簡易等価回路で見る電流帰還バイアス増幅回路

この回路は電流帰還バイアス増幅回路を書き換えたものです。

(1) 問題文のとおりに $R_\mathrm{B}$ をおくと、簡易等価回路は以下のように表されます。

$v_\mathrm{o}=-h_\mathrm{fe}i_\mathrm{b}R_\mathrm{C}R_\mathrm{L}/(R_\mathrm{C}+R_\mathrm{L})$ より、出力電流 $i_\mathrm{o}$ は以下の式で表されます。

したがって、電流増幅度 $A_\mathrm{i}$ は以下の式で与えられます。

上図の青矢印で示した閉路にキルヒホッフの電圧則を適用すると、以下のように $i_\mathrm{i}/i_\mathrm{b}$ が求められます。

したがって、電流増幅度 $K_\mathrm{i}$ は $R_\mathrm{B}$、$A_\mathrm{i}$ を用いて次式で表されます。

$v_\mathrm{i}=\{h_\mathrm{ie}+(h_\mathrm{fe}+1)R_\mathrm{E}\}i_\mathrm{b}$ より、入力インピーダンス $Z_\mathrm{i}$ は $R_\mathrm{B}$ を用いて次式で表されます。

(2) 下図のように $C_\mathrm{E}$ を挿入したとき、簡易等価回路は上図で $R_\mathrm{E}$ を短絡したものとなります。

したがって、上述の計算結果に $R_\mathrm{E}=0$ を代入することで、$C_\mathrm{E}$ 挿入時の電流増幅度や入力インピーダンスが求められ、その結果は以下のようになります。

※ 電圧増幅度だけでなく、電流増幅度や入力インピーダンスも前回の記事の練習問題3で扱った固定バイアス増幅回路における式と一致します。

% Common Emitter Amplifier (voltage divider bias)
\documentclass[border=3mm]{standalone}
\usepackage{tikz}
\usepackage{circuitikz}
\usetikzlibrary{calc}
\ctikzset{transistors/arrow pos=end}
\usepackage{newtxtext,newtxmath}
\pagecolor{white}
\begin{document}
\begin{tikzpicture}
\draw (0,0) node[npn](Tr) {};
\draw[thick] ($(Tr)-(0.35,0)$) circle [radius=13pt] node[above left=8pt] {Tr};
\draw(Tr.E)
    to[european resistor, l_=$R_\mathrm{E}$] ++(0,-2)
    coordinate(tmp3) % below Re
    to[short] ++(2.5,0)
    coordinate(tmp6) % below Rl
    to[short] ++(2.5,0)
    to[battery2, invert, l_=$V_\mathrm{CC}$] ++(0,5.6)
    to[short] ++(-5,0)
    coordinate(tmp1) % above Rc
    to[european resistor, l_=$R_\mathrm{C}$] ++(0,-2)
    to[short] (Tr.C);
\draw(tmp1)
    to[short, *-] ++(-1.5,0)
    to[european resistor, l_=$R_1$] ++(0,-2.8) |- (Tr.B)
    node[pos=0.5, coordinate] (tmp5) {};
\draw(tmp5) to[short, *-] (Tr.B);
\draw(tmp3)
    to[short, *-] ++(-1.5,0)
    to[european resistor=$R_2$, *-] (tmp5);
\draw(Tr.C)
    to[C, l_=$C_\mathrm{o}$, *-] ++(2.5,0)
    coordinate(tmp7)
    to[european resistor, l=$R_\mathrm{L}$, o-o] (tmp6);
\draw(tmp5)
    to[C, l=$C_\mathrm{i}$, -o] ++(-1.5,0)
    coordinate(tmp8);
\draw(tmp3)
    to[short] ++(-3,0)
    coordinate(tmp9)
    to[short, o-] ++(-1,0)
    to[european resistor, l=$R_\mathrm{S}$] ++(0,1.6)
    to[sV=$v_\mathrm{S}$] ++(0,1) |- (tmp8) to[short, -o] (tmp8);
\draw(tmp7) to[short, o-] ++(1.3,0);
\draw[-latex] ($(tmp6)+(1.2,0.2)$) -- ($(tmp7)+(1.2,-0.2)$)
    node[pos=0.5, right] {$V_\mathrm{o}$};
\draw[-latex] ($(tmp9)+(0,0.2)$) -- ($(tmp8)+(0,-0.2)$)
    node[pos=0.5, left] {$V_\mathrm{i}$};
%%% [BEGIN] Bypass capacitor %%%
\draw(Tr.E)
    to[short, *-] ++(1.3,0)
    to[C, l_=$C_\mathrm{E}$, -*] ++(0,-2);
%%%  [END]  Bypass capacitor %%%
\end{tikzpicture}
\end{document}

