Crystal Oscillator

Electronics Tutorial about Oscillators

Oscillators

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Introduction to OscillatorsOscillators are used in many electronic circuits and systems providing the central "clock" signal that controls the sequential operation of the entire system. Oscillators can produce a wide range of different wave shapes and frequencies that can be complicated or simple depending upon the application. Oscillators are also used in many pieces of test equipment producing either sinusoidal sine waves, square, sawtooth or triangular shaped waveforms or just pulses of a variable or constant width. Oscillators are basically an Amplifier with "Positive Feedback", (in-phase) and one of the many problems in electronic circuit design is stopping amplifiers from oscillating while trying to get oscillators to oscillate. Oscillators works because they overcome the losses of their feedback resonator circuit either in the form of a Capacitor, Inductor or both by applying DC energy at the required frequency into this resonator circuit. Then an Oscillator has a gain equal too or slightly greater than 1. In addition to these reactive components, an amplifying device such as an Operational Amplifier or Bipolar Transistor is required. Unlike an amplifier there is no external AC input required to cause the Oscillator to work as the DC supply energy is converted by the oscillator into AC energy at the required frequency.

Basic Feedback Circuit

Where: is a feedback fraction.

Oscillators are circuits that generate a continuous voltage output waveform at a required frequency with the values of the inductors, capacitors or resistors forming a frequency selective LC resonant (or tank) feedback network. The oscillators frequency is controlled using a tuned or resonant inductive/capacitive (LC) circuit with the resulting output frequency being known as the Oscillation Frequency and by making the oscillators feedback a reactive network the phase angle of the feedback will vary as a function of frequency and this is called Phase-shift. There are basically types of Oscillators

1. Sinusoidal Oscillators - these are known as Harmonic Oscillators and are generallya "LC Tuned-feedback" or "RC tuned-feedback" type Oscillator that generates a sinusoidal waveform which is of constant amplitude and frequency.

2. Non-Sinusoidal Oscillators - these are known as Relaxation Oscillators andgenerate complex non-sinusoidal waveforms that changes very quickly from one condition of stability to another such as "Square-wave", "Triangular-wave" or "Sawtoothed-wave" type waveforms.

ResonanceWhen a constant voltage but of varying frequency is applied to a circuit consisting of an inductor, capacitor and resistor the reactance of both the Capacitor/Resistor and Inductor/Resistor circuits is to change both the amplitude and the phase of the output signal as compared to the input signal due to the reactance of the components used. At high frequencies the reactance of a capacitor is very low acting as a short circuit while the reactance of the inductor is high acting as an open circuit. At low frequencies the reverse is true, the reactance of the capacitor acts as an open circuit and the reactance of the inductor acts as a short circuit. Between these two extremes the combination of the inductor and capacitor produces a "Tuned" or "Resonant" circuit that has a Resonant Frequency, ( r ) in which the capacitive and inductive reactance's are equaland cancel out each other, leaving only the resistance of the circuit to oppose the flow of current. This means that there is no phase shift as the current is in phase with the voltage. Consider the circuit below.

Basic LC Oscillatory Circuit

The circuit consists of an inductive coil, L and a capacitor, C. The capacitor stores energy in the form of an electrostatic field and which produces a potential (Static Voltage) across its plates, while the inductive coil stores its energy in the form of a magnetic field. The capacitor is charged up to the DC supply voltage, V by putting the switch in position A. When the capacitor is fully charged the switch is put to position B and the charged capacitor is now connected in parallel across the inductive coil so the capacitor begins to discharge itself through the coil. The voltage across C starts falling as the current through the coil begins to rise. This rising current sets up an electromagnetic field around the coil and when C is completely discharged the energy that was originally stored in the capacitor, C as an electrostatic field is now stored in the inductive coil, L as an electromagnetic field around the coils windings. As there is now no external voltage in the circuit to maintain the current within the coil, it starts to fall as the electromagnetic field begins to collapse. A back e.m.f. is induced in the coil (e = -Ldi/dt) keeping the current flowing in the original direction. This current now charges the capacitor, C with the opposite polarity to its original charge. C continues to charge until the current has fallen to zero and the electromagnetic field of the coil has collapsed completely. The energy originally introduced into the circuit through the switch, has been returned to the capacitor which again has an electrostatic voltage potential across it, although it is now of the opposite polarity. The capacitor now starts to discharge again back through the coil and the whole process is repeated, with the polarities changed and continues as the energy is passed back and forth producing an AC type sinusoidal voltage and current waveform. This oscillatory action of passing energy from the capacitor, C to the inductor, L and vice versa, would continue indefinitely if it was not for energy losses. Energy is lost in the resistance of the inductors coil, in the dielectric of the capacitor, and in radiation from the circuit so the oscillation steadily decreases until it dies away completely. Then in a practical LC circuit the amplitude of the oscillatory voltage decreases at each half cycle of oscillation and will eventually die away to zero. The oscillations are then said to be "Damped" with the amount of damping being determined by the Quality factor of the circuit.

