SAW resonators. Resonators based on surface acoustic waves (SAW). SAW filters with low losses

Resonators based on surface acoustic waves (SAW)

piezoelectric element resonator acoustic transducer

Structurally, SAW resonators are a substrate made of piezocrystalline material, on the surface of which comb conductive electrodes are located. They are called interdigitated transducers (IDTs) and are designed to convert electrical energy into acoustic energy and vice versa. The input IDT converts the input signal into an electric field that varies in space and time, which, due to the inverse piezoelectric effect, causes elastic deformations in the subelectrode region, propagating in the form of surface acoustic waves to the output IDT, where the waves are converted back into electrical voltage.

The most commonly used are single-phase and two-phase interdigital converters. A single-phase converter (Fig. 2.7, a) is a piezoelectric plate 2 with a comb of metal electrodes 1 applied to its working surface, and on reverse side- solid electrode 3. The two-phase converter (Fig. 2.7, b) has two electrode combs on the surface of the piezoelectric plate: 1 and 3.

Excited by the inverse piezoelectric effect, two surface waves propagate in opposite directions. The total wave is obtained by adding these waves. Elastic deformation of a piezoelectric material when an alternating voltage of frequency f is applied to an IDT excites a surfactant of the same frequency if the spatial period of the IDT lattice L is equal to the length of the surfactant in the medium lc. The operation of a two-phase converter corresponds to the condition L=lc / 2. Typically, the width of the IDT electrodes is equal to the distance between them and is the pitch of the surfactant structure, which is equal to a quarter of the wavelength of the surfactant. The local deformation of the sound pipeline that has arisen under a pair of adjacent pins, having traveled a distance of lc / 2 to the next gap, appears there at the moment when the next half-wave of the external voltage reaches its maximum and creates a new deformation there, in-phase with the incoming one. When a surfactant propagates along the sound pipeline, this process is repeated many times, and as a result, by the end of the IDT, the amplitude of the surfactant, gradually increasing, will reach a maximum. The more pairs of pins, the greater the amplitude of the SAW voltage of frequency f0=V/lc and the more strongly the SAWs whose frequencies differ from f0 are suppressed (in this case, the synchronism of the SAW movement and the change in the electric field between the pins is disrupted). This leads to a narrowing of the IDT bandwidth. The number of pairs of pins N and the bandwidth?f are related by the relation?f=f0 / N. Comparing it with the expression for the quality factor of the LC circuit Q=f0/?f, we have that the number of pairs of pins corresponds (Q=N) to the value of the quality factor of the IDT. Thus, the frequency-selective properties of the IDT are determined by the pitch of the pins h and the number of their pairs.

The frequency at which the conversion of high-frequency vibrations into surfactants is most effective is called the acoustic synchronization frequency. When the input oscillation frequency deviates from it, the conversion efficiency drops the more, the greater the distance between the pins and the further the input oscillation frequency is from the acoustic synchronization frequency. This factor determines the frequency properties of the SAW device.

With existing technology, it is difficult to obtain a pitch of less than 1 micron. This step corresponds to a frequency of about 2 GHz. The lower operating frequency is determined by the feasible length of the sound line and is selected around 10 MHz.

SAW resonators can be single-input or double-input. In a single-input resonator, the functions of energy input and output are carried out by one two-phase IDT (Fig. 2.9, a), in a two-input resonator (Fig. 2.9, b), one IDT provides generation, the second - reception of acoustic waves and their conversion into an electrical signal.

Single-input SAW resonators are implemented in the form of an extended IDT with a large number of electrodes. In this case, a sequential resonance occurs at the acoustic synchronization frequency f0 or a parallel resonance at the frequency fpar = f0(1 + f/N). The frequency properties of SAW resonators are determined mainly by the frequency dependence of the reflection coefficient of reflectors 4, while IDTs are elements of communication with the resonant cavity.

To reduce losses, multi-element IDTs with “split” electrodes, substrates with a low electromechanical coupling coefficient, and distributed reflectors with a high reflection coefficient are used.

SAW resonators, depending on the requirements for temperature instability, can be manufactured using any piezoelectric material. Most often, ST cut quartz is used in manufacturing, as it is the most temperature stable.

