ESE 232 Introduction to Electronic Circuits Professor Paul Min psm@wustl (314) 853-6200

ESE 232 Introduction to Electronic Circuits

Professor Paul [email protected](314) 853-6200

Bryan Hall 302A

mailto:[email protected]

Chapter 1. Signals and Amplifiers

Copyright 2004 by Oxford University Press, Inc.

Microelectronics • Integrated circuit technology• Billions of components• Typically implement in silicon wafer < 100 mm2

• Examples: microprocessors, memories, logic chips

ESE 232• Study of microelectronics• Analysis and design• Functional circuits


Electrical circuits

• Processes signals• Driven by power sources (voltage or current)• At every point in a circuit, voltage and current are

defined.

Signal (or power) represented in voltage(Thevenin form)

Signal (or power) represented in current(Norton form)

Equivalent and translatable

vs(t) = Rs is(t)


Signals

• Contain time-varying information. • Exist in various forms (mechanical, electrical, chemical,

acoustical, etc.)• Can be conveniently processed by electrical circuits.• Converting non-electrical signal to electrical signal is done by

transducer (or sensor).


Frequency Spectrum of Signals

• Often difficult to express signals in time (in mathematical form).

• Signals can be shown in frequency spectrum: Fourier series, Fourier transform, Z-transform, etc. → At what frequencies does the signal contain energy and by how much?


Fourier Series

• Example: sine-wave va(t) = Va sin wt

va(t) has all its energy at the angular frequency of w = 2πf.

f is frequency in Hz. T = 1/f is period in seconds.Magnitude of this sine-wave at the angular frequency w

is Va.


Example: square-wave

Time expression

Frequency expression

w0= 2π/T


Frequency Allocations in the U.S.A.


Digital v. Analog

• Analog signal: continuous value, continuous time• Digital signal: discrete value, discrete time

Sample QuantizeAnalog Signal

DigitalSignal

Continuous timeContinuous value

Discrete timeContinuous value

Discrete timeDiscrete value


Why Digital?

• Less expensive circuits• Privacy and security• Small signals (less power)• Converged multimedia• Error correction and reduction

Why Not Digital?

• More bandwidth• Synchronization in electrical circuits• Approximated information


Notation

•Total instantaneous quantities: lowercase symbols with uppercase subscripts (e.g., iC)

•dc quantities: uppercase symbols with upper case subscripts (e.g., IC)•Power supply voltages: uppercase V’s with double letter uppercase subscripts (e.g., VEE)•dc currents draw from power supply: uppercase I’s with double letter uppercase subscripts (e.g., ICC)•Incremental signal quantities: lowercase symbols with lower case subscripts (e.g., ic)


Amplifiers

• Amplification of input signal• Linear amplifier: vo(t) = Avi(t) (A: constant gain)• Voltage amplifier: changes input signal amplitude

Av = voltage gain = vo / vi

• Preamplifier: shaping in frequency (i.e., amplifies different frequency components differently).

• Power amplifier: gains in voltage and current

symbols


Transfer Characteristic


load power ( )= power gain =

input power ( )

= current gain

voltage gain in decibels 20log

current gain in decibels 20log

power gain in decibels 10log

O OLp

I I I

Oi

I

p v i

v

i

p

v iPA

P v i

iA

i

A A A

A dB

A dB

A dB


Power Supplies

dc 1 1 2 2

dissipated

dc

dc power delivered to amplifer:

power drawn from sources:

power delivered to load:

power dissipated in amplifier:

amplifier efficiency: 100

I

L

L

P V I V I

P

P

P

P

P


1 2

Example. Amplifier with 10 V power supplies.

