UNIT II- OSCILLATORS

Negative Resistance oscillator - Barhausen Criterion for oscillation in feedback

oscillator - Mechanism for start of oscillation and stabilization of amplitude - Analysis

of RC Oscillators using Cascade connection of Lowpass and highpass filters - Wein

Phase shift and twin-T network - Analysis of LC Oscillators - Colpitts Hartley, Clapp,

Franklin, Armstrong and Miller Oscillator - Frequency range of RC and LC Oscillator

- Quartz Crystal Construction Electrical equivalent circuit of Crystal - Crystal

Oscillator circuits - use of Logic Gates as linear amplifiers, oscillator and clock

generator circuits using logic gate amplifiers.

When the operating point enters the region of positive resistance, the

amplitude of oscillation is limited.

To obtain the maximum output, the quiescent point must be accurately located

at the center of the negative resistance region. The frequency of oscillation is

given by,

A tunnel diode has a characteristic with a negative resistance region between

voltages of approximately 0.1 and 0.3 V and can be used as an oscillator at

frequencies up to 100 0Hz.

2.2 BARKHAUSEN CRITERION:

The essential condition for maintaining oscillations are:

| βA | = 1, i.e. the magnitude of loop gain must be unity.

The total phase shift around the closed loop is zero or 360 degrees.

PRACTICAL CONSIDERATIONS:

The condition that | βA | = 1 gives a single and precise value of Aβ which

should be set through out the operation of the oscillator circuit.

But in practice, as transistor characteristics and performance of other circuit

components change with time, | βA | will become greater or less than unity.

Hence, in all practical circuits | βA | should be set greater than unity so that

the amplitude of oscillation will continue to increase without limit but such an

increase in amplitude is limited by the onset of the nonlinearity of operation in

the active devices associated with the amplifier is shown below.

In this circuit, Βa is larger than unity for positive feedback. This onset of

Non linearity is an essential feature of all practical oscillators.

2.3 MECHANISM FOR START OF OSCILLATION:

A circuit which produces electrical oscillations of any desired frequency is

known as oscillatory circuit or tank circuit.

A circuit which produces sinusoidal oscillations of any desired frequency is

known as sinusoidal oscillator.

A simple oscillatory circuit consists of a capacitor (C) and inductance (L) in

parallel as shown below

(1) In the position shown in figure (i), the upper plate of capacitor has deficit of

electrons and the lower plate has excess of electrons. Therefore, there

is a voltage across the capacitor and the capacitor has electro-static energy.

(2) When switch S is closed as shown in figure (ii), the capacitor will discharge

through inductance and the electron flow will be in the direction indicated by the

arrow. This current flow sets up magnetic field around the coil. Due to the inductive

effect, the current builds up slowly towards a maximum value. The circuit current will

be maximum when the capacitor is fully discharged. At this instant, electro-static

energy is zero but because electron motion is greatest, the magnetic field energy

around the coil is maximum. Obviously, the electro-static energy across the capacitor

is completely converted into magnetic field energy around the coil.

(3) Once the capacitor is discharged, the magnetic field will begin to collapse and

produce a counter e.m.f. according to Lenz‟s law, the counter e.m.f will keep the

current flowing in the same direction. The result is that the capacitor is now charged

with the opposite polarity, making upper plate of capacitor negative and lower plate

positive as shown in figure (iii).

(4) After the collapsing field has recharged the capacitor, the capacitor now

begins to discharges, current now flowing in the opposite direction. Figure (iv) shows

capacitor fully charged and maximum current flowing. The sequence of charge and

discharge results in alternating motion of electrons or an oscillating current. The

energy is alternately stored in the electric field of the capacitor (and the magnetic field

of inductance coil (L) . This interchange of energy between L and C is repeated over.

and again resulting in the production of oscillation.

So the charge and discharge of condenser through inductance results in

oscillating current and hence the electrical oscillations are set up in LC circuit

whose frequency is given by, f = 1/ 2π√LC.

WAVEFORM:

If there were no losses in the tank circuit to consume the energy, the

interchange of energy between L and C would continue indefinitely.

In a practical tank circuit, there are resistance and radiation losses in the coil

and dielectric losses in the capacitor.

During each cycle, a small part of the originally imparted. energy is used up to

overcome these losses.

The result is that the amplitude of oscillating current decreases gradually and

eventually it becomes zero when all the energy is consumed as losses.

Therefore, the tank circuit by itself will produce damped oscillations as shown

below.

STABILIZATION OF AMPLITUDE:

In all the oscillators the output waveform tends to be the maximum possible

output that the amplifier can produce.

Having large amplitudes will distort the output amplitude since the output

amplitude is limited only by the amplifier output range.

To minimize distortion and reduce the amplitude of the output waveform to an

acceptable level amplitude stabilization circuitry must be employed.