Damped Oscillations

The losses are mainly due to the resistance of the inductors windings called the "Real Resistance". If this real resistance is low the oscillations will die away slowly and if the coil resistance is high the oscillations die away more rapidly. The frequency of the oscillatory voltage depends upon the value of the inductance and capacitance in theLC circuit. We know that for Resonance to occur both the capacitive, XC and inductive, XL reactance's must be equal, XL = XC and opposite to cancel out each other out leaving only the resistance in the circuit to oppose the flow of current. Then the frequency at which this will happen is given as:

Then by simplifying the equation we get the final equation for Resonant Frequency in a tuned LC circuit as:

Where:

L is the Inductance in Henrys C is the Capacitance in Farads fr is the Output Frequency in HertzThis equation shows that if either L or C are decreased, the frequency increases. This output frequency is commonly given the abbreviation of ( fr ) to identify it as the Resonant Frequency.

To keep the oscillations going in an LC circuit we have to replace the energy lost in each oscillation and also to maintain the amplitude of the oscillations at a constant level. The amount of energy replaced must be equal that lost during each cycle because if too large the amplitude would increase until clipping of the supply rails occurs. Alternatively, if the amount of energy replaced is too small the amplitude would decrease to zero over time. The simplest way of replacing this energy is to take part of the output from theLC circuit, amplify it and then feed it back into the LC circuit again and this can be achieved using a voltage amplifier. To produce a constant oscillation, the level of the energy fed back to the LC network must be accurately

controlled. Then there must be some form of automatic amplitude or gain control when the amplitude tries to vary from a reference voltage either up or down. To maintain a stable oscillation the overall gain of the circuit must be equal to 1 or unity. Any less and the oscillations will not start or die away to zero, any more the oscillations will occur but the amplitude will become clipped by the supply rails causing distortion. Consider the circuit below.

Basic Transistor LC Oscillator Circuit

A Bipolar Transistor is used as the oscillators amplifier and the tuned LC circuit acts as the Collector load. Another coil L2 is connected between the Base and Emitter and whose electromagnetic field is "mutually" coupled with that of coil L. Mutual inductance exists between two circuits when the changing current in one circuit induces by electromagnetic induction a potential voltage in the other (transformer effect). So as the oscillations occur in the tuned circuit, electromagnetic energy is transferred from coil L to coil L2 and a voltage of the same frequency as that in the tuned circuit is applied between the Base and Emitter of the transistor. In this way the necessary automatic feedback voltage is obtained. The amount of feedback can be increased or decreased by altering the coupling between coils L and L2. When the circuit is oscillating its impedance is resistive and the Collector and Base voltages are 180o out of phase. In order to maintain oscillations the voltage applied to the tuned circuit must be "In-phase" with the oscillations occurring in the tuned circuit. Therefore, we must introduce an additional 180o phase shift into the feedback path between the Collector and Base. This is achieved by winding the coil of L2 in the correct direction relative to coil L giving us the correct amplitude and phase relationships for theOscillators circuit or by connecting a phase shift network between the output and input of the amplifier. LC Oscillators are therefore "Sinusoidal Oscillators" or more commonly "Harmonic Oscillators" that can generate high frequency sine waves for use in radio frequency (RF) type applications with the transistor amplifier being of a Bipolar Transistor or FET. Harmonic Oscillators come in many different forms because there are many different ways to construct an LC filter network and amplifier with the most common being the Hartley LC Oscillator, Colpitts LC Oscillator, Armstrong Oscillator and Clapp Oscillator to name a few.

Oscillators SummaryThe basic requirements for an Oscillatory circuit are given as follows.

1. The circuit MUST contain a reactive (frequency-dependant) component either an Inductor, (L) or a Capacitor, (C) and a DC supply voltage. 2. In a simple circuit oscillations become damped due to circuit losses. 3. Voltage amplification is required to overcome these circuit losses. 4. The overall gain of the amplifier must be at least 1, unity.

5. Oscillations can be maintained by feeding back some of the output voltage to the tuned circuit that is of the correct amplitude and in-phase, (0o). 6. Oscillations can only occur when the feedback is "Positive" (self-regeneration). 7. The overall phase shift of the circuit must be zero or 360o so that the output signal from the feedback network will be "In-phase" with the input signal.

