Question

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Answer 1

$\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\thicklines\put(1,1){\line(1,0){6.5}}\put(1,1.1){\line(1,0){6.5}}\put(1,1.2){\line(1,0){6.5}}\end{picture}$

$\blacksquare\:\:\:\underline{\underline{\red{Main\: Circuit }}}$

$\setlength{\unitlength}{1.2 mm}\begin{picture}(30,20)\thicklines\multiput(25,20)(0,4){4}{\line(3,2){3}}\multiput(25,20)(0,4){4}{\line(3,-2){3}}\put(28,18){\line(0,-1){8}}\put(28,34){\line(0,1){8}}\put(28,42){\line(1,0){20}}\put(48,42){\line(0,-1){25.5}}\put(16,10){\line(1,0){26}}\put(42,5){\line(0,1){10}}\put(42,12){\line(4,3){6.1}}\put(42,8){\line(4,-3){6.1}}\put(48,3.6){\line(0,-1){8}}\multiput(45.1,-18.2)(0,4){4}{\line(3,2){3}}\multiput(45.1,-18.2)(0,4){4}{\line(3,-2){3}}\put(48,-20.2){\line(0,-1){8}}\put(45,-28.2){\line(1,0){6}}\put(16,8){\line(0,1){4}}\put(14,8){\line(0,1){4}}\put(14,10){\line(-1,0){5}}\put(9,10){\circle*{1.5}}\put(5,9){ V_i }\put(40,-13){ R_L }\put(19,25){ R_B\:\:\:\:\:\:\:\:\:220\:k\Omega }\multiput(45,-28.2)(2,0){4}{\line(3,-2){3}}\put(48,0){\line(1,0){4}}\put(52,-2){\line(0,1){4}}\put(54,-2){\line(0,1){4}}\put(54,0){\line(1,0){2}}\put(56,0){\circle*{1.5}}\put(56.8,-0.7){ V_o }\put(49,-13){ 3.3\:k\Omega }\put(43.2,7){\vector(4,-3){2}}\end{picture}$

$\blacksquare\:\:\:\underline{\underline{\red{Equivalent\: Circuit }}}$

$\setlength{\unitlength}{1.19 mm}\begin{picture}(30,20)\linethickness{0.2mm}\multiput(25,20)(0,4){4}{\line(3,2){3}}\multiput(25,20)(0,4){4}{\line(3,-2){3}}\put(28,18){\line(0,-1){14}}\put(28,34){\line(0,1){14}}\put(19,48){\line(1,0){15}}\multiput(36,45.1)(4,0){4}{\line(2,3){2}}\multiput(36,45.1)(4,0){4}{\line(-2,3){2}}\put(50,48){\line(1,0){23}}\put(54,48){\line(0,-1){44}}\put(19,4){\line(1,0){54}}\multiput(63,20)(0,4){4}{\line(3,2){3}}\multiput(63,20)(0,4){4}{\line(3,-2){3}}\put(66,18){\line(0,-1){14}}\put(66,34){\line(0,1){14}}\put(19,48){\circle*{1}}\put(73,48){\circle*{1}}\put(54,22){\circle{6}}\put(54.05,20){\vector(0,1){3}}\put(55,16){ h_{fe}I_b }\put(56,48){\vector(1,0){4}}\put(20,48){\vector(1,0){4}}\put(27,48){\vector(1,0){4}}\put(23,45){ I_i }\put(30.5,45){ I_b }\large{\put(39,50){ h_{ie} }}\footnotesize{\put(55,49.5){ (1+h_{fe})I_b }}\put(28.5,25){ R_B }\put(59,24){ R_L }\put(67,43){ I_L }\put(66,45){\vector(0,-1){4}}\put(22,15){\line(0,-1){7}}\put(22,15){\vector(1,0){4}}\put(40,15){\line(0,-1){7}}\put(40,15){\vector(1,0){4}}\put(60,12){\line(0,-1){5}}\put(60,12){\vector(-1,0){4}}\put(72,12){\line(0,-1){5}}\put(72,12){\vector(-1,0){4}}\put(23,12){ R'_i }\put(41,12){ R_i }\put(56,9){ R_o }\put(68,9){ R'_o }\put(19,48){\line(0,-1){20}}\put(18,26){ V_i }\put(19,25){\line(0,-1){21}}\put(73,48){\line(0,-1){20}}\put(72,26){ V_o }\put(73,25){\line(0,-1){21}}\end{picture}$

$\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\thicklines\put(1,1){\line(1,0){6.5}}\put(1,1.1){\line(1,0){6.5}}\put(1,1.2){\line(1,0){6.5}}\end{picture}$

⇝ From the figure :-

$\longrightarrow \large{V_i=I_b.h_{ie}+(1+h_{fe})I_bR_L}$

⇝ Input Resistance :-

$\longrightarrow R_i=\dfrac{V_i}{I_b}$

$\longrightarrow R_i=h_{ie}+(1+h_{fe})R_L$

$\longrightarrow R_i=1260\Omega+101\times3300\Omega$

$\longrightarrow \boxed{R_i=334.5\:k\Omega}$

And

$\longrightarrow R'_i=R_B||R_i$

$\longrightarrow R'_i=\dfrac{R_B.R_i}{R_B+R_i}$

$\longrightarrow\boxed{ R'_i=132.7\:k\Omega}$

⇝ Voltage Gain :-

$\longrightarrow A_v=\dfrac{V_o}{V_i}$

$\longrightarrow A_v=\dfrac{I_L.R_L}{I_b.R_i}$

$\longrightarrow A_v=\dfrac{(1+h_{fe})I_bR_L}{I_b.R_i}$

$\longrightarrow A_v=\dfrac{(1+h_{fe})R_L}{R_i}$

$\longrightarrow A_v=\dfrac{101\times3.3}{334.5}$

$\longrightarrow \boxed{A_v=0.996}$

⇝ Output Resistance :-

$\longrightarrow R'_o=R_L||R_o$

$\longrightarrow R'_o=R_L||\dfrac{h_{ie}}{1+h_{fe}}$

$\longrightarrow R'_o=3.3\:k\Omega||\dfrac{1260\Omega}{101}$

$\longrightarrow \boxed{R'_o=12.4\Omega}$

$\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\thicklines\put(1,1){\line(1,0){6.5}}\put(1,1.1){\line(1,0){6.5}}\put(1,1.2){\line(1,0){6.5}}\end{picture}$

