RC oscillator

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

Contents

A simple example of a do-it-yourself RC audio oscillator is presented in. [1]

Description

RC oscillators are a type of feedback oscillator; they consist of an amplifying device, a transistor, vacuum tube, or op-amp, with some of its output energy fed back into its input through a network of resistors and capacitors, an RC network, to achieve positive feedback, causing it to generate an oscillating sinusoidal voltage. [2] [3] [4] They are used to produce lower frequencies, mostly audio frequencies, in such applications as audio signal generators and electronic musical instruments. [5] [6] At radio frequencies, another type of feedback oscillator, the LC oscillator is used, but at frequencies below 100 kHz the size of the inductors and capacitors needed for the LC oscillator become cumbersome, and RC oscillators are used instead. [7] Their lack of bulky inductors also makes them easier to integrate into microelectronic devices. Since the oscillator's frequency is determined by the value of resistors and capacitors, which vary with temperature, RC oscillators do not have as good frequency stability as crystal oscillators.

The frequency of oscillation is determined by the Barkhausen criterion, which says that the circuit will only oscillate at frequencies for which the phase shift around the feedback loop is equal to 360° (2π radians) or a multiple of 360°, and the loop gain (the amplification around the feedback loop) is equal to one. [8] [2] The purpose of the feedback RC network is to provide the correct phase shift at the desired oscillating frequency so the loop has 360° phase shift, so the sine wave, after passing through the loop will be in phase with the sine wave at the beginning and reinforce it, resulting in positive feedback. [7] The amplifier provides gain to compensate for the energy lost as the signal passes through the feedback network, to create sustained oscillations. As long as the gain of the amplifier is high enough that the total gain around the loop is unity or higher, the circuit will generally oscillate.

In RC oscillator circuits which use a single inverting amplifying device, such as a transistor, tube, or an op amp with the feedback applied to the inverting input, the amplifier provides 180° of the phase shift, so the RC network must provide the other 180°. [7] Since each capacitor can provide a maximum of 90° of phase shift, RC oscillators require at least two frequency-determining capacitors in the circuit (two poles), and most have three or more, [2] with a comparable number of resistors.

This makes tuning the circuit to different frequencies more difficult than in other types such as the LC oscillator, in which the frequency is determined by a single LC circuit so only one element must be varied. Although the frequency can be varied over a small range by adjusting a single circuit element, to tune an RC oscillator over a wide range two or more resistors or capacitors must be varied in unison, requiring them to be ganged together mechanically on the same shaft. [3] [9] The oscillation frequency is proportional to the inverse of the capacitance or resistance, whereas in an LC oscillator the frequency is proportional to inverse square root of the capacitance or inductance. [10] So a much wider frequency range can be covered by a given variable capacitor in an RC oscillator. For example, a variable capacitor that could be varied over a 9:1 capacitance range will give an RC oscillator a 9:1 frequency range, but in an LC oscillator it will give only a 3:1 range.

Some examples of common RC oscillator circuits are listed below:

A phase-shift oscillator RC phase shift oscillator.svg
A phase-shift oscillator

Phase-shift oscillator

In the phase-shift oscillator the feedback network is three identical cascaded RC sections. [11] In the simplest design the capacitors and resistors in each section have the same value and . Then at the oscillation frequency each RC section contributes 60° phase shift for a total of 180°. The oscillation frequency is

The feedback network has an attenuation of 1/29, so the op-amp must have a gain of 29 to give a loop gain of one for the circuit to oscillate

A twin-T oscillator Twin T oscillator.svg
A twin-T oscillator

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 if ; if it is connected as a negative feedback to an amplifier, and x>2, the amplifier becomes an oscillator. (Note: .)

Quadrature oscillator

The quadrature oscillator uses two cascaded op-amp integrators in a feedback loop, one with the signal applied to the inverting input or two integrators and an invertor. The advantage of this circuit is that the sinusoidal outputs of the two op-amps are 90° out of phase (in quadrature). This is useful in some communication circuits.

It is possible to stabilize a quadrature oscillator by squaring the sine and cosine outputs, adding them together, (Pythagorean trigonometric identity) subtracting a constant, and applying the difference to a multiplier that adjusts the loop gain around an inverter. Such circuits have a near-instant amplitude response to the constant input and extremely low distortion.

Low distortion oscillators

The Barkhausen criterion mentioned above does not determine the amplitude of oscillation. An oscillator circuit with only linear components is unstable with respect to amplitude. As long as the loop gain is exactly one, the amplitude of the sine wave would be constant, but the slightest increase in gain, due to a drift in the value of components will cause the amplitude to increase exponentially without limit. Similarly, the slightest decrease will cause the sine wave to die out exponentially to zero. Therefore, all practical oscillators must have a nonlinear component in the feedback loop, to reduce the gain as the amplitude increases, leading to stable operation at the amplitude where the loop gain is unity.

