From 54f1051920684208b287fb7e66000191a8db6e6b Mon Sep 17 00:00:00 2001 From: Kenryu Shibata Date: Tue, 6 Oct 2026 10:40:45 +0900 Subject: [PATCH] mostly finished t-3 --- assets/t-3/e1.png | Bin 0 -> 32739 bytes assets/t-3/e2.png | Bin 0 -> 38221 bytes bibs/t-3.bib | 52 ++++++++++++++++++++++++++++ out/report_t-3.pdf | Bin 0 -> 214372 bytes out/report_t-3.synctex.gz | Bin 0 -> 35440 bytes report_t-3.tex | 66 ++++++++++++++++++++++++++++++++++++ sections/t-3/exp-detail.tex | 55 ++++++++++++++++++++++++++++++ sections/t-3/exp-result.tex | 24 +++++++++++++ sections/t-3/reflection.tex | 59 ++++++++++++++++++++++++++++++++ sections/t-3/theory.tex | 33 ++++++++++++++++++ 10 files changed, 289 insertions(+) create mode 100644 assets/t-3/e1.png create mode 100644 assets/t-3/e2.png create mode 100644 bibs/t-3.bib create mode 100644 out/report_t-3.pdf create mode 100644 out/report_t-3.synctex.gz create mode 100644 report_t-3.tex create mode 100644 sections/t-3/exp-detail.tex create mode 100644 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k5o5sT@c(C*Fb?H81)LDA$_6TecI~>Xtq;n*aO?5^1IgT5bpQYW literal 0 HcmV?d00001 diff --git a/bibs/t-3.bib b/bibs/t-3.bib new file mode 100644 index 0000000..8a5416d --- /dev/null +++ b/bibs/t-3.bib @@ -0,0 +1,52 @@ +@inbook{fsd-2-fet, + title={半導体デバイスの基礎 中}, + author={Betty L. Anderson and Richard L. Anderson}, + translator={樺沢 宇紀}, + publisher={シュプリンガー・ジャパン株式会社}, + year={2008}, + month={05}, + part={3}, + chapter={7} +} +@inbook{fsd-3-bjt, + title={半導体デバイスの基礎 下}, + author={Betty L. Anderson and Richard L. Anderson}, + translator={樺沢 宇紀}, + publisher={シュプリンガー・ジャパン株式会社}, + year={2008}, + month={05}, + part={4}, + chapter={9} +} +@inbook{eco, + title={新訂電子回路概論}, + author={高木 茂考 and 堀桂 太郎}, + publisher={株式会社太洋社}, + year={2025}, + month={04}, + pages={34-47} +} +@inbook{eco-amp, + title={新訂電子回路概論}, + author={高木 茂考 and 堀桂 太郎}, + publisher={株式会社太洋社}, + year={2025}, + month={04}, + pages={65-115} +} +@online{bjt-ds, + title={2SC1815}, + author={LTD, UNISONIC TECHNOLOGIES CO.}, + url={https://akizukidenshi.com/goodsaffix/2SC1815_unisonic.pdf}, + year={2021}, + month={05}, + urldate={2026-10-03} +} +@online{nfet-ds, + title={MTA100N10KRI3}, + author={CYStech Electronics Corp.