% Simple Equivalent Circuit (w/o Ce)
\documentclass[border=3mm]{standalone}
\usepackage{tikz}
\usepackage{circuitikz}
\usepackage{newtxtext,newtxmath}
\pagecolor{white}
\begin{document}
\begin{tikzpicture}
%%% [BEGIN] equivalent circuit of common emitter BJT %%%
\draw (0,0) to[european resistor, l_=$h_\mathrm{ie}$] ++(0,-1.75);
\draw (1.5,0) to[american current source, l=$h_\mathrm{fe}i_\mathrm{b}$] ++(0,-1.75);
\draw (0,0) to[short, f<_=$i_\mathrm{b}$, -o] ++(-1,0);
\draw (1.5,0) to[short, -o] ++(1.5,0);
\draw (-1,-3.5) to[short, o-o] (3,-3.5);
\draw (0,-1.75) to[short] ++(1.5,0);
%%%  [END]  equivalent circuit of common emitter BJT %%%
\draw (0.75,-1.75) to[european resistor, l=$R_\mathrm{E}$, *-*] ++(0,-1.75);
\draw[-latex] (1.5,-3.3) -- (1.5,-1.95) node[pos=0.5, right] {$v_\mathrm{f}$};
%%% [BEGIN] input %%%
\draw (-2,0) to[european resistor, l_=$R_1$, *-*] ++(0,-3.5);
\draw (-1,0) to[european resistor, l_=$R_2$, *-*] ++(0,-3.5);
\draw (-1,0) to[short, -o] ++(-2,0) to[short, f<_=$i_\mathrm{i}$] ++(-1,0)
    to[sV_<=$v_\mathrm{S}$] ++(0,-1.5)
    to[european resistor, l_=$R_\mathrm{S}$] ++(0,-2)
    to[short] ++(1,0) to[short, o-] ++(2,0);
\draw[-latex] (-3,-3.3) -- (-3,-0.2) node[pos=0.5, left] {$v_\mathrm{i}$};
%%%  [END]  input %%%
%%% [BEGIN] output %%%
\draw (3,0) to[european resistor, l=$R_\mathrm{C}$, *-*] ++(0,-3.5);
\draw (3,0) to[short, -o] ++(1,0) to[short, f<=$i_\mathrm{o}$] ++(1,0)
    to[european resistor, l=$R_\mathrm{L}$] ++(0,-3.5) to[short] ++(-1,0)
    to[short, o-] ++(-1,0);
\draw[-latex] (4,-3.3) -- (4,-0.2) node[pos=0.5, right] {$v_\mathrm{o}$};
%%%  [END]  output %%%
\end{tikzpicture}
\end{document}

