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22.629000404448508 +100, 0.12790697802960094, -0.575 +300, 0.11912595995597372, 0.0005 +1000, 0.13083595787123853, -0.54 +3000, 0.2339775047946777, 0.0175 +10000, 1.1103465569966267, -0.7196666666666666 +30000, 5.469108250465964, -0.1436666666666667 +100000, 18.557929658732142, -0.2996666666666667 +300000, NaN, -0.14333333333333334 +1000000, NaN, 1.9835 diff --git a/assets/a-1/exp1-data-unadjusted.txt b/assets/a-1/exp1-data-unadjusted.txt index d5b72c9..dced3ff 100644 --- a/assets/a-1/exp1-data-unadjusted.txt +++ b/assets/a-1/exp1-data-unadjusted.txt @@ -1,7 +1,9 @@ -100, -0.11938231771144642 -300, 0.17395049078367358 -1000.0, 0.7685164726618712 -3000.0, 2.0711059211817617 -10000.0, 3.6629685926623363 -30000.0, 8.466203314149721 -100000.0, 25.36059471122112 +100, 0.11952579118058759, -0.7200000000000001 +300, 0.17723955593035218, -1.4366666666666668 +1000, 0.4411191860809871, -5.033333333333334 +3000, 1.244940988458407, -3.4499999999999997 +10000, 2.4258671800932605, -2.4 +30000, 6.7781659217833905, -0.8643333333333333 +100000, 19.8299212024026, 0.0003333333333332966 +300000, NaN, 2.7566666666666664 +1000000, NaN, 8.233333333333334 diff --git a/assets/a-1/exp1.gnuplot b/assets/a-1/exp1.gnuplot index 41834a8..6ac9bc0 100644 --- a/assets/a-1/exp1.gnuplot +++ b/assets/a-1/exp1.gnuplot @@ -17,9 +17,20 @@ set key left top set log x set xrange [1e2:1.5e5] -set xlabel "Frequency (Hz)" -set ylabel "Amplitude (dB)" +set multiplot layout 2,1 rowsfirst + +set xlabel +set ylabel "Gain (dB)" +set format x "" + +plot "exp1-data-unadjusted.txt" u 1:2 title "Unadjusted" with points pt '*', "exp1-data-adjusted.txt" u 1:2 title "Adjusted" with points pt 'x' + +unset key set xtics add ("1k" 1e3, "3k" 3e3, "10k" 1e4, "30k" 3e4, "100k" 1e5) +set xlabel "Frequency (Hz)" +set ylabel "Phase (deg)" -plot "exp1-data-unadjusted.txt" title "Unadjusted" with points pt '*', "exp1-data-adjusted.txt" title "Adjusted" with points pt 'x' +plot "exp1-data-unadjusted.txt" u 1:3 title "Unadjusted" with points pt '*', "exp1-data-adjusted.txt" u 1:3 title "Adjusted" with points pt 'x' + +unset multiplot diff --git a/assets/a-1/exp4-gnd.bmp b/assets/a-1/exp4-gnd.bmp new file mode 100644 index 0000000..e4d09b6 Binary files /dev/null and b/assets/a-1/exp4-gnd.bmp differ diff --git a/assets/a-1/exp4-gnd.png b/assets/a-1/exp4-gnd.png new file mode 100644 index 0000000..cf52388 Binary files /dev/null and b/assets/a-1/exp4-gnd.png differ diff --git a/assets/a-1/exp4-non-gnd.bmp b/assets/a-1/exp4-non-gnd.bmp