Popular sinewave feedback L-C tuned oscillators are listed below. These are principally used for generating RF oscillations.

- Tuned Collector Oscillator
- Tuned Based Oscillator
- Hartley Oscillation
- Colpitts Oscillator
- Clapp Oscillator
- Crystal Oscillator

## Tuned Collector Oscillator

Figure 1 gives the basic circuit. A parallel tuned L-C circuit placed in the collector circuit constitutes the load impedance and determines the frequency of oscillation. The output voltage developed across the tuned circuit is inductively coupled to the basic circuit through the coil L_{2}. The winding direction of the two coils L_{1} and L_{2} are so chosen that positive feedback takes place from the collector circuit to the base circuit. the dots are placed on coils L_{1} and L_{2}. When the dotted end of L_{1} is positive, the dotted end of L_{3} also become positive.

The tuned circuit in the collector circuit resonates at frequency . At this frequency, the impedance of the tuned circuit is purely resistive and large. The ac voltage drop across the inductor L_{1} from collector to ground is 180^{0} out of phase with the voltage from base to ground. The transformer winding directions are so chosen as to produce a phase shift of another 180^{0} assuming the secondary to be unloaded. Then the total loop phase shift is exactly 360^{0} or 0^{0} and oscillations are produced at the frequency of resonance . However, the secondary is always loaded to some extent. Hence the frequency of oscillation i.e. the frequency at which Barkhausen criterion is satisfied differs from the frequency of resonance of the tuned circuit.

Analysis using small signal equivalent circuit for the transistor and the Barkhausen criterion yields the following results:

- Condition for sustained oscillations:

…………………..(1)

Where M is the mutual inductance between coils L_{1} and L_{2} and R is the load resistance of the secondary coil L_{2} reflected to the primary coil L_{1}.

Resistances of the coils L_{1} and L_{2} have been neglected.

- Frequency of oscillation:

……………..(2)

Where is the frequency of resonance of L_{1} and L_{2} and equals .

From Eq. (2), we conclude that in tuned collector oscillator, the frequency of oscillation exceeds the frequency of resonance of the tuned circuit.

## Tuned Based Oscillator

Figure 2 gives the basic circuit. A parallel tuned L-C circuit placed in the base-to-ground circuit determines the frequency of oscillation. The output developed across the tuned circuit is inductively coupled to the collector circuit through the coil L_{2}. The winding direction of the coils L_{1} and L_{2} are so selected that positive feedback takes place from the collector circuit to the base circuit resulting in oscillations. The tuned circuit in the base circuit resonates at frequency . At this frequency, the impedance of the tuned circuit is purely resistive and large.

The voltage drop across the inductor L_{2} is 180^{0} out of phase with the base to ground voltage. The transformer winding direction are so chosen as to produce phase shift of another 180^{0} assuming the oscillator to be non-loaded. Then the total phase shift is exactly 360^{0} or zero degree. However, the secondary is always loaded to some extent. Hence the frequency of oscillation differs slightly from the frequency of resonance of the tuned circuit.

## Hartley Oscillator

Figure 3 gives thew circuit of Hartley oscillator using BJT. The collector supply voltage Vcc is applied to the collector through inductor L whose reactance is high compared with that of L_{2} and may, therefore, be neglected. Capacitor C_{b} has a low reactance at the frequency of oscillation and may also be neglected in the equivalent circuit. At dc i.e. zero frequency, C_{b}, therefore, prevents collector supply Vcc from getting short circuited by L in series with L_{2}. The parallel combination of R_{e} and C_{z} in conjunction with= R_{1} – R_{2} combination provides stabilized self-bias. The circuit operates as class C amplifier with infinity gain. The tuned circuit constituted by L_{1} – L_{2} – C determines the frequency of resonance. Since the tuned circuit extends right from the input circuit, the feedback needed for sustained oscillation takes place through the tuned circuit itself.

**Result of Analysis:** Analysis making use of the equivalent circuit and the Barkhausen criterion yields the following results:

- Condition for sustained oscillations ………(3)

If there exists mutual inductance M between coils L_{1} and L_{2} then the condition for sustained oscillation is,

…….(4)

- Frequency of oscillation,

….(5)

Where and ,

…..(6)

From Eq. (5) we conclude that in Hartley oscillator, the frequency of oscillation is slightly smaller than the frequency of series resonance of L_{1}, L_{2} and C.

