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# Hartley Oscillator

A very popular **local oscillator** circuit that is mostly used in **radio receivers** is the **Hartley Oscillator** circuit. The constructional details and operation of a Hartley oscillator are as discussed below.

## Construction

In the circuit diagram of a Hartley oscillator shown below, the resistors R_{1}, R_{2} and R_{e} provide necessary bias condition for the circuit. The capacitor C_{e} provides a.c. ground thereby providing any signal degeneration. This also provides temperature stabilization.

The capacitors C_{c} and C_{b} are employed to block d.c. and to provide an a.c. path. The radio frequency choke (R.F.C) offers very high impedance to high frequency currents which means it shorts for d.c. and opens for a.c. Hence it provides d.c. load for collector and keeps a.c. currents out of d.c. supply source

### Tank Circuit

The frequency determining network is a parallel resonant circuit which consists of the inductors L_{1} and L_{2} along with a variable capacitor C. The junction of L_{1} and L_{2} are earthed. The coil L_{1} has its one end connected to base via C_{c} and the other to emitter via C_{e}. So, L_{2} is in the output circuit. Both the coils L_{1} and L_{2} are inductively coupled and together form an **Auto-transformer**.

The following circuit diagram shows the arrangement of a Hartley oscillator. The tank circuit is **shunt fed** in this circuit. It can also be a **series-fed**.

## Operation

When the collector supply is given, a transient current is produced in the oscillatory or tank circuit. The oscillatory current in the tank circuit produces a.c. voltage across L_{1}.

The **auto-transformer** made by the inductive coupling of L_{1} and L_{2} helps in determining the frequency and establishes the feedback. As the CE configured transistor provides 180^{o} phase shift, another 180^{o} phase shift is provided by the transformer, which makes 360^{o} phase shift between the input and output voltages.

This makes the feedback positive which is essential for the condition of oscillations. When the **loop gain |βA| of the amplifier is greater than one**, oscillations are sustained in the circuit.

### Frequency

The equation for **frequency of Hartley oscillator** is given as

$$f = \frac{1}{2 \pi \sqrt{L_T C}}$$

$$L_T = L_1 + L_2 + 2M$$

Here, **L _{T}** is the total cumulatively coupled inductance;

**L**and

_{1}**L**represent inductances of 1

_{2}^{st}and 2

^{nd}coils; and

**M**represents mutual inductance.

**Mutual inductance** is calculated when two windings are considered.

### Advantages

The advantages of Hartley oscillator are

Instead of using a large transformer, a single coil can be used as an auto-transformer.

Frequency can be varied by employing either a variable capacitor or a variable inductor.

Less number of components are sufficient.

The amplitude of the output remains constant over a fixed frequency range.

### Disadvantages

The disadvantages of Hartley oscillator are

- It cannot be a low frequency oscillator.
- Harmonic distortions are present.

### Applications

The applications of Hartley oscillator are

- It is used to produce a sinewave of desired frequency.
- Mostly used as a local oscillator in radio receivers.
- It is also used as R.F. Oscillator.