% Simple Equivalent Circuit (w/ Ce)
\documentclass[border=3mm]{standalone}
\usepackage{tikz}
\usepackage{circuitikz}
\usepackage{newtxtext,newtxmath}
\pagecolor{white}
\begin{document}
\begin{tikzpicture}
%%% [BEGIN] equivalent circuit of common emitter BJT %%%
\draw (0,0) to[european resistor, l_=$h_\mathrm{ie}$, -*] ++(0,-3.5);
\draw (1.5,0) to[american current source, l=$h_\mathrm{fe}i_\mathrm{b}$, -*] ++(0,-3.5);
\draw (0,0) to[short, f<_=$i_\mathrm{b}$, -o] ++(-1,0);
\draw (1.5,0) to[short, -o] ++(1.5,0);
\draw (-1,-3.5) to[short, o-o] (3,-3.5);
%%%  [END]  equivalent circuit of common emitter BJT %%%
%%% [BEGIN] input %%%
\draw (-2,0) to[european resistor, l_=$R_1$, *-*] ++(0,-3.5);
\draw (-1,0) to[european resistor, l_=$R_2$, *-*] ++(0,-3.5);
\draw (-1,0) to[short, -o] ++(-2,0) to[short, f<_=$i_\mathrm{i}$] ++(-1,0)
    to[sV_<=$v_\mathrm{S}$] ++(0,-1.5)
    to[european resistor, l_=$R_\mathrm{S}$] ++(0,-2)
    to[short] ++(1,0) to[short, o-] ++(2,0);
\draw[-latex] (-3,-3.3) -- (-3,-0.2) node[pos=0.5, left] {$v_\mathrm{i}$};
%%%  [END]  input %%%
%%% [BEGIN] output %%%
\draw (3,0) to[european resistor, l=$R_\mathrm{C}$, *-*] ++(0,-3.5);
\draw (3,0) to[short, -o] ++(1,0) to[short, f<=$i_\mathrm{o}$] ++(1,0)
    to[european resistor, l=$R_\mathrm{L}$] ++(0,-3.5) to[short] ++(-1,0)
    to[short, o-] ++(-1,0);
\draw[-latex] (4,-3.3) -- (4,-0.2) node[pos=0.5, right] {$v_\mathrm{o}$};
%%%  [END]  output %%%
\end{tikzpicture}
\end{document}

% Voltage Divider Bias Circuit
\documentclass[border=3mm]{standalone}
\usepackage{tikz}
\usepackage{circuitikz}
\ctikzset{transistors/arrow pos=end}
\usepackage{newtxtext,newtxmath}
\pagecolor{white}
\begin{document}
\begin{tikzpicture}
\draw (0,0) node[npn](Tr) {};
\draw[thick] ($(Tr)-(0.35,0)$) circle [radius=13pt] node[above left=8pt] {Tr};
\draw[red, -latex] (0.2,-0.4) arc[x radius=0.6, y radius=0.6, start angle=320, delta angle=80]
    node[below right=4pt] {$v_\mathrm{CE}$};
\draw(Tr.C)
    to[short, f<_=$i_\mathrm{C}$] ++(2.6,0)
    to[european resistor, l_=$R_\mathrm{C}$] ++(0,-1.75)
    coordinate(tmp0) % below Rc
    to[short] ++(-2.6,0)
    to[european resistor, l=$R_1$] ++(-2,0)
    coordinate(tmp1) % left R1
    to[short] ++(0,0.95) |- (Tr.B)
    node[pos=0.5, circ] (tmp3) {}; % ;
\draw(tmp3) to[short, f_=$i_\mathrm{B}$] (Tr.B);
\draw(Tr.E)
    to[short] ++(0,-0.5)
    to[european resistor, l_=$R_\mathrm{E}$, -*] ++(0,-2)
    coordinate(tmp2); % below Re
\draw(tmp0)
    to[battery2, l=$V_\mathrm{CC}$, *-] ++(0,-2.3) |- (tmp2);
\draw(tmp1)
    to[short, *-] ++(0,-0.3)
    to[european resistor, l_=$R_2$] ++(0,-2) |- (tmp2)
    node[pos=0.5, circ] {};
%%% [BEGIN] Bypass capacitor %%%
\draw(Tr.E)
    to[short] ++(0,-0.5)
    to[short, *-] ++(1.3,0)
    to[C, l_=$C_\mathrm{E}$, -*] ++(0,-2);
%%%  [END]  Bypass capacitor %%%
%%% [BEGIN] I/O %%%
% --- Input ---
\draw(tmp3)
    to[short] ++(-0.5,0) to[C, l=$C_\mathrm{i}$] ++(-0.5,0)
    to[short, f_<=$i_\mathrm{i}$, -o] ++(-1,0) node (inp) {};
\draw(tmp2) to[short, *-o] ++(-4,0) node (inn) {};
\draw[-latex] (inn) -- (inp) node[right,pos=0.5] {$v_\mathrm{i}$};
% --- Output ---
\draw(Tr.C) to[short, -*] ++(2.6,0)
    to[short] ++(0.5,0) to[C, l_=$C_\mathrm{o}$] ++(0.5,0)
    to[short, f_<=$i_\mathrm{o}$, -o] ++(1,0) node (outp) {};
\draw(tmp2) to[short, -*] ++(2.6,0)
    to[short, -o] ++(2,0) node (outn) {};
\draw[-latex] (outn) -- (outp) node[left,pos=0.5] {$v_\mathrm{o}$};
%%%  [END]  I/O %%%
%%% [BEGIN] Load & Source %%%
\draw(outp.center) to[short, o-] ++(1,0)
    to[european resistor, l=$R_\mathrm{L}$] ++(0,-4) |- (outn.center)
    node[pos=0.5] {} to[short, -o] (outn.center);
\draw(inp.center) to[short, o-] ++(-1,0)
    to[sV_<=$v_\mathrm{S}$] ++(0,-1.5)
    to[european resistor, l_=$R_\mathrm{S}$] ++(0,-1.5) |- (inn.center)
    node[pos=0.5] {} to[short, -o] (inn.center);
%%%  [END]  Load & Source %%%
\end{tikzpicture}
\end{document}

