6.002
CIRCUITS AND
ELECTRONICS
Nonlinear Analysis
Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
6.002 Fall 2000
Lecture 6
Review
Discretize matter t LCA
m1 X KVL, KCL, i-v
m2 X Composition rules
m3 X Node method
m4 X Superposition
m5 X Thévenin, Norton
any
circuit
linear
circuits
Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
6.002 Fall 2000
Lecture 6
Review
Discretize value t Digital abstraction
X Subcircuits for given “switch”
setting are linear! So, all 5
methods (m1 – m5) can be
applied
VS
VS
A =1
B =1
RL
RL
C
A
C
RON
B
RON
SR MOSFET Model
Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
6.002 Fall 2000
Lecture 6
Today
Nonlinear Analysis
X Analytical method
based on m1, m2, m3
X Graphical method
X Introduction to incremental analysis
Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
6.002 Fall 2000
Lecture 6
How do we analyze nonlinear
circuits, for example:
Hypothetical
nonlinear
D
device
(Expo Dweeb ☺)
iD
V
+
vD
-
+
–
+ vD -
D
iD
iD
iD = aebvD
a
vD
0,0
(Curiously, the device supplies power when vD is negative)
Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
6.002 Fall 2000
Lecture 6
Method 1: Analytical Method
Using the node method,
(remember the node method applies for linear or
nonlinear circuits)
vD − V
+ iD = 0
R
iD = aebvD
2 unknowns
1
2
2 equations
Solve the equation by
trial and error
numerical methods
Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
6.002 Fall 2000
Lecture 6
Method 2: Graphical Method
Notice: the solution satisfies equations
1 and 2
iD
2
iD = aebvD
a
vD
iD
V vD
1 iD = −
R R
V
R
1
slope = −
R
vD
V
Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
6.002 Fall 2000
Lecture 6
Combine the two constraints
iD
V
1
R
~ 0 .4
a
¼
called “loadline”
for reasons you
will see later
vD
~ 0.5
e.g.
V =1
R =1
1
a=
4
b =1
V
1
vD = 0.5V
iD = 0.4 A
Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
6.002 Fall 2000
Lecture 6
Method 3: Incremental Analysis
Motivation: music over a light beam
Can we pull this off?
iD
+
vD LED
light
intensity
I D ∝ iD
vI music signal
iR
vI (t ) +
–
t
vI (t )
iD (t )
light
AMP
iR ∝ I R
light intensity IR
in photoreceiver
LED: Light
Emitting
expoDweep ☺
iR (t )
sound
nonlinear
linear
problem! will result in distortion
Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
6.002 Fall 2000
Lecture 6
Problem:
The LED is nonlinear
distortion
iD
iD
vD
vD = vI
t
vD
t
iD
vD
t
Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
6.002 Fall 2000
Lecture 6
If only it were linear …
iD
iD
vD
vD
t
it would’ve been ok.
What do we do?
Zen is the answer
… next lecture!
Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
6.002 Fall 2000
Lecture 6