Crystal and Ceramic Filters

The selectivity of a i lter is limited primarily by the Q of the circuits, which is generally the Q of the inductors used. With LC circuits, it is difi cult to achieve Q values over 200. In fact, most LC circuit Qs are in the range of 10 to 100, and as a result, the roll-off rate is limited. In some applications, however, it is necessary to  

Figure 1.01 How selectivity af ects the ability to discriminate between signals 

select one desired signal, distinguishing it from a nearby undesired signal (see Fig. 1-01). A conventional i lter has a slow roll-off rate, and the undesired signal is not, therefore, fully attenuated. The way to gain greater selectivity and higher Q, so that the undesirable signal will be almost completely rejected, is to use i lters that are made of thin slivers of quartz crystal or certain types of ceramic materials. These materials exhibit what is called piezoelectricity. When they are physically bent or otherwise distorted, they develop a voltage across the faces of the crystal. Alternatively, if an ac voltage is applied across the crystal or ceramic, the material vibrates at a very precise frequency, a frequency that is determined by the thickness, shape, and size of the crystal as well as the angle of cut of the crystal faces. In general, the thinner the crystal or ceramic element, the higher the frequency of oscillation. 

 

Crystals and ceramic elements are widely used in oscillators to set the frequency of operation to some precise value, which is held despite temperature and voltage variations that may occur in the circuit. 

    Crystals and ceramic elements can also be used as circuit elements to form i lters, specii cally bandpass i lters. The equivalent circuit of a crystal or ceramic device is a tuned circuit with a Q of 10,000 to 1,000,000, permitting highly selective i lters to be built. 

Crystal Filters. Crystal i lters are made from the same type of quartz crystals normally used in crystal oscillators. When a voltage is applied across a crystal, it vibrates at a specii c resonant frequency, which is a function of the size, thickness, and direction of cut of the crystal. Crystals can be cut and ground for almost any frequency in the 100-kHz to 100-MHz range. The frequency of vibration of crystal is extremely stable, and crystals are therefore widely used to supply signals on exact frequencies with good stability 

     The equivalent circuit and schematic symbol of a quartz crystal are shown in Fig. 1-02. The crystal acts as a resonant LC circuit. The series LCR part of the equivalent circuit represents the crystal itself, whereas the parallel capacitance CP is the capacitance of the metal mounting plates with the crystal as the dielectric. 

Figure 1-02 Quartz crystal. (a) Equivalent circuit. (b) Schematic symbol. 

Figure 1-03 Impedance variation with frequency of a quartz crystal 

Fig. 1-03 shows the impedance variations of the crystal as a function of frequency. At frequencies below the crystal’s resonant frequency, the circuit appears capacitive and has a high impedance. However, at some frequency, the reactances of the equivalent inductance L and the series capacitance CS are equal, and the circuit resonates. The series circuit is resonant when XL 5 XCS . At this series resonant frequency fS , the circuit is resistive. The resistance of the crystal is extremely low, giving the circuit an extremely high Q. Values of Q in the 10,000 to 1,000,000 range are common. This makes the crystal a highly selective series resonant circuit. 

   If the frequency of the signal applied to the crystal is above fS , the crystal appears inductive. At some higher frequency, the reactance of the parallel capacitance CP equals the reactance of the net inductance. When this occurs, a parallel resonant circuit is formed. At this parallel resonant frequency fP, the impedance of the circuit is resistive but extremely high. 

Because the crystal has both series and parallel resonant frequencies that are close together, it makes an ideal component for use in i lters. By combining crystals with selected series and parallel resonant points, highly selective i lters with any desired bandpass can be constructed. 

The most commonly used crystal i lter is the full crystal lattice shown in Fig. 0-04. It is a bandpass i lter. Note that transformers are used to provide the input to the i lter and to extract the output. Crystals Y1 and Y2 resonate at one frequency, and crystals Y3 and Y4 resonate at another frequency. The difference between the two crystal frequencies determines the bandwidth of the i lter. The 3-dB down bandwidth  is approximately 1.5 times the crystal frequency spacing. For example, if the Y1 to Y2 frequency is 9 MHz and the Y3 to Y4 frequency is 9.002 MHz, the difference is 9.002 2 9.000 5 0.002 MHz 5 2 kHz. The 3-dB bandwidth is, then, 1.5 3 2 kHz 5 3 kHz. 

     The crystals are also chosen so that the parallel resonant frequency of Y3 to Y4 equals the series resonant frequency of Y1 to Y2 . The series resonant frequency of Y3 to Y4 is equal to the parallel resonant frequency of Y1 to Y2 . The result is a passband with extremely steep attenuation. Signals outside the passband are rejected as much as 50 to 

 

Figure 1-04 Crystal lattice fi lter 

Figure 1-05 Crystal ladder fi lter. 

60 dB below those inside the passband. Such a i lter can easily discriminate between very closely spaced desired and undesired signals. 

Another type of crystal i lter is the ladder i lter shown in Fig. 1-05, which is also a bandpass i lter. All the crystals in this i lter are cut for exactly the same frequency. The number of crystals used and the values of the shunt capacitors set the bandwidth. At least six crystals must usually be cascaded to achieve the kind of selectivity needed in communication applications. 

  

Ceramic Filters. Ceramic is a manufactured crystallike compound that has the same piezoelectric qualities as quartz. Ceramic disks can be made so that they vibrate at a i xed frequency, thereby providing i ltering actions. Ceramic i lters are very small and inexpensive and are, therefore, widely used in transmitters and receivers. Although the Q of ceramic does not have as high an upper limit as that of quartz, it is typically several thousand, which is very high compared to the Q obtainable with LC i lters. Typical ceramic i lters are of the bandpass type with center frequencies of 455 kHz and 10.7 MHz. These are available in different bandwidths depending upon the application. Such ceramic i lters are widely used in communication receivers. 

    A schematic diagram of a ceramic i lter is shown in Fig. 1-06 For proper operation, the i lter must be driven from a generator with an output impedance of Rg and be terminated with a load of RL. The values of Rg and RL are usually 1.5 or 2 kV. 

Surface Acoustic Wave Filters. A special form of a crystal i lter is the surface acoustic wave (SAW) i lter. This i xed tuned bandpass i lter is designed to provide the exact selectivity required by a given application. Fig. 1-07 shows the schematic design 

Figure 1-06 Schematic symbol for a ceramic fi lter. 

Figure 1-07 A surface acoustic wave fi lter. 

Electronic Fundamentals for Communications

of a SAW i lter. SAW i lters are made on a piezoelectric ceramic substrate such as lithium niobate. A pattern of interdigital i ngers on the surface converts the signals into acoustic waves that travel across the i lter surface. By controlling the shapes, sizes, and spacings of the interdigital i ngers, the response can be tailored to any application. Interdigital i ngers at the output convert the acoustic waves back to electrical signals. 

       SAW i lters are normally bandpass i lters used at very high radio frequencies where selectivity is difi cult to obtain. Their common useful range is from 10 MHz to 3 GHz. They have a low shape factor, giving them exceedingly good selectivity at such high frequencies. They do have a signii cant insertion loss, usually in the 10- to 35-dB range, which must be overcome with an accompanying amplii er. SAW i lters are widely used in modern TV receivers, radar receivers, wireless LANs, and cell phones.