new file mode 100644 index 0000000..f5e353a Binary files /dev/null and b/assets/a-1/exp4-non-gnd.bmp differ diff --git a/assets/a-1/exp4-non-gnd.png b/assets/a-1/exp4-non-gnd.png new file mode 100644 index 0000000..7f0c310 Binary files /dev/null and b/assets/a-1/exp4-non-gnd.png differ diff --git a/assets/a-1/patch-exp1-bode.sed b/assets/a-1/patch-exp1-bode.sed new file mode 100644 index 0000000..c02a9d0 --- /dev/null +++ b/assets/a-1/patch-exp1-bode.sed @@ -0,0 +1 @@ +s/exp1-bode/.\/assets\/a-1\/exp1-bode/g; diff --git a/assets/a-1/unadjusted.txt b/assets/a-1/unadjusted.txt new file mode 100644 index 0000000..839ea06 --- /dev/null +++ b/assets/a-1/unadjusted.txt @@ -0,0 +1,10 @@ +hz, os rms, mm rms, phase +100, 3.00, 2.959, -720m -360m -1.08 +300, 3.02, 2.959, -1.30 -1.72 -1.29 +1k, 3.11, 2.956, -4.68 -5.39 -5.03 +3k, 3.37, 2.920, -2.60 -3.44 -4.31 +10k, 3.48, 2.632, -1.80 -2.16 -3.24 +30k, 3.52, 1.613, -1.30 -861m -432m +100k, 3.54, 0.361, -1.08 -359m 1.44 +300k, 3.55, NaN, 3.24 3.95 1.08 +1M, 3.52, NaN, 7.75 8.28 8.67 diff --git a/bibs/a-1.bib b/bibs/a-1.bib index e69de29..a8811e3 100644 --- a/bibs/a-1.bib +++ b/bibs/a-1.bib @@ -0,0 +1,72 @@ +@online{probe-ds, + title={TEXAS250}, + author={HONG KONG TEXAS CO., LTD}, + url={https://akizukidenshi.com/goodsaffix/Texas_Probe_PCN_20211213.pdf}, + year={2021}, + month={12}, + urldate={2026-04-26} +} +@online{multi-m-ds, + title={PC700 DIGITAL MULTIMETER INSTRUCTION MANUAL}, + author={三和電気計器株式会社}, + url={https://www.sanwa-meter.co.jp/japan/pdf/manual/digital_multimeters/PC700_JP.pdf}, + year={2014}, + month={04}, + urldate={2026-04-26} +} +@online{os-ds, + title={TBS1000B-EDUシリーズ・デジタル・オシロスコープ}, + author={Inc., Tektronix}, + url={https://download.tek.com/datasheet/TBS1000B-EDU-Series_Oscilloscope_Datasheet-JA-JA-3GZ300013.pdf}, + year={2018}, + month={11}, + urldate={2026-04-26} +} +@online{fg-ds, + title={FG-274 取扱説明書}, + author={TEXIO TECHNOLOGY}, + url={https://www.texio.co.jp/uploads/FG-274_B71-0173-11_J.pdf}, + year={2014}, + month={10}, + urldate={2026-04-26} +} +@online{os-trig-video, + title={The Basics of an Oscilloscope Trigger}, + author={Inc., Tektronix}, + url={https://www.tek.com/en/video/the-basics-of-an-oscilloscope-trigger}, + year={2021}, + month={04}, + urldate={2026-04-27} +} +@inbook{probe-comp:tester-and-os-usage-for-electronic-works, + title={電子工作のためのテスタ\&オシロスコープ活用}, + author={橋詰伸一}, + publisher={CQ出版株式会社}, + year={2010}, + month={05}, + pages={70-71} +} +@inbook{probe-atten:tester-and-os-usage-for-electronic-works, + title={電子工作のためのテスタ\&オシロスコープ活用}, + author={橋詰伸一}, + publisher={CQ出版株式会社}, + year={2010}, + month={05}, + pages={181} +} +@inbook{probe-rc:tester-and-os-usage-for-electronic-works, + title={電子工作のためのテスタ\&オシロスコープ活用}, + author={橋詰伸一}, + publisher={CQ出版株式会社}, + year={2010}, + month={05}, + pages={184} +} +@inbook{probe-gnd:tester-and-os-usage-for-electronic-works, + title={電子工作のためのテスタ\&オシロスコープ活用}, + author={橋詰伸一}, + publisher={CQ出版株式会社}, + year={2010}, + month={05}, + pages={187-189} +} diff --git a/out/report_a-1.pdf b/out/report_a-1.pdf index 2257620..779d2e2 100644 Binary files a/out/report_a-1.pdf and b/out/report_a-1.pdf differ diff --git a/out/report_a-1.synctex.gz b/out/report_a-1.synctex.gz index 9aa0495..74d3770 100644 Binary files a/out/report_a-1.synctex.gz and b/out/report_a-1.synctex.gz differ diff --git a/report_a-1.tex b/report_a-1.tex index 5a22029..c9728f0 100644 --- a/report_a-1.tex +++ b/report_a-1.tex @@ -1,13 +1,13 @@ \documentclass[japanese,xelatex,a4paper,10.5pt,ja=standard]{bxjsarticle} \usepackage{tex/preamble} -\usepackage{tex/depD-bib} \usepackage{tex/experiment-title} \usepackage{amsmath} \usepackage{amssymb} \usepackage{cleveref} \usepackage{multirow} \usepackage{pgf} +\usepackage{tex/depD-bib} \renewcommand\figurename{Fig. } \renewcommand\tablename{Table } @@ -20,8 +20,8 @@ \Crefname{figure}{Fig.}{Fig.} \crefname{table}{Table}{Tables} \Crefname{table}{Table}{Tables} -\crefname{equation}{式}{式} -\Crefname{equation}{式}{式} +\crefname{equation}{Eq.}{Eq.} +\Crefname{equation}{Eq.}{Eq.} \creflabelformat{equation}{(#1)} \newcommand\resetrefcounter{ @@ -33,7 +33,7 @@ \reportauthor{柴田健琉} \reporttitle{計測器の使い方} \reportdate{2026年}{04月}{14日} -\turnindate{2026年}{04月}{27日} +\turnindate{2026年}{04月}{28日} \schoolyear{2026} \grade{3} \department{電子制御工学科} @@ -43,8 +43,9 @@ \seatingnum{15} \addExperimentDate{2026年 04月 14日} \addExperimentDate{2026年 04月 21日} -\addResearcher{佐藤暖斗} -\addResearcher{森下轟弾} +\addExperimentDate{2026年 04月 27日} + +\addbibresource{./bibs/a-1.bib} \begin{document} \experimentTitle @@ -58,7 +59,6 @@ \input{./sections/a-1/exp-detail} \resetrefcounter - \clearpage \input{./sections/a-1/exp-result} \resetrefcounter @@ -66,4 +66,18 @@ \input{./sections/a-1/reflections} \resetrefcounter + \section{まとめ} + + 今回の実験より以下の事が分かった: + + \begin{itemize} + \item{マルチメータのモードが測定精度を左右する} + \item{測定機器の内部抵抗には注意すること} + \item{測定機器の電源にアースが付いている場合は接続することが望ましい} + \item{オシロスコープのプローブの校正は測定前に確認すること} + \item{オシロスコープのプローブの接続には十分注意すること} + \end{itemize} + + \printbibliography[title={参考文献}]{} + \end{document} diff --git a/sections/a-1/exp-detail.tex