written 3.5 years ago by |
Answer:
Step 1 - Calculate $I_{DQ}$
$V_G=\dfrac{R_2}{R_1+R_2} \times V_{DD}$
$V_G=\dfrac{110}{910+110} \times 20$
$\therefore V_G=2.156V$
Now , $V_S=I_{DQ}\times R_S=I_{DQ}\times 1.1$
$\therefore V_{GS}=(2.156-1.1I_{DQ})$
By schokley equation ,
$I_D=I_{DSS}[1-\dfrac{V_{GS}}{V_P}]^2$
$=10[1+\dfrac{2.156-1.1I_{D}}{3.5}]^2$
$1.21I_D^2-12.35I_D+25.60=0$
$\therefore I_D=7.31mA, \ I_D=2.89mA$
Now , $I_D\neq7.31mA$ because for this value of $I_D$ , $V_{DS}$comes out to be negative.
Hence , $ I_{DQ}=2.89mA$
Step 2 - Calculate $V_{GSQ}$
$\therefore V_{GSQ}=2.156-1.1I_{DQ}$
$\therefore V_{GSQ}=2.156-1.1 \times 2.89=-1.023V$
Step 3 - Obtain the value of $g_m$
$g_m=g_{mo}[1-\dfrac{V_{GS}}{V_P}]$
$g_{mo}=\dfrac{2 I_{DSS}}{V_p}=\dfrac{2 \times 10}{3.5}=5.71mS$
$g_m=5.71mS[1-\dfrac{-1.02}{-3.5}]=4.04mS$
Step 4 - Calculate $A_V, \ Z_i\ Z_0$
$\therefore A_V=-g_mR_D=-4.04 \times 10^{-3}\times 2.2 \times 10^3=-8.90$
$\therefore Z_i=R_1 \parallel R_2=910 \parallel110=98.13k \Omega$
$\therefore Z_0=R_D=2.2k\Omega$