Question

Calculate the overall voltage gain Gv of a common-source amplifier for which gm = 3 mA/V, ro = 100kΩ, RD =10kΩ, and RG =10MΩ. The amplifier is fed from a signal source with a Thevenin resistance of 1 MΩ, and the amplifier output is coupled to a load resistance of 20 kΩ.

Answer 1

Answer:

G_v = -17.046

Explanation:

Given:

- g_m = 3 mA/V

- r_o = 100 kohms

- R_D = 10 kohms

- R_G = 10 Mohms

- Thevian Resistance R_sig = 1 Mohms

- Coupled load resistor R_L = 20 kohms

Find:

Calculate the overall voltage gain Gv

Solution:

- For a common source amplifier the overall Voltage gain G_v is given by:

                      G_v = - (R_G / R_G + R_sig)*g_m* ( r_o || R_D || R_L )

Plug in the values:

                      G_v = - (10 / 10 + 1)*0.003* ( 100 || 10 || 20 )*10^3

                      G_v = - (30/11)*( 100 || 10 || 20 )

Where,

                   ( 100 || 10 || 20 ) is the equivalent resistance of parallel resistors.

                     1/R_eq = 1/100 + 1/10 + 1/20

                     1/R_eq = 4/25

                      R_eq = 25/4

Plug back in and evaluate:

                      G_v = - (30/11)*(25/4) = -17.046

Answer 2

Answer:

Gv = -17.045 v /v

Explanation:

gm = 3 mA/V, ro = 100kΩ, RD =10kΩ, and RG =10MΩ , Rth = 1 MΩ , RL =20 kΩ.

firstly we need to find the parallel resistance of the three resistances (ro || RD || RL )

$\frac{1}{R}$ =$\frac{1}{100}$ + $\frac{1}{20}$ +$\frac{1}{20}$

$\frac{1}{R}$ = $\frac{16}{100}$

RT = 6.25KΩ

the formular for the overall voltage gain is given as,

overall voltage gain Gv =  $\frac{RG}{RG + RTH}$ ×gm × RT

Gv =  $\frac{10}{10 + 1}$ × 3×10⁻³ × 6.25×10⁻³

Gv = -17.045 v /v