Page 450 - Maxwell House

430 Chapter 8

Sometimes the capacitive discontinuity in the cutoff waveguide might be replaced with
dielectric or ferrite inclusions. Note that the ferrite usage makes the filter tunable by the external
magnetic field. It is worthy to point out that the simulation and optimization of evanescent
filters practically impossible without the sophisticated numerical electromagnetic analysis.
8.4.10 Surface Acoustic Wave (SAW) Filters

The title of this section and following discussion probably looks strange in the book about
electrodynamics. Nevertheless, let us check the equation [21] describing the propagation of
25
acoustic waves in lossless homogeneous elastic media that can be represented in the form of
wave equation ∇ + (1 ) = 0. Here p is the acoustic pressure measured in Pascal
2
2
2
2
⁄
⁄
[Pa] and c [m/s] is the velocity of acoustic wave. Everything looks familiar does not it? That is
correct. As we have established in Chapter 4, the electromagnetic scalar potential measured in
2
2
2
2
voltage is the solution of the similar equation (4.23) ∇ + (1 ) = 0 ( = , =
⁄
⁄
= 0). It means that propagation of EM and acoustic waves must have much in common:
0,
both carry energy, have finite propagation velocity defined by media constants, certain
frequency, phase and wavelength. They interfere and diffract, obey the boundary conditions,
reflect and refract in the same manner at the boundary between media with different parameters.
You can continue this list of similarities. Note only that EM wave in free space are transverse,
i.e. their E- and H-fields oscillate from side to side, up and down, or any other direction just in
the plane perpendicular to the direction of propagation. Meanwhile, the propagating acoustic
waves (waves of pressure) are longitudinal and they move media molecules forwards and
backwards, i.e. in the direction of propagation. Although such difference is significant but not
critical for the following discussion.
Looking back we may notice that the dimensions and mass of any RF device are determined
primarily by the wavelength. Therefore, one of the straightforward paths to device
miniaturization is the reduction in wavelength. We followed this RF approach increasing the
dielectric constant of materials in usage thereby making the wavelength shorter. However,

even = 100 might give only a tenfold wavelength reduction that is proportional to √ =

10. Meanwhile, the acoustic wave speed much below the speed of light, depends mostly on
media density, and in general vary from 18 km/s = 18 ∙ 10 m/s in diamonds to 331 m/s in the
3
3
9
air. If so, the wavelength of acoustic wave in diamond is only 18 ∙ 10 ⁄ 10 = 0.018 mm at the
ultrasound frequency 1 GHz = 10 Hz. At the same frequency 1 GHz the RF wavelength is 30
9
mm in free space and 30/ √ = 3 mm in the same diamond, i.e. 167 (!) times longer than the

acoustic wave enjoys.
From the above discussion immediately follows that the substitution RF waves by the acoustic
waves might be the efficient procedure for developing a minuscule version of RF devices like
filters. However, we should first carry out the exchange energy between these two types of
waves. In Section 2.6 of Chapter 2, we have described the piezoelectrics (like Quartz) belonging
to the class of ferroelectrics. The RF voltage applied to piezoelectric crystal causes it to vibrate
thereby RF signal energy transfers into the acoustic energy of practically the same waveform.

25 Elasticity is the property of substance that enables it to change its length, volume, or shape in direct
response to a force effecting such a change and recover its original form upon the removal of the force.