diff --git a/08_bjt.tex b/08_bjt.tex index bb10c0b0bcd1b60e310caf34449e77e76de92563..b22358a1fbb1ee0da48b5bd2486b0f58649e7959 100644 --- a/08_bjt.tex +++ b/08_bjt.tex @@ -23,16 +23,16 @@ If $V_{BC}<0$ extraction of electrons from B to C, of holes from C to B. Collector current, focus on electron diffusion in base: \begin{align} - n_{pB}(0) & =n_{pB_0}e^{\frac{qV_{BE}}{kT}} \\ - n_{pB}(x) & =n_{pB}(0)(1-\frac{x}{W_B}) \\[1em] + n_{pB}(0) & =n_{pB_0}e^{\frac{qV_{BE}}{kT}} \\ + n_{pB}(x) & =n_{pB}(0)(1-\frac{x}{W_B}) \\[1em] \begin{split} J_{nB} &= qD_n\frac{\mathrm{d} n_{pB}}{\mathrm{d}x}\\ &= -qD_n\frac{n_{pB}(0)}{W_B} - \end{split} \\ + \end{split} \\ \begin{split} I_C &=-J_{nB}A_E\\ &=qA_E\frac{E_n}{W_B}n_{pB_0}e^{\frac{qV_{BE}}{kT}} - \end{split} \\ + \end{split} \\ I_C & = I_Se^{\frac{qV_{BE}}{kT}} \end{align} Base current, @@ -44,11 +44,11 @@ focus on hole injection and recombination in emitter: \begin{split} J_{pE}&=-qD_p\frac{\mathrm{d}p_{nE}}{\mathrm{d}x}\\ &=-qD_p\frac{p_{nE(-x_{BE})-p_{nE_0}}}{W_E} - \end{split} \\ + \end{split} \\ \begin{split} I_B&=-J_{pE}A_E\\ &=qA_E\frac{D_p}{W_E}p_{nE_0}\left( e^{\frac{qV_{VE}}{kT}} -1 \right) - \end{split} \\ + \end{split} \\ I_B & =\frac{I_S}{\beta}\left(e^{\frac{qV_{BE}}{kT}}-1\right) \\ I_B\approx\frac{I_C}{\beta} \end{align} @@ -88,15 +88,15 @@ For reverse, it is the same but $\beta_R\approx [0.1,5]\ll\beta$. \subsection{Ebers-Moll model} \begin{center} \begin{circuitikz} - \draw (0,0) node[left] {B} to [short,*-] ++(1,0) + \draw (0,0) node[left] {B} to [short,o-*] ++(1,0) to [Do,l=$\frac{I_S}{\beta_R}\left( e^{\frac{qV_{BC}}{kT}} -1 \right)$] ++(0,2) to [short] ++(2,0) to [I,l=$I_S\left( e^{\frac{qV_{BE}}{kT}} - e^{\frac{qV_{BC}}{kT}} \right)$,i=$$] ++(0,-4) to [short] ++(-1,0); \draw (1,0) to [Do,l_=$\frac{I_S}{\beta}\left( e^{\frac{qV_{BE}}{kT}}-1 \right)$] ++(0,-2) to [short] ++(1,0) - to [short,-*] ++(0,-1) node [below] {E}; - \draw (2,2) to [short,-*] ++(0,1) node[above] {C}; + to [short,*-o] ++(0,-1) node [below] {E}; + \draw (2,2) to [short,*-o] ++(0,1) node[above] {C}; \end{circuitikz} \end{center} diff --git a/09_bjt_small_signal.tex b/09_bjt_small_signal.tex index d617c7c905dacf574f60bbea026e13a406686c64..6084ab2bf2e331b5d7c5029c63161c8706e5e29e 100644 --- a/09_bjt_small_signal.tex +++ b/09_bjt_small_signal.tex @@ -8,9 +8,9 @@ to [short] ++(2,0) to [R,l=$r_{o}$] ++(0,-2) to [short] ++(-2,0) - to [short,i=$i_e$,-o] ++(0,-1)node[below]{E} + to [short,i=$i_e$,*-o] ++(0,-1)node[below]{E} ++(2,3) - to [short,i<=$i_c$,-o] ++(1,0) node[right]{C}; + to [short,i<=$i_c$,*-o] ++(1,0) node[right]{C}; % to [open,v_=$v_{ce}$] ++(0,-2); \end{circuitikz} \begin{circuitikz} @@ -21,7 +21,7 @@ to [short,-o,i=$i_c$]++(1,0) node[right]{C} ++(-1,0) to[R,l_=$r_{o}$] ++(0,2) to [short] ++(-4,0) - to [R,l=$r{be}$,v=$v_{be}$] ++(0,-2) + to [R,l=$r_{be}$,v=$v_{be}$] ++(0,-2) to [short,i=$i_b$,-o] ++(-1,0)node[left]{B} ; \end{circuitikz}