oscillators 2. lc oscillators. oscillators oscillators with lc feedback circuits for frequencies...

Oscillators

2. LC Oscillators

Oscillators

Oscillators With LC Feedback Circuits

For frequencies above 1 MHz, LC feedback oscillators are used.

We will discuss the Colpitts, Hartley and crystal-controlled oscillators.

Transistors are used as the active device in these types.

Z 1

Z 2

Z 3

Oscillators


Oscillators – Colpitts

The Colpitts

oscillator

utilizes a

tank circuit

(LC) in the

feedback

loop as

shown in

the figure.

R 2 R 4 C 4

C 3

LC 1 C 2

R 1 R 3 C 5 V out

Amplifier

Feedbackcircuit

V CC

LC feedback oscillators use resonant circuits in the feedback path. A popular LC oscillator is the Colpitts oscillator. It uses two series capacitors in the resonant circuit. The feedback voltage is developed across C1.

In

L

Vf Vout

AvVf

Vout

IC1 C2

Out

The effect is that the tank circuit is “tapped”. Usually C1 is the larger capacitor because it develops the smaller voltage.


OscillatorsOscillators With LC Feedback Circuits

L

C 2

C 1

If ZT = 0;

01

1

2

11

Cj

CjLj

;1

LCeqo

21

11

CCCeq Colpitts


The resonant frequency can be determined by the formula below.

T

rLC

f2

1

21

111

CCCT

21

21

CCCC

TC

Total capacitance (CT ) is ;


Conditions for oscillation and start up

Out In

V outV f

L

C 1 C 2

V f V out

A v

I1

2

2

1 C

C

IX

IX

V

V

c

c

out

f

2

11

C

CAv

L

Zin

C1 C2

Vout

If Q > 10, this formula gives good results.

2

2T

1

12πr

Qf

QLC

Recall that the total capacitance of two series capacitors is the product-over-sum of the individual capacitors. Therefore,

1 2

1 2

1

2π

rfC C

LC C

For Q < 10, a correction for Q is


Oscillators – Hartley

C 1

C 2 C 4

C 3

C 5

R 1 R 3

R 2 R 4

L 1 L 2

VCC

V out

Amplifier

Feedbackcircuit

The Hartley oscillator is similar to the Colpitts. The tank circuit has two inductors and one capacitor

The Hartley oscillator is similar to the Colpitts oscillator, except the resonant circuit consists of two series inductors (or a single tapped inductor) and a parallel capacitor. The frequency for Q > 10 is

In

AvVf

Vout

Out L1 L2

C

One advantage of a Hartley oscillator is that it can be tuned by using a variable capacitor in the resonant circuit.

T 1 2

1 1

2π 2πrf

L C L L C


If ZT = 0;

01

21

Cj

LjLj

CLLo

21

1

Oscillators


L 1

L 2

C Hartley


The calculation of the resonant frequency is the same.

CLf

T

r 2

1 21 LLLT

2

1

L

L

1

21

L

LAv

Oscillators – Crystal

The crystal-controlled oscillator is the most stable and

accurate of all oscillators. A crystal has a natural

frequency of resonance. Quartz material can be cut or

shaped to have a certain frequency.

Quartzwafer

XTAL

(a) Typical packaged crystal

(b) Basic construction (without case)

(b) Symbol (b) Electrical equivalent

L sC s

R s

C m

Since crystal has natural resonant frequencies of 20 MHz or less, generation of higher frequencies is attained by operating the crystal in what is called the overtone mode

Oscillators – Crystal

XTAL

C 1

V out

V CC

R 2 R 4

C C

R 1 R 3 C 2

Oscillators

3. Relaxation Oscillators

Oscillators – Relaxation

Relaxation oscillators make use of an RC timing and a device that changes states to generate a periodic waveform (non-sinusoidal).

1. Triangular-wave

2. Square-wave

3. Sawtooth


Triangular-wave oscillator

Triangular-wave oscillator circuit is a combination of a comparator and integrator circuit.

Comparator

IntegratorV out

C

R 1

R 3

R 2

A square wave can be taken as an output here.



Comparator output

+Vmax

V out

- Vmax

V UTP

V LTP



3

2

14

1

R

R

CRfr

2

3max R

RVVUTP

-

2

3max R

RVVLTP

For the triangular wave generator, the frequency is found from:

2

1 3

1

4r

Rf

R C R

–

+

R1

Vout

Integrator

–

+

Comparator

R3

R2

C

What is the frequency of the circuit shown here?