Amplitude stabilization operates by ensuring that oscillation ceases as the

amplifier output approaches a predetermined level.

As the output falls to an acceptable level the circuit continues to oscillate. For

phase shift oscillators the amplifier gain should always exceed 29 to sustain

oscillations.

2.4 ANALYSIS OF RC OSCILLATORS USING CASCADE CONNECTION

OF LOW PASS AND HIGH PASS FILTERS.

Oscillators produce the desired output waveform when the voltage feedback is

in phase with the in1 wave.

The phase shift between the voltage feedback and the input should be 0

degrees or 180 degrees.

If a transistor is used as the basic amplifying element it 9introduces a phase

shift of 1800 degrees.

A further phase shift of 1800 degrees should be introduced by the feedback

network, so that the output of the feed back network is in phase with the input

signal An RC network may be used as the feedback network Wein bridge

oscillator and RC phase shift oscillator are the RC oscillators used.

HIGH PASS COMBINATION:

The basic high pass filter is shown in the figure Since the reactance of the

capacitor decreases with increasing frequency the higher frequency

components of the input signal appear at the output with less attenuation than

the low frequency components .

At very high frequencies the capacitor acts almost as a short circuit and

virtually all the input appears at the output.

At 0 frequency the capacitor has infinite reactance and hence behaves as an

open circuit.

Any constant input voltage (D.C) is blocked and cannot reach the output.

Therefore C is called the blocking capacitor.

This basic configuration is the most common coupling circuit to obtain d.c

isolation between input and output.

SINUSOIDAL INPUT:

When a sinusoidal input Vin is applied the output signal Vo increases with the

increasing frequency.

Even in the case of a transmission network where no amplification is involved

and in which the output is always smaller than the input, the ratio Vo/Vin is

called the amplification or gain A of the circuit.

For the given circuit the gain A and the angle θ by which the output leads the

input are given by

LOW PASS COMBINATION:

The circuit shows a low pass filter. it passes the low frequencies but attenuates

the high frequencies because of the reactance of the capacitor C decreases with

increase in frequency.

At very high frequencies the capacitor acts as a short circuit and the output

falls to 0.

This basic low pass filter represents the situation that exists in a basic signal

source.

The terminals of the source are 0— 0‟.

Looking back at the source the source may be replaced by a Thevinins

equivalent.

The voltage Vi is the open circuit voltage and R is the output impedance of the

source assumed purely resistive.

The capacitance C represents all the capacitance which appears in shunt

across 0 -- 0‟.

This capacitance may arise from the wire used to couple the terminals 0 — 0‟

to a load or may arise as a result of the capacitive component of the

admittance presented by the load or from stray capacitance across terminals at

the signal source itself.

The network shown in the figure is similar to that of the high pass filter except

that the output is now taken across C instead of R.

Hence the mathematical solution for the low pass circuit can be obtained in a

similar way as for a high pass circuit.

SINUSOIDAL INPUT:

If the input voltage Vi is sinusoidal the magnitude „of the steady state gain A

and the angle θ by which the output leads the input are given by

2.5 WEIN BRIDGE OSCILLATOR:

This is audio frequency RC oscillator.

The advantage of this oscillator is that the frequency may be varied in the

range of 10 Hz to about 1‟ MHz whereas in RC oscillators, the frequency

cannot be varied.

The oscillator consists of two stages of R-C coupled amplifier and a feedback

network.

The block diagram is shown below.

The voltage across the parallel combination of R and C is fed to the input of

amplifier 1.

The net phase shift through the two amplifiers is zero.

Now the question is that why we could not feed the out tput of amplifier 2 to

amplifier 1 to provide regeneration needed for oscillation operation.

The answer is that amplifier 1 will amplify signals over a wide range of

frequencies and hence the direct coupling would result in poor frequency

stability.

By adding Wien-bridge feedback network, the oscillator becomes sensitive to

a signal of only one particular frequency. Hence good frequency stability is

obtained.

It is now essential that the feed back network should not introduce any phase

shift between its input and output voltages.

It can be shown that this is achieved at a frequency f= 1/2πRC when β= 1/3.

This is obtained by introducing two resistances R1 and R2 in the feedback

network as shown in figure;

We can vary the frequency of this oscillator by varying the two capacitors

simultaneously.

We can also change the range of the frequency of the oscillator by using

different values of resistors R.

Where f is the frequency of oscillation.

ADVANTAGES:

This gives good frequency stability.

By replacing R2 with a Thermistor amplitude stability of oscillator output voltage

can be increased.

Overall gain is high because of two transistors.

Frequency of oscillations can be changed.

Exceedingly good sine wave output.

DISADVANTAGES:

It requires two transistors and large number of components.

It cannot generate very high frequencies.

2.6 PHASE SHIFT OSCILLATOR:

The tuned circuit oscillators are good for generating high frequency.

oscillations.

For low frequencies, R-C oscillators are more suitable.