In most ordinary oscillators, the nonlinearity is simply the saturation (clipping) of the amplifier as the amplitude of the sine wave approaches the power supply rails. The oscillator is designed to have a small-signal loop gain greater than one. The higher gain allows an oscillator to start by exponentially amplifying some ever-present noise. [12]

As the peaks of the sine wave approach the supply rails, the saturation of the amplifier device flattens (clips) the peaks, reducing the gain. 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. [13] The net effect is the oscillator amplitude will stabilize 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. [14]

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. [15] However the oscillator must have gain significantly above one to start reliably.

So in oscillators that must produce a very low-distortion sine wave, 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. [16] [17] These oscillators exploit the resistance 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.

Wien bridge oscillator with automatic gain control. Rb is a small incandescent lamp. Usually, R1 = R2 = R and C1 = C2 = C. In normal operation, Rb self heats to the point where its resistance is Rf/2. Wien Bridge Oscillator.png
Wien bridge oscillator with automatic gain control. Rb is a small incandescent lamp. Usually, R1 = R2 = R and C1 = C2 = C. In normal operation, Rb self heats to the point where its resistance is Rf/2.

Wien bridge oscillator

One of the most common gain-stabilized circuits is the Wien bridge oscillator. [18] 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.

Related Research Articles

Electronic oscillator Type of electronic circuit

An electronic oscillator is an electronic circuit that produces a periodic, oscillating electronic signal, often a sine wave or a square wave or a triangle wave. Oscillators convert direct current (DC) from a power supply to an alternating current (AC) signal. They are widely used in many electronic devices ranging from simplest clock generators to digital instruments and complex computers and peripherals etc. Common examples of signals generated by oscillators include signals broadcast by radio and television transmitters, clock signals that regulate computers and quartz clocks, and the sounds produced by electronic beepers and video games.

Amplifier electronic device/component that increases the strength of a signal

An amplifier, electronic amplifier or (informally) amp is an electronic device that can increase the power of a signal. It is a two-port electronic circuit that uses electric power from a power supply to increase the amplitude of a signal applied to its input terminals, producing a proportionally greater amplitude signal at its output. The amount of amplification provided by an amplifier is measured by its gain: the ratio of output voltage, current, or power to input. An amplifier is a circuit that has a power gain greater than one.

Resonance Tendency to oscillate at certain frequencies

Resonance describes the phenomenon of increased amplitude that occurs when the frequency of a periodically applied force is equal or close to a natural frequency of the system on which it acts. When an oscillating force is applied at a resonant frequency of a dynamic system, the system will oscillate at a higher amplitude than when the same force is applied at other, non-resonant frequencies.

Relaxation oscillator Oscillator that produces a nonsinusoidal repetitive waveform

In electronics a relaxation oscillator is a nonlinear electronic oscillator circuit that produces a nonsinusoidal repetitive output signal, such as a triangle wave or square wave. The circuit consists of a feedback loop containing a switching device such as a transistor, comparator, relay, op amp, or a negative resistance device like a tunnel diode, that repetitively charges a capacitor or inductor through a resistance until it reaches a threshold level, then discharges it again. The period of the oscillator depends on the time constant of the capacitor or inductor circuit. The active device switches abruptly between charging and discharging modes, and thus produces a discontinuously changing repetitive waveform. This contrasts with the other type of electronic oscillator, the harmonic or linear oscillator, which uses an amplifier with feedback to excite resonant oscillations in a resonator, producing a sine wave. Relaxation oscillators are used to produce low frequency signals for applications such as blinking lights and electronic beepers and in voltage controlled oscillators (VCOs), inverters and switching power supplies, dual-slope analog to digital converters, and function generators.

<i>Q</i> factor Parameter describing the longevity of energy in a resonator relative to its resonant frequency

In physics and engineering, the quality factor or Q factor is a dimensionless parameter that describes how underdamped an oscillator or resonator is. It is approximately defined as the ratio of the initial energy stored in the resonator to the energy lost in one radian of the cycle of oscillation. Q factor is alternatively defined as the ratio of a resonator's centre frequency to its bandwidth when subject to an oscillating driving force. These two definitions give numerically similar, but not identical, results. Higher Q indicates a lower rate of energy loss and the oscillations die out more slowly. A pendulum suspended from a high-quality bearing, oscillating in air, has a high Q, while a pendulum immersed in oil has a low one. Resonators with high quality factors have low damping, so that they ring or vibrate longer.

Negative resistance the property that an increasing voltage results in a decreasing current

In electronics, negative resistance (NR) is a property of some electrical circuits and devices in which an increase in voltage across the device's terminals results in a decrease in electric current through it.