The Hartley OscillatorThe basic LC Oscillator circuit we looked at in the previous tutorial has no means of controlling the amplitude of the oscillations. If the electromagnetic coupling between L and L2 is too small there would be insufficient feedback and the oscillations would eventually die away to zero. Likewise if the feedback was too strong the oscillations would continue to increase in amplitude until they were limited by the circuit conditions producing distortion. It is possible to feed back exactly the right amount of voltage for constant amplitude oscillations. If we feed back more than is necessary the amplitude of the oscillations can be controlled by biasing the amplifier in such a way that if the oscillations increase in amplitude, the bias is increased and the gain of the amplifier is reduced. If the amplitude of the oscillations decreases the bias decreases and the gain of the amplifier increases, thus increasing the feedback. In this way the amplitude of the oscillations are kept constant and this is known as Automatic Base Bias. One big advantage of automatic base bias is that the oscillator can be made more efficient by providing a ClassB bias or even a Class-C bias as the Collector current flows during only part of the cycle and the quiescent Collector current is very small. Then this "self-tuning" Base oscillator circuit forms the basic configuration for the Hartley Oscillator circuit. In the Hartley Oscillator the tuned LC circuit is connected between the Collector and the Base of the transistor amplifier and as far as the oscillatory voltage is concerned, the emitter is connected to a tapping point on the tuned circuit coil. The feedback of the tuned tank circuit is taken from the centre tap of the inductor coil or two separate coils in series which are in parallel with a variable capacitor, C. An Hartley Oscillator can be made from any configuration that uses either a single tapped coil (similar to an Autotransformer) or a pair of series connected coils in parallel with a single capacitor as shown below.

Basic Hartley Oscillator Circuit

When the circuit is oscillating, the voltage at point X (collector), relative to point Y (emitter), is 180o out-of-phase with the voltage at point Z (base) relative to point Y. At the frequency of oscillation, the impedance of the Collector load is resistive and an increase in Base voltage causes a decrease in the Collector voltage. Then there is a 180o phase change in the voltage between the Base and Collector and this along with the original 180o phase

shift in the feedback loop provides the correct phase relationship of positive feedback for oscillations to be maintained. The amount of feedback depends upon the position of the "tapping point" of the inductor. If this is moved nearer to the collector the amount of feedback is increased, but the output taken between the Collector and earth is reduced and vice versa. Resistors, R1 and R2 provide the usual stabilizing DC bias for the transistor in the normal manner while the capacitors act as DC-blocking capacitors. In this Hartley Oscillator circuit, the DC Collector current flows through part of the coil and for this reason the circuit is said to be "Series-fed" with the frequency of oscillation of the Hartley Oscillator being given as.

Note: LT is the total inductance if two separate coils are used. The frequency of oscillations can be adjusted by varying the "tuning" capacitor, C or by varying the position of the iron-dust core inside the coil (inductive tuning) giving an output over a wide range of frequencies making it very easy to tune. Also the Hartley Oscillator produces an output amplitude which is constant over the entire frequency range. As well as the Series-fed Hartley Oscillator above, it is also possible to connect the tuned tank circuit across the amplifier as a shunt-fed oscillator as shown below.

Shunt-fed Hartley Oscillator Circuit

In the Shunt-fed Hartley Oscillator both the AC and DC components of the Collector current have separate paths around the circuit. Since the DC component is blocked by the capacitor, C2 no DC flows through the inductive coil, L and less power is wasted in the tuned circuit. The Radio Frequency Coil (RFC), L2 is an RF choke which has a high reactance at the frequency of oscillations so that most of the RF current is applied to the LC tuning tank circuit via capacitor, C2 as the DC component passes through L2 to the power supply. A resistor could be used in place of the RFC coil, L2 but the efficiency would be less.

Example No1

A Hartley Oscillator circuit having two inductors of 0.5mH each is tuned to resonate with a capacitor which can be varied from 100pF to 500pF. Determine the upper and lower frequencies of oscillation and the oscillators bandwidth. The frequency of oscillations for a Hartley Oscillator is given as:

The circuit consists of two inductive coils in series, so the total inductance is given as:

Upper Frequency

Lower Frequency

Oscillator Bandwidth

Colpitts OscillatorsIn some ways the Colpitts Oscillator is the opposite to the Hartley Oscillator we looked at in the previous tutorial. Like the Hartley oscillator, the tuned tank circuit consists of an LC resonance circuit connected between the Collector and Base of the transistor amplifier. The basic configuration of the Colpitts Oscillator resembles that of the Hartley Oscillator but the difference being is that the centre tapping is now made from a "Capacitive Voltage Divider" network instead of a tapped autotransformer type inductor as shown below.

