Oscillators Oscillators with LC Feedback Circuits.

Oscillators

Oscillators with LC Feedback Circuits

Oscillators

Oscillators With LC Feedback Circuits

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

•LC feedback oscillators use resonant circuits in the feedback path.

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

•Transistors are used as the active device in these types.

LC Oscillators – Colpitts

The Colpitts

oscillator utilizes a

tank circuit (LC) in

the feedback loop

to provide the

necessary phase

shift and to act as

a resonant filter

that passes only

the desired

frequency of

oscillation.

R 2 R 4 C 4

C 3

LC 1 C 2

R 1 R 3 C 5 V out

Amplifier

Feedbackcircuit

V CC

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.



The resonant frequency can be determined by the formula below.

T

rLC

f2

1

L

Zin

C1 C2

Vout2

2T

1

12πr

Qf

QLC

• Figure below shows the input impedance of the amplifier acts as a load on the resonant feedback circuit and reduces the Q of the circuit.

• The resonant frequency of a parallel resonant circuit depends on the Q, according to the formula below:


LC 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 except that the feedback circuit consists of two series inductors and a parallel capacitor.

The frequency of oscillation 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

LC Oscillators – Hartley

where LT = L1 + L2

LC Oscillators – Crystal-Controlled

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

LC Oscillators – Crystal-Controlled

XTAL

C 1

V out

V CC

R 2 R 4

C C

R 1 R 3 C 2

Oscillators

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.



• Assume that the output voltage of the comparator is at its maximum negative level.

• This output is connected to the inverting input of the integrator through R1, producing a positive-going ramp on the output of the integrator.

• When the ramp voltage reaches the UTP, the comparator switches to its maximum positive level.

•This positive level causes the integrator ramp to change to a negative-going direction.

•The ramp continues in this direction until the LTP of the comparator is reached and the cycle repeats.



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

Amplitude of the triangular output is set by establishing the UTP and LTP voltages according to the following formulas:

The frequency of both waveforms depends on the R1C time constant as well as the amplitude-setting resistors, R2 and R3. By varying R1, the fr can be adjusted without changing the output amplitude.

Determine the frequency of oscillation of the circuit in figure below. To what value must R1 be changed to make the frequency 20 kHz?

Oscillators – Relaxation - EXAMPLE

Answer: fr = 8.25 kHz, R1 = 4.13 kOhm

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).

END CHAPTER 5

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Oscillators Oscillators with LC Feedback Circuits.

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