From b2ff21cd12934d759884798f95649f09e92be1dd Mon Sep 17 00:00:00 2001 From: Alvie Rahman Date: Mon, 20 Mar 2023 14:21:30 +0000 Subject: [PATCH] add notes on piezoelectrics --- .../MMME2051_Lec7_Top1_Quiz.pdf | Bin 0 -> 78489 bytes ...ot-2023-03-16T11:15:41,326771312+00:00.png | Bin 0 -> 67312 bytes ...ot-2023-03-16T11:22:04,554599428+00:00.png | Bin 0 -> 18778 bytes ...ot-2023-03-16T11:28:48,428685773+00:00.png | Bin 0 -> 39283 bytes .../lecture_slides/MMME2051EMD_Lecture6A.pdf | Bin 0 -> 1038511 bytes .../lecture_slides/MMME2051EMD_Lecture6B.pdf | Bin 0 -> 790782 bytes .../lecture_slides/MMME2051EMD_Lecture7.pdf | Bin 0 -> 3056612 bytes .../piezoelectrics.md | 66 ++++++++++++++++++ .../MMME2051_Lec7_Top1_Quiz.pdf | Bin 0 -> 78489 bytes .../StrainGaugeHomework.pdf | Bin 0 -> 257151 bytes 10 files changed, 66 insertions(+) create mode 100644 uni/mmme/2051_electromechanical_devices/MMME2051_Lec7_Top1_Quiz.pdf create mode 100644 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n{q*l2>{tKgPk;W)zx?BW^xtg<`T2GE_&r|IUjw&)|M>qG$0GX2 literal 0 HcmV?d00001 diff --git a/uni/mmme/2051_electromechanical_devices/piezoelectrics.md b/uni/mmme/2051_electromechanical_devices/piezoelectrics.md new file mode 100755 index 0000000..aa79a6e --- /dev/null +++ b/uni/mmme/2051_electromechanical_devices/piezoelectrics.md @@ -0,0 +1,66 @@ +--- +author: Akbar Rahman +date: \today +title: MMME2051 // Piezoelectrics +tags: [ piezoelectrics, op_amps ] +uuid: ed7d0899-478d-4f0d-b0e9-634cdbb5b48a +lecture_slides: [ ./lecture_slides/MMME2051EMD_Lecture7.pdf ] +lecture_notes: [] +exercise_sheets: [ ./seminar_worksheets/MMME2051_Lec7_Top1_Quiz.pdf, ./seminar_worksheets/StrainGaugeHomework.pdf ] +--- + +Piezoelectricity is the charge that gets accumulated in some materials upon application of +mechanical stress + +$$Q \propto F$$ + +This relation allows the measurement of force using electric signals. + +![](./images/vimscrot-2023-03-16T11:15:41,326771312+00:00.png) + +\begin{align*} +Q &\propto F \\ +Q &= k_1F \\ + &= k_1Ma \\ +\frac{\mathrm d Q}{\mathrm dt} &= i = k_1M\frac{\mathrm da}{\mathrm dt} +\end{align*} + +# Integrating Amplifier + +Measuring current is expensive and difficult. +Integrating the current helps to measure a voltage instead, which is easier. +This is done using the following amplifier: + +![](./images/vimscrot-2023-03-16T11:22:04,554599428+00:00.png) + +\begin{align*} +V_\text{out} &= A_{OL}(V^+-V__) = -A_{OL}V__ \\ +V__ &= V_\text{out} - V_C +\end{align*} + +As input resistance of op amp is infinite: + +$$i_f = -i_n = -k_1M\frac{\mathrm da}{\mathrm dt}$$ + +From the capacitor equation: + +$$i_f = C_f \frac{\mathrm dV_C}{\mathrm dt} = -k_1M\frac{\mathrm da}{\mathrm dt}$$ + +Integrating both sides gives + +$$V_C = -\frac{k_1M}{C_f}a$$ + +And it can be found that + +\begin{align*} +V_\text{out} &= -A_{OL}(V_\text{out} - V_C) \\ +V_C &= -V\text{out} \frac{1+A_\text{OL}}{A_{OL}} +\end{align*} + +To get + +$$V_\text{out} = \frac{k_1M}{C_f}a$$ + +This circuit can be stacked to get velocity and displacement: + +![](./images/vimscrot-2023-03-16T11:28:48,428685773+00:00.png) diff --git a/uni/mmme/2051_electromechanical_devices/seminar_worksheets/MMME2051_Lec7_Top1_Quiz.pdf b/uni/mmme/2051_electromechanical_devices/seminar_worksheets/MMME2051_Lec7_Top1_Quiz.pdf new file mode 100644 index 0000000000000000000000000000000000000000..074c550442d6c02bfe87a42b7b07249b724e92d6 GIT binary patch literal 78489 zcmb@s1#}(Fjxc!5F*7@6X7)8RGegYGOffSvvtwqam}6#UW@b+8*k1d4GjHbX&i?!F zo|XFaEs#`wtJIQORb&bxVsuROY%pYfg?$};&3(Br%!G`Dc7~QPJUk3CCbnkI=7cOC zElLbx7S_%tjtpYf2F@lTCPsF~CVYG_PR@=d1~xG6Syh^n73*S1T~jsFoY(u+x`h~U z0oW5f61E}!c=(*0u;5wxdbdx?(sl`2uRL;$DdI}%E(_{U`Z8hE5K5uz1(rVkeHNIKZv5B}IThRpD?2j?maJqo zQ=cB+D#r%i3Im^>v*B2t_ngC%O8URb_}Y@ziX1LSYr&h{^#DD=o2zT3jYB_>_CV;<{&^H($p&GsN(`+^hOwzp`w zd}=YV=FT=ud+tr}PlO_%iRd`sCgZuT7#pFQQFHbwQ2PMj zV*nmmXkfoz%>ldzJd8^~j`uu8UXFd!lsS^pk7Toz(y)E~1e1;u^DZRwdd3l$E_)ks 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