Basic Colpitts Oscillator Circuit

The transistor amplifiers Emitter is connected to the junction of capacitors, C1 and C2 which are connected in series with the required external phase shift is obtained in a similar manner to that in the Hartley Oscillator. The amount of feedback is determined by the ratio of C1 and C2 which are generally "ganged" together to provide a constant amount of feedback. The frequency of oscillations for a Colpitts Oscillator is determined by the resonant frequency of the LC tank circuit and is given as:

where CT is the capacitance of C1 and C2 connected in series and is given as:.

The configuration of the transistor amplifier is of a Common Emitter Amplifier with the output signal 180o out of phase with regards to the input signal. The additional 180o phase shift require for oscillation is achieved by the fact that the two capacitors are connected together in series but in parallel with the inductive coil resulting in overall phase shift of the circuit being zero or 360o. Resistors, R1 and R2 provide the usual stabilizing DC bias for the transistor in the normal manner while the capacitor acts as a DC-blocking capacitors.

Example No1A Colpitts Oscillator circuit having two capacitors of 10pF and 100pF respectively are connected in parallel with an inductor of 10mH. Determine the frequency of oscillations of the circuit. The frequency of oscillations for a Colpitts Oscillator is given as:

The circuit consists of two capacitors in series, so the total capacitance is given as:

The inductor is of 10mH then the frequency of oscillation is:

Then the frequency of oscillations for the Oscillator is 527.8kHz

The RC OscillatorIn the Amplifiers tutorial we saw that a single stage amplifier will produce 180o of phase shift between its output and input signals when connected in a class-A configuration. For an oscillator to oscillate sufficient feedback of the correct phase, ie "Positive Feedback" must be provided with the amplifier being used as an inverting stage to achieve this. In a RC Oscillator the input is shifted 180o through the amplifier stage and 180o again through a second inverting stage giving us "180o + 180o = 360o" of phase shift which is the same as 0o thereby giving us the required positive feedback. In a Resistance-Capacitance Oscillator or simply an RC Oscillator, we make use of the fact that a phase shift occurs between the input to a RC network and the output from the same network. for example.

RC Phase-Shift Network

The circuit on the left shows a single Resistor-Capacitor network and whose output voltage "leads" the input voltage by some angle less than 90o. An ideal RC circuit would produce a phase shift of exactly 90o. The amount of actual phase shift in the circuit depends upon the values of the Resistor, Capacitor and the chosen frequency of oscillations with the phase angle ( ) being given as:

Phase Angle

In our simple example above, the values of R and C have been chosen so that at the required frequency the output voltage leads the input voltage by an angle of about 60o. Then by connecting together three such RC Networks in series we can produce a total phase shift in the circuit of 180o at the chosen frequency and this forms the bases of an RC Oscillator circuit.

We know that in an amplifier circuit either using a Bipolar Transistor or an Operational Amplifier, it will produce a phase-shift of 180o between its input and output. If a RC phase-shift network is connected between this input and output of the amplifier, the total phase shift will become 360o, ie. the feedback is "in-phase". Consider the circuit below.

Basic RC Oscillator Circuit

The RC Oscillator which is sometimes called a Phase Shift Oscillator, produces a sine wave output signal using regenerative feedback from the Resistor/Capacitor combination. This regenerative feedback from the RC network is due to the ability of the capacitor to store an electric charge, (similar to the LC tank circuit). This Resistor/Capacitor feedback network can be connected as shown above to produce a leading phase shift (Phase Advance Network) or interchanged to produce a lagging phase shift (Phase Retard Network) the outcome is still the same as the sine wave oscillations only occur at the frequency at which the overall phase-shift is 360o. By varying one or more of the resistors or capacitors in the phase-shift network, the frequency can be varied and generally this is done using a 3-ganged variable capacitor. If all the resistors, R and the capacitors, C are equal in value, then the frequency of oscillations produced by the oscillator is given as:

Where:

f is the Output Frequency in Hertz R is the Resistance in Ohms C is the Capacitance in Farads N is the number of RC stages and in our example N = 3Since the RC network in the RC Oscillator circuit also acts as an attenuator producing attenuation of -1/29th (Vo/Vi = ) per stage, the gain of the amplifier must be sufficient to overcome the losses and in our three mesh network above the amplifier gain must be greater than 29. the loading effect of the amplifier on the feedback network has an effect on the frequency of oscillations and can cause the oscillator frequency to be up to 25% higher than calculated. Then the feedback network should be driven from a high impedance output source and fed into a low impedance load such as a common emitter transistor amplifier but better still is to use an Operational Amplifier as it satisfies these conditions perfectly.

