Electronic Circuits - ETH Zeleccirc/docs/restricted/lecture01.pdf · ETH Integrated Systems Laboratory 2 Electronic Systems Electrical and electronic equipment is indispensable in

Prof. Dr. Qiuting HuangIntegrated Systems Laboratory

Electronic Circuits

1. Introduction

ETH 2Integrated Systems Laboratory

Electronic Systems

Electrical and electronic equipmentis indispensable in our daily lives


Electronics Industry Overview

World Production per Sector

• Electronics industry: ~1300 Billion Euro• Key driver for global economic growth

• Responsible for ~10% of global GDP (incl. service providers)

More than just consumer electronics

Automotive9%

HomeAppliances

6%

Telecoms21%

Audio/Video13%

Industrial &Medical

17%

Data Processing24%

Aero / Defense& Security

10%


Progress in Electronics and Enabled Applications

Improvements in electronics have drastically changed our daily lives

in the past 50 years.


Applications of Transistor Circuits

PCB with operational amplifiers to contact a temperature sensor to a microcontroller board.

Mixed analog and digital integrated circuit for biomedical applications developed at the IIS.

Backpack with solar collectors for hiking.

Miniaturized Device for Monitoring Oxygen Saturation

6ETH Integrated Systems Laboratory

Resistor

Capacitor

Inductor


Review of Passive Components

Range (SMD): 1 pF − 300 𝜇𝜇F

Range (SMD): 0.01 Ω − 10 MΩ

Range (SMD): 1 nH − 10 mH

𝑉𝑉R = 𝑅𝑅𝐼𝐼R

𝐼𝐼C = 𝐶𝐶dd𝑡𝑡𝑉𝑉C

𝑉𝑉L = 𝐿𝐿dd𝑡𝑡𝐼𝐼L

𝐼𝐼C = 𝐼𝐼S𝑒𝑒𝑉𝑉BE𝑉𝑉T 1 +

𝑉𝑉CE𝑉𝑉A

BJT Parameters


Bipolar Junction Transistor

𝐼𝐼B =𝐼𝐼C𝛽𝛽

𝐼𝐼E = 1 + 𝛽𝛽 𝐼𝐼B

𝛽𝛽

𝐼𝐼S𝑉𝑉A

𝑉𝑉T =𝑘𝑘𝑘𝑘𝑞𝑞≈ 26 mV

Current Gain

Early Voltage

Reverse Saturation Current

Physical Constants

𝑘𝑘𝑞𝑞𝑘𝑘

Boltzmann Constant

Elementary Charge

Temperature in K

𝐼𝐼C: Function of 2 Variables𝐼𝐼C = 𝐼𝐼C(𝑉𝑉BE,𝑉𝑉CE)

100 … 500

30 … 100 V

10−15 … 10−12A

Presenter

Presentation Notes

The early effect is still included, because the formula given here is not a function of 2 variables without V_A.

In general: 𝐼𝐼C = 𝐼𝐼C(𝑉𝑉BE,𝑉𝑉CE) function of 2 variables

𝐼𝐼C(𝑉𝑉BE,𝑉𝑉CE) = 𝐼𝐼S𝑒𝑒𝑉𝑉BE𝑉𝑉T (1 + 𝑉𝑉CE

𝑉𝑉A)


2-Dimensional I/V Characteristic

𝑉𝑉BE fixed: 𝐼𝐼C(𝑉𝑉CE)𝑉𝑉CE fixed: 𝐼𝐼C(𝑉𝑉BE)

𝑉𝑉BE [V]

[mA

]

[mA

]

𝑉𝑉BE1

𝑉𝑉BE2

𝑉𝑉BE3

𝑉𝑉BE4

𝑉𝑉CE [V]

Saturation

Forward Active

Presenter

Presentation Notes

3D Matlab Demonstration


Analytical Calculation of Transistor Circuits

𝐼𝐼C = 𝐼𝐼S𝑒𝑒𝑉𝑉BE𝑉𝑉T (1 +

𝑉𝑉CE𝑉𝑉A

)