When turning on the SAW resonator in electrical circuit an inductance is connected to its output in series with the load resistance, which compensates for the static capacitance of the IDT.

The main parameters of SAW resonators are:

• § operating frequency range: from units of megahertz to units of gigahertz;
• § frequency stability: (1...10)* 10-6 per year;
• § quality factor: depends on frequency (Q = 10400/f) and takes values ​​greater than 104. Large values ​​of quality factor are associated with the return of acoustic energy to the resonant cavity from reflective elements;
• § tuning accuracy: depends on the frequency and is in the range (150...1000)*10-6. Frequency adjustment is allowed within (1...10)*10-3 due to the introduction of an additional converter with varying load resistance.

Thanks to the use of surface acoustic waves, the frequency range of this type of filter is extended to high frequencies and can reach values ​​of several gigahertz. To implement surface wave filters, piezoelectrics similar to a quartz plate are used. However, quartz is rarely used to make broadband filters. Typically barium titanate or lithium niobate is used.

The difference in the operation of SAW filters from quartz or piezoceramic filters is that it is not the volumetric vibration of the piezoelectric that is used, but a wave propagating over the surface. In order to avoid the occurrence of body waves that can distort the frequency response, special design measures are taken.

SAW filters with linear phase response

Excitation of a surface wave on the surface of a piezoelectric plate is usually carried out using two metal strips deposited on its surface at a distance of λ/2. To increase the efficiency of the converter, the number of strips is increased. Figure 1 shows a simplified design of a surface acoustic wave filter.

Figure 1. Simplified design of a surfactant filter

This figure shows how a surface wave propagates and is again converted into electrical vibrations using a transducer similar to the input one. Please note that at the ends of the piezoelectric plate there are absorbers of acoustic waves, which eliminate their reflection. The fact that the wave propagates in two directions means that its energy is divided equally and half of it is absorbed by the absorber. As a result, the loss of the described device cannot be less than 3 dB. Another fundamental limitation is that some of the surfactant energy must remain at the output of the receiving converter. Otherwise, it will not be possible to realize the specified amplitude-frequency response. As a result, the loss in the passband for this type of filter on surface waves reaches 15 ... 25 dB

Their operating principle is similar to that of digital FIR filters. The impulse response is realized due to the length of the metal strips in the output piezoelectric transducer. When calculating, an ideal (rectangular) amplitude-frequency response is selected. An example of specifying the requirements for the frequency response of a bandpass filter is shown in Figure 2.

Figure 2. Shape of the idealized frequency response of the filter

Then, in order to obtain the impulse response, a Fourier transform is performed from the ideal frequency response. To reduce its length, and, consequently, the number of metal strips in the receiving converter, coefficients with low energy are discarded. An example of such an impulse response is shown in Figure 3.

Figure 3. Shape of the discrete impulse response of the SAW filter

However, when some coefficients are discarded, the shape of the amplitude-frequency characteristic is distorted. In the stopband, areas appear with a low suppression coefficient of unwanted frequency components.

To reduce these effects, the resulting impulse response is multiplied by a Hamming or Blackman-Harris time window. Each coefficient will be represented by its own pair of electrodes in the receiving converter of the acoustic wave into an electrical signal.

An example of the shape of the frequency response of a filter after processing its impulse response with a Blackman-Harris window is shown in Figure 4. The same figure shows the frequency response of the filter on surface acoustic waves, taking into account the inaccuracy in the manufacture of the length of the metal strips of the transducer.

Figure 4. Frequency response of a SAW filter using the Blackman-Harris window without and taking into account manufacturing inaccuracy

The undoubted advantage of this type of SAW filters is the excellent shape of the amplitude-frequency response. Another advantage is their linear phase characteristic, which provides significant advantages when creating equipment using digital types of modulation.

However, a significant drawback is the significant insertion loss at the center frequency of the passband. This does not allow you to use this type bandpass filters in the first stages of highly sensitive receivers of mobile radio communication systems and cell phones. For the same reason, it is undesirable to use these filters in the output stages of radio transmitters (the release of a significant part of the output oscillation power on the filter leads to its destruction).

