1. Chapter 5 – Oscillators – Part 2
LC Oscillators
Hartley Oscillator
Crystal Oscillator

2. LC Tuned Oscillators LC Oscillators RC Oscillators Phase-Shift
Wien-Bridge

3. Checkpoint – 1: Calculate the operating frequency of the following oscillator circuit, if C1 = μF and L1 = 175 mH. (Ans f = kHz).
Checkpoint – 2: Calculate the operating frequency of the following oscillator circuit, if C1 = μF and L1 = 150 mH

4. Block diagram of LC Oscillators

5. 1. Hartley Oscillator C B
A parallel LC resonator connected between collector and base.
Feedback is achieved by way of an inductive divider.
Oscillating frequency is determined by the resonance frequency. Resonant frequency

6. Checkpoint – 1: A single tuned amplifier with capacitive coupling consists tuned circuit having R=10, L=20mH and C=0.05F. Determine the (i) Resonant frequency (ii) Q-factor of the tank circuit (iii) Bandwidth of the amplifier.

7. Checkpoint – 2: A Hartley Oscillator circuit having two individual inductors of 0.5mH each (L1 = L2 = 0.5mH), are designed to resonate in parallel with a variable capacitor that can be varied from 100pF to 500pF. Determine the upper and lower frequencies of oscillation and also the Hartley oscillators bandwidth.

8. Transconductance, gm and oscillation condition

10. Op- Amp block diagram of Hartley Oscillator
The frequency selection network provides a phase shift of 180o.
Amplifier introduces
shift of 180o

11. 2. Colpitts Oscillator
A parallel LC resonator connected between collector and base.
Feedback is achieved by way of an capacitive divider.
Oscillating frequency is determined by the resonance frequency. Resonant frequency

12. Checkpoint – 3: The capacitance values of the two capacitors C1 and C2 of the resonant circuit of a colpitt oscillator are C1 = 20pF and C2 = 70pF.The inductor has a value of 22μH. What is the operating frequency of oscillator?

13. Checkpoint – 3: Calculate the operating frequency of the following oscillator circuit, if C1 = μF, C2 = μF, and L1 = 50 mH.
Checkpoint – 3: Calculate the operating frequency of the following oscillator circuit, if C1 = μF, C2 = μF, and L1 = 80 mH.

14. Colpitts Oscillator tends to be more stable than the Hartley
Hartley Oscillator
Colpitts Oscillator
Colpitts Oscillator tends to be more stable than the Hartley
Oscillator.
Hartley Oscillator
Colpitts Oscillator
The Hartley Oscillator uses a
tapped coil for the feedback
for oscillation, and these tend to be more difficult to make.
It is easier to tap 2 capacitors in series, as well as being cheaper to make, than to use a tapped coil for feedback purposes.
It is also easier to Frequency
Modulate the Colpitts design.

15. Crystal Oscillators
A piezoelectric crystal. (a) Circuit symbol.(b) Equivalent circuit
L, C, and R are related to the properties of the quarts crystal.
For a 90 kHz crystal, L = 137 H, Cs = pF, R = 15 k, and Cp = 3.5 pF ( Cp is the electrostatic capacitance of the electrodes)

16. (neglecting the small
resistance r, ).
A series resonance at
A parallel resonance at

17. Crystal reactance versus frequency (neglecting the small resistance r, ).
Parallel resonant frequency is always greater than the series resonant frequency.
Crystal reactance ( XL + XC) is capacitive both below and above the resonant frequencies.

18. Exercise : 1 - A piezoelectric crystal has L = 137 H, Cs = 0
Exercise : 1 - A piezoelectric crystal has L = 137 H, Cs = pF, and Cp = 3.5 pF. Find the parallel resonant
frequency and series resonant frequency.

19. Frequency response of a crystal

20. Series-tuned circuit
A series-tuned circuit has a minimum impedance at resonance.
Above resonance the series-tuned circuit acts INDUCTIVELY, and below resonance it acts CAPACITIVELY.
In other words, the crystal unit has its lowest impedance at the series-resonance frequency.
The impedance increases as the frequency is lowered because the unit acts as a capacitor.
The impedance of the crystal unit also increases as the frequency is raised above the series-resonant point because the unit acts as an inductor.
Therefore, the crystal unit reacts as a series-tuned circuit.

21. Parallel-tuned circuit
Since the series-tuned circuit acts as an inductor above the resonant point, the crystal unit becomes equivalent to an inductor and is parallel with the equivalent capacitor Ceq.
At some frequency above the series-resonant point, the crystal unit will act as a parallel-tuned circuit.
A parallel-tuned circuit has a MAXIMUM impedance at the parallel-resonant frequency and acts inductively below parallel resonance.
Therefore, at some frequency, depending upon the cut of the crystal, the crystal unit will act as a parallel-tuned circuit.

22. 2. A piezoelectric crystal has
Cs= .01pF
r = 5 Ω
Cp = 20 pF .
Find the parallel resonant frequency and series
resonant frequency.
Find the capacitance reactance at series resonant
frequency .
Find the inductance reactance at parallel resonant
frequency.
Find the capacitance reactance at parallel resonant

23. Amplifier introduces shift of 180o Z2 Z3 Z1
The frequency selection network provides a phase shift of 180o.
Amplifier introduces
shift of 180o Z1 Z2 Z3