10 nF

82 k

22 k

10 k

2

1 3

1

4

1 22 k

4 82 k 10 nF 10 k

r

Rf

R C R

= 671 Hz


Normally, the triangle wave generator uses fast comparators to avoid slew rate problems. For non-critical applications, a 741 will work nicely for low frequencies (<2 kHz). The circuit here is one you can construct easily in lab. (The circuit is the same as Example 16-4 but with a larger C.)

The waveforms are:

Both channels: 5 V/div 250 s/div

–

+

R1

V

V

out1

out2

–

+

R3

R2

C

33 k

10 k

10 k

0.1 F741

741

Square wave

Triangle wave


Oscillators – Square-wave

A square wave relaxation oscillator is like the

Schmitt trigger or Comparator circuit.

The charging and discharging of the capacitor

cause the op-amp to switch states rapidly and

produce a square wave.

The RC time constant determines the frequency.


C

R 1

R 3

R 2

V C

V fV out

Oscillators – Sawtooth voltage controlled oscillator (VCO)

R i

V IN

0 V

PUTV G

V out

V p

I

+-

Sawtooth VCO circuit is a combination of a Programmable Unijunction Transistor (PUT) and integrator circuit.

Oscillators – Sawtooth VCO

OPERATION

Initially, dc input = -VIN

• Vout = 0V, Vanode < VG

• The circuit is like an integrator.

• Capacitor is charging.

• Output is increasing positive going ramp.


OPERATION

R i

V IN

0 V

PUTV G

V out

V p

I

+-

0


OPERATION

When Vout = VP

• Vanode > VG , PUT turns ‘ON’

• The capacitor rapidly discharges.

• Vout drop until Vout = VF.

• Vanode < VG , PUT turns ‘OFF’

VP – maximum peak value

VF – minimum peak value


OPERATION

Oscillation frequency

-

FPi

IN

VVCR

Vf

1


EXAMPLE

In the following circuit, let VF = 1V.

a) Find;

(i) amplitude;

(ii) frequency;

b) Sketch the output waveform


EXAMPLE (cont’d)


EXAMPLE – Solution

a) (i) Amplitude

V 5.7151010

10

43

4

VRR

RVG

V 5.7 GP VV V 1FVand

So, the peak-to-peak amplitude is;

V 5.615.7 -- FP VV



a) (ii) Frequency

-

FPi

IN

VVCR

Vf

1

V 92.121

2 --

VRR

RVIN



a) (ii) Frequency

Hz 628

V1V5.7

1

μ0047.0k100

92.1

-f



b) Output waveform

2 ms

V out

1 V

7.5 V

t

ms 2628

11

fT

OscillatorsThe 555 timer as an oscillator

OscillatorsThe 555 Timer As An Oscillator

The 555 timer is an integrated circuit that can be

used in many applications. The frequency of

output is determined by the external components

R1, R2, and C. The formula below shows the

relationship.

extr CRRf

21 2

144


Duty cycles can be adjusted by values of R1 and R2. The duty cycle is limited to 50% with this arrangement. To have duty cycles less than 50%, a diode is placed across R2. The two formulas show the relationship;

Duty Cycle > 50 %

%1002

cycleDuty 21

21

RR

RR


Duty Cycle < 50 %

%100cycleDuty 21

1

RR

R


The 555 timer may be operated as a VCO with a control voltage applied to the CONT input (pin 5).

OscillatorsSummary

Sinusoidal oscillators operate with positive feedback.

Two conditions for oscillation are 0º feedback phase shift and feedback loop gain of 1.

The initial startup requires the gain to be momentarily greater than 1.

RC oscillators include the Wien-bridge, phase shift, and twin-T.

LC oscillators include the Colpitts, Clapp, Hartley, Armstrong, and crystal.

OscillatorsSummary (cont’d)

The crystal actually uses a crystal as the LC tank circuit and is very stable and accurate.

A voltage controlled oscillator’s (VCO) frequency is controlled by a dc control voltage.

A 555 timer is a versatile integrated circuit that can be used as a square wave oscillator or pulse generator.

END CHAPTER 5

oscillators 2. lc oscillators. oscillators oscillators with lc feedback circuits for frequencies...

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