% Simple Equivalent Circuit (w/o Ce)
\documentclass[border=3mm]{standalone}
\usepackage{tikz}
\usepackage{circuitikz}
\usepackage{newtxtext,newtxmath}
\pagecolor{white}
\begin{document}
\begin{tikzpicture}
%%% [BEGIN] equivalent circuit of common emitter BJT %%%
\draw (0,0) to[european resistor, l_=$h_\mathrm{ie}$] ++(0,-1.75);
\draw (1.5,0) to[american current source, l=$h_\mathrm{fe}i_\mathrm{b}$] ++(0,-1.75);
\draw (0,0) to[short, f<_=$i_\mathrm{b}$, -o] ++(-1,0);
\draw (1.5,0) to[short, -o] ++(1.5,0);
\draw (-1,-3.5) to[short, o-o] (3,-3.5);
\draw (0,-1.75) to[short] ++(1.5,0);
\draw (0.75,-1.75) to[european resistor, l=$R_\mathrm{E}$, *-*] ++(0,-1.75);
\draw[-latex] (1.5,-3.3) -- (1.5,-1.95) node[pos=0.5, right] {$v_\mathrm{f}$};
%%%  [END]  equivalent circuit of common emitter BJT %%%
%%% [BEGIN] input %%%
\draw (-1,0) to[european resistor, l_=$R_\mathrm{B}$, *-*] ++(0,-3.5);
\draw (-1,0) to[short, -o] ++(-1,0) to[short, f<_=$i_\mathrm{i}$] ++(-1,0)
    to[sV_<=$v_\mathrm{S}$] ++(0,-1.5)
    to[european resistor, l_=$R_\mathrm{S}$] ++(0,-2)
    to[short] ++(1,0) to[short, o-] ++(1,0);
\draw[-latex] (-2,-3.3) -- (-2,-0.2) node[pos=0.5, left] {$v_\mathrm{i}$};
%%%  [END]  input %%%
%%% [BEGIN] output %%%
\draw (3,0) to[european resistor, l=$R_\mathrm{C}$, *-*] ++(0,-3.5);
\draw (3,0) to[short, -o] ++(1,0) to[short, f<=$i_\mathrm{o}$] ++(1,0)
    to[european resistor, l=$R_\mathrm{L}$] ++(0,-3.5) to[short] ++(-1,0)
    to[short, o-] ++(-1,0);
\draw[-latex] (4,-3.3) -- (4,-0.2) node[pos=0.5, right] {$v_\mathrm{o}$};
%%%  [END]  output %%%
%%% [BEGIN] loop %%%
\draw[blue, latex-] (-0.15,-3.2) arc[x radius=0.5, y radius=0.5, start angle=280, delta angle=320];
%%%  [END]  loop %%%
\end{tikzpicture}
\end{document}

