit

15 Secondorder Stage Deign Circuit tage to yield ζω L C ω K T K ςω ω K ω C K K H ζω F Ω Ω K ω Ω Η ζω Ω F ω ω H MAE4 Linear Circuit

16 Circuit Synthei Given a table tranfer function T, realize it via a cct uing firtorder and econdorder tage α β γ T a b c α β T a b We are limited to table tranfer function to keep within the linear range of the OpAmp There i an exception When the untable T i part of a table feedback ytem Come to MAE43B to find out Tranitor cct deign i conceptually imilar MAE4 Linear Circuit 3