The Op-amp RC OscillatorOperational Amplifier RC Oscillators are more common than their Bipolar Transistors counterparts. TheRC network that produces the phase shift is connected from the op-amps output back to its "Non-inverting" input as shown below.

Op-amp RC Oscillator Circuit

As the feedback is connected to the non-inverting input, the operational amplifier is therefore connected in its "Inverting Amplifier" configuration which produces the required 180o phase shift while the RC network produces the other 180o phase shift at the required frequency. Although it is possible to cascade together two RC stages to provide the required 180o of phase shift, the stability of the oscillator at low frequencies is poor. One of the most important features of an RC Oscillator is its frequency stability which is its ability too provide a constant frequency output under varying load conditions. By cascading three or even four RCstages together the stability of the oscillator can be greatly improved. RC Oscillators with four stages are generally used because commonly available operational amplifiers come in quad IC packages so designing a 4-stage oscillator with 45o of phase shift relative to each other is relatively easy. RC Oscillators are stable and provide a well-shaped sine wave output with the frequency being proportional to 1/RC and therefore, a wider frequency range is possible when using a variable capacitor. However, RC Oscillators are restricted to frequency applications because of their bandwidth limitations to produce the desired phase shift at high frequencies.

Example No1Determine the frequency of oscillations of a RC Oscillator circuit having 3-stages each with a resistor and capacitor of equal values. R = 10k and C = 500pF The frequency of oscillations for a RC Oscillator is given as:

The circuit is a 3-stage oscillator which consists of three 10k resistors and three 500pF capacitors therefore the frequency of oscillation is given as:

Wien Bridge OscillatorsIn the previous RC Oscillators tutorial we saw that a resistor and capacitor can be connected together to produce an oscillating circuit. Another type of oscillator which uses a RC network in place of the conventional LC tuned circuit to produce a sinusoidal output waveform, is the Wien Bridge Oscillator. The Wien Bridge Oscillator is a two-stage RC coupled amplifier circuit that has good stability at its resonant frequency, low distortion and is very easy to tune making it a popular circuit as an audio frequency oscillator but the phase shift of the output signal is considerably different from the previous RC Oscillators. The Wien Bridge Oscillator uses a feedback circuit consisting of a series RC circuit connected with a parallel RC of the same component values producing a phase delay-advance circuit depending upon the frequency. Consider the circuit below.

RC Phase Shift Network

The above RC network consists of a series RC circuit connected to a parallel RC forming basically a High Pass Filter connected to a Low Pass Filter producing a very selective 2nd order frequency dependantBand Pass Filter with a high Q factor at the selected frequency. At low frequencies the reactance, Xc of the series capacitor is very high so the series capacitor acts like an open circuit and blocks any input signal, Vin and therefore there is no output signal, Vout. At high frequencies, the reactance of the parallel capacitor is very low so the parallel capacitor acts like a short circuit on the output so again there is no output signal. However, between these two extremes the output voltage reaches a maximum and the frequency at which this happens is called the Resonant Frequency, (r) as the circuits reactance equals its resistance, Xc = R. At this resonant frequency the output voltage is one third (1/3) of the input voltage.

Output Gain and Phase Shift

It can be seen that at very low frequencies the phase angle between the input and output signals is "Positive" (Phase Advanced), while at very high frequencies the phase angle becomes "Negative" (Phase Delay). In the middle of these two points the circuit is at its resonant frequency, (r) with the signals being "in-phase" or 0o and we can define this resonant frequency point with the following expression.

Resonant Frequency

Where:

fr is the Resonant Frequency in Hertz R is the Resistance in Ohms C is the Capacitance in FaradsThen this frequency selective RC network forms the basis of the Wien Bridge Oscillator circuit. If we now place this RC network across a Non-inverting amplifier the following oscillator circuit is produced.

Wien Bridge Oscillator

The output of the operational amplifier is fed back to the inputs "in-phase" with part of the feedback signal is connected to the inverting input terminal via the resistor divider network of R1 and R2, while the other part is fed back to the non-inverting input terminal via the RC network. Then at the selected resonant frequency, ( r ) the voltages applied to the inverting and non-inverting inputs will be equal and "in-phase" so the positive feedback will cancel the negative feedback signal causing the circuit to oscillate. Also the voltage gain of the amplifier circuit MUST be 3 as set by the resistor network, R1 and R2.