Tuned circuit is not a essential requirement for oscillation. The essential

requirement is that there must be a 1800 phase shift around the feedback

network and loop gain should be greater than unity.

The 180° phase shift in feedback signal can be achieved by a suitable RC

network consisting of three RC sections as shown below.

When a sinusoidal voltage of frequency f is applied to a circuit consisting of

resistor R and capacitor C in series, then the alternating current in the circuit

leads the applied voltage by certain angle known as phase angle.

The value of R and C may be selected in such a manner that for the frequency

f, the phase angle is 60°.

So using a ladder network of three R-C sections, desired 180° phase shift may

be produced.

CIRCUIT ARRANGEMENT:

The circuit arrangement of a phase shift oscillator using NPN transistor in

common-emitter configuration is shown below.

Here R — R provide dc emitter bias.

RL is the load which controls the collector voltage. Re-Ce combination

provides temperature stability and prevents ac signal degeneration.

The output of the amplifier goes to a feedback netwok which conists of three

identical R-C sections.

It should be remembered that the last section contains a resistance R=Rhie.

Since, this resistor is connected with the base of the transistor, the input

resistance hie of the transistor is added to it to give a total resistance.

CIRCUIT ACTION:

Here R-C network produces a phase shift of 1800 between input and output

voltages.

Since C-E amplifier produces a phase of 180°, the total phase change becomes

360° or 00 which is the essential requirement of sustáined oscillations.

The RC phase shift networks serve as frequency determining circuit.

Since only at a single frequency the net phase shift around the loop will be 360°

a sinusoidal waveform at this frequency is generated.

These oscillators are used for audio frequency ranges LC tuned circuits at low

frequencies become too much bulky and expensive moreover they suffer from

frequency instability and poor waveform.

FREQUENCY OF OSCILLATIONS:

The equivalent circuit is shown below:

The equivalent circuit can be simplified by making the following assumptions:

1. 1/hoe is much larger than RL, its effect can be neglected.

2. hre of the transistor is usually small and hence h is omitted from the circuit.

3. In practice RL is taken equal to R.

4. The current source is replaced by voltage source using Thevenin‟s theorem.

The simplified equivalent circuit in also shown below.

Thus for sustained oscillation, the value of hfe of transistor should be 56.

TWIN T NETWORK:

The twin “T” network is one of the few RC filter networks capable of

providing infinitely deep notch.

By combining the twin “T” with an operational amplifier voltage follower, the

usual drawbacks of the network are overcome.

The Quality factor is raised from the usual 0.3 to something greater than 50.

Further, the voltage folllower acts as a buffer, providing a low output

resistance; and the high input resistance of the op amp makes it possible to use

large resistance values in the “T” so only small capacitors are required, even at

low frequencies.

The fast response of follower allows the notch to be used at high frequencies.

Neither the depth of the h nor the frequency of the notch are changed when the

follower is added .

Figure low shows a twin T” network connected to an op amp to form a high

Q,60 Hz notch.

The junction of R3 and C3, which is normally connected to ground, i bootstrapped

to the output of the follower.

Because the output of the follower is I very low impedance, neither the depth nor

the frequency of the notch chang however, the Q is raised in oportion to the

amount of si fed back to R3 ai C3.

Figure below shows the response of a normal twin “T” and the response wi the

follower added.

ADJUSTABLE TWIN T:

In applications where the rejected signal-might deviate slightly from the null of

the notch network, it is advantageous to lower the Q of the network.

This insures some rejection over a wider range of input frequencies.

Figure below shows circuit Where the Q may be varied from 0.3 to 50.

A fraction of the output is fed back to R3 and C3 by a second voltage follower,

and the Q is dependent on the amount of signal fed back.

A second follower is necessary to drive the twin from a low-resistance source so

that the notch frequency and depth will not change with the potentiometer setting.

Depending on the potentiometer (RL) setting, the circuit in Figure, will have a

response that falls in the shaded area of the frequency response plot.

An interesting change in the high Q twin “T” occurs when components are not

exactly matched in ratio.

For example, an increase of 1 to 10 percent in the value of C3 will raise the Q,

while degrading the depth of the notch.

If the value of C3 is raised by 1,0 to 20 percent, the network provides voltage gain

and acts as a tuned amplifier.

A voltage gain of 400 was, obtained during testing.

Further increases in C3 cause the circuit to oscillate, giving a clipped sine wave

output.

The circuit is easy to use and only a few items need be considered for proper

operation.

To minimize notch frequency shift with temperature, silver mica, or

polycarbonate, capacitors should be used with precision resistors.

Notch depth depends on component match, therefore,. 0.1 percent resistors and 1

percent capacitors are suggested to minimize the trimming needed for a 60 dB

notch.

To insure stability of the op amp, the power supplies should be bypassed near the

integrated circuit package with .01 mF disc capacitors.