𝐼𝐼C =𝛽𝛽

𝛽𝛽 + 1𝐼𝐼E ≈ 𝐼𝐼E =

𝑉𝑉E𝑅𝑅E

𝑉𝑉out = 𝑉𝑉CC − 𝐼𝐼C𝑅𝑅L

𝑉𝑉E𝑅𝑅E

− 𝐼𝐼S𝑒𝑒𝑉𝑉in−𝑉𝑉E−𝑉𝑉EE

𝑉𝑉T = 0

Transcendental equation:No analytical solution

≈ 𝐼𝐼S𝑒𝑒𝑉𝑉BE𝑉𝑉T = 𝐼𝐼S𝑒𝑒

𝑉𝑉in−𝑉𝑉E−𝑉𝑉EE𝑉𝑉T

𝛽𝛽 ≫ 1

𝑉𝑉A ≫ 𝑉𝑉CE

Presenter

Presentation Notes

Next year. Check: do we want V_EE etc.? If yes -> new slide explaining it. If not -> change examples and drawings


Graphical Solution

𝐼𝐼E =𝑉𝑉E𝑅𝑅E

≈ 𝐼𝐼S𝑒𝑒𝑉𝑉in−𝑉𝑉E−𝑉𝑉EE

𝑉𝑉T

Solution 1: Graphical Solution

𝐼𝐼𝐶𝐶

𝐼𝐼C(𝑉𝑉in,1)

𝐼𝐼C

𝑉𝑉E




𝐼𝐼E =𝑉𝑉E𝑅𝑅E


Small Signal EquivalentSolution 2: Small Signal Equivalent• Set 𝑉𝑉CC = 𝑉𝑉EE = 0

𝑣𝑣E𝑅𝑅E

= 𝑔𝑔m(𝑣𝑣in − 𝑣𝑣E)

𝑖𝑖C =𝛽𝛽

𝛽𝛽 + 1𝑣𝑣E𝑅𝑅E

≈𝑣𝑣E𝑅𝑅E

𝑣𝑣out = −𝑖𝑖C𝑅𝑅L ≈ −𝑣𝑣E𝑅𝑅E

𝑅𝑅L = −𝒈𝒈𝐦𝐦𝑹𝑹𝐋𝐋

𝟏𝟏 + 𝒈𝒈𝐦𝐦𝑹𝑹𝐄𝐄𝒗𝒗𝐢𝐢𝐢𝐢

𝑣𝑣E =𝑔𝑔m𝑅𝑅E

1 + 𝑔𝑔m𝑅𝑅E𝑣𝑣in

𝑔𝑔m: transconductance

• Approximate 𝐼𝐼C = 𝐼𝐼S𝑒𝑒𝑉𝑉BE𝑉𝑉T for small

signals around the operating point as 𝑖𝑖C = d𝐼𝐼C

d𝑉𝑉BE(𝑣𝑣in − 𝑣𝑣E) = 𝑔𝑔m(𝑣𝑣in − 𝑣𝑣E)


