LC oscillators :

• LC oscillator is a type of oscillator where a LC (inductor-capacitor) tank circuit is used for giving the required positive feedback for sustaining the oscillations. The LC tank circuit is also termed as LC resonant circuit or LC tuned circuit. According to the Barkhausen criterion for sustained oscillations, a circuit will sustain stable oscillations only for frequencies at which the loop gain of the system is equal to or greater than 1 and the phase shift between input and output is 0 or an integral multiple of 2π. LC oscillators can realized using BJT, FET, MOSFET, opamp etc. Typical applications of LC oscillators include RF signal generators, frequency mixers, tuners, sine wave generators, RF modulators etc.

Types : 

• Tuned collector oscillator.

• Tuned base oscillator.

• Hartley oscillator.

• Colpitts oscilllator.

• Clapp oscillator.

Resonant Frequency of a LC Oscillator : 

$f_r=\dfrac{1}{2\pi\sqrt{LC}}$

Where:

L is the Inductance in Henries

C is the Capacitance in Farads

ƒr is the Output Frequency in Hertz

 This equation shows that if either L or C are decreased, the frequency increases. This output frequency is commonly given the abbreviation of ( ƒr ) to identify it as the “resonant frequency”.

To keep the oscillations going in an LC tank circuit, we have to replace all the energy lost in each oscillation and also maintain the amplitude of these oscillations at a constant level. The amount of energy replaced must therefore be equal to the energy lost during each cycle.

The basic conditions required for an LC oscillator resonant tank circuit are given as follows.

• For oscillations to exist an oscillator circuit MUST contain a reactive (frequency-dependant) component either an “Inductor” or a “Capacitor” as well as a DC power source.
• In a simple inductor-capacitor, LC circuit, oscillations become damped over time due to component and circuit losses.
• Voltage amplification is required to overcome these circuit losses and provide positive gain.
• The overall gain of the amplifier must be greater than one, unity.
• Oscillations can be maintained by feeding back some of the output voltage to the tuned circuit that is of the correct amplitude and in-phase, (0o).
• Oscillations can only occur when the feedback is “Positive” (self-regeneration).
• The overall phase shift of the circuit must be zero or 360o so that the output signal from the feedback network will be “in-phase” with the input signal.