2.8 ANALYSIS OF LC OSCILLATORS:

In the general form of a oscillator, any of the active devices such as Vacuum tube,

transistor, FET, Operational amplifier may be used in the amplifier section.

Z1, and Z2 are reactive elements constituting the feedback tank circuit which

determines the frequency of oscillations.

also provides temperature stabilization.

The radio frequency choke (R.F.C) offers very high impedance to high frequency

currents i.e., acts like a d.c short and open.

Thus it provide d.c load for collector and keeps a.c. currents out of d.c. s source.

The function of Cc and Cb to block d.c. and to provide an a.c. path.

Frequency determining network is a parallel resonant circuit consisting of

inductors L1 and L2 and a variable capacitor C, the junction of L1 and L2 is

earthed.

One side of L is connected to base via C and the other to emitter via C So, L the

input circuit.

Similarly one end of L is connected to collector via C and other end id connected

to emitter via Ce.

So, L is in the output circuit.

The two! are inductively coupled and form an auto ttansformer.

WORKING OF THE CIRCUIT:

When the collector supply voltage is switched on, a transient current produced in

the tank circuit.

The oscillatory current in the tank circuit produces voltage across L in this way a

feedback between output and input circuit accomplished through auto transformer

action.

So there is a phase reversal of 1800 between output and input.

The common-emitter amplifier also produces a further 180° phase shift between

input and output voltages.

Thus total phase shift becomes 360°.

This makes the feedback positive which is the essential condition for oscillations.

When the loop gain | β | of the amplifier is greater than one, oscillations are

sustained in the circuit.

FREQUENCY OF OSCILLATIONS:

The general equation for the oscillator is given by,

The figure shows the circuit diagram of colpitt‟s oscillator.

The circuit is same as that of Hartley oscillator except that the emitter tap is

connected between the capacitance‟s C1 and C2.

The resistors R and Re provide the necessary bias conditions for the circuit.

The parallel combination of Re and C in the emitter circuit is the stabilizing

circuit.

The function of Ce and Cb is to block d.c. and to provide an a.c. path.

The radio frequency choke offers very high impedance to high frequency

currents.

Thus it prevents radio frequency currents from reaching source of collector supply

voltage and prevents this source from short-circuiting the alternating output

voltage.

The frequency determining network is a parallel resonant circuit consisting f

capacitors C and C and the inductor L.

The junction of C and C is grounded. e voltage developed across provides the

regenerative feedback required for the stained oscillations.

CIRCUIT OPERATION:

When the collector supply voltage is switched on, a transient current is produced

in the tank circuit.

So damped harmonic oscillations are produced in the circuit.

The oscillations across C are applied to the base emitter junction and ax in the

amplified form in the collector circuit and supply losses to the tank circuit.

If terminal 1 is at positive potential with respect to terminal 3 at any instant,

terminal 2 will be at negative potential with respect to 3 at that instant because

terminal 3 is grounded.

Therefore points 1 and 2 are 1800 out of phase.

A further shift of 180° is produced by the transistor.

In this way, feedback is properly phased to produce continuous undamped

oscillations.

In other words, energy is supplied to the tank circuit in phase with the oscillations

and if βA is greater than one, oscillations are sustained in the circuit.

Equation (3) gives the condition for maintenance of oscillations.

2.11 CLAPP OSCILLATOR:

This is modified form of Colpitt‟s oscillator.

The main difference lies in the introduction of another capacitance C in series

with the coil L.

The capacitor C1 is made large so as to reduce the effect of collector capacitance

variations d2 collector voltage changes .

The frequency of oscillation is given by,

2.12 FRANKLIN OSCILLATOR:

The local oscillator for, a balanced modulator generating single or double

sideband amplitude modulated wave is based on the Franklin oscillator, that was

so popular in the first half of this century.

The Franklin circuit used two vacuum tubes, this circuit uses two direct coupled

FET‟s.

The Inductor Li is wound on a ceramic former, about 1/2 inch (12.5mm)

Diameter.

Ceramic coil former can be made from an old 1KW electric fire (heater) element

by nicking the element with a hacksaw, and breaking it on a hard surface.

Drilling holes in it will not help. The main tuning capacitor is a double bearing

type, value about 2Opf.

The trimmer cap is a good quality air spaced type. The 5Opf fixed cap (47pf

actually) is polystyrene.

The trimmer marked, 5p should be adjusted to the minimum value that gives

reliable operation, a 5mm ceramic trimmer, 3/20pf would be appropriate.

The VFO should be built in a well screened box.

The VFO output is about 700m Vpp, further amplification will be needed to drive

a high level diode, or mosfet mixer.

Here a digital VFO stabilizer is used, so good long term frequency stability will

not be too difficult to achieve.

The LO. AMP. Increases the VFO signal level to about +17 dBm (50 mW).

This uses a 2N2219A transistor.

