A

**Colpitts oscillator**An electronic oscillator is an electronic circuit that produces a repetitive electronic signal, often a sine wave or a square wave. They are widely used in innumerable electronic devices...

, invented in 1920 by American engineer

Edwin H. ColpittsEdwin Henry Colpitts was a communications pioneer best known for his invention of the Colpitts oscillator. As research branch chief for Western Electric in the early 1900s, he and scientists under his direction achieved significant advances in the development of oscillators and vacuum tube...

, is one of a number of designs for

electronic oscillatorAn electronic oscillator is an electronic circuit that produces a repetitive electronic signal, often a sine wave or a square wave. They are widely used in innumerable electronic devices...

circuits using the combination of an

inductanceIn electromagnetism and electronics, inductance is the ability of an inductor to store energy in a magnetic field. Inductors generate an opposing voltage proportional to the rate of change in current in a circuit...

(L) with a

capacitorA capacitor is a passive two-terminal electrical component used to store energy in an electric field. The forms of practical capacitors vary widely, but all contain at least two electrical conductors separated by a dielectric ; for example, one common construction consists of metal foils separated...

(C) for frequency determination, thus also called LC oscillator. The distinguishing feature of the Colpitts circuit is that the

feedbackFeedback describes the situation when output from an event or phenomenon in the past will influence an occurrence or occurrences of the same Feedback describes the situation when output from (or information about the result of) an event or phenomenon in the past will influence an occurrence or...

signal is taken from a voltage divider made by two

capacitorA capacitor is a passive two-terminal electrical component used to store energy in an electric field. The forms of practical capacitors vary widely, but all contain at least two electrical conductors separated by a dielectric ; for example, one common construction consists of metal foils separated...

s in series. One of the advantages of this circuit is its simplicity; it needs only a single inductor. Colpitts obtained US Patent 1624537 for this circuit.

The frequency is generally determined by the inductor and the two capacitors at the bottom of the drawing.

## Implementation

A Colpitts oscillator is the electrical dual of a

Hartley oscillatorThe Hartley oscillator is an electronic oscillator circuit that uses an inductor and a capacitor in parallel to determine the frequency. Invented in 1915 by American engineer Ralph Hartley, the distinguishing feature of the Hartley circuit is that the feedback needed for oscillation is taken from...

. Fig. 1 shows the basic Colpitts circuit, where two

capacitorA capacitor is a passive two-terminal electrical component used to store energy in an electric field. The forms of practical capacitors vary widely, but all contain at least two electrical conductors separated by a dielectric ; for example, one common construction consists of metal foils separated...

s and one

inductorAn inductor is a passive two-terminal electrical component used to store energy in a magnetic field. An inductor's ability to store magnetic energy is measured by its inductance, in units of henries...

determine the

frequencyFrequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...

of oscillation. The

feedbackFeedback describes the situation when output from an event or phenomenon in the past will influence an occurrence or occurrences of the same Feedback describes the situation when output from (or information about the result of) an event or phenomenon in the past will influence an occurrence or...

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 oscillatorThe Clapp oscillator is one of several types of electronic oscillator constructed from a transistor and a positive feedback network, using the combination of an inductance with a capacitor for frequency determination, thus also called LC oscillator.It was published by James Kilton Clapp in 1948...

).

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 transistor|- align = "center"| || PNP|- align = "center"| || NPNA bipolar transistor is a three-terminal electronic device constructed of doped semiconductor material and may be used in amplifying or switching applications. Bipolar transistors are so named because their operation involves both electrons...

s, other active components such as field effect transistors or

vacuum tubeIn electronics, a vacuum tube, electron tube , or thermionic valve , reduced to simply "tube" or "valve" in everyday parlance, is a device that relies on the flow of electric current through a vacuum...

s, capable of producing gain at the desired frequency, could be used.

### 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

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 resistanceNegative resistance is a property of some electric circuits where an increase in the current entering a port results in a decreased voltage across the same port. This is in contrast to a simple ohmic resistor, which exhibits an increase in voltage under the same conditions. Negative resistors are...

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

impedanceElectrical impedance, or simply impedance, is the measure of the opposition that an electrical circuit presents to the passage of a current when a voltage is applied. In quantitative terms, it is the complex ratio of the voltage to the current in an alternating current circuit...

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

transconductanceTransconductance, also known as mutual conductance, is a property of certain electronic components. Conductance is the reciprocal of resistance; transconductance, meanwhile, is the ratio of the current change at the output port to the voltage change at the input port. It is written as gm...

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 resistanceNegative resistance is a property of some electric circuits where an increase in the current entering a port results in a decreased voltage across the same port. This is in contrast to a simple ohmic resistor, which exhibits an increase in voltage under the same conditions. Negative resistors are...

. 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

mAThe ampere , often shortened to amp, is the SI unit of electric current and is one of the seven SI base units. It is named after André-Marie Ampère , French mathematician and physicist, considered the father of electrodynamics...

. The transconductance is roughly 40

mSThe siemens is the SI derived unit of electric conductance and electric admittance. Conductance and admittance are the reciprocals of resistance and impedance respectively, hence one siemens is equal to the reciprocal of one ohm, and is sometimes referred to as the mho. In English, the term...

. 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/or 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. 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 oscillatorThe Hartley oscillator is an electronic oscillator circuit that uses an inductor and a capacitor in parallel to determine the frequency. Invented in 1915 by American engineer Ralph Hartley, the distinguishing feature of the Hartley circuit is that the feedback needed for oscillation is taken from...

. 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/or 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 functionThe Describing function method of Nikolay Mitrofanovich Krylov and Nikolay Bogolyubov is an approximate procedure for analyzing certain nonlinear control problems. It is based on quasi-linearization, which is the approximation of the non-linear system under investigation by an LTI system transfer...

method.

## See also

- Armstrong oscillator
The Armstrong oscillator is named after its inventor, the electrical engineer Edwin Armstrong. It is sometimes called a tickler oscillator because the feedback needed to produce oscillations is provided using a tickler coil via magnetic coupling between coil L and coil T...

- Clapp oscillator
The Clapp oscillator is one of several types of electronic oscillator constructed from a transistor and a positive feedback network, using the combination of an inductance with a capacitor for frequency determination, thus also called LC oscillator.It was published by James Kilton Clapp in 1948...

- Hartley oscillator
The Hartley oscillator is an electronic oscillator circuit that uses an inductor and a capacitor in parallel to determine the frequency. Invented in 1915 by American engineer Ralph Hartley, the distinguishing feature of the Hartley circuit is that the feedback needed for oscillation is taken from...

- Relaxation Oscillator
A relaxation oscillator is an oscillator based upon the behavior of a physical system's return to equilibrium after being disturbed. That is, a dynamical system within the oscillator continuously dissipates its internal energy...

- Vačkář oscillator
A Vackář oscillator is a variation of the split-capacitance oscillator model. It is similar to a Colpitts oscillator or a Clapp oscillator in this respect. It differs in that the output level is relatively stable over frequency, and has a wider bandwidth when compared to a Clapp design.In 1949,...

- Wien bridge oscillator
A Wien bridge oscillator is a type of electronic oscillator that generates sine waves. It can generate a large range of frequencies. The oscillator is based on a bridge circuit originally developed by Max Wien in 1891....

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