Wien Bridge Oscillator SummaryThen for oscillations to occur in a Wien Bridge Oscillator circuit the following conditions must apply.

1. The Voltage gain of the amplifier must be at least 3. 2. The network can be used with a Non-inverting amplifier. 3. The input resistance of the amplifier must be high compared to R so that the RC network is not overloaded and alter the required conditions. 4. The output resistance of the amplifier must be low so that the effect of external loading is minimised.

5. Some method of stabilizing the amplitude of the oscillations must be provided because if the voltage gain of the amplifier is too small the desired oscillation will decay and if it is too large the waveform becomes distorted.

Example No1Determine the maximum and minimum frequency of oscillations of a Wien Bridge Oscillator circuit having a resistor of 10k and a variable capacitor of 1nF to 1000nF. The frequency of oscillations for a Wien Bridge Oscillator is given as:

Lowest Frequency

Highest Frequency

Crystal OscillatorsOne of the most important features of an oscillator is its Frequency Stability, or in other words its ability to provide a constant frequency output under varying conditions. Some of the factors that affect the frequency stability of an oscillator include: temperature, variations in the load and changes in the power supply. Frequency stability of the output signal can be improved by the proper selection of the components used for the resonant feedback circuit including the amplifier but there is a limit to the stability that can be obtained from normal LC and RC tank circuits. For very high stability a quartz crystal is generally used as the frequency determining device to produce another types of oscillator circuit known generally as Crystal Oscillators. When a voltage source is applied to a small thin piece of crystal quartz, it begins to change shape producing a characteristic known as the Piezo-electric Effect. This piezo-electric effect is the property of a crystal by which an electrical charge produces a mechanical force by changing the shape of the crystal and vice versa, a mechanical force applied to the crystal produces an electrical charge. Then, piezo-electric devices can be classed as Transducers as they convert energy of one kind into energy of another. This piezo-electric effect produces mechanical vibrations or oscillations which are used to replace the LC tank circuit and can be seen in many different types of crystal substances with the most important of these for electronic circuits being the quartz minerals because of their greater mechanical strength. The quartz crystal used in Crystal Oscillators is a very small, thin piece or wafer of cut quartz with the two parallel surfaces metallized to make the electrical connections. The physical size and thickness of a piece of quartz crystal is tightly controlled since it affects the final frequency of oscillations and is called the crystals "characteristic frequency". Then once cut and shaped the crystal can not be used at any other frequency. The crystals characteristic or resonant frequency is inversely proportional to its physical thickness between the two metallized surfaces. A mechanically vibrating crystal can be represented by an equivalent electrical circuit consisting of low Resistance, large Inductance and small Capacitance as shown below.

Quartz Crystal

A quartz crystal has a resonant frequency similar to that of a electrically tuned tank circuit but with a much higher Q factor due to its low resistance, with typical frequencies ranging from 4kHz to 10MHz. The cut of the crystal also determines how it will behave as some crystals will vibrate at more than one frequency. Also, if the crystal is not of a parallel or uniform thickness it have two or more resonant frequencies having both a fundamental frequency and harmonics such as second or third harmonics. However, usually the fundamental frequency is more stronger or pronounced than the others and this is the one used. The equivalent circuit above has three reactive components and there are two resonant frequencies, the lowest is a series type frequency and the highest a parallel type resonant frequency. We have seen in the previous tutorials, that an amplifier circuit will oscillate if it has a loop gain greater or equal to 1 and it has positive feedback. In a Crystal Oscillator circuit the oscillator will oscillate at the crystals fundamental series resonant frequency as the crystal always wants to oscillate when a voltage source is applied to it. However, it is also possible to "tune" a crystal oscillator to any even harmonic of the fundamental frequency, (2nd, 4th, 8th etc.) and these are known generally as Harmonic Oscillators whileOvertone Oscillators vibrate at odd multiples of the fundamental frequency, 3rd, 5th, 11th etc). Generally, crystal oscillators that operate at overtone frequencies do so using their series resonant frequency.

Colpitts Crystal OscillatorThe design of a Crystal Oscillator is very similar to the design of the Colpitts Oscillator we looked at in the previous tutorial, except that the LC tank circuit has been replaced by a quartz crystal as shown below.

