ECE/ENGRD 2100

Introduction to Circuits for ECE

Lecture 9

Large-Signal Analysis of Nonlinear Circuits

ECE/ENGRD 2100 2

Announcements

• Upcoming due dates:– Prelab 2 due by 12:20 pm on Tuesday February 12, 2019– Homework 2 due by 11:59 pm on Friday February 15, 2019– Lab report 2 due by 11:59 pm on Friday February 22, 2019

• Lab 2 is this week (starting Tuesday February 12, 2019)

• Prelim 1 on Thursday February 21, 2019 from 7:30 – 9 pm in 203 Phillips

ECE/ENGRD 2100 3

𝑣"

𝑖"

Examples of Two-Terminal Nonlinear Devices

Ideal Diode Real Diode

𝑣"

𝑖"

~0.7V

𝑣"

𝑖"

𝑣"

𝑖"

Zener Diode

𝑣"

𝑖"

~0.7V

−V+

𝑣"

𝑖" Quadratic Devicemade by shorting two

terminals of a MOSFET

𝑣,

𝑖,

V-

𝑣,

𝑖,

Q

ECE/ENGRD 2100 4

Analysis of Circuits with Nonlinear Devices

• Following techniques still work when circuits have nonlinear components:– Brute Force (KVL, KCL and Element Constitutive Relationships)– Mesh and Loop Analysis– Node Analysis

• Superposition does not work when circuits have nonlinear components

ECE/ENGRD 2100 5

Analysis of Circuits with One Nonlinear Device

NL NL

ECE/ENGRD 2100 6

Nonlinear Device Circuit – Example 1

𝑣,

𝑖,

1V

𝑖, = 10if𝑣, < 1V

0.5 𝑣, − 16mAif𝑣, ≥ 1V𝑣,

𝑖,

Q

5V1kΩ

Q 𝑣,

𝑖,

ECE/ENGRD 2100 7

Nonlinear Device Circuit – Example 1 (Cont.)

𝑖, = 10if𝑣, < 1V

0.5 𝑣, − 16mAif𝑣, ≥ 1V5V

1kΩQ 𝑣,

𝑖,

ECE/ENGRD 2100 8

Example 1: Graphical Analysis using Load Line

𝑣,

𝑖,

1 53

3

1

5

mA

V

𝑖, = 10if𝑣, < 1V

0.5 𝑣, − 16mAif𝑣, ≥ 1V5V

1kΩQ 𝑣,

𝑖,

ECE/ENGRD 2100 9

Zener Diode

𝑣"

𝑖"

~0.7V

−V+

𝑣"

𝑖"

• Behaves mostly like a normal diode

• Reverse breakdown occurs typically with a sharper knee at designed voltage

EngineeredReverse

Breakdown

ECE/ENGRD 2100 10

Regulated Power Supply using Zener Diode

V=R=

𝑖?𝑣?

V= = 9V

R= = 3Ω

V+ = 5V

V=R=

𝑖?𝑣?V+

Supply LoadZener

𝑖?

𝑣?9V

5V

3A

ECE/ENGRD 2100 11

Regulated Power Supply (Cont.)

V= = 9V

R= = 3Ω

V+ = 5V

V= − R=𝑖?R=

𝑣?𝑣A

𝑣A

𝑖A

V+

𝑖A

𝑖?

𝑣?9V

5V

3A

ECE/ENGRD 2100 12

Piecewise Linear (Approximate) Analysis

𝑣A

𝑖A

V+

𝑣A

𝑖A

V= − R=𝑖?R=

𝑣?𝑣A

𝑖AV= − R=𝑖?

R=𝑣?