b/sections/a-1/exp-detail.tex index e9fb54d..94cb580 100644 --- a/sections/a-1/exp-detail.tex +++ b/sections/a-1/exp-detail.tex @@ -2,25 +2,30 @@ \subsection{実験器具} -今回の実験で使用した装置は以下の通りである: +今回の実験で使用した機材は以下の通りである: \begin{itemize} \item {SANWA, PC700 マルチメータ} \item {Tektronix, TBS 1072B-EDU デジタルオシロスコープ} \item {TEXIO, FG-274 ファンクションジェネレータ} - \item {Hong kong Texas, TEXAS250 プローブ x2} + \item {HONG KONG TEXAS, TEXAS250 プローブ x2} + \item {ブレッドボード} + \item {47 $\Omega{} \pm 5\%$} + \item {10k $\Omega{} \pm 5\%$} + \item {100k $\Omega{} \pm 5\%$} \end{itemize} \subsection{実験1 - プローブの補正} \begin{enumerate} - \item{オシロスコープとFGを用意する} + \item{オシロスコープとFGを用意する.} \item{パッシブプローブを接続し,トリマを回転させ波形を歪ませ,記録する.プローブはアッテネーション(x10)を有効にしておく.} + \item{比較・位相測定用に補正済のプローブを接続する.} \item{ 補正不足の状態でプローブをFGの出力に接続し, 100 Hz, 300 Hz, 1 kHz, 3kHz, 10kHz, 100kHz, 1MHzの正弦波の振幅をオシロスコープで測定・記録する. 同時にFGの出力を交流電圧・周波数測定モード$(\tilde{\text{V}}/\text{Hz})$にしたマルチメータに接続しそれぞれで振幅を測定・記録する. - 入力電圧振幅も記録しておく. + 入力電圧振幅も記録しておく.別チャンネルの基準波形を元に位相をオシロスコープで測定・記録する. } \item{プローブを補正し,3と同様に測定・記録を行なう.} \end{enumerate} diff --git a/sections/a-1/exp-result.tex b/sections/a-1/exp-result.tex index 67a1046..c0d9d72 100644 --- a/sections/a-1/exp-result.tex +++ b/sections/a-1/exp-result.tex @@ -41,7 +41,7 @@ \label{fig:bode-line} \end{figure} -この実験で周波数が高くなるにつれ,未補正での振幅が変化することを確認した.また,マルチテスタで測定した入力電圧振幅が周波数が高くなるにつれ小さくなり,最終的に測定不能となった. +この実験で周波数が高くなるにつれ,未補正での振幅が変化することを確認した.また,マルチテスタで測定した入力電圧振幅が周波数が高くなるにつれ小さくなり,最終的に1 MHzで測定不能となった. 補正時では未補正時よりも振幅が最大約2.3 dB低下した. @@ -80,4 +80,26 @@ \subsection{実験4} +電圧波形は以下となった: +\begin{figure}[tbh] + \begin{minipage}[c]{0.45\hsize} + \centering + \includegraphics[width=6cm]{./assets/a-1/exp4-gnd.png} + \caption{From Common Ground} + \label{fig:exp4-gnd} + \end{minipage} + \begin{minipage}[c]{0.45\hsize} + \centering + \includegraphics[width=6cm]{./assets/a-1/exp4-non-gnd.png} + \caption{From Floating Voltage} + \label{fig:exp4-non-gnd} + \end{minipage} +\end{figure} + +\cref{fig:exp4-gnd}では黄色の波形が節点Aの,青色の波形が節点Bの節点Cを基準電位とした電圧となっている. + +\cref{fig:exp4-non-gnd}では黄色の波形が節点Aの,青色の波形が節点Cの節点Bを基準電位とした電圧となっている. + +節点Bを基準電位とした時,節点Cの波形が得られなかったが,手順の演算を行なったところ,節点Cを基準電位とした節点Aの電圧波形が得らたことを確認できた. +また,オシロスコープの電源にはアースを接続することでより精度よく,低ノイズで測定できることを実験中に確認した. diff --git a/sections/a-1/reflections.tex b/sections/a-1/reflections.tex index d89b168..6f47cba 100644 --- a/sections/a-1/reflections.tex +++ b/sections/a-1/reflections.tex @@ -6,38 +6,56 @@ オシロスコープのプローブにはトリマとアッテネーションがある.