Colpitts Crystal Oscillator

These types of Crystal Oscillators are designed around the common emitter amplifier stage of a Colpitts Oscillator. The input signal to the base of the transistor is inverted at the transistors output. The output signal at the collector is then taken through a 180o phase shifting network which includes the crystal operating in a series resonant mode. the output is also fed back to the input which is "in-phase" with the input providing the necessary positive feedback. Resistors, R1 and R2 bias the resistor in a Class Aoperation and resistor Re is chosen so that the loop gain is slightly greater than unity. Capacitors, C1 and C2 are made as large as possible in order that the frequency of oscillations can approximate to the series resonant mode of the crystal and is not dependant upon the values of these capacitors. The circuit diagram above of the Colpitts Crystal Oscillator circuit shows that capacitors, C1and C2 shunt the output of the transistor and which reduces the feedback signal. Therefore, the gain of the transistor limits the maximum values of C1 and C2. The output amplitude should be kept low in order to avoid excessive power dissipation in the crystal otherwise could destroy itself by excessive vibration.

Pierce OscillatorAnother common design of crystal oscillator is that of the Pierce Oscillator. The Pierce oscillator is a crystal oscillator that uses the crystal as part of its feedback path and therefore has no resonant tank circuit. The Pierce Oscillator uses a JFET as its amplifying device as it provides a very high input impedance with the crystal connected between the output Drain terminal and the input Gate terminal as shown below.

Pierce Crystal Oscillator

In this simple circuit, the crystal determines the frequency of oscillations and operates on its series resonant frequency giving a low impedance path between output and input. There is a 180 phase shift at resonance, making the feedback positive. The amplitude of the output sine wave is limited to the maximum voltage range at the Drain terminal. Resistor, R1 controls the amount of feedback and crystal drive while the voltage across the radio frequency choke, RFC reverses during each cycle. Most digital clocks, watches and timers use a Pierce Oscillator in some form or other as it can be implemented using the minimum of components.

Microprocessor ClocksWe can not finish a Crystal Oscillators tutorial without mentioning something about Microprocessor clocks. Virtually all microprocessors, microcontrollers, PICs and CPU's generally operate using a Crystal Quartz Oscillator as its frequency determining device to generate their clock waveform because as we already know, crystal oscillators provide the highest accuracy and frequency stability compared to Resistor/Capacitor or Inductor/Capacitor oscillators. The CPU clock dictates how fast the processor can process the data and a microprocessor having a clock speed of 1MHz means that it can process data internally 1 million times a second at every clock cycle. Generally all that's needed to produce a microprocessor clock waveform is a crystal and two ceramic capacitors of values ranging between 15 to 33pF as shown below.

Microprocessor Oscillator

Most microprocessors, microcontrollers and PICs have two oscillator pins labelled OSC1 and OSC2 to connect to an external quartz crystal, RC network or even a Ceramic resonator. In this application theCrystal Oscillator produces a train of continuous square wave pulses whose frequency is controlled by the crystal which inturn regulates the instructions that controls the device. For example, the master clock and system timing.

Example No1A series resonant crystal has the following values after being cut, R = 1k, C = 0.05pF and L = 3H. Calculate the fundamental frequency of oscillations of the crystal. The frequency of oscillations for Crystal Oscillators is given as:

Then the fundamental frequency of oscillations for the crystal is given as 411 kHz

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VSS4Spread Spectrum CMOS 5.0 x 3.2 x 1.1 4 pin SMD

Spread Spectrum for EMI reduction 12 to 168

RoHS and Lead Free Assembly Compliant

XO

VCC1-FIB35 x 7 x 1.8 4 pin SMD RoHS and Lead Free Assembly Compliant Low Jitter SMD Package

106.25

HCMOS

XO

PX-700 C12501 to 800 ACMOS TTL LVPECL LVDS 5 x 7 x 1.9 SMD Mil Temp range and Class B screening optional, Previously MC032 and MC033, MC029 Shock Survival >15,000g RoHS Compliant Low Jitter

XO

PX-701 C12601 to 175 HCMOS LVPECL LVDS 5 x 7 x 2.3 6 pin SMD RoHS and Lead Free Assembly Compliant Reflow Process Compatible Low Jitter Low Phase Noise Tight Stability SONET Minimum Clock Specification

XO

PX-501 C13101 to 700 HCMOS PECL LVDS Sinewave 14.4 x 9.5 x 5.9 SMD RoHS and Lead Free Assembly Compliant Surface Mount Package Reflow Process Compatible AT-Cut Crystal SONET Minimum Clock Specification Good phase noise

XO

PX-500 C13001 to 800 ACMOS TTL LVPECL 14.2 x 9.14 x 3.68 SMD Mil Temp Range and Class B screening optional, Previously MC042, MC342, MC037

XO

VCE1TTL HCMOS 9 x 14 x 4.7 4 pin SMD

1 to 66.667

RoHS and Lead Free Assembly Compliant Industry Standard Plastic Package

XO

Additional Crystal Oscillators top of page

Programmable Crystal OscillatorsCrystal Oscillator Series

Legacy Part No.