The Transistor Amplifier

𝐼𝐼C

𝑉𝑉CE

Operating

Point

𝐼𝐼C

𝑉𝑉BE

Gain depends on theoperating point



𝐼𝐼C

𝑉𝑉CE

Operating

Point

𝐼𝐼C

𝑉𝑉BE


𝐼𝐼C

𝑉𝑉CE

Operating

Point

𝐼𝐼C

𝑉𝑉BE




𝑉𝑉CE

𝐼𝐼C

𝑉𝑉BE



𝐼𝐼C



Transistor Amplifier – Nonlinear Distortion

Operating

Point

𝐼𝐼C𝐼𝐼C

𝑉𝑉CE𝑉𝑉BE𝑉𝑉BE2

𝑉𝑉BE3

𝑉𝑉BE1

𝑉𝑉BE2

𝑉𝑉BE3

𝑉𝑉BE1


BJT – Small Signal Parameters

𝐼𝐼C

𝑉𝑉BE

d𝐼𝐼C

d𝑉𝑉BE

𝑔𝑔m

𝑔𝑔𝜋𝜋

𝑔𝑔o𝐼𝐼C

𝑉𝑉CE

=𝐼𝐼S𝑉𝑉A𝑒𝑒𝑉𝑉BE𝑉𝑉T

𝐼𝐼C = 𝛽𝛽𝐼𝐼B

=𝜕𝜕

𝜕𝜕𝑉𝑉BE𝐼𝐼S 𝑒𝑒

𝑉𝑉BE𝑉𝑉T 1 +

𝑉𝑉CE𝑉𝑉A

=𝐼𝐼C𝑉𝑉T

=𝜕𝜕𝐼𝐼C𝜕𝜕𝑉𝑉BE

=𝑔𝑔m𝛽𝛽

=1𝛽𝛽𝜕𝜕𝐼𝐼C𝜕𝜕𝑉𝑉BE

=𝜕𝜕𝐼𝐼B𝜕𝜕𝑉𝑉BE

=𝐼𝐼C

𝑉𝑉A + 𝑉𝑉CE

=𝜕𝜕𝐼𝐼C𝜕𝜕𝑉𝑉CE

=𝜕𝜕

𝜕𝜕𝑉𝑉CE𝐼𝐼S 𝑒𝑒

𝑉𝑉BE𝑉𝑉T 1 +

𝑉𝑉CE𝑉𝑉A


BJT – Small Signal Equivalent

𝑟𝑟𝜋𝜋 =1𝑔𝑔𝜋𝜋

=𝛽𝛽𝑔𝑔m

𝑟𝑟o =1𝑔𝑔o

=𝑉𝑉A + 𝑉𝑉CE

𝐼𝐼C≈𝑉𝑉A𝐼𝐼C

𝑉𝑉A ≫ 𝑉𝑉CE

𝑔𝑔m =𝐼𝐼C𝑉𝑉T

20Integrated Systems Laboratory

Small Signal Equivalent – Numerical Example

𝑟𝑟𝜋𝜋 =𝛽𝛽𝑔𝑔m

=


=4.6 S

0.15 S0. 77 S

3.3 kΩ649 Ω109 Ω

ETH


Example: Common Emitter Amplifier




Example: Common Emitter AmplifierLarge Signal: Replace the linear part by its Thévenin equivalent



VTHE =VCCRB2

RB1 + RB2

RTHE =RB1RB2

RB1 + RB2



𝑉𝑉BE = 𝑉𝑉THE − 𝐼𝐼B𝑅𝑅THE = 𝑉𝑉T ln𝛽𝛽𝐼𝐼B𝐼𝐼S

VTHE =VCCRB2

RB1 + RB2

RTHE =RB1RB2

RB1 + RB2

𝑉𝑉BE ≈ 0.7 V = 𝑉𝑉THE − 𝐼𝐼B𝑅𝑅THE

𝐼𝐼B =𝑉𝑉THE − 𝑉𝑉BE

𝑅𝑅THE

𝑰𝑰𝐁𝐁 =𝑽𝑽𝐂𝐂𝐂𝐂𝑹𝑹𝐁𝐁𝐁𝐁

𝑹𝑹𝐁𝐁𝟏𝟏 + 𝑹𝑹𝐁𝐁𝐁𝐁− 𝑽𝑽𝐁𝐁𝐄𝐄

𝑹𝑹𝐁𝐁𝟏𝟏 + 𝑹𝑹𝐁𝐁𝐁𝐁𝑹𝑹𝐁𝐁𝟏𝟏𝑹𝑹𝐁𝐁𝐁𝐁

𝑰𝑰𝐂𝐂 = 𝜷𝜷𝑰𝑰𝐁𝐁


Example: Common Emitter AmplifierSmall Signal




, 𝑟𝑟𝜋𝜋 =𝛽𝛽𝑔𝑔m

Small Signal

𝑟𝑟o =𝑉𝑉A𝐼𝐼C




, 𝑟𝑟𝜋𝜋 =𝛽𝛽𝑔𝑔m

Small Signal

𝑣𝑣out = −𝑔𝑔m𝑣𝑣in(𝑅𝑅L||𝑟𝑟o)

𝐴𝐴V =𝑣𝑣out𝑣𝑣in

= −𝑔𝑔m(𝑅𝑅L| 𝑟𝑟o ≈ −𝑔𝑔m𝑅𝑅L

𝑟𝑟o =𝑉𝑉A𝐼𝐼C

𝑅𝑅L ≪ 𝑟𝑟o

The voltage divider 𝑅𝑅B1,𝑅𝑅B2sets the bias voltage for the BJT.