SAW filters with low losses

The basis for constructing filters based on surface acoustic waves with low losses are SAW resonators. The operating principle of these resonators is based on the reflection of a surface acoustic wave by reflective gratings. The distance between the conducting strips (or grooves in the piezoelectric plate) is equal to half the wavelength. The distance between the reflectors is chosen as a multiple of the acoustic wavelength at the resonator tuning frequency. As a result, a standing wave appears between the reflectors. The design of SAW resonators of this type is shown in Figure 5.

Figure 5. Design of a surface acoustic wave resonator (SAW resonator)

A photograph of a section of the surface of such a SAW resonator is shown in Figure 6. In this figure, a section of the surface is highlighted with a dotted line and shown nearby in an enlarged view. For clarity, the dimensions are shown in the photo.

Figure 6. Photograph of a section of the surface of a SAW resonator

As an option, the SAW resonator can be made on a long emitter of surface acoustic waves. In this case, the wave is reflected from distant elements of the emitter. A similar design is shown in Figure 7.

Figure 7. Another version of the SAW resonator

A SAW resonator is no different in its characteristics from a conventional quartz resonator, which uses volumetric acoustic waves. His electrical diagram corresponds to a series resonant circuit. To ensure stability of characteristics, they are manufactured on quartz plates. The typical quality factor of this circuit is 12000. The equivalent circuit of a surface acoustic wave resonator is shown in Figure 8.

Figure 8. Equivalent circuit of a surface acoustic wave resonator

Using SAW resonators, filters similar to conventional ones are implemented. Narrowband bandpass filters are usually implemented using this principle. Their operating principle is based on the well-known and Chebyshev. Losses in the passband are determined by the quality factor of the resonators and can be 2 ... 3 dB, which allows the use of this type of SAW filters in the input stages of receivers and output stages of transmitters.

A surface wave resonator can be made with two converters, the design of which is shown in Figure 9. The use of two converters allows the input and output of the filter to be galvanically isolated.

Figure 9. Design of a resonator with two piezoelectric transducers

In this resonator, the reflectors are made not in the form of short-circuited strips of metal, but in the form of grooves in a piezoelectric material. The grooves cause reflection in the same way as short-circuited strips of metal. The equivalent circuit of this resonator is shown in Figure 10. Such a circuit solution allows the input and output of the device to be galvanically isolated.

Figure 10. Equivalent circuit of a resonator with two piezoelectric transducers

Several resonators can be implemented on one piezoelectric plate. They can be connected to each other electrically or through acoustic communication. The design of a surface wave filter with two resonators connected acoustically is shown in Figure 11.

Figure 11. Design of a surface wave filter with two resonators

The equivalent circuit of this filter is shown in Figure 12. In it, the SAW resonators form two poles, as in a bandpass or second-order Butterworth.

Figure 12. Equivalent circuit of a surface wave filter with two resonators

The typical amplitude-frequency response implemented by such a filter is shown in Figure 13.

Figure 13. Frequency response of a filter with two resonators

The considered design is equivalent to a quartz twin. For communication between twos, a coupling capacitor is usually used. A similar design of a surface wave filter is shown in Figure 14.

Figure 14. Four-cavity SAW filter

The equivalent electrical circuit of the filter, the design of which is shown in Figure 14, is shown in Figure 15.

Figure 15. Equivalent circuit of a four-cavity SAW filter

Photo of a surfactant filter with open lid is shown in Figure 16. A ten-kopeck coin is located nearby for size comparison.

Figure 16. Appearance SAW filter

Another type of bandpass filters based on surface waves with low losses is built using a ladder scheme. The schematic diagram of a U-shaped ladder filter with three resonators is shown in Figure 15.

Figure 15. Scheme of a ladder filter based on SAW resonators

The equivalent circuit of this filter is shown in Figure 16.

Figure 16. Equivalent circuit of a ladder filter based on SAW resonators

A typical arrangement of SAW resonators in a ladder filter is shown in Figure 17.

Figure 17. Design of a ladder filter based on SAW resonators

Appearance of a ladder filter on surface waves with an open top cover shown in Figure 18.

