1、表面聲波元件及信號處理,Chapter 9 IDT Finger Reflections & Radiation Conductance,Surface acoustic wave reflections from the edges of the metallic electrode fingers of an IDT can have a significant influence on its operation, as well as on overall SAW device response. These reflections can either be desirable or
2、 undesirable, depending on the application.An undesirable feature can be degradation of both the amplitude & phase response in some filters designs, unless minimized, such as through the use of split electrode.,9-1,表面聲波元件及信號處理,IDT Finger Reflections & Radiation Conductance,In recent years, however,
3、finger reflections have been used to advantage in the design of RF front-end filters, antenna duplexers, and RF interstage filters employing LSAW substrates.SAW reflections from the finger edges of an IDT affect its operation in two important ways.A reduction in the average SAW velocity under the ID
4、T reducing its center frequencyA distortion of its radiation conductance.對uniform IDT asymmetric conductance with a peak at a lower frequency than for the unperturbed response.,9-2,表面聲波元件及信號處理,對於一般的metallization thickness, 此項distortion 可以忽略不計(如果工作頻率在100MHz以下).當頻率增加時，則須加以考慮，尤其是在應用於RF front-end 的元件時(頻
5、率為900MHz or higher).The film-thickness ratio h/l for the metallization of an IDT is an important SAW design parameter. This chapter examines this parameter and its influence on the radiation conductance of an IDT. In addition, the Mason equivalent circuit model will be further examined for incorpora
6、tion of finger-reflection effects.,IDT Finger Reflections & Radiation Conductance,9-3,表面聲波元件及信號處理,IDT Film-Thickness Ratio and Radiation Conductance,In SAW filter fabrication, thin-metal films are deposited to form the IDTs. While these metal films define IDT geometry and provide electrical contact,
7、 they also need to be light enough so that they do not dampen the surface wave excessively.Because of its low density, aluminum (or an aluminum ally) is the preferred metal for such fabrications.Its thickness h is usually in the range h = 500-2000 (1=10-8cm), to provide both a good electrical contac
8、t & low resistance.,9-4,表面聲波元件及信號處理,The film-thickness ratio h/l is an important design parameter when finger reflections are of concern.The effects of electrode metallization on the IDT frequency response can often be neglected when h/l 1% (其值與頻率有關).A large film-thickness ratio will affect the resp
9、onse characteristics of an IDT in two ways. First, the average SAW velocity under the IDT will be reduced from the free-surface value and will result in a reduction in its center frequency. Moreover, acoustic reflections from - and between IDT fingers will give rise to a charge in its radiation cond
10、uctance.,IDT Film-Thickness Ratio and Radiation Conductance,9-5,表面聲波元件及信號處理,For illustrative purposes, three variant forms of radiation conductance are introduced here : Ga(f), Gam(f), Gamf(f)Ga(f) : free-surface 條件下的radiation conductanceGam(f) : 與Ga(f)雷同，速度採用free-surface與metallized surface的平均值，忽略fi
11、nger reflections.Gamf(f) : 包括速度偏移及finger reflection的影響. Radiation conduction 為an asymmetric frequency response.,IDT Film-Thickness Ratio and Radiation Conductance,9-6,表面聲波元件及信號處理,The IDTs examined here are those for a uniform SAW filter, with the single-electrode (solid electrode) geometry and metal
12、lization ratio h=0.5.,Reflections from IDTs with Single-Electrode Geometries,9-7,表面聲波元件及信號處理,The actual mass of the metal electrodes will dampen the surface wave. This damping can be reduces by using thin-film electrodes made of a light metal(選用aluminum而不用gold). However, their electrical resistance
13、must not be significant(完全阻隔電性).In consequence, typical aluminum-film thickness are in the range of 500-2000.,Reflections from IDTs with Single-Electrode Geometries,9-8,表面聲波元件及信號處理,To first order, the fractional velocity decrease (dv/v)m due to this mass-loading in the metallized regions can be expr
14、essed in terms of the film-thickness ratio h/l.r : dielectric constant of substrateF 與 metal employed 及 substrate 有關(metal : aluminum or 其之合金)F = 0.037 for lithium niobate = 0.01 for quartz,Reflections from IDTs with Single-Electrode Geometries,9-9,表面聲波元件及信號處理,Also considered here is an additional p
15、urturbation that relates to the fractional velocity decrease (dv/v)p of the SAW under metallized regions due to the “shorting” of surface piezoelectric fields given by,Reflections from IDTs with Single-Electrode Geometries,9-10,表面聲波元件及信號處理,AS well as causing mass-loading, however, the deposited meta
16、l film will also change the effective “stiffness” of the propagating surface. 與metal及壓電材料有關. “It can actually cause the SAW velocity to increase, in competition with the change due to mass loading”.For piezoelctric substrates with large values of K2, LiNbO3. 第一項will be the dominant one.For ST-X quar
17、tz, 第二項及第三項為主要的影響因素。,Reflections from IDTs with Single-Electrode Geometries,9-11,表面聲波元件及信號處理,Impedance Discontinuities in Equivalent SAW Tx. Line,If propagation of the forementioned surface waves is modealled in terms of an equivalent SAW tx. line, velocity changes at such IDT surface discontinuitie
