Hartley Oscillator

Hartley Oscillator

AU : May-04, 10, 13, 17, Dec.-10, 11, 12, 13, 14

• It uses two inductive reactances and one capacitive reactance in its feedback network. Depending on the active device used in amplifier stage, the two types of Hartley oscillators are,

i) BJT Hartley oscillator ii) FET Hartley oscillator.

1. Transistorised Hartley Oscillator

• The Fig. 10.9.1 shows the practical circuit of Hartley oscillator using BJT as an active device. The resistances R₁ R₂ and R_E are the biasing resistors.

• The RFC is radio frequency choke whose reactance value is very high at high frequency and can be treated as open circuit. While for d.c. operation, it is shorted hence does not cause problems for d.c. operation.

• Due to RFC, the isolation between a.c. and d.c. operation is achieved. The Ccl and CC2 are the coupling capacitors while CE is the emitter bypass capacitor. The CE amplifier provides phase shift of 180°.

• In the feedback circuit, as the centre of Ll and L2 is grounded, it provides additional phase shift of 180°. This satisfies Barkhausen condition. In this oscillator,

• The inductance Li + L2 is equivalent inductance denoted as Leq. To satisfy I API = 1, the hfe of the BJT used must be L₁/L₂.

H_fe = L₁ / L₂

• Practically Li and L2 are wound on a single core and there exists a mutual inductance M between them. The circuit is shown in the Fig. 10.9.2.

In this case, L_eq  = L₁ + L₂ + 2_M

• If capacitor C is kept variable, frequency can be varied over wide range.

2. Derivation of Frequency of Oscillations

• The output current is collector current which is h_fe I_b' where I_b is base current. Assuming coupling capacitors shorted, the capacitor C gets connected between collector and base.

• As emitter is grounded for a.c. analysis, L1 is between emitter and base while L2 is between emitter and collector. The equivalent circuit is shown in the Fig. 10.9.3.

• h_ie is the input impedance of the transistor. The output current is I_b while input current is hfe Ib- Convert current source to voltage source as shown in the Fig. 10.9.4.

• In practice, and L2 may be wound on a single core so that there exists a mutual inductance between them denoted as M.

• In such a case, the mutual inductance is considered while determining the equivalent inductance Leq. Hence,

L_eq = L₁ + L₂ + 2 M

• If L₁ and L₂ are assisting each other then sign of 2M is positive while if L-^ and L2 are in series opposition then sign of 2M is negative.

• The expression for the frequency of the oscillations remain same as given by equation (10.9.3).

• A practical circuit where the mutual inductance exists between L1 and L2, of transistorised Hartley oscillator is shown in the Fig. 10.9.5.

Ex. 10.9.1 A Hartley oscillator is found to oscillate at 1.66 MHz. The oscillator uses a capacitor of 1 nF in tuned circuit. If one of the inductors in tuned circuit is 5 pH, find the value of other inductor.

Sol. :

Ex. 10.9.2 Calculate the frequency of oscillations of a Hartley oscillator having = 0.5 mH, =1 mH and C = 0.2 μF.

Ex. 10.9.3 In a transistorised Hartley oscillator the two inductances are 2 mH and 20 pH while the frequency is to be changed from 950 kHz to 2050 kHz. Calculate the range over which the capacitor is to be varied.

Sol. : The frequency is given by,

Hence C must be varied from 2.98 pF to 13.89 pF, to get the required frequency variation.

Ex. 10.9.4 In a Hartley oscillator, L_I = 15 mH and C = 50 pF. Calculate L₂ for a frequency of 168 kHz. The mutual inductance between L₁ and L₂ is 5 pH. Also find the required gain of the transistor to be used for the oscillations.

Sol. : For a Hartley oscillator,

3. Advantages, Disadvantages and Applications

• The advantages are,

i) The frequency can be easily varied by variable capacitor.

ii) The output amplitude remains constant over the frequency range.

iii) The feedback ratio of L1 to L2 remains constant.

iv) It can be operated over wide range of frequency.

• The disadvantages are,

i) The output is rich in harmonics hence not suitable for pure sine wave requirement.

ii) Poor frequency stability. 

• The applications are,

i) Used as local oscillator in T.V. and radio receivers.

ii) In function generators.

iii) In radio frequency sources.

Review Questions

1. Draw and explain the operation of a Hartley oscillator. Derive the equation for fr and h_fe.

AU : May-04, 10, 13, 17, Dec.-l0, 11, 18, Marks 16

2. Draw the circuit diagram and explain the principle of operation of Hartley oscillator.

AU : Dec.-12, 13, 14, Marks 8

3. A Hartley oscillator circuit has C = 500 pF, L1 = 20 µH and L₂ = 2 mH. Find the frequency of oscillations.     

(Ans.: 45.01 kHz)

4. In a Hartley oscillator Lj =20 qH, = 2 mH and C is variable. Find the range of C if frequency is to be varied from 1 MHz to 2.5 MHz. Neglect mutual inductance.

(Ans.: 2.0244 pF to 12.6525 pF)