Figure 18. External view of the ladder SAW filter and its central resonator

The most famous domestic manufacturer of surface acoustic wave filters is AEK LLC (for example, filter A177-44.925M1). To bring its input and output resistance to the standard value of 50 Ohms, the manufacturer recommends using a resistance filter-transformer solution that is already well known to us. And since this is a low-pass filter, it will simultaneously eliminate the problems of imperfect amplitude-frequency characteristics in the high-frequency region, which can be caused by the triple echo effect or the influence of a body wave.

Figure 19. SAW filter matching circuit with a standard resistance value of 50 Ohms

Filters produced by the foreign company EPCOS contain all the matching circuits inside the housing, so it is enough to provide a signal source resistance and a load resistance of 50 Ohms, and we will get the desired frequency response.

As already indicated, single-input resonators are in many ways similar quartz resonators on volumetric types of vibrations. Therefore, the practical circuits of self-oscillators based on these two types of resonators are largely similar. These schemes will be discussed in more detail in Chapter. 4, but here we just note that they can be built using three-terminal active elements, primarily such as transistors, or using active two-terminal devices, the most typical representative of which is a tunnel diode. Let us consider how the material presented above in Chap. 2 can be applied to self-oscillators with single-input SAW resonators.

Let us consider as an example the self-oscillator circuit in Fig. 2.16. The SAW resonator is connected between the collector and the base of the transistor. It is clear that in such a circuit the resonator can only operate in the frequency range where its input impedance is inductive in nature, that is, in the region between the frequencies of series and parallel resonances. Let's imagine the diagram in Fig. 2.16 in the form of Fig. 2.17, i.e. in the form of a circuit similar to the self-oscillator circuit in Fig. 2.1. If in all the formulas of § 2.1-2.6 we substitute the Y-parameters of the circuit instead of the Y-parameters of the SAW laser or a two-input SAW resonator feedback rice. 2.17, then we obtain shortened equations for a self-oscillator with a single-input resonator (Fig. 2.16 in the form (2.20). Let us consider in more detail the process of finding the natural frequencies of a linear resonant system ω k and the control resistance R.

Feedback circuit for the circuit in Fig. 2.17 is characterized by the following matrix of Y-parameters [similar to (2.2)]:

where Y p is the input conductivity of a single-input SAW resonator.

Then, similarly to (2.8), we obtain the following characteristic equation, from which it will be possible to determine ω k and α * k:

where z p is the input resistance of the SAW resonator, equal to z p = 1/Y p.

Equations (2.65) and (2.66) were obtained to simplify mathematical calculations under the assumption that the input and output linear conductivities of the AE are equal to zero. In general, if these conductivities are reactive, then they can be formally attributed to capacitances C 1 and C 2. If they are essentially resistive in nature, then equations (2.65) and (2.66) will become more complicated.

From (2.65) and (2.66) it is clear that if the AE is inertialess, i.e. φ = 0, then from (2.65) we have

Consequently, the resonant frequency of the linear system of the self-oscillator ω k will be the one at which the reactive component of the input resistance of the surfactant resonator will be equal to the resistance of the chain of series-connected capacitors C 1 and C 2 connected to its input.

Using the material from § 1.9, it is easy to obtain from (2.67) or (2.65) the values ​​of ω k. For the case φ = 0, the graphical solution (2.67) is presented in Fig. 2.18. In the general case, we obtain two values ​​of the natural frequency ω k: ω" k and ω" k.

If the frequency ω k is determined, then from (2.66) we can determine R. In Fig. Figure 2.19 shows the graphical definition of R. It can be seen that the frequency ω" k corresponds to a greater value of the control resistance R than the frequency ω" k. This explains that the system, in the absence of a nonlinear component of the AE input current, usually operates near the frequency that corresponds to a larger value of R.

For all other circuits for switching on a single-input SAW resonator for a self-oscillator on a three-pole AE, it is possible similarly to the self-oscillator in Fig. 2.16, obtain shortened equations (2.20). For different switching schemes they will differ only in the coefficients of the equations.