18、s will also change the equivalent electrical impedance parameters.,9-12,表面聲波元件及信號處理,At the boundary between region 1 & 2, the reflection coefficient 12 at the leading metal edge, for surface waves incident from the left, is z1 : free space region 的阻抗 (SAW)z2 : metallized layer 下的阻抗Likewise, the refl
19、ection coefficient r21 at the back edge is If metallization ratio h = 0.5 相當於l/4 at center frequency(什麼速度下), 則,Impedance Discontinuities in Equivalent SAW Tx. Line,9-13,在1 2的邊界上,表面聲波元件及信號處理,Similarly, all other metal fingers in the receiving IDT will be in-phase at center frequency, so that the refl
20、ected SAW signal components will be additive.,Impedance Discontinuities in Equivalent SAW Tx. Line,9-14,表面聲波元件及信號處理,Because these reflected waves can be further reflected from the input IDT, spurious passband ripples of amplitude & phase can ensue in the same manner as for triple-transit interferenc
21、e. Multiple reflections can also occur between fingers of the same IDT, giving rise to spurious resonance. The impedance perturbation in the metallized region will be small if the metal fingers are thin & have low density, or it they are buried in quartz.,Impedance Discontinuities in Equivalent SAW
22、Tx. Line,9-15,表面聲波元件及信號處理,The resultant reflection coefficient rs for the single electrode (with h = 0.5) at center frequency(if we neglect multiple reflections between IDT fingers)To a good approximation, the ratio of reflected SAW power Pr to incident power Pi on an array of N single electrodes at
23、 center frequency :,Impedance Discontinuities in Equivalent SAW Tx. Line,9-16,表面聲波元件及信號處理,Impedance Discontinuities in Equivalent SAW Tx. Line,9-17,表面聲波元件及信號處理,Self-Coupling and Mutual-Coupling Coefficients,在metallized surface 影響下的速度可改寫如下：上述之參數(如 , 及 )，可經由實驗量測得到。(給予不同之h/l值) self coupling coefficient
24、 k11 :ko : wave vector at center frequencyk11 is also called a velocity-shift coefficient, as it relates to the decrease in the center frequency of an IDT due to surface loading.,9-18,表面聲波元件及信號處理,Self-Coupling and Mutual-Coupling Coefficients,9-19,表面聲波元件及信號處理,The normalized mutual-coupling coefficie
25、nt k12 relates the coupling between oppositely directed surface waves in a reflection grating or in an IDT.,Self-Coupling and Mutual-Coupling Coefficients,9-20,表面聲波元件及信號處理,Effects on IDT Radiation Conductance,The average shifted-velocity Va under an IDT due to metallization , Vo : free-surface SAW v
26、elocity , average shifted center frequency unperturbed radiation conductance :因為,9-21,表面聲波元件及信號處理,Effects on IDT Radiation Conductance,Ex : Shifted Radiation Conductance of IDT Due to Velocity shift. ST-X quartz, l0 = 12.54 mm, Np =200, h/l0 = 0.02, uniform aperture width W = 20l0. Determine (a) f0
27、(b) Va (c) fa (d) Gam(f)Sol : (a) (b)由 (c),9-22,表面聲波元件及信號處理,Effects on IDT Radiation Conductance,(d),9-23,表面聲波元件及信號處理,The Equivalent Circuit for an IDT Section with Negligible Finger Reflections,9-24,表面聲波元件及信號處理,上圖假設acoustic finger reflections are negligible.全部region的速度皆假設為free-surface SAW velocity
28、Vo 。只有一個acoustic impedance (Zo) . turns ratio , W : acoustic apertured & s are appropriate piezoelectric & compliance constants.,The Equivalent Circuit for an IDT Section with Negligible Finger Reflections,9-25,表面聲波元件及信號處理,假設 = 1,The Equivalent Circuit for an IDT Section with Negligible Finger Refle
29、ctions,9-26,表面聲波元件及信號處理,The 2 2 acoustic sub-matrix ya represents an equivalent SAW tx-line section for an IDT finger.,The Equivalent Circuit for an IDT Section with Negligible Finger Reflections,9-27,表面聲波元件及信號處理,The Equivalent Circuit for an IDT Section with Finger Reflections,9-28,表面聲波元件及信號處理,因為在f
30、ree-surface 及metallized surface 下的速度不相同：V0 & Vm 。所以阻抗Z0也不等於Zm，造成reflection。Average shifted frequency fa In order to calculate the overall response of the free acoustic transmission submatrices, ABCD matrix manipulations must be employed, because Z or Y matrix cannot be directly multiplied.,The Equiv
31、alent Circuit for an IDT Section with Finger Reflections,9-29,表面聲波元件及信號處理,The Equivalent Circuit for an IDT Section with Finger Reflections,9-30,表面聲波元件及信號處理,Transit angle q 的定義如下 ： ：for unmetallized region ：for metallized region (？)Unmetallized region 的ABCD matrix Ru,The Equivalent Circuit for an ID
32、T Section with Finger Reflections,9-31,表面聲波元件及信號處理,Metallized region 的ABCD matrix RmThe total submatrix Rt for the three cascaded sections of transmission line :,The Equivalent Circuit for an IDT Section with Finger Reflections,9-32,表面聲波元件及信號處理,上述是針對一個electrode，如果有Np finger pairs,The Equivalent Circ
33、uit for an IDT Section with Finger Reflections,9-33,表面聲波元件及信號處理,Resultant admittance matrix including finger reflections,The Equivalent Circuit for an IDT Section with Finger Reflections,9-34,表面聲波元件及信號處理,由matched boundary conditions ：,The Equivalent Circuit for an IDT Section with Finger Reflections,9-35,表面聲波元件及信號處理,The Equivalent Circuit for an IDT Section with Finger Reflections,9-36,