}, + url={https://akizukidenshi.com/goodsaffix/MTA100N10KRI3.pdf}, + year={2020}, + month={04}, + urldate={2026-10-03} +} diff --git a/out/report_t-3.pdf b/out/report_t-3.pdf new file mode 100644 index 0000000000000000000000000000000000000000..986ca5528cc3b216104873bf5e79ffcdb1abbf7b GIT binary patch literal 214372 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teSG(?KmGROmyfiuFYo^3QbYdb*T4Vr{m);1`{Coe{{@srS?5JF0|0@p2`vBs literal 0 HcmV?d00001 diff --git a/report_t-3.tex b/report_t-3.tex new file mode 100644 index 0000000..23b0e64 --- /dev/null +++ b/report_t-3.tex @@ -0,0 +1,66 @@ +\documentclass[japanese,xelatex,a4paper,10.5pt,ja=standard]{bxjsarticle} + +\usepackage{tex/preamble} +\usepackage{tex/experiment-title} +\usepackage{amsmath} +\usepackage{amssymb} +\usepackage{array} +\usepackage{multirow} +\usepackage{subcaption} +\usepackage{pgfmath} +\usepackage{pgffor} +\usepackage{tex/depD-bib} +\usepackage{tex/depD-format} + +\reportauthor{柴田健琉} +\reporttitle{トランジスタの特性} +\reportdate{2026年}{09月}{29日} +\turnindate{2026年}{10月}{06日} +\schoolyear{2026} +\grade{3} +\department{電子制御工学科} +\subject{電子制御工学実験1} +\reportid{T-3} +\expgroup{4班} +\seatingnum{15} +\addResearcher{後藤 昊大} +\addResearcher{佐藤 暖斗} +\addResearcher{高橋 健太} +\addExperimentDate{2026年 07月 23日} +\addExperimentDate{2026年 09月 29日} + +\addbibresource{./bibs/t-3.bib} + +\begin{document} + \experimentTitle + + \section{実験目的} + + 今回の実験では代表的な3端子半導体素子の特性とその測定方法を確認するために行った. + + \input{sections/t-3/theory} + \resetrefcounter + + \input{sections/t-3/exp-detail} + \resetrefcounter + + \newpage + + \input{sections/t-3/exp-result} + \resetrefcounter + + \input{sections/t-3/reflection} + \resetrefcounter + + \section{まとめ} + + 今回の実験で以下の事象・事実を確認した: + + \begin{itemize} + \item{BJTやMOSFETの出力特性は非線形である} + \item{BJTやMOSFETはそれぞれ電流と電圧で信号を増幅出来る} + \end{itemize} + + \printbibliography[title={参考文献}]{} + +\end{document} diff --git a/sections/t-3/exp-detail.tex b/sections/t-3/exp-detail.tex new file mode 100644 index 0000000..50fa8cb --- /dev/null +++ b/sections/t-3/exp-detail.tex @@ -0,0 +1,55 @@ +\section{実験条件・実験手順} + +\subsection{実験器具} + +\begin{itemize} + \item{ADALM2000} + \item{Scopyを導入したPC} + \item{抵抗器($100 \ \Omega , 10 \ \text{k}\Omega , 100 \ \text{k}\Omega$)} + \item{N チャネル MOSFET (MTA100N10KRI3)} + \item{NPN BJT (2SC1815L-GR-T92)} + \item{ブレッドボード} + \item{ジャンパーワイヤ 複数} +\end{itemize} + +\subsection{実験1} + +ADALM2000の波形生成機能と直流電圧源とオシロスコープを用いてMOSFETのドレイン電流とゲート-ソース間電圧の関係を調べる. +\Cref{fig:exp-1_cd}の回路をブレッドボード上で作成し, +100 Hz, 2.5 $\text{V}_{\text{pp}}$, 直流成分\\1.25 