Let's consider a self-oscillator with a single-input SAW resonator on a two-pole active element. The simplest scheme A similar self-oscillator is shown in Fig. 2.20.

Since the frequency dependence of the input conductivity of the SAW resonator, as already indicated, is quite complex, further consideration (as before) for simplicity will be carried out under the assumption that the self-excitation margin is small, i.e. that the frequency band of possible self-oscillations is significantly less than the passband SAW resonator. Let us attribute the linear part of the AE to the linear resonant system of the self-oscillator, and display the nonlinear component of its current as a current source i(u). Then the equivalent circuit of the self-oscillator under consideration can be depicted in the form of Fig. 2.21. In this case, the following equality is true.

Surface acoustic wave resonators for short-range radio systems

V. Novoselov

Surface acoustic wave resonators for short-range radio systems

This article is devoted to surface acoustic wave (SAW) resonators and aims to attract the attention of Russian manufacturers of modern technology to these devices and provide as much information as possible about SAW resonators for choosing a technical solution for building a radio channel at a frequency of 433.92 MHz.

JSC Angstrem has mastered the production of surfactant resonators with a frequency of 433.92 MHz (RK1912, RK1412, RK1825), which is carried out in a single technological process with semiconductor ICs on a powerful production line. Currently, the enterprise satisfies the need of the Russian market for these resonators and has a reserve capacity for a significant increase in production.

SAW resonators have very successfully proven themselves as an element for stabilizing the frequency of a master oscillator for low-power transmitting devices. Such devices, thanks to technical capabilities SAW resonators have found very wide application in short-range radio systems. Especially for devices belonging to this class of systems, a frequency band of 1.72 MHz is allocated in the frequency range 433.05...434.79 MHz. The use of the range is regulated by the European standard I-ETS 300 220 (433.92 MHz).

Over the past years, the frequency 433.92 MHz, which is the average frequency of the allocated range, has been increasingly used in the countries of the European region for the system remote control car door locks and its security alarm.

Technical solutions for portable transmitters in the form of a key fob, developed using a SAW resonator and used in the automotive industry, are currently spreading to other areas. The idea of ​​​​using portable transmitters with a frequency of 433.92 MHz from the region mobile systems Remote control of door locks, garage doors, barriers, ship models and toys is increasingly penetrating stationary systems in which a short-range radio channel ensures the exchange of signals between units. Eliminating the need for wiring in a number of applications is a major selling point.

An example of a successful stationary application of a radio channel at a frequency of 433.92 MHz is a security and fire alarm cottage or apartment. All system actuator sensors are battery-powered and contain a radio transmitter. A single system receiver monitors all sensors inside the home. Installation of such a system is simple and quick, since it comes down to attaching the sensors.

Wireless transmission information at 433.92 MHz also turned out to be attractive for a home weather station. The values ​​of temperature, humidity, atmospheric pressure, wind speed, and illumination are transmitted digitally via radio from autonomous outdoor sensors to the monitor of the receiving unit indoors. The growth in the acquisition of such weather stations in European countries is associated solely with the battery power of all system units and the complete absence of wires connecting the units. Another example of the use of SAW resonators at a frequency of 433.92 MHz is a car security system that monitors pressure and temperature in each wheel of a passenger car using a radio channel. The system instantly warns the driver about a decrease in pressure and the tire heating up. Reducing driving speed in such conditions not only prevents an accident, but also allows, in some cases, to drive several hundred kilometers more to repair services, preserving the tire. The transmitter is mounted on each wheel and remains operational for the life of the tire.

All of the listed examples of the use of transmitters at a frequency of 433.92 MHz and many others are based on the main advantages of SAW resonators:

• quartz frequency stability over time and temperature range;
• low level of phase noise, providing exceptionally high purity of the spectrum of the generated signal;
• high quality factor;
• relatively high level of permissible power dissipation;
• high resistance to external mechanical influences;
• miniature;
• high reproducibility of equivalent parameters;
• variety of types and designs;
• low price.

Below we present the design elements of a surfactant resonator and highlight their relationship with the characteristics; the values ​​of the main parameters achieved in modern resonators of Russian and foreign companies are given.