それぞれ測定の精度を左右する重要なパラメータである. -トリマはプローブ内部で並列接続された可変コンデンサのキャパシタンスを変える効果がある. +トリマは\cref{fig:probe-equiv-circuit}のようにプローブ内部で並列接続された可変コンデンサのキャパシタンスを変える効果がある. +これによりプローブのインピーダンスを変化させ交流電圧を正しく計測できるようになる\supercite{probe-comp:tester-and-os-usage-for-electronic-works}. \begin{figure}[tbh] \centering \begin{circuitikz} \draw (0, 1) to [short,o-] ++(2,0) to [R, l={$R_{\text{in}}$}] ++(0,-2); - \draw (2, 1) to [short,*-] ++(2,0) to [C, l={$C_{\text{in}}$}] ++(0,-2); - \draw (4, 1) to [short,*-] ++(2,0) to [vC, l={$C_{\text{comp}}$}] ++(0,-2); + \draw (2, 1) to [short,*-] ++(2,0) to [C, l={$C_{\text{in}}$}] ++(0,-1) to [vC, l={$C_{\text{comp}}$}] ++(0,-1); + + %\draw (2, 1) to [short,*-] ++(2,0) to [C, l={$C_{\text{in}}$}] ++(0,-2); + %\draw (4, 1) to [short,*-] ++(2,0) to [vC, l={$C_{\text{comp}}$}] ++(0,-2); + %\draw (6,-1) to [short,-*] ++(-2,0); + \draw (4,-1) to [short,-*] ++(-2,0) to [short,-o] ++(-2,0); - \draw (6,-1) to [short,-*] ++(-2,0); \end{circuitikz} \caption{Equivalent Circuit Diagram of Oscilloscope Probe} + \label{fig:probe-equiv-circuit} \end{figure} アッテネーションは測定範囲を変更できるもので,プローブの最低電圧レンジ:オシロスコープの最低電圧レンジの比で表示されている. -例えば10:1のプローブを使いオシロスコープでの最低電圧レンジが10 mV/divの場合,プローブの最低電圧レンジは100 mV/divとなる.この設定では50 mV/divのような低電圧の測定に向かないので1:1での測定が必要となる. +例えば10:1のプローブを使いオシロスコープでの最低電圧レンジが10 mV/divの場合,プローブの最低電圧レンジは100 mV/divとなる.この設定では50 mV/divのような低電圧の測定に向かないので1:1での測定が必要となる\supercite{probe-atten:tester-and-os-usage-for-electronic-works}. \subsubsection{マルチテスタの測定結果の変化} \cref{fig:bode-line}より,10 kHzを境に振幅が大きくなっていく様子が分かる. -これはマルチメータの定格測定周波数レンジ(15 \textasciitilde{} 10 kHz)を超えたためと思われる. +これはマルチメータの定格測定周波数レンジ(15 \textasciitilde{} 10 kHz)を超えたためと思われる\supercite{multi-m-ds}. \subsubsection{トリガ} +画面上で流れている波形はトリガレベルを調節することで止めることで観察しやすくする,これがトリガの効果である.オシロスコープは連続的に電圧を波形として表示する特性上,表示タイミングが合わないと波形表示が乱れたり,左右に動いてしまう. + +デジタルオシロスコープとアナログオシロスコープでは回路が異なるが,どちらもトリガレベルと測定波形を比較し,測定電圧がトリガレベル以上(立上がり)または以下(立下がり)になった時にトリガ(実行)し,トリガ前後波形を表示するようになっている.トリガによる測定開始タイミングの一致が安定した波形表示に寄与している\supercite{os-trig-video}. + +トリガにも様々な種類があり,特定のパルス幅・ロジックレベル・一定期間以上電圧レベルを維持した時などがある\supercite{os-trig-video}. + \subsection{実験2} +実験手順1で得た値を\cref{equ:rms-to-pp}に代入して計算すると$V_{\text{pp}}$は1.923 Vとなった. +これは2 $\text{V}_{\text{pp}}$から-3.833 \%の誤差率となる. + +実験手順2の実効値を同様に代入・計算すると$V_{\text{rms}}$は0.163 Vとなり,0.15 Vからの誤差率は+8.423 \%となった. + +この誤差はマルチメータでの小電圧の測定に向いた交流mV モードではなく誤差の大きい交流V モードで測定したことに起因すると考えられている\supercite{multi-m-ds}. + \subsection{実験3} \Cref{tb:v-btwn-diff-r}では一見オームの法則に反しているように見える. しかし,調査するとFGの内部抵抗による分圧回路の出力であると判明した. -FGのデータシートによると内部抵抗は$50 \Omega$であると分かった.なので,実験3の回路図は\cref{fig:actual-cd-exp3}となった. +FGのデータシートによると内部抵抗は$50 \Omega$であると分かった\supercite{fg-ds}.