The transformer is wound on a small ferrite ring (the same type as used for the

balanced modulator), 6 turns bifilar winding.

Twist two lengths of pvc insulated wire together, use two different colors T low

pass filter is designed to work at 11.5 MHz.

The inductor is 12 Turns on a T50-2 core.

If your rig has a different L.O. frequency, you will need to re-calculate the LPF

component values.

The 5R resistor is two 10 R resistors in parallel.

APPLICATION OF FRANKLIN OSCILLATOR:

The simple, two diode balanced modulator is still one of the best ways of

generating a DSB/SSB signal.

The local oscillator used here is Franklin oscillator.

You can use Silicon switching diodes, 1N914, 1N4148, Germanium point

contact diodes, 1N34, or Schottky (Hot Carrier) diodes.

Both transistors are BC548‟s, for the reasons mentioned above.

The transformer is wound on a high permeability (ui = 850) ferrite core.

2K2 resistor at the output, supplies a few mA to a diode switch in my receiver.

This allows the same crystal filter to be used for transmit and receive.

If only transmitter is built, this resistor should be omitted.

The modules constructed so far will work on any band.

Decide what band you want to use, work out the local oscillator frequency,

allowing for the IF offset, then build a suitable oscillator / PLL / DDS.

An SSB transceiver requires the 80 Metre band.

The IF frequency here is 7.8MHz, the local oscillator frequency range required

is, 1 1.3 MHz to 11.6 MHz to cover from 3.5 to 3.8 Mhz.

This local Franklin oscillator can easily be modified to work on other

frequencies, if you are using a different IF.

2.13 ARMSTRONG OSCILLATOR:

The basic circuit of an Armstrong oscillator is shown in the figure.

The tank circuit comprises of the inductor L1 and capacitor C1.

Coil L1 is inductively coupled with coil L2.

When the plate supply voltage Ebb is first connected the current flows through

the plate circuit.

This current flows through coil L2 and since it is inductivey coupled to coil L1, a

voltage is induced in the latter.

This voltage is in such direction that grid of the tube is driven positive.

This increases the plate current ia faster rate and the induced voltage in coil Li

increases further.

Thus a high positive voltage is built up across the tank circuit.

Capacitor Cl charges with a positive polarity on its top plate.

During this process since the grid is positive the grid current changes the capacitor

Cg to the peak value with the polarity shown.

As the p1 current approaches its saturation point the rate of rise of plate current

decreases therefore the induced voltage decreases.

Capacitor Cg therefore discharges through the resistance Rg.

This makes the grid negative and therefore a chain reaction is setoff.

With the grid becoming negative the plate current starts decreasing and as a result

the magnetic field of L2 is wiped out.

This induces a negative voltage in coil L1.

The capacitor Cg is still discharging and this drives the tube to a cut off region

and therefore the plate current becomes zero.

The negative induced voltage across L1 causes C1 to discharge and then charge

up again to the peak value of the negative induced voltage.

The tube is cut off and Cl is charged with a negative polarity at its top plate.

During the next half cycle, the tank circuit takes out the tube from its cut off

region.

Cl starts to discharge through Li and the grid is raised in potential till the tube

starts again.

As soon as the tube conducts, the energy is transferred from the plate circuit to the

tank circuit.

Capacitor C1, charges up again to the peak value of positive voltage.

The entire cycle repeats itself as described.

The output is taken from coil L3 which is inductively coupled to L1.

MILLER OSCILLATOR:

Circuit below shows the diagram of a crystal controlled Miller oscillator.

A tuned LC circuit in the drain section is adjusted near the crystal parallel

resonant frequency.

The crystal oscillator has a series and a parallel resonant frequency.

The parallel resonant frequency of the crystal is fp=1/2π√C+Cm/LCCm. This This parallel frequency of the crystal made equal to the resonant frequency of the

output.

The tuned circuit consists of an inductor and a capacitor in parallel with each other

with respect to supply source.

In practice, some resistance R is always present with the inductor.

The value of R is negligible small as compared to other impedances.

It should be noted that IL = Vs / XL and Ic = Vs /Xc where, XL and Xc are the

impedances of inductor and capacitor respectively.

Further I = I L+ IC We know that the current in inductor lags Vs by 90° while the

current in capacitor leads Vs by 900.

Thus the two currents are out of phase with each other.

When alternating voltage is applied across the parallel circuit, the frequency of

oscillations will be the same as that of applied voltage.

However, at particular frequency of applied voltage, the inductive reactance XL

equals the capacitive reactance Xc.

Now the circuit behaves as purely resistive circuit.

The phenomenon is call as resonance. The miller oscillator gives a sinusoidal

output at the required frequency.

The maximum gate source signal occurs at the crystal anti resonant frequency

controlling the circuit operating frequency.

