Oscillators with LC Feedback Circuits

• LC Feedback elements are used for the generation of higher frequencies of oscillation.

• Because of lower unity gain frequency of most op amps, discrete transistors are often used as the gain elements in LC Feedback oscillators.

• Colpitts, Clapp, Hartley, Armstrong and Crystal controlled oscillators are the examples

The Colpitts Oscillator• LC feedback circuit provides the required

phase shift and acts as resonant filter that passes only the desired frequency of oscillation.

Conditions for Oscillation and Startup

• Values of C1 and C2 determine the attenuation as

or

But for Oscillation

For the oscillator to be self starting,

OR

Loading Effect on Feedback Circuit

Input impedance of the amplifier acts as a load on the resonant feedback circuit and reduces the quality factor of the circuit

When Q>10,

When Q<10, the resonant frequency is significantly reduced

To avoid this loading effect, we can use JFET instead of BJT as it has very high input impedance as compared to BJT.

The concept of Reflected Load and Impedance Matching using Transformer Coupling

Matching Audio amplifier with an output resistance of 800 ohm to an 8 ohm speaker using transformer coupling

The Clapp Oscillator

• Clapp oscillator is a variation of Colpitts

• An additional capacitance C3 in series with the inductor

• This new capacitance is in series with C1

and C2 within the tank circuit

• Total capacitance is given by

If C3 is much smaller than C1 and C2 ,then C3 almost entirely controls the resonant frequency

Since one end of each of C1 and C2 is grounded, junction capacitance and other stray capacitances appear in parallel with these altering their values

C3 is not affected yet and hence helps to provide a more accurate and stable frequency of oscillation

The Hartley Oscillator

OR

Loading Effect is the same as in the case of Colpitts, i.e, to reduce the quality factor hence reducing the resonant frequency.

The Armstrong Oscillator

•Uses transformer coupling for feedback provision of the signal voltage.

•Sometimes called tickler oscillator in reference to transformer secondary of tickler coil.

•Less common as compared to previous ones mainly because of transformer size and cost.

•The frequency of oscillation is set by the inductance of primary winding, Lpri in parallel with C1

Crystal Controlled Oscillators• Most stable and accurate type of feedback oscillators• Exhibits a very high Q (values of several thousand are

typical)• Piezoelectric crystal is used in the feedback loop for the

frequency control• Quartz crystal is normally used in electronic applications

in the form of a quartz wafer• Piezoelectric Effect: when a changing mechanical stress

is applied across the crystal to cause it to vibrate, a voltage is developed at the frequency of mechanical vibration

• Conversely when an ac voltage is applied across the crystal, it vibrates at the frequency of applied voltage

• The greatest vibration occurs at the natural resonant frequency.

• Natural resonant frequency is determined by the physical dimensions and by the way the crystal is cut.

Quartz wafer is mounted between two electrodes and enclosed in a protective can

Series-Parallel RLC circuit can operate either in series or parallel resonance

At the series resonance, the inductive reactance is cancelled by the reactance of CS and now RS determines the impedance of the crystal

Parallel resonance occurs when the inductance reactance and reactance of Cm

are equal

Parallel resonant frequency is usually at least 1kHz higher than the series resonant frequency

Crystal used as series resonant circuit

Maximum feedback is provided at series resonant frequency where impedance of the crystal is minimum.

CC is used to fine tune the oscillator frequency by pulling the resonant frequency of the crystal slightly up or down

Crystal used as parallel resonant circuit (modified Colpitts configuration)

Impedance of the crystal is maximum at parallel resonance and maximum voltage is develops across the capacitors

The voltage across the capacitor C1 is fed back to the input

Modes of Oscillation in the Crystals

There are two modes of oscillation

Fundamental Mode:

• It is the lowest natural resonant frequency of oscillation.

• It depends upon the crystal mechanical dimensions, type of cut and inversely proportional to the thickness of crystal slab.

• Upper limit on fundamental frequency is set by the thickness of crystal slab as it cannot be cut too thin without fracturing.

• For most crystals, this upper limit is less than 20MHz.

Overtone Mode:

• Overtones are the approximate integer multiples of the fundamental frequency

• Usually these are the odd multiples of the fundamental