𝑅𝑅E defines 𝐼𝐼E

𝑉𝑉B = 𝑉𝑉THE − 𝐼𝐼B𝑅𝑅THE ≈𝑉𝑉CC𝑅𝑅B2𝑅𝑅B1+𝑅𝑅B2

𝑉𝑉E = 𝑉𝑉B − 𝑉𝑉BE 𝐼𝐼C ≈ 𝐼𝐼E = 𝑉𝑉E

𝑅𝑅E

𝐼𝐼B = 𝐼𝐼C𝛽𝛽


Biasing of a BJT

𝐼𝐼E ≈ 𝐼𝐼C

Large Signal


Example: Biasing of a BJT

Design the biasing network for𝑅𝑅L = 1kΩ, 𝛽𝛽 = 500, 𝑉𝑉CC= 5 V

What we would like to have: Output DC level: 𝑉𝑉out = 0 V Output signal swing: 𝑉𝑉swing = 2 V Transistor in active region, 𝑉𝑉BE ≈ 0.7 V

How large is 𝑉𝑉𝑅𝑅B2? What we know

𝐼𝐼C = 𝐼𝐼S𝑒𝑒𝑉𝑉BE𝑉𝑉T 1 + 𝑉𝑉CE

𝑉𝑉A= 𝐼𝐼𝑠𝑠𝑒𝑒

𝑉𝑉B−𝑉𝑉E𝑉𝑉T 1 + 𝑉𝑉C−𝑉𝑉E

𝑉𝑉A 𝑉𝑉C = 𝑉𝑉CC − 𝐼𝐼C𝑅𝑅L ≈ 𝑉𝑉CC − 𝐼𝐼E𝑅𝑅L,𝛽𝛽 ≫ 1 𝑉𝑉E = −𝑉𝑉CC + 𝑉𝑉𝑅𝑅E = −𝑉𝑉CC + 𝐼𝐼E𝑅𝑅E

𝑉𝑉CE,min = 0.2 V























𝑉𝑉CE = 𝑉𝑉C − 𝑉𝑉E = 𝑉𝑉out + 𝑉𝑉cc − 𝑉𝑉swing − 𝑉𝑉𝑅𝑅E ≥ 𝑉𝑉CE,min𝑉𝑉𝑅𝑅E ≤ 𝑉𝑉CC + 𝑉𝑉out − 𝑉𝑉swing − 𝑉𝑉CE,min = 2.8 V𝑉𝑉𝑅𝑅B2 = 𝑉𝑉𝑅𝑅E + 𝑉𝑉BE = 3.5 V

Thevenin: 𝑉𝑉𝑅𝑅B2 = 𝑉𝑉THE − 𝐼𝐼B𝑅𝑅THE ≈ 𝑉𝑉THE

𝑉𝑉𝑅𝑅B2 ≈2𝑉𝑉CC𝑅𝑅B2𝑅𝑅B1+𝑅𝑅B2

⟹ 𝑅𝑅B2 =𝑉𝑉𝑅𝑅B2 𝑅𝑅B1+𝑅𝑅B2

2𝑉𝑉CC Choosing 𝑅𝑅B1 + 𝑅𝑅B2 = 10 kΩ

𝑅𝑅B2 = 𝟑𝟑.𝟓𝟓 𝐤𝐤𝐤𝐤, 𝑅𝑅B1 = 𝟔𝟔.𝟓𝟓 𝐤𝐤𝐤𝐤

𝑅𝑅E =𝑉𝑉𝑅𝑅E𝐼𝐼E

= 𝟓𝟓𝟔𝟔𝟓𝟓 𝐤𝐤 with 𝐼𝐼E ≈ 𝐼𝐼C = 𝑉𝑉CC−𝑉𝑉out𝑅𝑅L



𝐼𝐼B =𝑉𝑉THE − 𝑉𝑉BE

𝑅𝑅THE + 1 + 𝛽𝛽 𝑅𝑅E= 9.9 𝜇𝜇A 𝑉𝑉𝑅𝑅B2 = 𝑉𝑉THE − 𝐼𝐼B𝑅𝑅THE = 3.48 V

𝐼𝐼E

Check the result: desired is𝐼𝐼B = 𝐼𝐼C

𝛽𝛽= 10 𝜇𝜇A, 𝑉𝑉𝑅𝑅B2 = 3.5 V

𝑉𝑉THE = 𝐼𝐼B𝑅𝑅THE + 𝑉𝑉BE + 𝐼𝐼B 1 + 𝛽𝛽 𝑅𝑅E


General 3 Terminal Element

• The BJT is an example of a 3 terminal element

• There are also other realizations, like the MOSFET

𝑥𝑥

𝑧𝑧

Example of 𝑓𝑓(𝑥𝑥,𝑦𝑦) for a device with an exponential characteristic in 𝑥𝑥

Example of 𝑓𝑓(𝑥𝑥,𝑦𝑦) for a device with a quadratic characteristic in 𝑥𝑥

𝑧𝑧

𝑦𝑦𝑥𝑥𝑦𝑦

𝑓𝑓(𝑥𝑥,𝑦𝑦0) 𝑓𝑓(𝑥𝑥,𝑦𝑦0)

