Signal Generators and Waveform-Shaping Circuitscc.ee.nchu.edu.tw/~aiclab/teaching/Electronics3/lect13.pdf · Signal Generators and Waveform-Shaping Circuits ... Only at this frequency

Ching-Yuan Yang

National Chung-Hsing UniversityDepartment of Electrical Engineering

Signal Generators and Waveform-Shaping Circuits

Microelectronic Circuits

13-1 Ching-Yuan Yang / EE, NCHUMicroelectrics (III)

Outline

Basic Principles of Sinusoidal Oscillators

Op Amp-RC Oscillator Circuits

LC and Crystal Oscillators

Bistable Multivibrators

Generation of Square and Triangular Waveforms Using Astable

Multivibrators

Generation of a Standardized Pulse – The Monostable Multivibrator

Integrated-Circuit Timers


Basic Principles of Sinusoidal Oscillators


Basic Structure of Sinusoidal Oscillators

Loop gain: )()()( ssAsL β≡

Characteristic equation: 0)(1 =− sL

The oscillation criterion: 1)()()( =≡ ωβωω jjAjL

At ω0 the phase of the loop gain should be zero and the magnitude of the loop gain should be unity. (Barkhausen criterion)

For the circuit to produce sustained oscillations at a frequency ω0 the characteristic equation has to have roots at s = ± ω0.

A positive-feedback loop is formed by an amplifier and frequency-selective network.

Transfer function:

)()(1)(

)(ssA

sAsAf β−

=


In an actual oscillator circuit, no input signal is present (xs = 0):

the feedback signal xf = βxo should be sufficiently large so that when multiplied by A it produces xo , Axf = xo , that is

Aβxo = xo Aβ = 1

At ω0, the phase of the loop should be zero and the magnitude of the loop gain should be

unity.

The stability of the frequency of oscillation is determined by the manner in which the

phase φ(ω ) of the feedback loop varies with frequency. This can be seen if one imagines

a change in phase Δφ due to a change in one of the circuit components.

Dependence of the oscillator frequency stability on the slope of the phase response:

A steep phase response (that is, large dφ /dω )

results in a small Δω0 for a given change in

phase Δφ (resulting from a change in a circuit

component).


Oscillator

Linear region of the circuit: linear oscillation

Nonlinear region of the circuit: amplitude stabilization


Nonlinear Amplitude Control

The oscillation condition – the Barkhausen criterion:

Aβ = 1 at ω = ω0

However, the temperature changes and Aβ becomes slightly less than unity.

Oscillation will cease in this case.

In order to ensure oscillation in the presence of temperature and process variations, we typically choose the loop gain to be at least twice or three times the required value.

If Aβ exceeds unity, oscillations will grow in amplitude. We therefore need a mechanism for forcing Aβ to remain equal to unity at the desired value of output amplitude.

This task is accomplished by providing a nonlinear circuit for gain control.

Gain-control mechanism:

To ensure that oscillations will start, Aβ is slightly greater than unity.

Sustain oscillations at the desired amplitude.


Limiter Circuit for Amplitude Control

Linear portion: (linear region)

If

O vR

Rv

1

−=

32

2

32

3

RRR

vRR

RVv OA +

++

=

54

5

54

4

RRR

vRR

RVv OB +

++

−=


Limit portion: (nonlinear region)

For , A D o

D

D

V V V L

R R RL V V

R R R

R RV V

R R

−

−

= − =

⎛ ⎞+= − −⎜ ⎟+⎝ ⎠

⎛ ⎞= − − +⎜ ⎟

⎝ ⎠

2 3 3

2 2 3

3 3

2 2

1

⎟⎟⎠

⎞⎜⎜⎝

⎛++=+

5

4

5

4 1RR

VRR

VL D

Rf is removed


Op Amp-RC Oscillator Circuits


Wien-Bridge Oscillator

Wien-bridge oscillator without amplitude stabilization

sCRsCR

RR

ZZ

Z

RR

sLsp

p

13

11)( 1

2

1

2

++

+=

+⎟⎟⎠

⎞⎜⎜⎝

⎛+=

⎟⎠⎞

⎜⎝⎛ −+

+=

CRCRj

RR

jL

ωω

ω1

3

1)( 1

2

Oscillation

(phase = 0, |L(jω)| = 1)

2 1

1

20 ==

RR

CRω


Wien-bridge oscillator with a limiter used for amplitude control


Wien-bridge oscillator with an alternative method for amplitude stabilization


Phase-Shift Oscillator

The basic structure of the phase-shift oscillator

It consists of a negative-gain amplifier (−K ) with a three-section (third-order) RC ladder network in the feedback.

The circuit oscillates at the frequency for which the phase shift of the RC network is 180o.

Only at this frequency will the total phase shift around the loop be 0 or 360o.