ˆGiven: ( ) sin , ( ) 9sin , 1 , 0.1 mA

9.5 mA

9= = 9 V/V (or 19.1 dB)

1ˆ9 V 9ˆ 9 mA 90 A/A (or 39.1 dB)ˆ1 k 0.1

I O L I

v

OO i

I

L

v t wt v t wt R k I

I I

A

II A

I

P

dc

dissipated dc

dc

9 9 1 0.140.5 mW, 0.05 mW

2 2 2 29 90 810 W/W (or 29.1 dB)

10 9.5 10 9.5 190 mW

190 0.05 40.5 149.6 mW

100 21.3%

rms rms rms rmso o I i i

p v i

I L

L

V I P V I

A A A

P

P P P P

P

P


Amplifier Saturation

maximum output

minimum output

To avoid saturation:

Iv v

L Lv

A A


at

quiescent point: instantaneous input: ( ) instantaneous output: ( )

input voltage is dc shifted by : ( ) ( )

output voltage: ( ) ( ) where ( ) ( ) and

i o

I I I i

OO O o o v i v

I

Q v t v t

V v t V v t

dvv t V v t v t A v t A

dv

Q

Nonlinear Transfer Characteristics and Biasing

•To avoid saturation, input signal should be shifted. → Biasing•Input signals are biased to operate in the middle of linear region.


4011

Example. transistor amplifier transfer characteristic:

10 10 for 0 V and 0.3 V

0.3 V. At 0.3 V, 0.690 V.

is highest when is lowest, i.e., 0 V.

Therefore,

IvO I O

O I

O I I

v e v v

L v v

v v v

L

0.673

when 0 V. 10 V.

We want to find such that 5 V.

0.673 V

= = -200 V/V I

O I

I O

I

Ov

I v

v v L

V V

V

dvA

dv


Circuit Models for Voltage Amplifiers

To make gain larger, make smaller. This also decouples the effects of unknown value of .

Ideal amplifiers have 0.

If , . This decouples

L o Lo vo i v vo

L o i L o

o L

o

L v vo

R v Rv A v A A

R R v R R

R R

R

R A A

the voltage gain of the amplifer from the values of .

If , then . Input is reduced by a voltage divider.

We want . Ideally, .

Overall voltage gain:

L

ii i s

i s

i s i

ovo

s

R

RR v v

R R

R R R

v RA

v

i L

i s L o

R

R R R R


Cascaded Amplifiers

Multiple stages of amplifiers put together.

Each stage may serve different purpose ( . ., power gain,

followed by voltage gain).

e g

High Ri with gain 10(Signal may be small.)

Modest Ri with gain 100(Provide gain.)

Small Ri with gain 1(Buffer output for next

stage.)


1

21

1

32

2

33

1 2 31

1

10.909 V/V

1 100

10010 9.9 V/V

100 1

10100 90.9 V/V

10 1

101 0.909 V/V

10 100

818 V/V

i

s

iv

i

iv

i

Lv

i

Lv v v v

i

L L

s i

v M

v M k

v kA

v k k

v kA

v k k

vA

v

vA A A A

v

v v

v v

1 1

6

1

8

1 1

743.6 V/V

/1008.18 10 A/A

/1

66.9 10 W/W

i iv

s s

o Li

i i

L oLp

i i

v vA

v v

i vA

i v M

v iPA

P v i


Different Amplifier Types

General Relationship: o mvo is m o

i i

R RA A G R

R R


Example 1.4. Small signal model for Bipolar Junction Transistor (BJT)

B: Base, E: Emitter, C: Collector

Emitter as common ( . ., ground) Common Emitter Ai e mplifier

Let 5 , = 2.5 , g 40 m A/V, 100 , and 5 . s m o LR k r k r k R k

BJT

and ||

|| 63.5 V/V. If , 66.7 V/V

be s o m be L os

o om L o o

s s s

rv v v g v R r

r R

v r vg R r r

v r R v


Frequency Response

With a sinusoidal input to a linear amplifier, the output is a sinusoid with

the same frequency, but with different amplitude and phase shift.

( ) : Transfer function of amplifier

( ) o

i

T w

VT w

V and ( )

Need to determine ( ) and ( ) for all frequencies.

