RC oscillator

Linear electronic oscillator circuits, which generate a sinusoidal output signal, are composed of an amplifier and a frequency selective element, a filter. An oscillator circuit which uses an RC network, a combination of resistors and capacitors, for its frequency selective part is called an RC oscillator.

Amplitude control

A sine wave oscillator is a quasi-linear circuit. For a linear system to oscillate, it must satisfy the Barkhausen stability criteria: the loop gain must be unity and phase shift around the loop must be an integer multiple of two pi. Barkhausen also does not set the amplitude: a linear oscillator could be at any amplitude. From a practical standpoint, it is impossible to set the loop gain to exactly one. What happens instead is the oscillator is designed to have a small-signal loop gain of a little more than one. The higher gain allows an oscillator to start by exponentially amplifying some ever-present noise.^[1]

As the oscillator amplitude builds, some nonlinearity in the circuit will cause the incremental gain to decrease at higher amplitudes. For example, the oscillator might have a loop gain of 3 for small signals, but that loop gain instaneously drops to zero when the output reaches one of the power supply rails.^[2] The net effect is the oscillator amplitude will stablize when average gain over a cycle is one. If the average loop gain is greater than one, the output amplitude increases until the nonlinearity reduces the average gain to one; if the average loop gain is less than one, then the output amplitude decreases until the average gain is one. The nonlinearity that reduces the gain may also be more subtle than running into a power supply rail.^[3]

The result of this gain averaging is some harmonic distortion in the output signal. If the small-signal gain is just a little bit more than one, then only a small amount of gain compression is needed, so there won't be much harmonic distortion. If the small-signal gain is much more than one, then significant distortion will be present.^[4]

If an oscillator is to produce a very low-distortion sine wave, then a system that keeps the gain roughly constant during the entire cycle is used. A common design uses an incandescent lamp or a thermistor in the feedback circuit.^[5]^[6] These oscillators exploit theresistance of a tungsten filament of the lamp increases in proportion to its temperature (a thermistor works in a similar fashion). The lamp both measures the output amplitude and controls the oscillator gain at the same time. The oscillator's signal level heats the filament. If the level is too high, then the filament temperature gradually increases, the resistance increases, and the loop gain falls (thus decreasing the oscillator's output level). If the level is too low, the lamp cools down and increases the gain. The 1939 HP200A oscillator uses this technique. Modern variations may use explicit level detectors and gain-controlled amplifiers.

Example oscillators

Phase-shift oscillator

A common design is the phase-shift oscillator.^[7]

Twin-T oscillator

Another common design is the "Twin-T" oscillator as it uses two "T" RC circuits operated in parallel. One circuit is an R-C-R "T" which acts as a low-pass filter. The second circuit is a C-R-C "T" which operates as a high-pass filter. Together, these circuits form a bridge which is tuned at the desired frequency of oscillation. The signal in the C-R-C branch of the Twin-T filter is advanced, in the R-C-R - delayed, so they may cancel one another for frequency $f={\frac {1}{2\pi RC}}$ if $x=2$ ; if it is connected as a negative feedback to an amplifier, and x>2, the amplifier becomes an oscillator.

Wien bridge

Another common design is the Wien bridge oscillator.^[8] In this circuit, two RC circuits are used, one with the RC components in series and one with the RC components in parallel. The Wien Bridge is often used in audio signal generators because it can be easily tuned using a two-section variable capacitor or a two section variable potentiometer (which is more easily obtained than a variable capacitor suitable for generation at low frequencies). The archetypical HP200A audio oscillator is a Wien Bridge oscillator.

References

^ Strauss, Leonard (1970), "Almost Sinusoidal Oscillations — the linear approximation", Wave Generation and Shaping (second ed.), McGraw-Hill, pp. 663–720 at page 661, "It follows that if $A β > 1$ in the small-signal region, the amplitude will build up until the limiter stabilizes the system...."
^ Strauss 1970, p. 694, "As the signal amplitude increases, the active device will switch from active operation to the zero-gain regions of cutoff and saturation."
^ Strauss 1970, pp. 703–706, Exponential limiting—bipolar transistor.
^ Strauss 1970, p. 664, "If gross nonlinear operation is permitted, the limiter will distort the signal and the output will be far from sinusoidal."
^ Strauss 1970, p. 664, "Alternatively, an amplitude-controlled resistor or other passive nonlinear element may be included as part of the amplifier or in the frequency-determining network."
^ Strauss 1970, pp. 706–713, Amplitude of Oscillation—Part II, Automatic Gain Control.
^ Department of the Army (1962) [1959], Basic Theory and Application of Transistors, Technical Manuals, Dover, pp. 178–179, TM 11-690
^ Department of the Army 1962, pp. 179–180

[1] Strauss, Leonard (1970), "Almost Sinusoidal Oscillations — the linear approximation", Wave Generation and Shaping (second ed.), McGraw-Hill, pp. 663–720 at page 661, "It follows that if $A β > 1$ in the small-signal region, the amplitude will build up until the limiter stabilizes the system...."

[2] Strauss 1970, p. 694, "As the signal amplitude increases, the active device will switch from active operation to the zero-gain regions of cutoff and saturation."

[3] Strauss 1970, pp. 703–706, Exponential limiting—bipolar transistor.

[4] Strauss 1970, p. 664, "If gross nonlinear operation is permitted, the limiter will distort the signal and the output will be far from sinusoidal."

[5] Strauss 1970, p. 664, "Alternatively, an amplitude-controlled resistor or other passive nonlinear element may be included as part of the amplifier or in the frequency-determining network."

[6] Strauss 1970, pp. 706–713, Amplitude of Oscillation—Part II, Automatic Gain Control.

[7] Department of the Army (1962) [1959], Basic Theory and Application of Transistors, Technical Manuals, Dover, pp. 178–179, TM 11-690

[8] Department of the Army 1962, pp. 179–180

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]