The basis of the SAW resonator is a quartz plate cut from a quartz single crystal. The orientation of the plate relative to the axes of the single crystal forms a shear.

A thin layer of metal is applied to the surface of the quartz plate. Aluminum is most often used. Using photolithography, a resonator structure is formed in the metal, consisting of one or two counter-pin converters (IDTs) and two reflective gratings.

The main elements of the resonator design are shown in Fig. 1.

Figure 1. Structures and equivalent circuits of resonators: a) single-input resonator; b) two-input resonator; c) coupled resonator

An electrical high-frequency signal through converters creates mechanical (acoustic) vibrations on the surface of quartz, propagating in the form of a wave. This wave is called a surface acoustic wave (SAW). The speed of surfactants in quartz is 100,000 times less than the speed electromagnetic wave. Slow propagation of an acoustic wave is the basis for the miniaturization of SAW devices. Maximum conversion efficiency is achieved at the synchronism frequency, that is, at such a frequency of the supplied electrical signal when the wavelength of acoustic vibrations coincides with the spatial period of the converter electrodes. At a frequency of 433.92 MHz, the wavelength of acoustic vibrations is 7 microns.

Two gratings at the synchronous frequency work like two mirrors, reflecting an acoustic wave. Due to the conservation and accumulation of energy mechanical vibrations in the area between the gratings at the resonant frequency, a high-quality oscillatory system is formed. The length of the entire system is several hundred wavelengths. In this case, the total length of the quartz substrate of the resonator with a frequency of 433.92 MHz does not exceed 3 mm.

The accuracy of setting the resonant frequency and high reproducibility of all parameters of the resonator at a frequency of 433.92 MHz are achieved by using group production on quartz plates with a diameter of 100 mm and modern technological equipment for microelectronic production.

There are three main types of resonators: single-input, two-input and coupled. In Fig. Figure 1 shows the structures of these types of resonators and shows the corresponding equivalent circuits, which model the frequency response quite well near the resonant frequency. All three types of resonators in mass production are produced in a housing with three terminals: two isolated, and one connected to the housing. In accordance with the growing global market demand for surface-mounted (SMD) ceramic resonators, the industry is increasing their production volumes. Typically, the 433.92 MHz resonator uses a 5x5mm SMD package (QCC8). The production of 433.92 MHz resonators in metal-glass housings of the TO-39 and SIP-4M types is maintained. The appearance and main dimensions of these buildings are shown in Fig. 2.

Figure 2. Appearance and drawings of the hulls: a) TO-39 hull; b) SIM-4M housing; c) QCC8 housing

Let's look at some features of connecting the resonator to the terminals inside the housing. The crystal element of a single-input resonator (two-terminal network) is connected to two insulated terminals of the housing. This makes it possible to use the resonator as a four-terminal network. A characteristic form of the transmission coefficient S21 for such a connection of a single-input resonator is shown in Fig. 3. With a two-pole connection of a single-input resonator, only the reflection coefficient S11 can be used, the form of which is shown in Fig. 4.

Figure 3. Single-input resonator. Module and phase of transmission coefficient S 21

Figure 4. Single-input resonator impedance in pie chart

The crystal element of a two-input resonator (four-port network) can be connected to the terminals of the housing in the form of 4 configurations. Two of them (I and II in Fig. 1c

Figure 5. Frequency characteristics of a two-input resonator: a) two-input resonator, 0 degrees. Module and phase of transmission coefficient S21; b) two-input resonator, 0 degrees. S11 and S21 in pie chart; c) two-input resonator, 180 degrees. Module and phase of transmission coefficient S21; d) two-input resonator, 180 degrees. S11 and S21 in a pie chart

It is important to note here that only a two-input resonator with = 180º allows external (on-board) connection of signal pins. In this case, a single-input resonator is formed with one terminal grounded, the type of frequency response of which corresponds to that shown in Fig. 4.

A coupled resonator (Fig. 1c) consists of two single-input resonators, between which a weak coupling is established, allowing vibration energy to penetrate from one resonant structure to another. Currently, a design has become widespread in which single-input resonators are located on a single quartz substrate parallel to one another at a distance of several wavelengths of acoustic vibrations. A coupled resonator is more likely a filter on coupled resonators, however, the phase response of such a device when used in a voltage-controlled generator makes it possible to expand the frequency tuning range. As can be seen from Fig. 6, the phase of the transmission coefficient of the coupled resonator varies in the range of ±180º, while for a two-input resonator this value is ±90º.