𝑓𝑓(𝑥𝑥0,𝑦𝑦)𝑓𝑓(𝑥𝑥0,𝑦𝑦)

MOSFET Parameters


MOSFET – Large Signal Summary

𝐾𝐾𝐾

𝑉𝑉t𝑊𝑊/𝐿𝐿

Intrinsic transconductance coefficient

Threshold voltage

Gate width / Gate length

Characteristic length𝜆𝜆

𝐼𝐼D =𝐾𝐾′

2𝑊𝑊𝐿𝐿

𝑉𝑉GS − 𝑉𝑉t 2 1 + 𝜆𝜆𝑉𝑉DS , 𝑉𝑉DS > 𝑉𝑉GS − 𝑉𝑉t,𝑉𝑉GS > 𝑉𝑉t


MOSFET – I/V Characteristics

−1𝜆𝜆

𝐼𝐼D =𝐾𝐾′

2𝑊𝑊𝐿𝐿

𝑉𝑉GS − 𝑉𝑉t 2 1 + 𝜆𝜆𝑉𝑉DS , 𝑉𝑉DS > 𝑉𝑉GS − 𝑉𝑉t

𝑽𝑽𝐃𝐃𝐃𝐃 < 𝑽𝑽𝐆𝐆𝐃𝐃 − 𝑽𝑽𝐭𝐭 𝑽𝑽𝐃𝐃𝐃𝐃 > 𝑽𝑽𝐆𝐆𝐃𝐃 − 𝑽𝑽𝐭𝐭


MOSFET – Small Signal Parameters

𝑉𝑉GS

𝐼𝐼𝐷𝐷

𝑉𝑉DS

d𝑉𝑉DSd𝐼𝐼D

d𝑉𝑉DSd𝐼𝐼D

=𝐾𝐾′

2𝑊𝑊𝐿𝐿

2(𝑉𝑉GS − 𝑉𝑉t) 1 + 𝜆𝜆𝑉𝑉DS

≈𝐾𝐾′

2𝑊𝑊𝐿𝐿 2(𝑉𝑉GS − 𝑉𝑉t)

𝑔𝑔m =𝜕𝜕𝐼𝐼D𝜕𝜕𝑉𝑉GS

=𝜕𝜕

𝜕𝜕𝑉𝑉GS𝐾𝐾′

2𝑊𝑊𝐿𝐿 𝑉𝑉GS − 𝑉𝑉t 2 1 + 𝜆𝜆𝑉𝑉DS

𝜆𝜆𝑉𝑉DS ≪ 1

=𝜕𝜕

𝜕𝜕𝑉𝑉DS𝐾𝐾′

2𝑊𝑊𝐿𝐿

𝑉𝑉GS − 𝑉𝑉t 2 1 + 𝜆𝜆𝑉𝑉DS

=𝐾𝐾′𝑊𝑊2𝐿𝐿 𝑉𝑉GS − 𝑉𝑉t 2𝜆𝜆

𝐼𝐼D

𝑉𝑉GS

d𝐼𝐼D

d𝑉𝑉GS

𝑔𝑔o =𝜕𝜕𝐼𝐼D𝜕𝜕𝑉𝑉DS

𝜆𝜆𝑉𝑉DS ≪ 1

=2𝐾𝐾′𝑊𝑊𝐿𝐿 𝐼𝐼D

= 𝐼𝐼D𝜆𝜆

1 + 𝜆𝜆𝑉𝑉DS≈ 𝜆𝜆𝐼𝐼D


MOSFET – Small Signal Equivalent Summary

𝑟𝑟o =1𝑔𝑔o

≈1𝜆𝜆𝐼𝐼D

𝑔𝑔m =2𝐾𝐾′𝑊𝑊𝐿𝐿

𝐼𝐼D

The BJT and the MOSFET can be used to amplify signals. Their V-I characteristics are nonlinear. For small signals the transistors behave almost linearly,

and small signal models can be used. The operating points of the transistors have to be set

through biasing. A BJT can be biased using a voltage divider.


Summary

Documents

Electronic Circuits - ETH Zeleccirc/docs/restricted/lecture01.pdf · ETH Integrated Systems Laboratory 2 Electronic Systems Electrical and electronic equipment is indispensable in