Applications of LC oscillators; Colpitts oscillator

Applications of tuned LC oscillators

• Generating the local oscillator signal in radio, TV and communication receivers (superheterodyne).
• Carrier generation in transmitters (AM and FM), with a varactor for frequency modulation.
• RF signal generators and test equipment.
• Frequency synthesizers and phase-locked loops (VCO stage).
• Mixers and frequency converters in cell phones, wireless devices and radar.
• Induction heating and metal detectors.

LC oscillators are used at radio frequencies (from about 100 kHz to a few hundred MHz). RC oscillators are used at audio frequencies, because the L and C values would be too large at low frequencies.

Colpitts oscillator circuit (BJT, common emitter)

                 +VCC
                  |
        +---------+
        |         |
      [R1]      [RFC]
        |         |
        |         +----||---+---------+
        |         |    Cc2  |         |
        |         C        [C1]       |
  +-----+------B--|  Q1     |        [L]
  |     |         E        GND        |
  |   [R2]        |         |         |
  |     |       [RE]||[CE] [C2]       |
  |    GND        |         |         |
  |              GND        |         |
  |                         |         |
  +---------||--------------+---------+
            Cc1

The collector is coupled through Cc2 to the top of the tank. C1 runs from the top of the tank to ground, C2 from ground to the bottom of the tank, and L is across the whole C1-C2 series combination. The bottom of the tank is coupled back to the base through Cc1. The output is taken from the collector (or the tank).

Tank connections in a simple form:

 Collector o----+------+
                |      |
               [C1]    |
                |     [L]
 Emitter/GND o--+      |
                |      |
               [C2]    |
                |      |
 Base        o--+------+

C1 is between collector and ground, C2 between base and ground (emitter), and L is across the series combination. Bias: voltage divider R1, R2; emitter resistor RE with bypass capacitor CE; RF choke in the collector supply.

Derivation of frequency

Neglecting loading by the transistor (hie, hoe), the tank is L in parallel with the series combination of C1 and C2:

Ceq = C1 C2 / (C1 + C2)

At resonance the inductive and capacitive reactances are equal: ωL = 1/(ω Ceq)

f = 1 / (2π √(L Ceq)) = 1 / (2π √( L C1 C2 / (C1 + C2) ))

(A more exact derivation using the h-parameter model gives the same frequency when the transistor loading is negligible.)

Condition for oscillation: with Aβ ≥ 1 and β = C1/C2, the transistor gain must satisfy

hfe ≥ C2/C1

Example: L = 100 µH, C1 = 1 nF, C2 = 1 nF: Ceq = 0.5 nF; f = 1/(2π√(100×10⁻⁶ × 0.5×10⁻⁹)) = 712 kHz.