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EMT212 – Analog
Electronic II
LC Oscillator
1
Oscillators With LC Feedback
Circuits
For frequencies above 1 MHz, LC feedback oscillators
are used.
We will discuss the Colpitts, Hartley and crystalcontrolled 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.
2
LC Oscillator circuit using an ideal Op-amp
with non-zero output impedance Ro and its
equivalent ideal circuit
3
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
4
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,
5
Thus,
where ω0 is the oscillation frequency. Using the two previous
equation we finally get
Since (ω0) 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.
6
Oscillators With LC Feedback
Circuits
oscillator circuit name depending on the choice of the reactance
7
Colpitts Oscillators
The Colpitts oscillator utilizes a tank circuit (LC) in the feedback
loop. The resonant frequency can be determined by the formula
below.
1
fr 
2 LCT
1
1
1


CT C1 C2
8
Colpitts Oscillators
Conditions for oscillation and start up

Vf
Vout
Av 
IX c1 C2


IX c 2 C1
1

C1
Av 
C2
9
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.
fr 
1
2 LT C
LT  L1  L2
L1

L2
1
L2
Av  
 L1
10
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.
11
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.
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