T w

T w T w


1 2

1 2

1 2

Constant gain between and . Should operate in this region.

Gain dropping away from and . Signals are distorted

at frequencies away from and

We say the amplifier has the bandwi

w w

w w

w w

1 2dth between and .w w

Typically

3 dB


First Order Systems: systems with a single time constant

circuits have a single time constant

circuits have a single time constant

General solution (during a time period: initial

RC RC

LRL

R

Final Initial Final

time final time)

( )

Frequency domain analysis ( : angular variable, : Laplace variable)

1 1 , or , or

t

t

x t x x x e

w s

R R C L jwL sLjwC sC



Low pass RC circuit

No distortion means constant amplitude gain and linear phase shift.


High pass RC circuit

No distortion means constant amplitude gain and linear phase shift.


1

1Example 1.5. and ||

11

1 1 1

1 1 1

iii i

i s i i isi s s

i i si i

oLo i

s oL o s s ii

i L s i

RsCZ V

V V Z R CRZ R VR sC R

sC R

VRV V

R RR R V R RsCR R R R

constant Function of s

Time constant: ||s ii i s i

s i

R RC C R R

R R


Only the input circuit is a first order system (or single time constant circuit).

Output circuit is a zero order system ( . ., no energy storing element).

Overall transfer function ( ) 1

1o

i e

K KT s

s sw

0

( : 3 dB frequency)

1 1

1 1

o

o

s os s

i L

w

VK

R RVR R


Different Shapes of Amplifier Frequency Response

For all devices, the transfer function loses amplitude

gain at high frequency because of internal capacitance.

Simple low pass configuration.

Direct coupled amplifier

Amplifier can block low frequency components

(including DC) by putting a capacity in series

with input (i.e,. input circuit is a high pass circuit).

Capacitively coupled amplifier

Amplifier can "filter-in" only selective frequency

components. Typically higher order circuits.

Tuned amplifier


Logic Inverter

Circuit symbol• input 1 (high) → out put 0 (low)• input 0 (low) → out put 1 (high)

Transfer function• high vi (> 0.690V) → low vo (≈ 0.3V)

• low vi (≈ 0V) → high vo (≈ VDD)

• linear region for mid value of vi

Linear region for ordinary amplifier operation (transition region)

Nonlinear (saturation) region for digital binary logic operation


Noise Margin• For cascaded inverters• Noise margin for high input NMH = VOH - VIH

• Noise margin for low input NML = VIL - VOL


Ideal Inverter

NMH = NML =VDD / 2


Abstract Implementation of Inverter

voltage controlled switch.

When vI is low, switch is open, leaving the vertical path disconnected.→ vo = VDD is an open circuit voltage.

When vI is high, switch connects the vertical path.→ vo is a low level voltage determined largely by Voffset, a characteristic of the voltage controlled switch.(Ron is typically small.)


Propagation Delay• Change of output after input change is not instantaneous.• Internal capacitance of devices causes the delay.



offset

on

offsoffset

When the switch is on (input high), it provides the vertical path with

and . The capacity is open circuit at steady state. Thus the steady state

output value is low: DDOL

V

R

V VV V

et

onon

0.55 V.

When the switch becomes off (input becomes low), the vertical path is

connected by the capacitor only. The final value of output is because

once again, the capacitor becomes an DD

RR R

V

8 810 10

open circuit at steady state.

Assuming the input changes at 0,

(0 ) ( ) (0 ) (where )

5 (0.55 5) 5 4.45

Define to be the time for output to go from low

t

o o o o

t t

PLH

t

v t v v v e RC

e e

t

to the half way point

1 1to the final high output value. 5 0.55

2 2From this we get, =6.9 ns.

o PLH OH OL

PLH

v t V V

t

Documents

ESE 232 Introduction to Electronic Circuits Professor Paul Min psm@wustl (314) 853-6200