Quartz Crystal Oscillators

Quartz Crystal Oscillator has a quite significant difference that distinguishes it from other types of oscillators.

One of the most important features of any oscilator is its frequency stability, that is, its ability to provide a constant frequency output under changing load conditions.

Some of the factors that affect the frequency stability of an oscilator usually include: changes in temperature, changes in load, as well as several changes in DC power supply voltage.

The frequency stability of the output signal can be greatly improved by the correct selection of components used for the resonance feedback circuit, including the amplifier. However, there is a limit to the stability that can be obtained from normal LC and RC tank circuits.

quartz crystal oscillator

To achieve a very high level of oscillator stability, a quartz crystal is often used as a frequency determination device to produce another type of oscillator circuit known as a quartz crystal oscillator (XO or XTAL).

When a voltage source is applied to a small, thin piece of quartz crystal, Piezo begins to change shape by producing a feature known as the electric effect. This Piezo-electric Effect is the property of a crystal in 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.

Next, piezo-electric devices can be classified as converters, as they convert one type of energy into the energy of another (from electricity to mechanical or mechanical to electricity). This piezo-electric effect produces mechanical vibrations or oscillations that can be used to replace the standard LC tank circuit in previous oscillators.

There are many different types of crystal matter that can be used as oscillators, the most important for electronic circuits, partly due to their larger mechanical strength.

quartz crystal oscillator
Quartz Crystal

The quartz crystal used in a quartz crystal oscillator is a very small, thin piece or cut quartz plate, metallized two parallel surfaces to make the necessary electrical connections. The physical size and thickness of a quartz crystal fragment are severely controlled during production as it affects the final or basic frequency of oscillations. The basic frequency is often referred to as the "characteristic frequency" of crystals.

Once cut and shaped, the crystal cannot be used at any other frequency. In other words, its size and shape determine the base oscillation frequency.

The frequency of crystals is inversely proportional to the physical thickness between the two metallized surfaces. A mechanically vibrating crystal can be represented by an equivalent electrical circuit consisting of low resistance R, a large inductans L and small capacitance C, as shown below.

quartz crystal oscillator
Quartz Crystal Oscillator Equivalent Model

The equivalent electrical circuit for the quartz crystal indicates a series of RLC circuits representing the mechanical vibrations of the crystal in parallel with a capacitance representing the electrical connections of the crystal. Quartz crystal oscillators tend to work towards "serial resonances".

The equivalent impedance of the crystal has a series of resonances in which Cs resonates with the Ls inducedance at the working frequency of the crystals. This frequency is called crystal series frequency, εs. In addition to this serial frequency, there is a second frequency point that occurs as a result of parallel resonance when Ls and Cs enter resonance with parallel capacitor Cp.

Crystal Impedance Against Frequency

quartz crystal oscillator

The slope of the crystal impedance above indicates this as the frequency increases along the terminals. At a certain frequency, the interaction between the serial capacitor Cs and the inductor Ls creates a series resonance circuit that minimizes crystal impedance and is equal to Rs. This frequency point is called crystal series resonance frequency εs and is crystal capacitive below εs.

As the frequency rises above this serial resonance point, it acts as a crystal inductor until the frequency reaches the parallel resonance frequency. At this frequency point, the interaction between the serial inductor, Ls and parallel capacitor, Cp, creates a parallel adjusted LC tank circuit and therefore reaches the maximum value of impedance along the crystal.

Then we can see that a quartz crystal is a combination of a series and parallel adjusted resonance circuits that are released at two different frequencies with a very small difference between the two, depending on the cut of the crystal. In addition, since the crystal can operate at its own serial or parallel resonance frequencies, a crystal oscillator circuit must be adjusted to one or another frequency, since you cannot use both together.

Depending on the circuit characteristics, a quartz crystal can act as a capacitor, an inductor, a series resonance circuit or a parallel resonance circuit, and to show this more clearly, we can also draw the reassurance of the crystals against the frequency, as shown.

Crystal Reactance Against Frequency

quartz crystal oscillator

The slope of the reactance against the above frequency indicates that the serial reactance at the εs frequency is inversely proportional to Cs because it appears crystal capacitive below and above εp. Between the frequencies εs and εp, the crystal appears inductive as the two parallel capacitances take each other.

