CN109586679B - 一种压电谐振器等效电参数及谐振频率的测量方法 - Google Patents
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Abstract
本发明公开了一种压电谐振器等效电参数及谐振频率的测量方法,通过测量压电谐振器的相位‑频率曲线,测得谐振频率与反谐振频率;然后再分别测量相位‑频率曲线在谐振频率与反谐振频率处的斜率,并计算谐振角频率和反谐振角频率,利用非线性方程组求解出压电谐振器的等效电参数。
Description
技术领域
本发明属于电子技术领域,更为具体地讲,涉及一种压电谐振器等效电参数及谐振频率的测量方法。
背景技术
静电驱动的压电谐振器都可以等效为BVD(Butterworth-Van Dyke)模型(V.E.Bottom,Introduce to crystal unite design.York:Van Nostrand RcinholdCompany, pp:82,1987.)。多种压电材料可以用BVD模型来描述,如石英晶体,钽酸锂,压电陶瓷PZT。多种形态的压电谐振器可以用BVD模型来描述,如体声波BAW 谐振器,声表面波SAW谐振器,石英晶体微天枰QCM,薄膜体声波(FBAR)谐振器等。
BVD模型等效参数的测量方法很多,如CI-miter法,基于阻抗仪的测量方法,IEC6044基于π网络零相位技术的石英晶体器件等效参数测量方法,基于谐振频率、反谐振频率、负载谐振频率和负载反谐振频率的计算方法(王艳、谌海云、刘东,一种石英晶体谐振器的等效电参数的测量方法.CN201610556735.1) 等。
目前市面上出售的测量等效参数的仪器包括,阻抗仪,矢量网络分析仪等。如,中国香港Kolinker Industrial Equipments Limited公司KH1800/KH1820,美国 SAUNDERS&ASSOCIATES,LLC公司W-2200MR,美国Wayne Kerr Electronics公司6500精密阻抗分析仪等。
目测主要采用的是基于IEC60444的测量方法。谐振电阻代替动态电阻。仿真表明,在谐振器Q值较低时,两者误差超过20%。(刘东,晶体振荡器温度补偿技术的研究[D].电子科技大学,2017.)
中国专利CN201610556735.1(王艳、谌海云、刘东,一种石英晶体谐振器的等效电参数的测量方法.CN201610556735.1)所提方法在理论上没有上述误差,但是实际操作较困难。这是因为频率随着温度漂移,细小的温度变化就导致计算结果巨大的误差。刘东等提出了基于谐振频率、反谐振频率、负载谐振频率、负载反谐振频率、相频曲线在谐振频率的导数和相频曲线在反谐振频率的导数计算等效参数的方法。(D.Liu,X.H.Huang,J.G.Hu,Y.L.Tang,and Y.Wang, "Measurement of quartz crystal unit parameters based onthe precise derivation of zero phase frequency,"Electronics Letters,vol.53,p.2,Feb 2017.)刘东2017所述方法需要测量谐振器不带负载电容时的相位-频率曲线,以及谐振器带负载电容时的相位-频率曲线。其方法需要测量两个相位-频率曲线,并且需要知道负载电容的值。因而,其方法操作复杂,不便于集成于科学仪器(如,矢量网络分析仪、阻抗仪等)的软件模块。
上述所有方法也没有考虑谐振频率、反谐振频率、负载谐振频率和负载反谐振频率的测量误差。例如,IEC60444方法所测谐振频率受导线长度以及负载变化影响测量准确度,图1即演示了导线长度与负载变化引起的误差。这种误差会传导至参数测量,从而影响参数测量准确度。
发明内容
本发明的目的在于克服现有技术的不足,提供一种压电谐振器等效电参数及谐振频率的测量方法,不需要阻抗匹配或π型网络或负载电容等外围电路,测出谐振频率、反谐振频率和等效电参数。
为实现上述发明目的,本发明一种压电谐振器等效电参数及谐振频率的测量方法,其特征在于,包括以下步骤:
(1)、测量压电谐振器的相位-频率曲线,并找到相位-频率曲线中的零相位点,即得到谐振频率fr与反谐振频率fa;