Figure 6. Coupled resonator. Module and phase of transmission coefficient S 21

The stability of all characteristics that affect the frequency of the oscillator is the main factor in the design of the resonator. The stability is based on a quartz single crystal. In relation to SAW resonators, three most significant stability indicators can be distinguished:

• drift or change in frequency over a long period of time (aging);
• phase noise or frequency change in a very short time;
• temperature shift in frequency caused by changes in ambient temperature.

The frequency drift is associated with a weakening of the quartz tension that arose during the manufacture of the resonator. The amount of drift decreases over time. For modern SAW resonators, the relative change in frequency over the first year is in the range from 50·10 -6 to 10·10 -6. Artificial aging techniques can reduce these values ​​to 1·10 -6.

The low level of phase noise, and hence the purity of the spectrum of the stabilized signal of generators based on SAW resonators, surpasses all other known technical solutions, with the exception of cryogenic technology. Many years of research into the mechanisms of the occurrence of phase noise in SAW devices have made it possible to optimize the design and manufacturing technology of the resonator, as well as the generator circuit. Exceptionally high results have been achieved. The power spectral density of the phase noise of the 500 MHz generator with a SAW resonator was -145 dBc/Hz when detuned by 1 kHz and -184 dBc/Hz when detuned by 100 kHz or more. Without dwelling in detail on the phase noise of the resonator, it should be noted that in order to obtain extremely high spectral characteristics of the generator, it has been established that the frequency must be stabilized at a signal level of 13...23 dBm. The design of such a resonator differs significantly from mass-produced resonators, usually designed for a signal level of 0 dBm.

The magnitude of the temperature shift in the frequency of the SAW resonator is set by the choice of the quartz cutoff. For mass production, the ST cut is used, for which the dependence of frequency on temperature has the form of an inverted parabola shown in Fig. 7. There are quartz cuts with better temperature stability. Currently, they have not found application in mass production due to the higher cost of resonators.

Figure 7. View of the temperature-frequency characteristic of the resonator

Extremum point temperature T for the ST cut can be set when designing the resonator at any point in the operating temperature range. A typical range is considered to be from -40 to +85ºС. Selecting the To value in the middle of the operating range (+22.5ºС) obviously allows you to minimize the frequency drift at extreme temperatures.

The slope of the parabola is a constant, the value of which for ST-cut quartz is -0.032·10 -6. The temperature shift in frequency for any temperature deviation from To can be calculated using the formula shown in Fig. 7. For a frequency of 433.92 MHz and T 0 = +22.5ºС, the calculation of the frequency drift when heating the resonator to +85ºС gives 54 kHz.

It is important to note that during the production process of resonators, errors arise that slightly shift the actual value of To. Typically, the deviation tolerance To is ±10ºС. Some resonator manufacturers use a rougher tolerance of ±15ºC. For 433.92 MHz, the To shift leads to an additional temperature shift in frequency at one of the boundaries of the temperature range. In this case, the overall frequency shift from the influence of temperature can be -73 kHz (for To = 10ºС) and -83 kHz (for To = 15ºС).

Deserves attention Russian developers the fact that foreign manufacturers, focusing on the warm climate of southern countries, position To +35ºС and even +40ºС, without always indicating this in the reference information. For a climate in which above-zero temperatures predominate, such a shift To makes it possible to reduce the frequency drift in real temperatures. The use of such a resonator in equipment for the Russian climate leads to unreasonably large frequency shifts at subzero temperatures.

The table shows typical values ​​of the main parameters of single-input resonators with a frequency of 433.92 MHz, which are produced by Angstrem OJSC according to Technical Specifications TU 6322-013-07598199-2002.

