LC Oscillators
• LC parallel resonant circuit
• used for high frequency domain
• frequency selective feedback network
Zech  Z C || Z L
Zech 
L/C
1 

j  L 

C 

1
ZC 
jC
Z L  jL
Resonance frequency:
Thompson’s relation
f0 
1
2 LC
The parallel LC circuit connected in series with a load acts as a
band-stop filter having infinite impedance at the resonant
frequency of the LC circuit.
1/7
How the LC circuit and the basic amplifier will be connected ?
Three points oscillator, one transistor amplifier
vo
Principle
scheme,
for variable
signals
The basic amplifier is an inverting one (CE), so the divider Z2, Z3
must introduce a -180o phase shift; Z2, Z3 will have opposite signs.
Z3 and Z1 should be similar to obtain an LC parallel resonant
circuit between collector and base.
2/7
Small-signal equivalent circuits for three points oscillators
vo
vo
C1C3
C
C1  C3
f0 
1
2 L2C
L  L1  L3
f0 
1
2 LC2
3/7
Optional
+VPS
+VPS
Colpitts
Hartley
4/7
Quartz-crystal oscillator
C p  C s
R  very low value
can be neglected
• Series resonance
fs 
symbol
equivalent
circuit
• Parallel resonance
C
Cs C p
Cs  C p
 Cs
1
2 LCs
range: tens of KHz … hundreds of MHz
fp 
1
2 LC
 fs
5/7
Optional
+VPS
quartz-crystal
sinusoidal oscillator
• advantage: very stable frequency, high quality factor
• disadvantage: oscillates on a fixed frequency (quartz frequency)
6/7
Quartz is amongst one of the most common minerals in the
Earth's continental crust. It has a hexagonal crystal structure
made of trigonal crystallized silica (silicon dioxide, SiO2)
The crystal oscillator circuit sustains oscillation by taking a
voltage signal from the quartz resonator, amplifying it, and
feeding it back to the resonator. The rate of expansion and
contraction of the quartz is the resonant frequency, and is
determined by the cut and size of the crystal.
During startup, the circuit around the crystal applies a random noise
(ac)signal to it, and purely by chance, a tiny fraction of the noise
will be at the resonant frequency of the crystal. The crystal will
therefore start oscillating in synchrony with that signal. As the
oscillator amplifies the signals coming out of the crystal, the
crystal's frequency will become stronger, eventually dominating the
output of the oscillator. Natural resistance in the circuit and in the
quartz crystal filter out all the unwanted frequencies.
7/7