## Colpitts Oscillator

Figure 4 gives the basic circuit. The collector supply voltage Vcc is applied to the collector through the inductor L_{c} whose reactance is high compared with the reactance of capacitor C_{2}. Hence L_{c} may be omitted from the equivalent circuit. Parallel combination of R_{c} and C_{z} along the resistor R_{1} – R_{2} provides the stabilized self-bias. The tuned circuit consists of capacitor C_{1} and C_{2} and inductor L. It extends from the collector circuit to the base circuit and basically determines the frequency of oscillation. The feedback is through the tank circuit itself.

**Result of Analysis:** Analysis making use of the small signal h-parameter model and the Barkhausen criterion yields the following results:

- Condition for sustained oscillation …..(7)
- Frequency of oscillation …….(8)

Where and and is the frequency of resonance of C_{1}, C_{2} and L and is given by

…(9)

From Eq. (8) we conclude that in the case of Colpitts oscillator, the frequency of oscillation is slightly greater than the frequency of series resonance of C_{1}, C_{2} and L.

## Clapp Oscillator

Figure 5 gives the basic circuit of Clapp oscillator. It is modified version of Colpitts oscillator. The main difference between the two circuits lies in the introduction of another capacitance C_{3} in series with the coil L.

The capacitance C_{1} is made so large as to reduce the effect of collector capacitance variation due to collector voltage change. The emitter junction capacitance depends on the emitter current. In the circuit of Fig 5, resistor R_{2} in the biasing network may be in the form of a thermistor so that the emitter current gets reduced at high temperatures.

The frequency of oscillation is given by,

……(10)

Capacitors C_{1} and C_{2} are kept fixed while capacitor C_{3} is used for tuning purpose.

Further

In that case, the frequency of oscillation is approximately given by,

……(11)

Thus, the frequency of oscillation is nothing but the frequency of series resonance of L and C_{3}.

This condition for sustained oscillation is, …..(12)

High frequency stability is obtained by (i) enclosing the entire circuit in a constant temperature chamber and (ii) by maintaining the operating voltage constant with the help of a zener diode.

## Crystal Oscillator

### Piezo-electric Quartz Crystal

For excellent stability of frequency of oscillation in the RF range, we may use a piezo-electric quartz crystal in place of the L-C tuned circuit in the oscillator. Fig 6 gives the electrical equivalent circuit of a piezo-electric quartz crystal.

In Fig 6, element R_{1} L_{2} C_{1} from a series resonance circuit resonating at frequency f_{s}. The impedance of this series circuit at resonance is restive and equal to R_{1}. Complete circuit including C_{2} along with R_{1} L_{2} C_{1} forms a parallel tuned circuit resonating at frequency f_{p}. under parallel resonance condition at f_{p}, the impedance of the complete tuned circuit is again resistive but extremely large. Frequency f_{p} is greater than f_{s} but extremely close to it. When piezo-electric quartz crystal is used in place of conventional L-C tuned circuit in an oscillator, the frequency of oscillation is determined by the value of elements R_{1} L_{1} C_{1} and C_{2} but this frequency must lie in the frequency range from f_{s} to f_{p}. Since f_{s} and f_{p} are extremely close, an extremely high order of stability of frequency of oscillation is obtainable in a crystal oscillator i.e. an oscillator using quartz crystal.

## Crystal Oscillator Circuit

A huge variety of crystal oscillator circuits are possible depending on (i) which active device is used, BJT or FET and (ii) part of the circuit where crystal is placed.

### Tuned Gate-Tuned Drain Crystal Oscillator

Figure 1 shows an FET crystal oscillator of tuned gate-tuned drain type. Here drain-to-gate capacitance C_{dg} forms the feedback path from drain (output) to the gate (input). Stray wiring capacitance C_{s} also gets added to this circuit. For sustained oscillation, it is necessary that the L-C tuned circuit in the drain circuit and the quartz crystal equivalent crystal equivalent circuit in the gate circuit be inductive. Hence this circuit will oscillate at a frequency which lies between the frequencies f_{s} and f_{p} of the crystal. Hence high stability of frequency of oscillation results.

### Colpitts Crystal Oscillator using BJT

Figure 2 shows crystal oscillator using Colpitts circuit using BJT. Here crystal is placed in place of inductor L of Colpitts tuned circuit. in this case also, the frequency od oscillation lies in the range determined by frequencies f_{s} and f_{p} of the quartz crystal.