A resistor–capacitor circuit, or RC filter or RC network, is an electric circuit composed of resistors and capacitors. It may be driven by a voltage or current source and these will produce different responses. A first order RC circuit is composed of one resistor and one capacitor and is the simplest type of RC circuit.

The Hartley oscillator is an electronic oscillator circuit in which the oscillation frequency is determined by a tuned circuit consisting of capacitors and inductors, that is, an LC oscillator. The circuit was invented in 1915 by American engineer Ralph Hartley. The distinguishing feature of the Hartley oscillator is that the tuned circuit consists of a single capacitor in parallel with two inductors in series, and the feedback signal needed for oscillation is taken from the center connection of the two inductors.

Regenerative circuit

A regenerative circuit is an amplifier circuit that employs positive feedback. Some of the output of the amplifying device is applied back to its input so as to add to the input signal, increasing the amplification. One example is the Schmitt trigger, but the most common use of the term is in RF amplifiers, and especially regenerative receivers, to greatly increase the gain of a single amplifier stage.

Voltage-controlled oscillator Electronic oscillator controlled by a voltage input

A voltage-controlled oscillator (VCO) is an electronic oscillator whose oscillation frequency is controlled by a voltage input. The applied input voltage determines the instantaneous oscillation frequency. Consequently, a VCO can be used for frequency modulation (FM) or phase modulation (PM) by applying a modulating signal to the control input. A VCO is also an integral part of a phase-locked loop. VCOs are used in synthesizers to generate a waveform whose pitch can be adjusted by a voltage determined by a musical keyboard or other input.

A Colpitts oscillator, invented in 1918 by American engineer Edwin H. Colpitts, is one of a number of designs for LC oscillators, electronic oscillators that use a combination of inductors (L) and capacitors (C) to produce an oscillation at a certain frequency. The distinguishing feature of the Colpitts oscillator is that the feedback for the active device is taken from a voltage divider made of two capacitors in series across the inductor.

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 for the measurement of impedances. The bridge comprises four resistors and two capacitors. The oscillator can also be viewed as a positive gain amplifier combined with a bandpass filter that provides positive feedback. Automatic gain control, intentional non-linearity and incidental non-linearity limit the output amplitude in various implementations of the oscillator.

A phase-shift oscillator is a linear electronic oscillator circuit that produces a sine wave output. It consists of an inverting amplifier element such as a transistor or op amp with its output fed back to its input through a phase-shift network consisting of resistors and capacitors in a ladder network. The feedback network 'shifts' the phase of the amplifier output by 180 degrees at the oscillation frequency to give positive feedback. Phase-shift oscillators are often used at audio frequency as audio oscillators. A simple example of a do-it-yourself phase-shift audio oscillator for hobbyists is presented in.

In control systems theory, the describing function (DF) method, developed by Nikolay Mitrofanovich Krylov and Nikolay Bogoliubov in the 1930s, and extended by Ralph Kochenburger 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 a linear time-invariant (LTI) transfer function that depends on the amplitude of the input waveform. By definition, a transfer function of a true LTI system cannot depend on the amplitude of the input function because an LTI system is linear. Thus, this dependence on amplitude generates a family of linear systems that are combined in an attempt to capture salient features of the non-linear system behavior. The describing function is one of the few widely applicable methods for designing nonlinear systems, and is very widely used as a standard mathematical tool for analyzing limit cycles in closed-loop controllers, such as industrial process controls, servomechanisms, and electronic oscillators.

Detector (radio)

In radio, a detector is a device or circuit that extracts information from a modulated radio frequency current or voltage. The term dates from the first three decades of radio (1888-1918). Unlike modern radio stations which transmit sound on an uninterrupted carrier wave, early radio stations transmitted information by radiotelegraphy. The transmitter was switched on and off to produce long or short periods of radio waves, spelling out text messages in Morse code. Therefore, early radio receivers had only to distinguish between the presence or absence of a radio signal. The device that performed this function in the receiver circuit was called a detector. A variety of different detector devices, such as the coherer, electrolytic detector, magnetic detector and the crystal detector, were used during the wireless telegraphy era until superseded by vacuum tube technology.

Parametric oscillator

A parametric oscillator is a driven harmonic oscillator in which the oscillations are driven by varying some parameter of the system at some frequency, typically different from the natural frequency of the oscillator. A simple example of a parametric oscillator is a child pumping a playground swing by periodically standing and squatting to increase the size of the swing's oscillations. The child's motions vary the moment of inertia of the swing as a pendulum. The "pump" motions of the child must be at twice the frequency of the swing's oscillations. Examples of parameters that may be varied are the oscillator's resonance frequency and damping .