なので,実験3の回路図は\cref{fig:actual-cd-exp3}となった. \begin{figure}[tbh] \centering @@ -64,3 +82,38 @@ FGのデータシートによると内部抵抗は$50 \Omega$であると分か \Cref{equ:exp3-vr}の$E$に1を,$R_{internal}$に50を,そして$R$に47と10kを代入して計算を行うとそれぞれ0.485,0.995となり,実験値と近い値となった. \subsection{実験4} + +オシロスコープのプローブのグラウンドは内部で接続されている. +なので\cref{fig:bad-ex-probing}のようにプローブを接続するとオシロスコープ内で短絡し,測定回路またはオシロスコープを破損・故障させる恐れがある\supercite{probe-gnd:tester-and-os-usage-for-electronic-works}. + +\begin{figure}[tbh] + \centering + \begin{circuitikz} + \draw (0,0) to [short, o-] ++(1,0) to [R] ++(2,0) -- ++(2,0) to [D] ++(2,0) to [short, -o] ++(1,0); + \draw (1,0) to [short, *-o] ++(0,-1) node[below] {CH1}; + \draw (3,0) to [short, *-o] ++(0,-1) node[below] {CH1 GND}; + \draw (5,0) to [short, *-o] ++(0,-1) node[below] {CH2}; + \draw (7,0) to [short, *-o] ++(0,-1) node[below] {CH2 GND}; + \draw (3,-1.5) -- ++(0,-0.5) -- ++(4,0) -- ++(0,0.5); + \draw (5,-2) node[below] {Short circuit across diode}; + \end{circuitikz} + \caption{Bad Example of Oscilloscope Probing} + \label{fig:bad-ex-probing} +\end{figure} + +2チャンネルによる同時測定ではオシロスコープの演算機能を駆使した差動測定が可能である. +\cref{fig:diff-probing}のようにプローブを接続し,演算機能でCH1 - CH2の波形を表示すればダイオードにかかる電圧をCH2で,抵抗器にかかる電圧をCH1 - CH2で確認できる. +またグラウンドを気にせずに任意の2点間の電位差を測定できる差動プローブというものでも同じ結果が得られる. + +\begin{figure}[tbh] + \centering + \begin{circuitikz} + \draw (0,0) to [short, o-] ++(1,0) to [R] ++(2,0) to [D] ++(2,0) to [short, -o] ++(2,0); + \draw (1,0) to [short, *-o] ++(0,-1) node[below] {CH1}; + \draw (3,0) to [short, *-o] ++(0,-1) node[below] {CH2}; + \draw (6,0) to [short, *-o] ++(0,-1) node[below] {CH1 GND \& CH2 GND}; + \end{circuitikz} + \caption{Example of Differential Probing with Passive Probes} + \label{fig:diff-probing} +\end{figure} + diff --git a/sections/a-1/theory.tex b/sections/a-1/theory.tex index 60c24a4..ee82120 100644 --- a/sections/a-1/theory.tex +++ b/sections/a-1/theory.tex @@ -9,22 +9,69 @@ 直流成分は電流・電圧などの電気的要素の平均値としてあらわれ,交流成分はその平均値の差分の時間変化としてあらわれる. +\begin{figure}[tbh] + \begin{minipage}[c]{0.3\hsize} + \centering + \begin{tikzpicture}[domain=0:4] + \draw[->] (-0.2,0) -- (4.2,0) node[right] {$t$}; + \draw[->] (0,-1.2) -- (0,2.2) node[above] {$V$}; + \draw[thick] plot (\x, 1); + \end{tikzpicture} + \caption{DC Voltage} + \end{minipage} + \begin{minipage}[c]{0.3\hsize} + \centering + \begin{tikzpicture}[domain=0:4] + \draw[->] (-0.2,0) -- (4.2,0) node[right] {$t$}; + \draw[->] (0,-1.2) -- (0,2.2) node[above] {$V$}; + \draw[thick] plot (\x, {sin(1.57*\x r)}); + \end{tikzpicture} + \caption{AC Voltage} + \end{minipage} + \begin{minipage}[c]{0.3\hsize} + \centering + \begin{tikzpicture}[domain=0:4] + \draw[->] (-0.2,0) -- (4.2,0) node[right] {$t$}; + \draw[->] (0,-1.2) -- (0,2.2) node[above] {$V$}; + \draw[thin,color=gray,dashed] plot (\x, 1); + \draw[thick] plot (\x, {sin(1.57*\x r) + 1}); + \end{tikzpicture} + \caption{DC Voltage + AC Voltage} + \end{minipage} +\end{figure} + \subsection{インピーダンス} 交流回路でのインピーダンスとは直流回路における抵抗に相当する電圧と電流の比である.