Table. Typical values ​​of the main parameters of resonators RK1825, RK1912, RK1412

Parameter name, unit of measurement	Letter designation	RK1825	RK1912	RK1412
1. Nominal resonance frequency, MHz	f 0	433,92	433,92	433,92
2. Tuning accuracy, kHz, no more for group 50, according to group 75, by group 150	F	±35 ±60 ±135	±35 ±60 ±135	±35 ±60 ±135
3. Insertion loss in the 50 Ohm path, dB	a	1,1	1,25	1,25
4. Own quality factor	Qu	12400	12100	12100
5. Static capacitance, pF	Co	2,5	2,10	2,10
6. Dynamic resistance, Ohm	Rm	13,8	16	16
7. Maximum change in operating frequency in the temperature range (-40; +85ºС), kHz	Ft	60	60	60
8. Housing type		QCC8	To-39	SIP-4M

Resonators RK1912, RK1412 are manufactured using a single crystalline element and differ only in the design of the housing. The frequency characteristics of these resonators have the form shown in Fig. 8.

Figure 8. Characteristics of resonators RK1912 and RK1412: a) modulus and phase of the transmission coefficient in the 50 Ohm path; b) resonator impedance on a pie chart

Characteristics for the RK1825 resonator, produced in a ceramic housing for surface mounting printed circuit board, shown in Fig. 9.

Figure 9. Characteristics of the RK1825 resonator: a) modulus and phase of the transmission coefficient in the 50 Ohm path; b) resonator impedance on a pie chart

Single-input resonator. SAW resonators are widely used in highly stable oscillators, bandpass filters and sensors of physical quantities. The design of a single-input SAW resonator is shown in Fig. 1.12. It includes an interdigitated transducer located on the surface of the piezoelectric medium, with reflective structures located to the right and left of it. The main piezoelectric material for SAW resonators is highly stable quartz slices. However, when resonators are used in SAW filters, other piezoelectric materials are also used, such as lithium niobate and lithium tantalate.

Due to the in-phase nature of the partial surface waves excited by the IDT and reflected by the reflective structures, a standing wave with a period equal to twice the period of the reflective structure (RS) is formed in the substrate under the structure. The phase matching conditions for reflected waves are satisfied only in a narrow frequency band near f0 ≈VPAW /(2p) . In the same frequency band, there is a sharp change in the input conductivity of the resonator and, as a consequence, the parameter S11() of the device’s scattering matrix (Fig. 1.13). Scattering matrix coefficients are complex quantities and are widely used to describe the properties of passive multiport networks. Parameter S11() has the meaning of the reflection coefficient of the incident high-frequency voltage wave from the load, which is the resonator. With perfect matching, there is no reflected wave, and all supplied electrical power is absorbed in the resonator. In this case, in relative units S11 0 (in decibels S11 →−∞).

Rice. 1.12. Single-input resonator topology

Rice. 1.13. Single-input resonator module S11()

Single-input SAW resonators are widely used as sensors, such as pressure or torque. In addition, single-input SAW resonators are used in highly stable oscillators in the frequency range from 100 MHz to 1 GHz. Another important application of single-input resonators is that they are the main element of low-loss SAW impedance filters, including those used in mobile phones.

Two-input resonator. The design of a two-input SAW resonator is shown in Fig. 1.14. A two-input resonator includes two interdigitated transducers located on the surface of the sound pipe in one acoustic channel. Reflective structures are located to the right and left of the transducers. The period of electrodes in the IDT and OS, the distance between two IDTs, as well as the distance between the IDT and OS are selected so that the partial surface acoustic waves excited by the transducers and reflected by the OS are in phase. The amplitude-frequency response of a two-input resonator has a form similar to the frequency response of a narrow-band filter (Fig. 1.15). An important characteristic of a resonator is its quality factor, which can be estimated by the approximate relation

Q ≈f0 /f3, (1.9)

where f3 is the frequency band of the resonator at a level of –3 d..

Rice. 1.14. Topology of a two-input SAW resonator

Rice. 1.15. Frequency response of a two-input SAW resonator

In the case of using a resonator as part of a generator, the quality factor determines such important characteristics of the generator as the spectral density of phase noise and the stability of the oscillation frequency. SAW resonators are widely used to create highly stable oscillators in the frequency range up to 2.5 GHz.