Then the formula of the crystal series resonance frequency is given as follows:

quartz crystal oscillator
Serial Resonance Frequency

The parallel resonance frequency occurs when the rectane of the εp, serial LC leg is equal to the Cp recess of the parallel capacitor and is given as follows:

quartz crystal oscillator
Parallel Resonance Frequency

Quartz Crystal Oscillator Question Sample 1

A quartz crystal has the following values: Rs = 6.4Ω, Cs = 0.09972pF and Ls = 2.546mH. If the capacitance in the terminal is measured at Cp 28.68pF, calculate the basic oscillation frequency and secondary resonance frequency of the Crystal.

Crystals series resonance frequency, εS:

quartz crystal oscillator

Parallel resonance frequency of the crystal, εP:

quartz crystal oscillator

We can see that the difference between εs and εp, the basic frequency of the crystal, is less than about 18kHz (10,005MHz – 9,987MHz). However, in this frequency range, the crystal's Q factor (Quality Factor) is extremely high because the inductive or resistant values of the crystal are much higher. At the serial resonance frequency, the Q factor of our crystal is given as follows:

quartz crystal oscillator

Then the Q factor of our crystal sample, about 25,000, is due to this high XL/R ratio. The Q factor of most crystals is between 20,000 and 200,000 compared to a good LC-tuned tank circuit that we have previously examined and will be much less than 1000. This high Q factor value also contributes to higher frequency stability in the working frequency of the crystal, making it ideal for creating crystal oscillator circuits.

Thus, we found that a quartz crystal has a resonance frequency similar to that of an electrically tuned LC tank circuit, but has a much higher Q factor. This is mainly due to its low series resistance, Rs. As a result, quartz crystals are an excellent choice of components for use in oscillators, especially very high frequency oscillators.

Typical crystal oscillators can vary at oscillation frequencies from approximately 40 kHz to 100 MHz, depending on circuit configurations and the amplifier used. The cut of the crystal also determines how it behaves, as some crystals vibrate at multiple frequencies, producing additional oscillations called upper tones.

Also, if the crystal does not have a parallel or uniform thickness, it can have two or more resonance frequencies, which both produce the basic frequency and produce harmonics such as the second or third harmonics.

In general, the basic oscillation frequency for a quartz crystal will be this, although it is much stronger or more pronounced than the secondary harmonics around it. In the graphs above we found that one crystal equivalent circuit has three reactive components, two capacitors plus one inductor, so there are two resonance frequencies, the lowest serial resonance frequency and the highest parallel resonance frequency.

In previous lessons, we have seen that an amplifier circuit will be released if it has a cycle gain equal to or greater than one, and the feedback is positive. In a Quartz Crystal Oscillator circuit, the crystal is released at the basic parallel resonance frequency of the crystals, as it always wants to be released when a voltage source is applied to it.

However, a crystal oscilator can be 4., 8.vb.) It is also possible to "adjust" to any pair harmonic, and while these are often known as Harmonic Oscillators, Upper Tone Oscillators vibrate at single times the basic frequency. , 3., 5., 11.vb.). In general, crystal oscillators operating at high tone frequencies do so using serial resonance frequencies.

Colpitts Quartz Crystal Oscillator

Crystal oscillator circuits are usually created using bipolar transistors or FET's. This is due to the fact that although transactional amplifiers can be used in many different low frequency (≤100kHz) oscillator circuits, transactional amplifiers do not have bandwidth to work successfully at higher frequencies suitable for crystals above 1MHz.

The design of a Crystal Oscillator is very similar to that of the Colpitts Oscillator, which we examined in the previous course, except that the LC tank circuit that provides feedback oscillations is replaced with a quartz crystal, as shown below.

quartz crystal oscillator
Colpitts Crystal Oscillator

This type of Crystal Oscillators are designed around a common collector (emitter-tracker) amplifier. The R1 and R2 resistance network adjusts the DC pre-redeem level at the base, while the emitter resistance adjusts the RE output voltage level. Resistance R2is set as large as possible to prevent loading into the parallel connected crystal.

The transistor is a 2N4265, a general purpose NPN transistor that connects in a common collector configuration and can operate at switching speeds exceeding 100Mhz, well above the basic frequency of crystals that can be between about 1MHz and 5MHz.

The above circuit diagram of the Colpitts Crystal Oscillator circuit indicates that the C1 and C2 capacitors are snuffing the output of the transistor, which reduces the feedback signal. Therefore, the gain of the transistor limits the maximum values of C1 and C2. To prevent excessive loss of power in the crystal, the output amplitude must be kept low, otherwise it can self-destruct with excessive vibration.