Pierce oscillator

The Pierce oscillator is a type of electronic oscillator particularly well-suited for use in piezoelectric crystal oscillator circuits. Named for its inventor, George W. Pierce (1872–1956), the Pierce oscillator is a derivative of the Colpitts oscillator. Virtually all digital IC clock oscillators are of Pierce type, as the circuit can be implemented using a minimum of components: a single digital inverter, one resistor, two capacitors, and the quartz crystal, which acts as a highly selective filter element. The low manufacturing cost of this circuit and the outstanding frequency stability of the quartz crystal give it an advantage over other designs in many consumer electronics applications.

In electronics, a differentiator is a circuit that is designed such that the output of the circuit is approximately directly proportional to the rate of change of the input. A true differentiator cannot be physically realized, because it has infinite gain at infinite frequency. A similar effect can be achieved, however, by limiting the gain above some frequency. The differentiator circuit is essentially a high-pass filter.
An active differentiator includes some form of amplifier, while a passive differentiator is made only of resistors, capacitors and inductors.

Parasitic oscillation is an undesirable electronic oscillation in an electronic or digital device. It is often caused by feedback in an amplifying device. The problem occurs notably in RF, audio, and other electronic amplifiers as well as in digital signal processing. It is one of the fundamental issues addressed by control theory.

Transimpedance amplifier Amplifier that converts current to voltage

In electronics, a transimpedance amplifier (TIA) is a current to voltage converter, almost exclusively implemented with one or more operational amplifiers. The TIA can be used to amplify the current output of Geiger–Müller tubes, photo multiplier tubes, accelerometers, photo detectors and other types of sensors to a usable voltage. Current to voltage converters are used with sensors that have a current response that is more linear than the voltage response. This is the case with photodiodes where it is not uncommon for the current response to have better than 1% nonlinearity over a wide range of light input. The transimpedance amplifier presents a low impedance to the photodiode and isolates it from the output voltage of the operational amplifier. In its simplest form a transimpedance amplifier has just a large valued feedback resistor, Rf. The gain of the amplifer is set by this resistor and because the amplifier is in an inverting configuration, has a value of -Rf. There are several different configurations of transimpedance amplifiers, each suited to a particular application. The one factor they all have in common is the requirement to convert the low-level current of a sensor to a voltage. The gain, bandwidth, as well as current and voltage offsets change with different types of sensors, requiring different configurations of transimpedance amplifiers.

References

  1. ↑ I made this audio oscillator on a breadboard , retrieved 2022-01-06
  2. 1 2 3 Mancini, Ron; Palmer, Richard (March 2001). "Application Report SLOA060: Sine-Wave Oscillator" (PDF). Texas Instruments Inc. Retrieved August 12, 2015.
  3. 1 2 Gottlieb, Irving (1997). Practical Oscillator Handbook. Elsevier. pp. 49–53. ISBN   0080539386.
  4. ↑ Coates, Eric (2015). "Oscillators Module 1 - Oscillator Basics". Learn About Electronics. Eric Coates. Retrieved August 7, 2015.
  5. ↑ Coates, Eric (2015). "Oscillators Module 3 - AF Sine Wave Oscillators" (PDF). Learn About Electronics. Eric Coates. Retrieved August 7, 2015.
  6. ↑ Chattopadhyay, D. (2006). Electronics (fundamentals And Applications). New Age International. pp. 224–225. ISBN   81-224-1780-9.
  7. 1 2 3 "RC Feedback Oscillators". Electronics tutorial. DAEnotes. 2013. Retrieved August 9, 2015.
  8. ↑ Rao, B.; Rajeswari, K.; Pantulu, P. (2012). Electronic Circuit Analysis. India: Pearson Education India. pp. 8.2–8.6, 8.11. ISBN   978-8131754283.
  9. ↑ Eric Coates, 2015, AF Sine Wave Oscillators, p. 10
  10. ↑ Groszkowski, Janusz (2013). Frequency of Self-Oscillations. Elsevier. pp. 397–398. ISBN   978-1483280301.
  11. ↑ Department of the Army (1962) [1959], Basic Theory and Application of Transistors, Technical Manuals, Dover, pp. 178–179, TM 11-690
  12. ↑ 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 Aβ > 1 in the small-signal region, the amplitude will build up until the limiter stabilizes the system...."
  13. ↑ 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."
  14. ↑ Strauss 1970 , pp. 703–706, Exponential limiting—bipolar transistor.
  15. ↑ Strauss 1970 , p. 664, "If gross nonlinear operation is permitted, the limiter will distort the signal and the output will be far from sinusoidal."
  16. ↑ 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."
  17. ↑ Strauss 1970 , pp. 706–713, Amplitude of Oscillation—Part II, Automatic Gain Control.
  18. ↑ Department of the Army 1962 , pp. 179–180
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