2.15 FREQUENCY RANGE OF RC AND LC OSCILLATORS :

RC Oscillators:

RC Oscillator provides sinewaves or squarewaves over the range of 0Hz to

10MHz with a 1/2 watt of output power.

A fixed 1Vrms sine wave output is also provided, independent of the main

output, and can be used for synchronizing a scope r as an auxiliary output.

For increased frequency accuracy, a synchronizing input is provided to lock

the oscillator to a more precise external frequency source

Unlike function generators which offer sine waves and square waves, is

basically Wein Bridge oscillator that generates true sine waves without

discontinuities or peaks.

The sine wave exhibits <0.1% distortion over the frequency range of 100Hz

to 100kHz, rising to 0.5% at 10Hz and 4% at 10MHz.

The square wave has a rise and fall time (10% to 90%) of<40ns, with

symmetry of 99% up to 1MHz.

The half watt of power over the entire range is outstanding for a general

oscillator, and along with a frequency response of 0.025dB, and frequency of

0.002%, makes the Model 4300B ideal for meter calibration, response

measurements and amplifier testing.

Unavoidable capacitive loading limits the usefulness of any generator without

low internal impedance and high power output ability.

The 50 ohm impedance minimizes signal losses due to resistive and capacitive

loading, and the half watt of power is essential for driving loads without over

loading.

Attenuation calibration of 0.2dB accuracy is obtained by means of an 8

position push-button switch calibrated in 10dB steps.

A continuous output control combined with the attenuator provides 90dB of

attenuation. Amplitude stability is within ±0.02%.

LC OSCILLATOR:

An ideal oscillator is an active device that produces a‟ single frequency output

for a DC input.

Moreover, the signal exists as a purely sinusoidal waveform with a fixed, with

respect to time, output power and frequency.

However, in practice the output signal is not fixed or confined to a single

frequency.

If one views the spectrum of an oscillator, it‟ appears as a continuum of

frequencies with decreasing amplitude distributed about the desired frequency.

This “sideband” noise is referred to as phase noise.

In a typical application one specifies the phase noise from the desired

frequency in dBc per Hz.

For example, at I KHz offset t phase noise must be greater than 90 dBc per Hz.

The “cleaner an oscillator the lower the phase noise.

Another „deviation from the ideal oscillator occurs in the „frequency stability

with respect to time;

This is due to aging and thermal variation of the resonator an surrounding

circuitry.

Thus, one usually specifies an aging limit and temperature stability factor.

Frequency stability, over a broad range of temperature, is usually

accomplished by employing a biasing network of thermistors that compensate

the oscillator circuit with a quadratic least-squares fit.

This class of oscillator is, termed temperature compensated crystal oscillator.

However, the best stability obtainable usually ,on the order of 1 ppb.

Higher stability, on the order; of 1 ppb, is achievable using ovenized crystal

oscillators, or OCXO‟s.

These oscillators have a built-in oven that keeps the crystal at a constant

temperature typically equal to the turning point of the crystal.

Most engineering applications require a frequency source that is electronically

tunable.

This is a necessity for any modulation scheme used in information transfer.

Tuning is typically accomplished by the use a varactor diode in the resonant

circuit. The diode capacitance is a function of the applied voltage.

Thus, the applied voltage controls the output frequency of the oscillator.

The prefix for such a device is a VC, or voltage controlled.

Therefore for example a voltage controlled crystal oscillator is called a

VCXO.

When the voltage tuning and temperature compensating features are

combined it is called a VCTCXO or TCVCXO.

If an inductor or micro strip is used as the resonator the nomenclature VCO is

used.

Similarly a dielectric oscillator is termed a DRO. In the case of no temperature

compensation or voltage control the device is called a clock oscillator.

These are primarily used as fixed reference sources for digital circuits, where

stability is not as critical.

Frequency ranges, stability, and phase noise differ for each technology.

LC oscillators are great for low stability, broad tuning, and inexpensive

applications.

The frequency range is confined to below 3 GHz with noise floors near 120

dBc per Hz.

Micro strip is similar to LC but spans from I GHz and up with much better

stability.

DRO‟s have a similar frequency range as micro strip but offer better noise

characteristics.

However, tuning range is much less Crystal oscillators or XO‟s offer the

greatest stability but suffer from the lowest tuning range.

Phase noise is typically the best for this group of oscillators, particularly for

the OCXO‟s.

The frequency range is limited to below 600 MHz.

Early frequency standards were simply variable tuned circuits, known as wave

meters.

These instruments were calibrated against the output of a rotary high-

frequency alternator whose frequency, and its harmonics, was determined

from the constants of the machine and its speed of rotation at that time, the

alternator was the only source of accurate calibrating frequencies.

The wave meter is subject to considerable error and, even with present

precision manufacturing and calibrating facilities, the dependable accuracy is

in the neighborhood of only 0.1% to 0.25%.

