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

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

Checkpoint – 1: Calculate the operating frequency of the following oscillator circuit, if C1 = 0.033 μF and L1 = 175 mH. (Ans f = 2.094 kHz). Checkpoint – 2: Calculate the operating frequency of the following oscillator circuit, if C1 = 0.047 μF and L1 = 150 mH

Block diagram of LC Oscillators

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

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.

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.

Transconductance, gm and oscillation condition

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

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

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?

Checkpoint – 3: Calculate the operating frequency of the following oscillator circuit, if C1 = 0.003 μF, C2 = 0.003 μF, and L1 = 50 mH. Checkpoint – 3: Calculate the operating frequency of the following oscillator circuit, if C1 = 0.005 μF, C2 = 0.005 μF, and L1 = 80 mH.

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.

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 = 0.0235 pF, R = 15 k, and Cp = 3.5 pF ( Cp is the electrostatic capacitance of the electrodes)

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

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.

Exercise : 1 - A piezoelectric crystal has L = 137 H, Cs = 0 Exercise : 1 - A piezoelectric crystal has L = 137 H, Cs = 0.0235 pF, and Cp = 3.5 pF. Find the parallel resonant frequency and series resonant frequency.

Frequency response of a crystal

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.

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.

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

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