Answer 2

$\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\thicklines\put(1,1){\line(1,0){6.5}}\put(1,1.1){\line(1,0){6.5}}\put(1,1.2){\line(1,0){6.5}}\end{picture}$

$\blacksquare\:\:\:\underline{\underline{\red{Equivalent\: Circuit }}}$

$\setlength{\unitlength}{1.19 mm}\begin{picture}(30,20)\linethickness{0.2mm}\multiput(25,20)(0,4){4}{\line(3,2){3}}\multiput(25,20)(0,4){4}{\line(3,-2){3}}\put(28,18){\line(0,-1){14}}\put(28,34){\line(0,1){14}}\put(19,48){\line(1,0){15}}\multiput(36,45.1)(4,0){4}{\line(2,3){2}}\multiput(36,45.1)(4,0){4}{\line(-2,3){2}}\put(50,48){\line(1,0){23}}\put(54,48){\line(0,-1){44}}\put(19,4){\line(1,0){54}}\multiput(63,20)(0,4){4}{\line(3,2){3}}\multiput(63,20)(0,4){4}{\line(3,-2){3}}\put(66,18){\line(0,-1){14}}\put(66,34){\line(0,1){14}}\put(19,48){\circle*{1}}\put(73,48){\circle*{1}}\put(54,22){\circle{6}}\put(54.05,20){\vector(0,1){3}}\put(55,16){ h_{fe}I_b }\put(56,48){\vector(1,0){4}}\put(20,48){\vector(1,0){4}}\put(27,48){\vector(1,0){4}}\put(23,45){ I_i }\put(30.5,45){ I_b }\large{\put(39,50){ h_{ie} }}\footnotesize{\put(55,49.5){ (1+h_{fe})I_b }}\put(28.5,25){ R_B }\put(59,24){ R_L }\put(67,43){ I_L }\put(66,45){\vector(0,-1){4}}\put(22,15){\line(0,-1){7}}\put(22,15){\vector(1,0){4}}\put(40,15){\line(0,-1){7}}\put(40,15){\vector(1,0){4}}\put(60,12){\line(0,-1){5}}\put(60,12){\vector(-1,0){4}}\put(72,12){\line(0,-1){5}}\put(72,12){\vector(-1,0){4}}\put(23,12){ R'_i }\put(41,12){ R_i }\put(56,9){ R_o }\put(68,9){ R'_o }\put(19,48){\line(0,-1){20}}\put(18,26){ V_i }\put(19,25){\line(0,-1){21}}\put(73,48){\line(0,-1){20}}\put(72,26){ V_o }\put(73,25){\line(0,-1){21}}\end{picture}$

$\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\thicklines\put(1,1){\line(1,0){6.5}}\put(1,1.1){\line(1,0){6.5}}\put(1,1.2){\line(1,0){6.5}}\end{picture}$

✏ From the figure :-

$\longrightarrow \large{V_i=I_b.h_{ie}+(1+h_{fe})I_bR_L}$

✏ Input Resistance :-

$\longrightarrow\footnotesize{ R_i=\dfrac{V_i}{I_b}}$

$\longrightarrow\footnotesize{ R_i=h_{ie}+(1+h_{fe})R_L}$

$\longrightarrow\footnotesize{ R_i=1260\Omega+101\times3300\Omega}$

$\longrightarrow\footnotesize{ \boxed{R_i=334.5\:k\Omega}}$

And

$\longrightarrow \footnotesize{R'_i=R_B||R_i}$

$\longrightarrow \footnotesize{R'_i=\dfrac{R_B.R_i}{R_B+R_i}}$

$\longrightarrow\boxed{ R'_i=132.7\:k\Omega}$

✏ Voltage Gain :-

$\longrightarrow\footnotesize{ A_v=\dfrac{V_o}{V_i}}$

$\longrightarrow \footnotesize{A_v=\dfrac{I_L.R_L}{I_b.R_i}}$

$\longrightarrow\footnotesize{ A_v=\dfrac{(1+h_{fe})I_bR_L}{I_b.R_i}}$

$\longrightarrow \footnotesize{A_v=\dfrac{(1+h_{fe})R_L}{R_i}}$

$\longrightarrow \footnotesize{A_v=\dfrac{101\times3.3}{334.5}}$

$\longrightarrow \boxed{A_v=0.996}$

✏ Output Resistance :-

$\longrightarrow\footnotesize{ R'_o=R_L||R_o}$

$\longrightarrow \footnotesize{R'_o=R_L||\dfrac{h_{ie}}{1+h_{fe}}}$

$\longrightarrow\footnotesize{ R'_o=3.3\:k\Omega||\dfrac{1260\Omega}{101}}$

$\longrightarrow \boxed{R'_o=12.4\Omega}$

$\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\thicklines\put(1,1){\line(1,0){6.5}}\put(1,1.1){\line(1,0){6.5}}\put(1,1.2){\line(1,0){6.5}}\end{picture}$