While the wave meter does have a definite place in radio engineering, its

inherent inaccuracies are far too great for frequency standardization purposes.

2.16 QUARTZ CRYSTAL CONSTRUCTION:

In case of LC and RC oscillators, the frequency of operation does not remain

strictly constant. The reason is that the values of resistors and inductors, which are

the frequency determining factors, changes with temperature.

For high degree of frequency stability, crystal oscillators are. used. Quartz

crystals are generally used in crystal oscillators.

The principle of crystal oscillators depends upon piezoelectric effect.

PIEZOELECTRIC EFFECT:

The natural shape of a quartz crystal is hexagonal.

When a wafer is cut such that the flat surfaces are perpendicular to X-axis, it is

called x cut crystals.

On the other hand, when a wafer is cit such that flat surfaces are perpendicular to

Y-axis, it is called as y cut crystals.

The crystals exhibit the property that when a mechanical stress is applied across

one face of the crystal, a potential difference is developed across the opposite

faces of the crystal.

Conversely, when a potential difference is applied across one faces, a mechanical

stress is produced along other faces.

This is known as piezoelectric effect.

When a piezoelectric crystal is subjected to a proper alternating potential, it

vibrates mechanically.

The amplitude of mechanical vibrations become maximum when the frequency of

alternating voltages is equal to the natural frequency of the crystal.

WORKING OF QUARTZ CRYSTAL:

In order to use the crystal in electronic circuit, it is placed between two metal

plates. The arrangement is equivalent to a capacitor with crystal as dielectric as

shown below.

When an alternating voltage is applied, the crystal starts vibrating with the

frequency of applied voltage.

If the frequency of applied voltage is made equal to the natural frequency of

crystal, resonance takes place and crystal vibrates with maximum amplitude.

EQUIVALENT CIRCUIT OF CRYSTAL:

The equivalent circuit of a crystal is shown below.

When the crystal is not vibrating, it is equivalent to a capacitance C

This is due to the fact that two metal plates are separated by a dielectric.

The vibrating crystal can be represented by a series LCR circuit shunted by

Cm .

The inductance L is electrical equivalent of mass of vibrating crystal, C is

electrical equivalent of mechanical compliance and resistance R represents the

electrical equivalence of mechanical friction.

The circuit has the following two resonant frequencies:

Lower series resonance frequency fs.

Parallel resonant frequency fp.

LOWER SERIES RESONANCE FREQUENCY:

At this frequency, the crystal offers a very high impedance to external circuit.

Crystals are available at frequencies of 15 KHz and above.

Commercially available crystals can „generally be used in the frequency range

about 15 KHz to 10MHz.

The values of L,C,R,Cm are such that the two frequencies fs and fp differ by very

small amount.

This fact gives rise to great frequency stability of crystal oscillator.

The resonant frequencies are temperature dependent.

The frequency difference can be made less that 1 part in 1010

by keeping the

crystal in temperature controlled ovens.

2.17 CRYSTAL OSCILLATOR:

A variety of crystal oscillator circuit is possible.

The below figure shows a transistor crystal oscillator suggested by Pierce.

In the circuit, R R2 and Re provide a voltage divider stabilized d.c. bias circuit.

The Capacitor Ce provides a.c. bypass of emitter resistor.

The capacitor C blocks any d.c. between collector and base.

The RFC provides d.c. collector load and also prevents any a.c. signal from

entering the d.c. supply.

Here the crystal is excited in series resonance mode because it is connected as

series element in feedback path from collector to base.

ADVANTAGES:

They have a high order of frequency stability.

The quality factor (Q) of the crystal is very high.

The Q factor of the crystal may be high as 10,000 compared to about 100 of L-C

tank.

DIS ADVANTAGES:

They are fragile and consequently can only be used in low power circuits.

/The frequency of oscillations cannot be changed appreciably.

Use Of Logic Gates As Linear Amplifiers, Oscillator And Clock Generator uits

Using Logic Gate Amplifiers:

LOGIC GATES AS LINEAR AMPLIFIERS:

It will be shown that the Digital Linear Amplifier offers a new level in transfer

function linearity since it becomes virtually impossible to stray away from

digitized linear transfer function.

It will also be shown that it offers a very high degree of power efficiency since

linear amplifiers are not required.

The power signal sources are simply gated on or off and may be operating near or

in saturation.

A ten example of a Digital Amplitude Modulator was presented in the first of

these two on the subjects of the Digital Amplitude Modulator and the Digital

Linear amplifier.

The 10-bit straight binary representation of the modulating voltage wave- is used

to turn on the drive to ten corresponding binarily related RF carrier power sources

which are summed by means of a cascade of isolated 3 dB hybrid power

combiners.

The Digital Amplitude Modulator is reproduced here in the figure:

OBTAINING DIGITAL LINEAR AMPLILFICATION:

A modulated signal may be fully described by the position of its voltage vector,

V(t) (or equivalently, its current vector) in the two dimensional plane described by

polar coordinates where R(t) represents the vector magnitude as function of time.