Vの三角波をMOSFETのゲートに入力し, シャント抵抗を用いて電流を測定する. +なお, MOSFETの\\ドレインには5 Vの定電圧を印加した. +オシロスコープでは縦軸がシャント抵抗両端の電圧, 横軸がゲート-\\ソース間電圧であるようなXYプロットとして表示させた. + +\begin{figure}[H] + \centering + \begin{circuitikz} + \draw (0, 0) node[above]{$V_p = 5 \ \text{V}$} to [short, o-] ++(0,-1) to [R={$R_1 = 100 \ \Omega$}] ++(0,-2) node[nigfete, anchor=D](q){}; + \draw (q.G) to [short, -o] ++(-1,0) node[left]{W1, 1+}; + \draw (q.D) to [short, *-o] ++(1,0) node[right]{2-}; + \draw (q.S) node[ground]{} to [short, *-o] ++(1,0) node[right]{1-}; + \draw (0,-1) to [short, *-o] ++(1,0) node[right]{2+}; + \end{circuitikz} + \caption{Circuit Diagram for Experiment 1} + \label{fig:exp-1_cd} +\end{figure} + +\subsection{実験2} + +ADALM2000の波形生成機能とオシロスコープを用いてNPNトランジスタのコレクタ電流とコレクタ-エミッタ間電圧の関係を調べる. +\Cref{fig:exp-2_cd}の回路をブレッドボード上で組む. +0.6 Vから4.6 Vまでが1 V間隔であるような階段上の波形をベースに入力し, それぞれの段でコレクタ電圧0 Vから5 Vまで走査させるような三角波を入力する. +シャント抵抗でコレクタ電流を測定し, 同時にコレクタ-エミッタ間電圧を測定する. +オシロスコープでは縦軸がシャント抵抗両端の電圧, 横軸がコレクタ-エミッタ間電圧であるようなXYプロットとして表示させた. + +\begin{figure}[H] + \centering + \begin{circuitikz} + \draw (0,0) node[above]{W1} to [short, o-] ++(0,-1) to [R={$R_1 = 100 \ \Omega$}] ++(0,-2) node[npn,anchor=C](q){}; + \draw (-3,0) node[above]{W2} to [short, o-] ++(0,-1) to [R={$R_2 = 100 \ \text{k}\Omega$}] ++(0,-2) |- (q.B); + \draw (q.C) to [short, *-o] ++(1,0) node[right]{1+, 2-}; + \draw (0,-1) to [short, *-o] ++(1,0) node[right]{2+}; + \draw (q.E) node[ground]{} to [short, *-o] ++(1,0) node[right]{1-}; + \end{circuitikz} + \caption{Circuit Diagram for Experiment 2} + \label{fig:exp-2_cd} +\end{figure} diff --git a/sections/t-3/exp-result.tex b/sections/t-3/exp-result.tex new file mode 100644 index 0000000..7647ca1 --- /dev/null +++ b/sections/t-3/exp-result.tex @@ -0,0 +1,24 @@ +\section{実験結果} + +\subsection{実験1} + +1.2 V付近で電流が急激に流れ始め, 1.8 V付近で電流の増加が頭打ちとなった. + +\begin{figure}[H] + \centering + \includegraphics[width=10cm]{./assets/t-3/e1.png} + \caption{$I_{D}$ vs. $V_{GS}$ of Experiment 1} + \label{fig:exp1_res} +\end{figure} + +\subsection{実験2} + +複数電圧での電流特性が重ね合わさった波形が出力された. +波形にはノイズが多少乗っているがそれぞれ, 急激な電流変化の後に変化が緩やかになった. + +\begin{figure}[H] + \centering + \includegraphics[width=10cm]{./assets/t-3/e2.png} + \caption{$I_{C}$ vs. $V_{CE}$ of Experiment 2} + \label{fig:exp2_res} +\end{figure} diff --git a/sections/t-3/reflection.tex b/sections/t-3/reflection.tex new file mode 100644 index 0000000..96c2616 --- /dev/null +++ b/sections/t-3/reflection.tex @@ -0,0 +1,59 @@ +\section{考察} + +\subsection{実験1} + +\Cref{fig:exp1_res}によると, $V_{GS}$ = 1.82 V付近で定電流となった. +これは, このMOSFETの閾値電圧$V_{GS\text{(th)}}$の0.6 Vから2.2 Vの範囲に収まっている\supercite{nfet-ds}. + +データシートの$I_{D}$ vs. $V_{DS}$グラフによると, $V_{GS}$ = 2.5 V, $V_{DS}$ = 5.0 Vでは約7.5 A流すことが出来るとあるが\supercite{nfet-ds}, \cref{fig:exp1_res}では45.64 mAしか流れていない. +これは, シャント抵抗が電流を制限してしまっているのが原因だと考えられる. オームの法則により$V_{DS} = R_{1}I_{D}$となり, $5 = 100I_{D}$なので, 最大の$I_{D}$は50 mAとなっている. + +MOSFETを用いた増幅回路はゲートに直流のバイアス電圧を掛け, 交流の信号を乗せることで電流を増幅することが出来る. +その電流をドレインに接続した抵抗を用いて電圧降下を発生させる事で電圧増幅を行う. +この時, $g_m$を相互コンダクタンス, $Z_o$を出力インピーダンスとすると電圧増幅度は\cref{equ:fet-av}となる\supercite{eco-amp}. +\begin{equation} + \label{equ:fet-av} + A_v = g_m Z_o +\end{equation} +バイアス電圧とドレイン抵抗を上手に設計できれば, ある程度の利得を確保できる. +例えば, \cref{fig:exp1_res}でゲート-ソース間に約1.57 Vを掛け, そこに0.1 Vの振幅を持つ交流信号を乗せるとドレイン電流は約4.74 mA から 約40.1 mAの範囲で変化する. +データシートによると, 相互コンダクタンスは6 Sであるので, 出力インピーダンスを低くする事が出来る. +また, MOSFETは電圧制御形なのでバイアス電圧を作り出す分圧抵抗の値を大きくすることが出来る. + +\subsection{実験2} + +実験では階段状の電圧波形をベースに入力した. この時流れる電流はオームの法則により$I_{B} = \frac{V_{B}}{R_2}$となる. +よって, $V_{B} = 0.6, \ 1.6, \ 2.6, \ 3.6, \ 4.6 \ \text{[V]}$ではそれぞれ, $I_{B} = 6.0, \ 16, \ 26, \ 36, \ 46 \ \text{[}\mu\text{A]}$となる. +また, \cref{fig:exp2_res}からそれぞれのベース電圧での飽和電流を概算すると, $I_{D\text{(sat)}} = 0.03, \ 2.26, \ 4.82, \ 7.37, \ 9.92 \ \text{[mA]}$となった. + +これらの値から電流利得を計算するとそれぞれ, $\beta = 5.00, \ 141, \ 185, \ 205, \ 216$となった. $V_{B} = 0.6 \ \text{V}$での利得が他より小さいのは素子が完全に活性していないためだと思われる. それ以外はデータシートに記載されている$70 \leq h_{FE} \leq 700$の範囲内となった\supercite{bjt-ds}. + +コレクタ-ベース間電圧を増加させるとトランジスタ内のp-n接合に逆電圧を印加する際に発生する空乏層の幅が増加する. +これにより, 元々幅が狭いベースのn形・p形半導体を更に狭くし, コレクタ-エミッタ間の電流がより流れやすくなり, 電流利得が上昇する. + +この現象はアーリー効果と呼ばれ, 電流利得の増加の度合いを示す指標としてアーリー電圧がある. +アーリー電圧が高ければ高いほどコレクタ電圧の増加による利得の変化が少なくなる. +アーリー電圧はあるベース電流における$I_{C}$ - $V_{CE}$特性の電流飽和領域での1次近似式の根の絶対値として求められる\supercite{fsd-3-bjt}. + +\Cref{fig:exp2_res}を例に取ると, 電流飽和領域での1次近似式は\cref{equ:early}となる. +\begin{equation} + \label{equ:early} + f(x) = \frac{i_2 - i_1}{v_2 - v_1}(x - v_1) + i_1 = \frac{10.4 \ \text{mA} - 9.92 \ \text{mA}}{3.326 \ \text{V} - 0.448 \ \text{V}}(x - 0.448 \ \text{V}) + 9.92 \ \text{mA} +\end{equation} +この式の根の絶対値を求めるとアーリー電圧\cref{equ:va}が求まる. +\begin{equation} + \label{equ:va} + \begin{split} + f(x) &= 0 \\ + x &= -\frac{i_1(v_2 - v_1)}{i_2 - i_1} + v_0 \\ + V_{A} &= |x| \approx 59478 \ \text{[V]} + \end{split} +\end{equation} +電流利得とアーリー電圧の積をとると$1.285 \times 10^7$程度となった. データシートにはアーリー電圧に関する記載が無かったため, +この値から言えることは電流利得は測定範囲内では十分に一定だという事実のみである. + +BJTを用いた増幅回路はMOSFETでの増幅回路と同様にベースに直流のバイアス電圧を印加し, 交流の信号を入力する. +しかし, MOSFETの時とは違い, BJTは電流制御形なので正しくバイアスをかけるには電流に余裕を持たせる必要があるので入力インピーダンスは相対的に低くなる. +電流増幅度は$h_{fe}$として示され, コレクタ電流$i_c$とベース電流$i_b$との関係は$i_c = h_fe i_b$と線形性を示す\supercite{eco}. + +例えば, $h_{FE} = h_{fe} = 216$とし, \cref{fig:exp2_res}の特性より, 2.313 Vを中心に持ってくるようなコレクタ抵抗を適切に設計すれば, $V_{BE} = 2.6 \ \text{V}$を中心とした小さな交流信号を入力すると, 電流は216倍, 電圧は0から電源電圧まで増幅することが出来る. diff --git a/sections/t-3/theory.tex b/sections/t-3/theory.tex new file mode 100644 index 0000000..300d928 --- /dev/null +++ b/sections/t-3/theory.tex @@ -0,0 +1,33 @@ +\section{理論} + +\subsection{トランジスタ} + +トランジスタは電気を用いて電流を制御する素子である. トランジスタは大きく分けて2種類ある: バイ\\ポーラジャンクショントランジスタ(BJT)と電界効果トランジスタ(FET)である. しかし, 単にトランジスタと呼ぶ場合は大抵BJTのことである. + +BJTには3つの端子があり, それぞれコレクタ(C), エミッタ(E), ベース(B)と呼ばれている. BJTには2種類あり, コレクタ・べース・エミッタの順で使用されている半導体の形によってnpn形とpnp形に分けられる. ベースには薄い半導体を, コレクタとエミッタにはベースと対となる形の半導体を使用してベースを挟み込むように配置されている. npn形はベース-エミッタ間に順電圧を, pnp形には逆電圧を掛けることでコレクタ-エミッタ間に電流が流れる. このベースに流れる電流を変化させることでコレクタ-エミッタ間の電流を制御することができる\supercite{eco}. + +\begin{figure}[H] + \centering + \begin{circuitikz} + \draw (-2,0) node[npn,anchor=C](q1){} (q1.B) node[left]{B} (q1.C) node[above]{C} (q1.E) node[below]{E} ++(0,-1) node{npn}; + \draw (2,0) node[pnp,anchor=E](q2){} (q2.B) node[left]{B} (q2.E) node[above]{E} (q2.C) node[below]{C} ++(0,-1) node{pnp}; + \end{circuitikz} + \caption{Symbols of BJT} + \label{fig:bjt-sym} +\end{figure} + +\subsection{MOSFET} + +電界効果トランジスタ(FET)はBJTと同じく3つの端子を持つ素子であり, 端子の名称はドレイン(D), ソース(S), ゲート(G)となる. FETには接合形とMOS(Metal Oxide Semiconductor, 酸化金属半導体)の2種類あるがここではより一般的に使用されているMOSFETを説明する. + +MOSFETはドレイン・ソースに使用する半導体の形によってNチャネルとPチャネルに分けることができ, 更にゲートに使用される半導体の性質によって, エンハンスメント形とデプレッション形がある. エンハンスメント形ではNチャネルのゲート-ソース間には順電圧を, Pチャネルのには逆電圧を掛けることで素子が活性される. デプレッション形ではそれぞれのチャネルでの動作が逆となる. このゲート-ソース間の電圧を変化させることでドレイン-ソース間に流れる電流を制御することができる\supercite{eco}. + +\begin{figure}[H] + \centering + \begin{circuitikz} + \draw (-2,0) node[nigfete, anchor=D](q1){} (q1.G) node[left]{G} (q1.D) node[above]{D} (q1.S) node[below]{S} ++(0,-1) node{Nch. MOSFET}; + \draw (2,0) node[pigfete, anchor=S](q2){} (q2.G) node[left]{G} (q2.S) node[above]{S} (q2.D) node[below]{D} ++(0,-1) node{Pch. MOSFET}; + \end{circuitikz} + \caption{Symbols of Enhancement MOSFET} + \label{fig:mosfet-enh-sym} +\end{figure}