(2)、测量相位-频率曲线在谐振频率fr处的斜率,记为Δ1;以及测量相位- 频率曲线在反谐振频率fa处的斜率,记为Δ2;
(3)、计算谐振角频率为ωr=2πfr,反谐振角频率为ωa=2πfa;
(4)、将ωr、ωa、Δ1、Δ2带入如下的非线性方程组,求解出压电谐振器的等效电参数:静态电容C0、动态电容C1、动态电感L1和动态电阻R1;
其中,Phaseoffset为相位偏移量,Pashe(f)为相位-频率函数,f为相位-频率曲线上的频点。
本发明的发明目的是这样实现的:
本发明一种压电谐振器等效电参数及谐振频率的测量方法,通过测量压电谐振器的相位-频率曲线,测得谐振频率与反谐振频率;然后再分别测量相位- 频率曲线在谐振频率与反谐振频率处的斜率,并计算谐振角频率和反谐振角频率,利用非线性方程组求解出压电谐振器的等效电参数。
同时,本发明一种压电谐振器等效电参数及谐振频率的测量方法还具有以下有益效果:
(1)、本发明不需要阻抗匹配、调整仪器相位零点等附加操作,也不需要π型网络、负载电容等外加电路,仅用一条相位-频率曲线,经计算得到压电谐振器四个等效电参数;
(2)、现有的IEC方法测量谐振频率受导线长度、负载变化引起的误差的影响;本发明避免了误差的影响,可以直接计算出导线长度、负载变化引起的相位零点漂移,频率测量更准确,不会将频率测量误差传导给参数测量;
(3)、计算参数高度符合所测相位-频率曲线,因此,参数测量精度高;
(4)、相较于IEC方法,本发明所测R1不受谐振器Q值变化影响,因此动态电阻R1测量更加准确;
(5)、现有的IEC方法所测动态电容C1受谐振器M值影响,M值越小误差越大;而本发明由于没有采用近似模型,因此理论上不受此影响,进而动态电容C1测量不受谐振器M值影响;
(6)、静态电容C0是谐振频率段的容值。相较于IEC方法所测静态电容 C0是高于谐振频率段的容值,本发明方法所测静态电容C0是谐振频率段的容值,因此容值更准确。
附图说明
图1是IEC方法谐振频率测量误差与导线长度、负载变化的关系图;
图2是压电晶体的BVD等效模型;
图3是三种测量方案框图对比;
图4是ADS仿真原理图;
图5是ADS仿真结果图;
图6是QCM水负载实测相位-频率曲线以及计算参数复原相位-频率曲线。
具体实施方式
下面结合附图对本发明的具体实施方式进行描述,以便本领域的技术人员更好地理解本发明。需要特别提醒注意的是,在以下的描述中,当已知功能和设计的详细描述也许会淡化本发明的主要内容时,这些描述在这里将被忽略。
实施例
图2是压点晶体的BVD等效模型。
在本实施例中,压电谐振器可以为高Q值晶体压电谐振器、石英晶体微天平压电谐振器和微机电系统压电谐振器。如图2所示,将压电晶体串入矢量网络分析仪,测量S21特性,转换为相位测量模式。此外,压电谐振器的材质可以为石英、鉭酸锂、硅酸镓镧、压电陶瓷PZT和氮化铝AlN。
然后对本发明一种压电谐振器等效电参数及谐振频率的测量方法进行说明,包括以下步骤:
S1、通过矢量网络分析仪实测出压电谐振器的相位-频率曲线,并找到相位- 频率曲线中的零相位点,即得到谐振频率fr与反谐振频率fa;
S2、测量相位-频率曲线在谐振频率fr处的斜率,记为Δ1;以及测量相位- 频率曲线在反谐振频率fa处的斜率,记为Δ2;
S3、计算谐振角频率为ωr=2πfr,反谐振角频率为ωa=2πfa;
S4、将ωr、ωa、Δ1、Δ2带入如下的非线性方程组,求解出压电谐振器的等效电参数:静态电容C0、动态电容C1、动态电感L1和动态电阻R1;
其中,Phaseoffset为相位偏移量,Pashe(f)为相位-频率函数值,f为相位-频率曲线上的频点。
在本实施例中,设相位-频率曲线上共计N个频点,则f可以表示为 f1,f2,…,fN;
那么,第i个频点fi的相位-频率函数值Pashe(fi)满足:
那么,每个频点的相位差为:
ΔPashei=Pashe(fi)+Phaseoffset-Pashemeasure(fi)
其中,Pashemeasure(fi)表示第i个频点fi的实测相位值;
然后求取它们的均方根误差,即:
通过不断改变Phaseoffset,使得RMSE最小,此时,所计算的等效参数、谐振频率与反谐振频率就是最后的结果。
图3是三种测量方案的对比框图。
在本实施例中,IEC测量方案如图3(a)所示,刘东2017所述方法如图3 (b)所示,和本发明测量方案如图3(c)所示。