The reason for using a three-section RC network is that three is the minimum number of sections (that is, lowest order) that is capable of producing a 180o phase shift at a finite frequency.


Practical phase-shift oscillator with a limiter for amplitude stabilization

To start oscillations, Rf has to be made slightly greater than the minimum required value. Although the circuit stabilizes more rapidly, and provides sine waves with more stable amplitude, if Rf is made much larger than this minimum, the price paid is an increased output distortion.


Quadrature Oscillator

vO2


Break the loop at X, loop gain

vO2 is the integral of vO1

vO2 and vO2−90 degrees phase difference

quadrature

( ) O

X

vL s

v s C R≡ = −2

2 2 21

oscillation frequencyCR1

0 =ω


Active-Filter Tuned Oscillator

Block diagram of the active-filter tuned oscillator

High-distortion v2

High-Q bandpass low-distortion v1


Practical implementation of the active-filter tuned oscillator


LC and Crystal Oscillators


A General Form of LC-Tuned Oscillator Configuration

Many oscillator circuits fall into a general form shown below

Z1, Z2, Z3 : capacitive or inductive


If , ,

for inductance for capacitance

For to

'

' ( ) ( )

( )( ) ( )

v Lo

L o

o

v

v

A v Zv

Z R

Zv v

Z Z

A Z ZvT

v R Z Z Z Z Z Z

Z jX Z jX Z jX

X L XC

A X XT j

jR X X X X X X

T

ωω

ω

−=

+

=+

−= =

+ + + += = =

= = −

=+ + − +

13

113

1 3

1 213

13 0 1 2 3 2 1 3

1 1 2 2 3 3

1 2

0 1 2 3 2 1 3

1

be real

or ( )v v v

X X X

A X X A X A XT T

X X X X X X

+ + =−

= = =− + +

1 2 3

1 2 1 1

2 1 3 1 3 2

0


With oscillation

|T| = 1 and ∠T = 0, 360, 720, … degrees.

i.e., T = 1

So, X1 & X2 must have the same sign (Av is positive)

X1 & X2 are L, X3 = −(X1 + X2) is C

or X1 & X2 are C, X3 = −(X1 + X2) is L.

Transistor oscillators

Collpitts oscillator

X1 & X2 are CS, X3 is L.

(feedback is achieved by using a capacitive divider)

Hartley oscillator

X1 & X2 are LS, X3 is C.

(feedback is achieved by using an inductive divider)

or ( )X L XC

ωω

= = −1


LC-tuned oscillators

Two commonly used configurations of LC-tuned oscillators:

Colpitts Hartley

⎟⎟⎠

⎞⎜⎜⎝

⎛+

=

21

21

01

CCCC

L

ωCLL )(

1

210 +=ω

(capacitive divider feedback) (inductive divider feedback)


Equivalent circuit of the Colpitts oscillator

0)1(1

22

12 =+⎟⎠⎞

⎜⎝⎛ +++ πππ VLCssCR

VgVsC m

01

)( 2122

213 =⎟

⎠⎞

⎜⎝⎛ +++++

RgCCs

RLC

sCLCs m

[ ] 0)(1

213

212

2

=−++⎟⎟⎠

⎞⎜⎜⎝

⎛−+ CLCCCj

RLC

Rgm ωωω

Oscillation:

RgCC

m=1

2

⎟⎟⎠

⎞⎜⎜⎝

⎛+

=

21

21

01

CCCC

L

ω

For oscillations to start, the loop gain must be made greater than unity.

gmR > C2 /C1


Complete circuit for a Colpitts oscillator

Oscillator amplitude:

LC tuned oscillators are known as self-limiting oscillators. (As oscillation grown in amplitude, transistor gain is reduced below its small-signal value)

Output voltage signal will be a sinusoid of high purity because of the filtering action of the LC tuned circuit.

Hartley oscillator can be similarity analyzed.


LC-tuned oscillators – Crystal oscillators

Piezoelectric crystal (is high-Q device)Circuit symbol Equivalent circuit

1( ) 0

11

(Assume )

ps

Z s rsC

sL sC

= =+

+

pssp

s

p CLCCCsLCs

sCsZ

)(11

)( 2

2

+++

=

ss LC

1=ω

⎟⎟⎠

⎞⎜⎜⎝

⎛

+

=

ps

ps

p

CC

CCL

1ω

(series resonance)

(parallel resonance)

Note:

⌦ ωp > ωs

⌦ Since Cp >> Cs, then ωp ≈ ωs

⌦ Resonance frequency:

ssLC

ωω =≈1

0


The crystal reactance is inductive over the narrow frequency band between ωs and ωp.

