1. 1 LC Oscillator EMT212 – Analog Electronic II

2. 2 Oscillators With LC Feedback Circuits For frequencies above 1 MHz, LC feedback oscillators are used. We will discuss the Colpitts, Hartley and crystal- controlled oscillators. BJT amplifier can usually obtain higher oscillating frequency than using standard operational amplifier. In this case the high frequency hybrid - model [1] must be used to properly model the transistor behavior.

3. 3 LC Oscillator circuit using an ideal Op-amp with non-zero output impedance Ro and its equivalent ideal circuit

4. 4 Let’s suppose that the amplifier is ideal but has a non zero output resistance Ro Applying the voltage divider equation twice we have the two equation and

5. 5 After some algebra we finally get Let’s consider the case of the LC tunable oscillators, i.e. the impedances are purely reactive (real part equal to zero) Then the previous ß becomes, For ß to be real,

6. 6 Thus, where ω 0 is the oscillation frequency. Using the two previous equation we finally get Since (ω 0 ) must be positive, X1 and X2 must have the same sign, which means that they have to be the same kind of reactance, two capacitors or two inductors.

7. 7 Oscillators With LC Feedback Circuits oscillator circuit name depending on the choice of the reactance

8. 8 Colpitts Oscillators The Colpitts oscillator utilizes a tank circuit (LC) in the feedback loop. The resonant frequency can be determined by the formula below.

9. 9 Colpitts Oscillators Conditions for oscillation and start up

10. 10 Hartley Oscillators The Hartley oscillator is similar to the Colpitts. The tank circuit has two inductors and one capacitor. The calculation of the resonant frequency is the same.

11. 11 Crystal Oscillators The crystal-controlled oscillator is the most stable and accurate of all oscillators. A crystal has a natural frequency of resonance. Quartz material can be cut or shaped to have a certain frequency. We can better understand the use of a crystal in the operation of an oscillator by viewing its electrical equivalent.

12. 12 Oscillators With LC Feedback Circuits Since crystal has natural resonant frequencies of 20 MHz or less, generation of higher frequencies is attained by operating the crystal in what is called the overtone mode.