% Block Diagram of Negative Feedback Amplifier
\documentclass[border=3mm]{standalone}
\usepackage{tikz}
\usepackage{circuitikz}
\usetikzlibrary{positioning}
\usepackage{newtxtext,newtxmath}
\pagecolor{white}
\begin{document}
\begin{tikzpicture}[>=latex,
    block/.style={draw, rectangle, minimum width=1.2cm, minimum height=0.8cm, align=center},
    sum/.style={draw, circle, minimum size=1.5mm, inner sep=0pt}]
    \node[block] (A) at (1.5, 1.4) {$A$};
    \node[block] (beta) at (1.5, 0.4) {$\beta$};
    \node[sum, left=0.8cm of A] (sum) {};
    \node[left=0.8cm of sum] (Vi) {$v_\mathrm{i}$};
    \node[right=1.6cm of A] (Vo) {$v_\mathrm{o}$};
    \draw[->] (Vi) -- (sum) node[pos=0.8, above] {$+$};
    \draw[<-] (A) -- (sum) node[above right] {$v_\mathrm{a}$};
    \draw[->] (A) -- (Vo) 
        node[pos=0.5, circle, fill=black, minimum size=1.5mm, inner sep=0pt, outer sep=0pt] (branch) {};
    \draw[->] (branch) |- (beta);
    \draw[->] (beta) -| (sum) node[pos=0.9, right] {$-$} node[pos=0.5, above right] {$v_\mathrm{f}$};
\end{tikzpicture}
\end{document}

% Block Diagram of Voltage Divider Bias Amplifier
\documentclass[border=3mm]{standalone}
\usepackage{tikz}
\usepackage{circuitikz}
\usetikzlibrary{positioning}
\usepackage{newtxtext,newtxmath}
\pagecolor{white}
\begin{document}
\begin{tikzpicture}[>=latex,
    block/.style={draw, rectangle, minimum width=1.2cm, minimum height=0.8cm, align=center},
    sum/.style={draw, circle, minimum size=1.5mm, inner sep=0pt}]
    \node[block] (A) at (1.5, 1.4) {$-\dfrac{h_\mathrm{fe}R_\mathrm{o}}{h_\mathrm{ie}}$};
    \node[block] (beta) at (1.5, 0) {$-\dfrac{(h_\mathrm{fe}+1)R_\mathrm{E}}{h_\mathrm{fe}R_\mathrm{o}}$};
    \node[sum, left=0.8cm of A] (sum) {};
    \node[left=0.8cm of sum] (Vi) {$v_\mathrm{i}$};
    \node[right=1.6cm of A] (Vo) {$v_\mathrm{o}$};
    \draw[->] (Vi) -- (sum) node[pos=0.8, above] {$+$};
    \draw[<-] (A) -- (sum); % node[above right] {$v_\mathrm{a}$};
    \draw[->] (A) -- (Vo) 
        node[pos=0.5, circle, fill=black, minimum size=1.5mm, inner sep=0pt, outer sep=0pt] (branch) {};
    \draw[->] (branch) |- (beta);
    \draw[->] (beta) -| (sum) node[pos=0.9, right] {$-$}; % node[pos=0.5, above right] {$v_\mathrm{f}$};
\end{tikzpicture}
\end{document}