• Consider two amplifiers connected in cascade .For one amplifier, the power gain is $G_1$ and its noise factor is $F_1$; while the corresponding figures for the other amplifier $G_2$ and $F_2$ respectively.

• Step 1: the noise power due to input source $V_s$ will be,

  $P_{ni}$= kTB

• The amplifier 1 has noise factor $F_1$.Hence , total noise power at the input of amplifier 1 will be ,

  Total $P_{ni}$= $F_1$ kTB -------(1)

• Step 2: the amplifier contributes the noise power of $P_{na}=(F-1)kTB$ .Hence due to amplifier 2, this component of noise power will be$P_{na}=(F_2-1)kTB$.

• This noise power will appear at the input of amplifier 2.In addition to this power, there will be noise power amplified by amplifier 1.

• From equation(1),the noise power at output of amplifier 1 will be $G_1$ $F_1 kTB$ .Note that total $P_ni$ is multiplied by gain $G_1$.The total power at the input of amplifier 2 will be ,noise power at input of amplifier 1 = $G_1 F_1 kTB + (F_2-1)kTB$ …..(2)

• Step 3:The noise power at the output of amplifier 2 will be obtained by, $P_{no}=G_2$×(noise power at input of the amplifier 2)

= $G_2 (G_1 F_1 kTB + (F_2-1)kTB )$ …..(3)

• Step 4:we know that $P_{no}=FGP_{ni}$

  $F=\frac{P_{no}}{GP_{ni} }$

• The overall gain of the cascade connection will be $G=G_2 G_1$.Putting expressions for G, $P_{no}$ and $P_{ni}$ in above equation ,

• This is the noise factor of the cascade connection.

• The argument can be easily be extended for additional amplifiers in cascade .Then

• This is known as “Friss formula”.