In cases involving SSB, VSB, the X-QAMs or the XVSBs where both amplitude

and phase modulation take place, it is not sufficient to simply amplitude modulate

as the method of Figure suggests.

A means to derive the required simultaneous phase modulation of the carrier

generator is also required.

Figure below shows an approach where the amplitude and phase modulation is

applied to a low signal level modulator designed for the fonts desired as if it were

to be used in an “ordinary scheme” of IF modulation,up conversion and

amplification such as that use for high high Definition Television or Digital

Television Broadcast, DTV.

The signal to be transmitted is complete at the IF stage even though it is not on

frequency for transmission.

It may also be spectrally inverted if high side RF conversion is the standard, but it

is the lF signal that contains all of the amplitude and phase information required to

continue with the derivation of the Digital Linear Amplifier.

Figure above shows the first step in the derivation of the Digital Linear Amplifier.

A baseband signal is modulating an IF carrier as usual for the format and system

of choice.

The modulated IF signal may be SSB, analog television which is VSB, a digital

format such as one of the QAMs or any signal which is planar, i.e. does not

have orthogonal carriers.

The IF signal is split into two paths.

One path demodulates the amplitude with no regard to phase such as a simple

diode detector.

The other is limited or clipped then phase detected with no regard to amplitude.

Levels at adjusted according to system needs.

Since the IF signal is not yet on the transmission frequency, the phase detected

signal in figure may be up-convert with a mixer and local oscillator.

Phase information is not lost during the up conversion since it simply adds another

term to the argument of the up-conversion oscillator.

Figure below shows the Digital Linear Amplifier with the amplitude and phase

information added back into the system for proper reconstruction of the complete

signal at the RF frequency not shown in figure below are leveling circuit Digital

delay lines are necessary in the lines.

PRACTICAL CONSIDERATIONS:

It may seem that the Digital Linear Amplifier shown in figure above is cumbersome

and may be difficult to keep in alignment.

Some considerations include:

a, Proper time alignment of the signals arriving at the power combiners.

b. Turn-on turn-off (rise and fall) times of the power amplifiers.

c. Regulation of the output power of all amplifiers.

d. The amplifiers must be designed as if they are gated on all of the time or for a

period as short as sample period.

e. Maintaining ten bit coordination in all ways.

• For (a), digital delay lines are available in fractional nanosecond and tens of

nanosecond intervals. Generally these devices are switch or logic level selectable and

certainly may be controlled by a microprocessor.

• For (b), rise and fall times required are inversely proportional to modulating

bandwidth. An experimental analog television transmitter showed that the bandwidth

of each amplifier should be at least 20 times greater than the modulation signal for

switching glitches to be lower than 60 dB down from the carrier.

• For analog television with a 4.18 MHz bandwidth, the rise and fall times for

each amplifier should be less than 12 nS.

For SSB voice communication, the rise and fall times need not be nearly as past, but

on the order of 17µs.

• Considerations (c ) and (d) are related in that the regulation bandwidth of the power

supplies for the amplifiers must be such that as an amplifier generates heat when it is

driven, its gain will decline causing the output power to droop.

• This must be sensed and the power supply voltage automatically adjusted

accordingly.

• Consideration (e) requires that all amplifiers must be connected to a common

reference in order to maintain the proper binary power relationship as a function of

time.

• This may be nearly impossible in a ten bit system, but there is a way to greatly

reduce the complexity of the Digital Linear Amplifier.

• It was mentioned early on that there are several reasons why the Digital Linear

Amplifier is superior to the conventional amplifier.

One is the inherent reduced inter modulation distortion since it is virtually impossible

to deviate from a straight-line transfer curve.

• The other is power efficiency since none of the amplifiers need to be linear. A look

at power efficiency indicates that the Digital Linear Amplifier is most efficient when

it is making the highest power.

• The efficiency of the power combiner cascade is theoretically 100% when all

amplifiers are gated on.

• It declines from there, but when less power is required down the slope of the

modulating signal, efficiency is a less important issue.

• Efficiency is the highest when the most power is needed.

The overall system power efficiency is then the efficiency of the power amplifiers

(assuming that the combiners are lossless) which may be in the eighties of percent if

class C amplifiers are used.

Comp1exity may be greatly reduced with very little sacrifice in power

efficiency and no reduction in linearity if it is realized that 87.5% of the

power generated by the ten bit Digital Linear Amplifier is generated in the

three highest o significant bits.

CONCLUSION:

The Digital Linear Amplifier concept and theoretical design has been presented with

he hope that it will find its rightful place in the digital age of the twenty-first century.

It has been proven only in the laboratory for analog television at a peak power of 1000

watts, but the concept is so simple and elegant that it deserves in other areas of RF

power transmission.