INTRINSIC GAIN METHOD EX-1

FINDING GAIN OF DEGENERATED & CASCODE AMPLIFIER 

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In this post, we shall discuss two basic amplifiers. 

Q1) Find the gain.

Solution: 

From the signal flow, it is evident that the amplifier is in CS mode.

Let's directly write the gain expression. What is the Intrinsic Gain Method? 

$GAIN=V_{IN} \times \frac{R_{LOAD}}{R_{LOAD}+R_{OUT}}$

Now, ${R_{LOAD}=R_{D}}$ ; ${R_{OUT}=r_{0}+M \times R_{S}}$, where $M= 1+g_{m}r_{0}$

How did I write the above expression? Go check.

$GAIN= -g_{m}r_{0} \times \frac {R_{D}}{R_{D}+(r_{0}+M \times R_{S})} \approx -g_{m}r_{0}\times \frac {R_{D}}{M \times R_{S}} \approx -\frac{R_{D}}{R_{S}}$

Let's try to solve it by another method called, $G_{m}r_{out}$ method and match the results with the above result.

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Another Method: 

We know the equivalent transconductance of the source-degenerated CS is $G_{M}= - \frac {g_{m}}{1+g_{m}R_{S}}$

$R_{eq}=R_{LOAD} || R_{OUT} \approx R_{D}$

$GAIN=G_{M}R_{eq}=- \frac {g_{m}}{1+g_{m}R_{S}} \times R_{S}$

Considering, $g_{m}R_{S}>>1$

$GAIN \approx -\frac{R_D}{R_S}$, which matches with the previous result.

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Q2) Find the gain.

           

Solution: Let's draw the schematic for a small signal.

The above diagram shows that M1 and M2 are in CS and CG mode respectively. 

$GAIN= -g_{m1}r_{01} \times M_{2} \times \frac {R_{LOAD}}{R_{LOAD}+R_{OUT}}$

 where, $R_{LOAD}= r_{03}+M_3 \times r_{04} \approx M_3 \times r_{04}$

             $R_{OUT}= r_{02}+M_2 \times r_{01} \approx M_2 \times r_{01}$ 

Now,

The $GAIN= -g_{m1} \times \frac {M_{2} \times r_{01} \times R_{LOAD}}{R_{LOAD}+R_{OUT}}$ =$-g_{m1}(R_{LOAD}|| R_{OUT})$

Let's also try with  $G_{m}r_{out}$ method.

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Another Method: 

$\frac{I_{SC}}{V_{IN}}= G_{M}=-g_{m1} \frac {r_{01}}{\frac{1}{g_{m2}}+r_{01}} \approx -g_{m1}$

$GAIN=G_MR_{eq}=-g_m \left(R_{LOAD}||R_{OUT} \right)$, which matches with above result.

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We will solve more complex circuits in the upcoming posts.

Check previous posts of the series we started "INTRINSIC GAIN METHOD".

PART1: INTRINSIC GAIN METHOD

PART2: INTRINSIC GAIN METHOD PARAMETERS 

PART3: FINDING EQUIVALENT IMPEDANCE

For part 5 follow our blog and don't forget to comment

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