振荡器电路中晶体的高稳定性

The stability of good quality RC oscillators can be expected to be around 0.1%, while normally we can assume the stability of LC oscillators to be up to 0.01%. When a much higher level of stability is required, we have to use a crystal based oscillator circuit.

与LC网络相比，晶体在振荡器电路中是如此重要的主要原因，它们的高度稳定性高，确保了实际上没有高输出幅度的精确振荡频率。

LC resonance vs Crystal Resonance

As opposed to the electro-magnetic resonance associated with an LC circuit, we find an electro-mechanical resonance from the piezo-electric crystal. The only difference is that crystals could simply be processed through machines to get high precision results in terms of natural frequencies as close as 10 parts per million (ppm).

Which Material is used in Crystals

大量的晶体材料,石英的happens to be a main example, have got the characteristics through which these are able to generate an electric field when exposed to mechanical stress. On the other hand, a quartze material tend to get physically deformed as soon as these are exposed to an electric field. This phenomenon is called the piezo-electric effect. As a result, you are able to cut a crystal to make it physically oscillate at some specified frequency as soon as it is exposed to an AC electric field.

尽管石英是最常用的物质之一，但在几种应用中也适用于锂钽酸盐，氧化镁 - 氧化锗，锂铌酸锂和铝 - 磷酸盐。

Additionally, you will find ceramic elements like the PZT ceramics being used for making crystals, which involves solid solutions of lead, zirconium and titanium. Yet another piezo-electric category includes polymers like polyvinyl chloride and difluorpolyethylene. For these materials, the piezo-electric characteristics is determined by how these are processed.

A fine plastic film using the above material is first warmed and then subjected to a powerful electrical field, and subsequently cooled down at room temperature. This process helps in the polarization of the substance, which subsequently gets the piezo-electric attributes.

Crystal Electronic Modelling

寻找电子视角，可以实现如下所示的RLC电路作为模拟晶体的工作的模型。

电感L可以比较的质量quartz piece. The capacitor C compares to the the rigidity of the quartz piece. The resistor R corresponds to the energy losses taking place due to the physical distortions happening in the crystal.

另一电容器CO的行为类似于涂覆在石英材料的两侧的导电电极之间的电容。

Normally, L can be a extremely large inductance while C is extremely low in value. For instance, in a crystal which is appropriately cut for vibrating at 200 kHz, L can be 27 H, C can be basically 0.024 pF, R can be 2 kΩ and C0 can be 9 pF.

The magnitudes like these are generally used while modelling the crystal behavior in computer simulations. The L to C ratio utilized is extremely high which we're able to obtain by making use of genuine electronic parts, providing the crystal an extremely high Q (quality factor).

晶体通常具有Q系数大约100,000，而最LC网络的Q仅在几百个范围内。

串联操作晶体和并联谐振模式

You can operate crystals in the series resonance mode or in parallel resonance mode. When applied in the series resonance mode, the crystal behaves like a capacitor and inductance connected in series. The crystal impedance can be minimal (corresponding to R only).

When utilized in the parallel resonance mode, which can be somewhat larger, the crystal works like an inductor and capacitor hooked up in parallel. In this mode the crystal's impedance increases to the highest level at the applied resonance frequency.

Crystals are often cut in a way that allows them to operate optimally in either series or the parallel resonance modes.

The cut of the crystal determines how the crystal would oscillate, the manner in which it will vibrate, and the size of the crystal film that will be required for the implementation. In case, the crystal is excited for a longitudinal vibration function, the resonant frequency can be roughly calculated using the following given formula.

F_O.= 2.7 x 10^3./L

Here L denotes the size parameter of the crystal, where the unit will be in meter. The numerical constant in the formula symbolizes the phase velocity of the crystal's vibration.

Therefore, if the required frequency fo is selected to be 100 kHz, then L must be 2.7cm. In case fo is required to be 10 MHz, L would be 0.27 mm

晶体基波和泛音频率

此外，它们通常以允许它们以基本模式或谐波（泛音）模式操作的方式切割。

The overtones are the odd harmonics of the fundamental frequency of the crystal, that makes sure that the crystal is able to operate at the fundamental as well at its harmonics. For example if we have a crystal cut to oscillate at 100 kHz, then it should also oscillate at 300 kHz, 500 kHz, 700 kHz and at other bigger harmonics.

