Colpitts oscillator
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Early schematic of a Colpitts circuit, using a vacuum tube, redrawn from the patent publication.
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A
Colpitts oscillator, invented in 1920 by American engineer
Edwin H. Colpitts, is one of a number of designs for
electronic oscillator circuits using the combination of an
inductance (L) with a
capacitor (C) for frequency determination, thus also called
LC oscillator. The distinguishing feature of the Colpitts circuit is that the
feedback signal is taken from a
voltage divider made by two
capacitors
in series. One of the advantages of this circuit is its simplicity; it
needs only a single inductor. Colpitts obtained US Patent 1624537
[1] for this circuit.
The frequency is generally determined by the inductor and the two capacitors at the bottom of the drawing.
Implementation
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Figure 3: Practical common base Colpitts oscillator (with an oscillation frequency of ~50 MHz)
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A Colpitts oscillator is the electrical dual of a
Hartley oscillator. Fig. 1 shows the basic Colpitts circuit, where two
capacitors and one
inductor determine the
frequency of oscillation. The
feedback needed for oscillation is taken from a
voltage divider
made of two capacitors, whereas in the Hartley oscillator the feedback
is taken from a voltage divider made of two inductors (or a single,
tapped inductor).
As with any oscillator, the amplification of the active component
should be marginally larger than the attenuation of the capacitive
voltage divider, to obtain stable operation. Thus, a Colpitts oscillator
used as a
variable frequency oscillator
(VFO) performs best when a variable inductance is used for tuning, as
opposed to tuning one of the two capacitors. If tuning by variable
capacitor is needed, it should be done via a third capacitor connected
in parallel to the inductor (or in series as in the
Clapp oscillator).
Fig. 2 shows an often preferred variant, where the inductor is also
grounded (which makes circuit layout easier for higher frequencies).
Note that feedback energy is fed into the connection between the two
capacitors. This amplifier provides current, not voltage, amplification.
Fig. 3 shows a working example with component values. Instead of
bipolar junction transistors, other active components such as
field effect transistors or
vacuum tubes, capable of producing gain at the desired frequency, could be used.
Theory
Oscillation frequency
The ideal frequency of oscillation for the circuits in Figures 1 and 2 are given by the equation:
where the series combination of C1 and C2 creates the effective capacitance of the LC tank.
Real circuits will oscillate at a slightly lower frequency due to
junction capacitances of the transistor and possibly other stray
capacitances.
Instability criteria
Colpitts oscillator model used in analysis at left.
One method of oscillator analysis is to determine the input impedance
of an input port neglecting any reactive components. If the impedance
yields a
negative resistance
term, oscillation is possible. This method will be used here to
determine conditions of oscillation and the frequency of oscillation.
An ideal model is shown to the right. This configuration models the
common collector circuit in the section above. For initial analysis,
parasitic elements and device non-linearities will be ignored. These
terms can be included later in a more rigorous analysis. Even with these
approximations, acceptable comparison with experimental results is
possible.
Ignoring the inductor, the input
impedance can be written as
Where
is the input voltage and
is the input current. The voltage
is given by
Where
is the impedance of
. The current flowing into
is
, which is the sum of two currents:
Where
is the current supplied by the transistor.
is a dependent current source given by
Where
is the
transconductance of the transistor. The input current
is given by
Where
is the impedance of
. Solving for
and substituting above yields
The input impedance appears as the two capacitors in series with an interesting term,
which is proportional to the product of the two impedances:
If
and
are complex and of the same sign,
will be a
negative resistance. If the impedances for
and
are substituted,
is
If an inductor is connected to the input, the circuit will oscillate
if the magnitude of the negative resistance is greater than the
resistance of the inductor and any stray elements. The frequency of
oscillation is as given in the previous section.
For the example oscillator above, the emitter current is roughly 1
mA. The transconductance is roughly 40
mS. Given all other values, the input resistance is roughly
This value should be sufficient to overcome any positive resistance
in the circuit. By inspection, oscillation is more likely for larger
values of transconductance and smaller values of capacitance. A more
complicated analysis of the common-base oscillator reveals that a low
frequency amplifier voltage gain must be at least four to achieve
oscillation.
[2] The low frequency gain is given by:
If the two capacitors are replaced by inductors and magnetic coupling is ignored, the circuit becomes a
Hartley oscillator. In that case, the input impedance is the sum of the two inductors and a negative resistance given by:
In the Hartley circuit, oscillation is more likely for larger values of transconductance and larger values of inductance.
Oscillation amplitude
The amplitude of oscillation is generally difficult to predict, but it can often be accurately estimated using the
describing function method.
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