The Impedance Model - MIT OpenCourseWare

6.002

CIRCUITS AND ELECTRONICS

The Impedance Model

Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].

6.002 Fall 2000 Lecture 17

Review

Sinusoidal Steady State (SSS) Reading 13.1, 13.2

vI = Vi cost +?

R

+

C vO ?

SSS

Focus on steady state, only care about vP as vH dies away.

Focus on sinusoids.

Sinusoidal Steady State (SSS) Reading 13.1, 13.2

Reading: Section 13.3 from course notes.

Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].

6.002 Fall 2000 Lecture 17

Review

Vi cost

1

usual set circuit up model DE

vP

Vp cos[t + Vp ]

nightmare trig.

sneak in

Vi e jt drive

complex algebra

Vp 2

take

3 vH

4

real total

part

The Sneaky Path

Vp e j t

Vi

1+ jRC

Vp contains all the information we need:

Vp Amplitude of output cosine Vp phase

Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].

6.002 Fall 2000 Lecture 17

Review vO = Vp cos(t + Vp )

Vp

Vi

1

1

2

1

1+ 2R2C2

Bode plot

Vp = 1 = H ( j) transfer

Vi 1+ jRC

function

remember demo

1 RC

= 1 RC

break frequency

Vp

Vi

0

= 1

RC

tan-1 - RC 1

- 4

- 2

The Frequency View

Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].

6.002 Fall 2000 Lecture 17

Is there an even simpler way

to get Vp ?

Vp

= 1+

Vi

jRC

Divide numerator and denominator by jC.

1

Vp = Vi

j C

1 +R

j C

Hmmm... looks like a voltage divider relationship.

Vp

= Vi

ZC ZC +

R

Let's explore further...

Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].

6.002 Fall 2000 Lecture 17

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