IEC方案需要pi型网络以便于阻抗匹配,并且IEC方案测量的误差较大。
刘东2017所述方法测量方案,需要负载电容与串联电阻,测量误差和电阻有关。该方案还需要切换带负载电容与带负载电容两种模式,这不便于集成于测量方法为仪器的软件模块。
本发明方案不需要外接电路,不需要阻抗匹配,直接串联于矢量网络分析仪。本方案操作简便,没有理论误差,测量误差小。测量相位-频率曲线4个点,既能计算谐振频率、反谐振频率,以及四个等效参数。参数反演的相位-频率曲线与实测曲线在800多个点都吻合,这800多个点的均方根误差低至0.1107。
实施例1
用ADS(Advanced Design System)软件进行仿真实验,原理图如图4所示,仿真的相位-频率曲线如图5所示。得到的结果如表1所示。
表1
R<sub>1</sub>(Ω) | L<sub>1</sub>(mH) | C<sub>1</sub>(fF) | C<sub>0</sub>(pF) | |
设定值 | 14.0000 | 75.0000 | 3.3600 | 3.0000 |
计算值 | 14.0050 | 75.0000 | 3.3600 | 3.0000 |
实施例2
和实施例1类似的方法,改变动态电阻R1的设定,用IEC方法计算谐振电阻Rr,用我们的方法分别计算的动态电阻R1,结果如表2所示。
表2
由表2可见,我们的方法计算的动态电阻和设定值更解决。IEC方法随着设定值的增加,误差增大。并且我们计算的R1小于IEC计算的R1.
实施例3
矢量网络分析仪N9913A实测一个QCM晶片滴上水滴之后的参数。N9913A 所测相位-频率曲线如图6实线所示。根据我们的非线性方程组及其MATLAB 数值解法,得到的等参数如表3所示。
表3
根据我们的参数反演的相位-频率曲线如图6虚线所示,可见反演曲线与实测曲线-几乎重合。
根据IEC方法测量的谐振电阻Rr也在表3中给出。可见我们所测R1比IEC 所测Rr小,这和仿真结果是一致的。同时,也可见,在QCM带液体负载时, Rr和R1差距很大。IEC的方法将会存在较大误差。
实施例4
测量不同负载引起的相位偏移。同一个QCM晶体分别处于空载,水滴负载,油滴负载情况下,由我们方法所测的相位偏移如表4所示。
表4
可见本发明能够直接测量负载变化引起的零相位点漂移。因而,本发明不存在IEC方法因负载变化引起的测量误差,如图1所示。
实施例5
测量不同导线长度引起的相位偏移。测量两个不同长度支架的石英晶体,分别编号1#和2#.由我们方法所测的相位偏移如表5所示。
表5
可见我们的方法,不仅能直接测量负载变化或者是导线长度引起的相位偏移,没有IEC方法负载变化与导线长度变化引起的测量误差。
尽管上面对本发明说明性的具体实施方式进行了描述,以便于本技术领域的技术人员理解本发明,但应该清楚,本发明不限于具体实施方式的范围,对本技术领域的普通技术人员来讲,只要各种变化在所附的权利要求限定和确定的本发明的精神和范围内,这些变化是显而易见的,一切利用本发明构思的发明创造均在保护之列。
Claims (4)
1.一种压电谐振器等效电参数及谐振频率的测量方法,其特征在于,包括以下步骤:
(1)、测量压电谐振器的相位-频率曲线,并找到相位-频率曲线中的零相位点,即得到谐振频率fr与反谐振频率fa;
(2)、测量相位-频率曲线在谐振频率fr处的斜率,记为Δ1;以及测量相位-频率曲线在反谐振频率fa处的斜率,记为Δ2;
(3)、计算谐振角频率为ωr=2πfr,反谐振角频率为ωa=2πfa;
(4)、将ωr、ωa、Δ1、Δ2带入如下的非线性方程组,求解出压电谐振器的等效电参数:静态电容C0、动态电容C1、动态电感L1和动态电阻R1;
其中,Phaseoffset为相位频移量,Pashe(f)为相位-频率函数,f为相位-频率曲线上的频点。
3.根据权利要求1所述的一种压电谐振器等效电参数及谐振频率的测量方法,其特征在于,所述的压电谐振器包括高Q值晶体压电谐振器、石英晶体微天平压电谐振器和微机电系统压电谐振器。
4.根据权利要求1所述的一种压电谐振器等效电参数及谐振频率的测量方法,其特征在于,所述压电谐振器的材质为石英、鉭酸锂、硅酸镓镧、压电陶瓷PZT和氮化铝AlN中的一种。
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