Pierce (Drilling) Oscitor

Another common design of the quartz crystal oscillator is the design of the Pierce Oscillator. The Pierce oscillator is very similar by design to the previous Colpitts oscillator and is very suitable for applying crystal oscillator circuits using a crystal as part of the feedback circuit.

The Pierce oscillator is basically a series of resonance-adjusted circuits that use a JFET for the main upgrade device (unlike the parallel resonance circuit of the Colpitts oscillator), since FET's provide very high input impedances with crystal connected between the Channel and the Door via capacitor C1. shown below.

quartz crystal oscillator
Pierce Crystal Oscillator

In this simple circuit, it determines the frequency of crystal oscillations and operates at a serial resonance frequency, giving a low impedance path between output and input. There's 180 phase shifts in resonance, which makes feedback positive. The amplitude of the output sinus wave is limited to the maximum voltage range in the channel terminal.

Resistance controls the amount ofR1 feedback, and the crystal drive reverses the voltage at the radio frequency, while the RFC reverses in each cycle. Most digital clocks, watches, and timers use the Pierce Oscitor because it can be applied using the minimum component.

In addition to using transistors and FET's, we can also create a simple basic parallel resonant crystal oscillator similar to the work of the Pierce oscillator using a CMOS inverter as a gain element. The basic quartz crystal oscilator consists of a single inverted Schmitt trigger logic door, an inductive crystal and two capacitors, such as the TTL 74HC19 or CMOS 40106, 4049 types. These two capacitors determine the value of the load capacitance of the crystals. Serial resistance helps limit drive current in the crystal and also insulates the inverter output from the complex impedance created by the capacitor-crystal meth.

CMOS Crystal Oscillator

quartz crystal oscillator

The crystal oscillates at a serial resonance frequency. The CMOS inverter is initially pressed into the middle of the working zone by the feedback resistance R1. This ensures that the Q point of the inverter is in a high-earning region. A resistance of 1MΩ is used here, but as long as its value is greater than 1MΩ, there is no problem. An additional inverter is used to buffer the output from the oscillator to the connected load.

Inverter 180 provides the additional 180o'o required for oscillationof that phase shift and crystal capacitor network. The advantage of the CMOS crystal oscillator is that it always automatically recalibrates itself to maintain this 360 oscillationphase shift.

Unlike previous transistor-based crystal oscillators that produce sinusoidal output waveforms, the CMOS Inverter oscillator uses digital logic gates, so output is a square wave that swings between HIGH and LOW. Naturally, the maximum operating frequency depends on the switching characteristics of the logic gate used.

Microprocessors and Crystal Oscillators

We can't finish quartz crystal oscillator training without mentioning the crystal oscillators used with microprocessors. Almost all microprocessors, microcontrollers, PIC's and CPUs usually work using a Quartz Crystal Oscillator as a frequency determination device to create clock waveforms, since as we already know, crystal oscillators provide the highest accuracy and frequency stability compared to the resistance capacitor. You can also get enough information about the standalone Arduino circuit here.

CPU clock determines how fast the processor can run and process data with a microprocessor, PIC or microcontroller with a clock speed of 1MHz, which means that it can process data internally one million times per hour cycle. Usually all it takes to produce a microprocessor clock waveform is a crystal and two ceramic capacitors with values ranging from 15 to 33pF, as shown below.

quartz crystal oscillator

Most microprocessors, microcontrollers and PIC have two oscillator inputs labeled OSC1/XTAL1 and OSC2/XTAL2 to connect to an external quartz crystal circuit, standard RC oscillator network and even a ceramic resonator. In this type of microprocessor application, the Quartz Crystal Oscillator produces a continuous sequence of square wave pulses whose basic frequency is controlled by the crystal itself. This basic frequency regulates the flow of instructions that control the processor device. For example, the main time and system schedule.

Quartz Crystal Oscillator Question Sample 2

After a quartz crystal is cut, it has the following values: Rs = 1kΩ, Cs = 0.05pF, Ls = 3H, and Cp = 10pF. Calculate crystal sequences and parallel oscillation frequencies.

The serial oscillation frequency is calculated as follows:

quartz crystal oscillator

The parallel oscillation frequency is calculated as follows:

quartz crystal oscillator

Then the oscillation frequency for the crystal will be between 411kHz and 412kHz.