Frequency Range (MHz)

Output Logic

Package (mm)

Crystal Oscillator Features Smallest Available XO Quick Delivery

VL-821 VCS31 to 200 CMOS 3.2 x 2.5 x 1.2 4 pin SMD

XO

RoHS and Lead Free Assembly Compliant

VP-700 VPC11.544 to 160 (Up to 125 MHz for 3.3Vdc) HCMOS / TTL 7.5 x 5 x 1.8 mm Quick Turn Programmable

XO

VPE1

1 to 125

HCMOS / TTL

14 x 9.8 x 4.7 mm

Quick Turn Programmable

XO

VM-7007.0 x 5.0 x 0.9 mm QFN

1 to 150

CMOS

Standard Foot Print 1.8V 2.5V 3.3 V Available Quick Turn Capability

XO

RoHS Compliant

VM-8005.0 x 3.2 x 0.9 mm QFN

1 to 150

CMOS

Standard Foot Print 1.8V 2.5V 3.3 V Available Quick Turn Capability

XO

RoHS Compliant Standard Foot Print 1.8V 2.5V 3.3 V Available Quick Turn Capability Low Cost

VM-8203.2 x 2.5 x 0.9 mm QFN

1 to 150

CMOS

XO

RoHS Compliant Standard Foot Print 1.8V 2.5V 3.3 V Available Quick Turn Capability Low Cost

VM-8402.5 x 2.0 x 0.9 mm QFN

1 to 150

CMOS

XO

RoHS Compliant

Archived Programmable Crystal Oscillators top of page

Precision Crystal OscillatorsPrecision Crystal Oscillator Series

Legacy Part No.

Frequency Range

Output Logic

Package

Precision Crystal Oscillator Features

VMEM5Q/3Q/2Q5.0 X 3.2 X 1.1 mm 3.2 X 2.5 X 0.85mm 2.5 X 2.0 X 0.85mm Vibration Insensitive for Military/Rugged Enviroments

1MHz - 30MHz

CMOS

XO

XO-400

15MHz - 250MHz

Complementary PECL

20.32 x 12.70 x 10.29

Ultra low jitter

XO

CO-401

CO-402

PX-400

CO-441TTL HCMOS ACMOS

CO-442XO

1 Hz - 200 MHz

4 Pin 14 Pin

Low Profile

CO-431/451

CO-432/452

CO-406XO

16kHz - 100MHz

Surface Mount DIP TTL HCMOS ACMOS ECL PECL 14 Pin Flatpack

Many custom options Many custom options

PX-340

CO-407

1 Hz to 700 MHz

CO-447XO

CO-437/457

PX-422

CO-408

CO-448XO

10kHz - 60MHz

HCMOS ACMOS

Ceramic LCC

Small size

CO-446XO

1Hz - 175MHz

CO-449XO

1Hz - 100MHz

HCMOS ACMOS FCT ACT

Surface Mount DIP

Low profile

4 Pin DIP

Small size

CO-434/454

PX-260XO

CO-484

4MHz - 700MHz

16 Pin DIP

ECL / PECL / Sinewave

10K, 10KH, ECLinPS, 10E/EL

CO-436/456

5MHz - 200MHz

Gull wing metal DIP

XO

CO-233/233HXO

4MHz - 500MHz

Sinewave

Solder seal metal can

PCB mount, low phase noise Reduced size, PCB mount Reduced size, PCB mount

CO-233F/FWXO

CO-285WXO

CO-285PXO

PX-200 CO-487

16 Pin Flatpack

Miniature hybrid design

XO

CO-286WXO

500.1MHz-1.3GHz

Solder seal metal can

Small size to 1.3GHz Very high frequency to 2.6GHz

CO-287WXO

1.31GHz-2.6GHz 16kHz - 60MHz TTL 14 Pin DIP

M55310/16

Class "S" also available

XO

M55310/19

12 x 12

1MHz - 60MHz

TTL

TTL, 40 Pad LCC

XO

M55310/21

16.5 x 16.5

1MHz - 60MHz

TTL

TTL; 20 Lead Flatpack

XO

M55310/2614 Pin DIP or 4 Pin DIP

0.01MHz - 65MHz

HCMOS

XO

M55310/27

1MHz - 85MHz

HCMOS

9 x 14

HCMOS; ceramic SMD J lead

XO

M55310/28

1MHz - 85MHz

TTL

9 x 14

TTL; ceramic SMD J lead

XO

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