CIRCUITS AND ELECTRONICS

Transcription

1 6.002x CIRCUITS AND EECTRONICS The Impedance Model!!! Reading: Section 3.3 from text

2 Review Sinusoidal Steady State (SSS) Reading 3., 3.2 v I i cost R C v SSS Focus on sinusoids. Focus on steady state, only care about v P as v H dies away. 2

3 Review Sinusoidal Steady State SSS Approach i cost sneak in i e jωt drive usual circuit model complex algebra The Sneaky Path set up DE nightmare trig. p 2 p cosé ë wt Ð p ù û take real part 3 v H 4 total p contains all the information we need: p p p e Amplitude of output cosine Phase jt i j RC 3

4 Review Frequency response - magnitude p i jrc H j transfer function v p i jrc cos t p p The Frequency iew 4

5 Review Frequency response - phase S p i tan RC 0 RC BIAS R C GS v C v O 4 2 The Frequency iew 5

6 Effort Is there an even simpler way to get p? p i jrc agony easy p Usual diff eqn. approach i jrc sneaky approach? Is there any even simpler way without DEs? 6

7 The Impedance Model Is there an even simpler way to get p? Consider resistor: Resistor v R i R R 7

8 The Impedance Model -- Capacitor Consider capacitor: Capacitor v C i C C 8

9 The Impedance Model -- Inductor Consider Inductor: Inductor v i 9

10 The Impedance Model -- Inductor Consider Inductor: Inductor v i i I v l l e e st st v di dt 0

11 The Impedance Model -- Summary capacitor inductor resistor

12 Back to RC example v I R C v C Is there an even simpler way to get p? c I c Z C capacitor Z c C I Z C sc c impedance 2

13 Back to RC example v I R C v C Is there an even simpler way to get p? c I c Z C capacitor Z c C I Z C sc c impedance Impedance model: Z R R i c I c Z C sc 3

14 There you have it Effort agony easy Usual diff eqn. approach sneaky approach super sneaky no DEs! Impedance method Today t 4

15 Signal Notation 5

16 Impedance Method Summary 6

17 Another example, recall series RC Remember, we want only the steady-state response to sinusoid (SSS) 7

18 Another example, recall series RC Remember, we want only the steady-state response to sinusoid (SSS) 8

19 Effort The Big Picture i coswt p cosé ë wt Ð p ù û usual circuit model set up DE nightmare trig. agony easy Usual diff eqn. approach sneaky approach Super sneaky no DEs t i e st drive impedance-based circuit model complex algebra complex algebra take real part No D.E.s, No trig! 9

20 Back to et s study this transfer function r i C jr jr 2 i I r C R r Review complex algebra in Appendix C of textbook 20

21 Graphically r i RC 2 C 2 RC 2 i I r C R r Find limit ow : High : : C 2

22 Graphically r i RC 2 C 2 RC 2 i I r C R r Observe ow : High : C : 22

23 Effort Is there an even simpler way to get p? p i jrc agony easy p Usual diff eqn. approach i jrc sneaky approach? Is there any even simpler way without DEs?

24 The Impedance Model Is there an even simpler way to get p? Consider resistor: Resistor v R i R R

25 The Impedance Model -- Capacitor Consider capacitor: Capacitor v C i C C 2

26 The Impedance Model -- Inductor Consider Inductor: Inductor v i 3

27 The Impedance Model -- Inductor Consider Inductor: Inductor v i i I v l l e e st st v di dt

28 The Impedance Model -- Summary capacitor inductor resistor 2

29 Back to RC example v I R C v C Is there an even simpler way to get p? c I c Z C capacitor Z c C I Z C sc c impedance

30 Back to RC example v I R C v C Is there an even simpler way to get p? c I c Z C capacitor Z c C I Z C sc c impedance Impedance model: Z R R i c I c Z C sc

31 There you have it Effort agony easy Usual diff eqn. approach sneaky approach super sneaky no DEs! Impedance method Today t 2

32 Signal Notation

33 Impedance Method Summary 2

34 Another example, recall series RC Remember, we want only the steady-state response to sinusoid (SSS)

35 Another example, recall series RC Remember, we want only the steady-state response to sinusoid (SSS)

36 Effort The Big Picture i coswt p cosé ë wt Ð p ù û usual circuit model set up DE nightmare trig. agony easy Usual diff eqn. approach sneaky approach Super sneaky no DEs t i e st drive impedance-based circuit model complex algebra complex algebra take real part No D.E.s, No trig!

37 Back to et s study this transfer function r i C jr jr 2 i I r C R r Review complex algebra in Appendix C of textbook

38 Graphically r i RC 2 C 2 RC 2 i I r C R r Find limit ow : High : : C 2

39 Graphically r i RC 2 C 2 RC 2 i I r C R r Observe ow : High : C :