回路計測の際には入力と出力でのインピーダンスが重要になる. \subsection{振幅と実効値} -交流の大きさを表す指標は主にピークツピーク値と実効値がある.ピークツピーク値は最大値と最小値の振れ幅を示す.実効値は交流の時間に対する二乗平均値であり,以下の式で求まる: +交流の大きさを表す指標は主にピークツピーク値と実効値がある.交流電圧$v(t)$に対するピークツピーク値$V_{\text{pp}}$は以下の式となる: + +\begin{equation} + V_{\text{pp}} = \max{(v(t))} - \min{(v(t))} +\end{equation} + +実効値は交流の時間に対する二乗平均値であり,以下の式で求まる: \begin{equation} V_{\textrm{rms}} = \sqrt{\frac{1}{T}\int_{0}^{T} v(t)^2 dt} \end{equation} +ここで$T$は交流電圧の周期[s]である. -また,正弦波交流でのピークツピーク値と実効値には以下の関係がある: +また,正弦波交流$v(t) = V_{m}\sin{(\omega{}t)}$でのピークツピーク値と実効値には以下の関係がある: -\begin{equation} - V_{\textrm{rms}} = \frac{V_{\textrm{pp}}}{2\sqrt{2}} +\begin{equation}\label{equ:rms-to-pp} + \begin{split} + V_{\text{pp}} &= V_{m} - (-V_{m}) = 2V_{m} \\ + V_{\textrm{rms}} &= \sqrt{\frac{1}{T}\int_{0}^{T} v(t)^2 dt} \\ + &= \sqrt{\frac{\omega{}}{2\pi}\int_{0}^{\frac{2\pi}{\omega{}}} \left(V_{m}\sin{(\omega{}t)}\right)^2 dt} \\ + &= \sqrt{\frac{\omega{}}{2\pi}\int_{0}^{\frac{2\pi}{\omega{}}} \left(\frac{V_{\text{pp}}}{2}\sin{(\omega{}t)}\right)^2 dt} \\ + &= \sqrt{\frac{{V_{\text{pp}}^{2}}}{4} \cdot{} \frac{\omega}{2\pi} \int_{0}^{\frac{2\pi}{\omega}} \frac{1-\cos{(2\omega{}t)}}{2} dt} \\ + &= \sqrt{\frac{{V_{\text{pp}}^{2}}}{8} \cdot{} \frac{\omega}{2\pi} \left(t - \frac{1}{2\omega{}}\sin{(2\omega{}t)}\right)^{\frac{2\pi}{\omega}}_{0}} \\ + &= \sqrt{\frac{{V_{\text{pp}}^{2}}}{8}} \\ + V_{\textrm{rms}} &= \frac{V_{\textrm{pp}}}{2\sqrt{2}} + \end{split} \end{equation} \subsection{マルチメータ} diff --git a/tex/depD-bib.sty b/tex/depD-bib.sty index b049b62..f7fbb63 100644 --- a/tex/depD-bib.sty +++ b/tex/depD-bib.sty @@ -2,12 +2,11 @@ \ProvidesPackage{depD-bib} \renewbibmacro*{cite}{ - \printtext[bibhyperref]{% \printfield{labelprefix}% \printfield{labelnumber})% \ifbool{bbx:subentry} {\printfield{entrysetcount}} - {}}} + {}} \DeclareFieldFormat{title}{"\mkbibemph{#1}"} \DeclareFieldFormat{chapter}{#1\bibstring{章}} \DeclareFieldFormat{pages}{#1\bibstring{頁}} diff --git a/tex/preamble.sty b/tex/preamble.sty index edd6468..26c7559 100644 --- a/tex/preamble.sty +++ b/tex/preamble.sty @@ -12,7 +12,7 @@ \usepackage{fontspec} \usepackage[mono=false]{libertine} \usepackage{noto} -\setmonofont{0xProto} +\setmonofont{Moralerspace Argon} \usepackage[european]{circuitikz}