Collpitts crystal oscillator:


Equivalent circuit:

Crystal oscillator circuit

s p

ss

C C C C

LCω ω

<<

≈ =

, ,1 2

01

crystal

===

Z C

Z C

Z

1 2

2 1

3


A Colpotts (or Pierce) crystal oscillator utilizing a CMOS inverter as an amplifier





Multivibrators (3 types)

Bistable : two stable states

Monostable : one stable state

Astable : no stable state

Bistable

Has two stable states

Can be obtained by connecting an amplifier in a amplifier in a positive-feedback loop having a loop gain greater than unity. i.e. βA >1 where β = R1/(R1+R2).


A Positive-Feedback Loop Capable of Bistable Operation

A physical analogy for the operation of the bistable circuit.

The ball cannot remain at the top of the hill for any length of time (a state of unstable equilibrium or metastability); the inevitably present disturbance will cause the ball to fall to one side or the other, where it can remain indefinitely (the two stable states).


The Bistable Circuit with the Negative Input of the Op Amp Connected to an Input Signal

The bistable circuit can be switched to the positive state (vO = L+) by applying a negative trigger signal vI magnitude greater than that of the negative threshold VTL.

The bistable circuit as a memory element

Schmitt trigger

+= LVTH β −= LVTL β

21

1

RRR+

=β


A Bistable Circuit with Noninverting Transfer Characteristics

21

1

21

2

RRR

vRR

Rvv OI +

++

=+

2

1

2

1

RR

LV

RR

LV

TH

TL

−

+

−=

−=


Application of the Bistable Circuit as a Comparator

Block-diagram representation and transfer characteristic for a comparator having a reference, or threshold, voltage VR.

Comparator characteristic with hysteresis


Illustrating the use of hysteresis in the comparator characteristics as a means of rejecting interference

Can reject interference


Making the Output Levels More Precise

Limiter circuits are used to obtain more precise output levels for the bistablecircuit.

L+ = VZ1 + VD

L− = −(VZ2 + VD),

where VD is the forward diode drop.

L+ = VZ + VD1 + VD2

L− = −(VZ + VD3 + VD4)


Generation of Square and Triangular Waveforms Using Astable Multivibrators


Astable Multivibrators

Connecting a bistable multivibrator with inverting transfer characteristics in a feedback loop with an RC circuit results in a square-wave generator


Circuit implementation Waveforms

τβ teLLLv −−++− −−= )( τ = CR

v− = βL+ at t = T1( )β

βτ−

−= +−

11

ln1LL

T

( )β

βτ−

−= −+

11

ln2LL

T

T = T1 + T2 ββτ

−+

=11

ln2


Generation of Triangular Waveforms

CRL

TVV TLTH +=

−

1

+

−=

LVV

CRT TLTH1

CRL

TVV TLTH −−

=−

2

−−−

=L

VVCRT TLTH

2


Generation of a Standardized Pulse – The MonostableMultivibrator


Monostable Multivibrator – One Shot

−

−−−

=−−=

LTv

eVLLtv

B

RCtDB

β)(

)()( 311

⎟⎟⎠

⎞⎜⎜⎝

⎛−−

=−−

−

LLLV

RCT D

β1

31 ln

For VD1 << |L−|, ⎟⎠

⎞⎜⎝

⎛−

≈β1

1ln31RCT


Integrated-Circuit Timers


555 IC Timer

Widely used as both a monostable and astable multivibrator

Use as monostable multivibrator

Discharge transistor

X11

001

110

Qn00

Qn+1SnRn

CCTH

CCTL

CCC n

VV

VV

Vv R

=

=

≥ =

23

32

13


555 Timer Connected to Implement a Monostable Multivibrator

( )( )

for

0

at

( )

( )

( )

.

t CRC CC CC

t CRCC CE sat

C TH CC

v V V V e t T

V e V V

v V V t T

−

−

= − − ≤ ≤

= − ≈ ≈

= = =

0 0

1 0

23

CRCRT 1.13ln ≈=

1 t CRCCV e−−( )


555 Timer Connected to Implement an Astable Multivibrator

. at 32

)( )(

HCCTHC

RRCtTLCCCCC

TtVVv

eVVVv BA

===

−−= +−

)(69.02ln)( BABAH RRCRRCT +≈+=

CCTL VV31

=

VC: VTL → VTH VC: VTH → VTL

. at 31

LCCTLC

CRtTHC

TtVVv

eVv B

===

= −

BBL CRCRT 69.02ln ≈=

CCTH VV3

2=

Period of o/p:

0.69( 2 )H L

A B

T T T

R R C

= += +

BA

BA

LH

H

RRRR

TTT

2

cycleDuty

++

=

+≡


Homework

Problems 4, 13, 18, 24, 30, 40

Documents

Signal Generators and Waveform-Shaping Circuitscc.ee.nchu.edu.tw/~aiclab/teaching/Electronics3/lect13.pdf · Signal Generators and Waveform-Shaping Circuits ... Only at this frequency