晶体限制

我们在晶体中可能发现的缺点之一是，当晶体被切割以包括大的基波频率时，最终可能最终厚度极薄。由于这，它很容易变得容易受到物理损坏和破损。

The highest frequency limit for fundamental mode crystals is approximately 70 Hz. Crystals made for operating at frequencies which may be in the range of many hundred MHz are cut such that they get a somewhat lower fundamental range but can be controlled in harmonic mode.

通过这种方法，可以获得晶体的最大振荡频率约为500MHz。

晶体中的热稳定性

在某些振荡器应用中，热稳定性至关重要。温度系数由晶体切割的方式决定。作为一个例子，流行的AT-CUT提供温度系数约为±0.002％的晶体，温度范围为-55℃至+ 105℃。

该温度系数范围相当于大多数电容器的某个％。

For getting an increased stability the crystal are often treated in an ‘oven’. In this process the crystal is cut so that it is able to acquire a minimum temperature coefficient at a temperature which may be higher than room temperature. Here, the oven is maintained at this specified higher than room temperature.

You may find disadvantages in this process due to the involvement of high power used in the oven, the involvement of huge bulky oven, and the amount of time taken by the oven to get heated.

However, the highly improved result that we get is an enhanced thermal stability for the crystal, approximately ±5 parts per ten million.

As high frequency communication channels increase, and as the clock speeds in digital circuits increase, crystals are gradually getting replaced by ceramic resonators. These ceramic resonators are usually tiny discs of PZT ceramics or similar piezo-electric components which are efficient at working with frequencies in the Gigahertz range.

Crystals in Oscillators

由于它们的高稳定性晶体被用来替代或部分地替代到大多数振荡器电路中的LC谐振电路级。

As an example, the crystal-controlled model of the Colpitts oscillator includes a crystal and a capacitor as opposed to the inductor L1.

When a crystal is installed in place of an inductor, the frequency gets a lot more accurately set. In this type of oscillator circuit, the crystals are generally controlled in parallel resonance mode, possessing highest possible impedance in the resonant frequency and thus generating an output frequency with very high amplitude.

The Pierce oscillator demonstrated in the following figure is an example which exhibits a crystal working in the series resonance mode. Feedback is directed by means of the crystal and it attains the maximum level as the crystal resonates in the series mode, using minimum impedance.

Observe that this oscillator can work reliably with the need of a tuned circuit, depending simply on the crystal to decide its oscillating frequency. Crystal oscillators are not only very accurate with their functioning, they are in addition one of the fastest of the oscillators, typically. Present day digital circuits demand extremely fast clocks to operate them, with frequencies that may range in hundreds of megahertz.

Surface Acoustic Wave Devices

您将找到一些使用曲面声波（SAW）器件的最快振荡器。它们是具有许多电极的压电物质的微小条，如下所示。

在可以是输入端的一端，当在电极之间施加电场时，它会导致条带的外部变形。该动作产生沿着条带的表面积行进的振动波。这表现得像声波，其能够以非常高的速度跨越条带，与大约3000米/秒的声速一样快。在一秒钟的一部分之后，一旦波浪流入延伸到另一端，这可以是条带的输出，所涉及的电场会产生跨链接电极的电位差。

由于两个端部上的电极之间的间隙确定了哪个频率将更强烈地进料到锯中并从另一端检索，锯通常在带通滤波器中施加。波浪穿过条带的波所需的时间提供了滤波器的滤波器的特性。

When used as an element of an oscillator, a SAW delay line can be used exactly in the above manner at the RC network of a phase shift filter. The time taken to create a phase shift of 180° is incredibly brief, and therefore, the frequency of this kind of oscillators is tremendously high. Normally, they range up to around 2 GHz. Oscillators that work with dielectric resonators in the feedback loop can even go beyond the 2 GHz range. At this level we could be effectively into the microwave spectrum, which possess their own specialized characteristics.