Find the relation between 2 variables

AI Thread Summary
The discussion revolves around finding the relationship between two variables, Vin and Vout, using a set of equations derived from Kirchhoff's Current Law (KCL). The original poster (OP) presents a complex equation and seeks clarification on the accuracy of three derived equations involving variables V1 and Vx. Participants confirm the equations' correctness and discuss the need for clearer communication, suggesting the use of LaTeX for better readability. Ultimately, the OP successfully finds the solution using the method of determinants and expresses gratitude for the assistance received. Sharing the solution is encouraged for the benefit of others.
Debdut
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Homework Statement
Find the relation between Vin and Vout
Relevant Equations
V1 = (-gm1 * Vin + s* C1 * Vout) / (gmc + s * C1)
gmc * V1 + s * C2 * Vout = Vx * (s * rb * C2 + 1) / rb
s * C1 * (V1 - Vout) + s * C2 * (Vx - Vout) = gm2 * Vx + Vout / ro2
Here is the equation I obtain after simplification, I don't know if it is correct:
gmc * V1 + s * C2 * Vout = [{s * (C1 + C2) * ro2 + 1} * Vout - s * C1 * ro2 * V1] * (s * rb * C2 + 1) / {ro2 * rb * (s * C2 - gm2)}

I need to eliminate V1 to find the relation between Vin and Vout.
 
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Can you post the complete problem statement ?
And please understand that telepathy isn't everyone's forte, so tell us what this is about.

##\ ##
 
BvU said:
Can you post the complete problem statement ?
And please understand that telepathy isn't everyone's forte, so tell us what this is about.

##\ ##
I don't know if they rewrote, but he explained in the line at the bottom. Though , OP , please use Latex to write your question.
 
Debdut said:
V1 = (-gm1 * Vin + s* C1 * Vout) / (gmc + s * C1)
gmc * V1 + s * C2 * Vout = Vx * (s * rb * C2 + 1) / rb
s * C1 * (V1 - Vout) + s * C2 * (Vx - Vout) = gm2 * Vx + Vout / ro2
For clarity's sake, is the following an accurate statement of the three equations?

##\qquad \textrm{Eqn 1: } V_1 = \dfrac{-g_{m_1} V_{in} + sC_1V_{out}}{g_{m_c} + sC_1}##

##\qquad \textrm{Eqn 2: } g_{m_c} V_1 + s C_2 V_{out} = V_x \dfrac{s r_b C_2 + 1}{r_b}##

##\qquad \textrm{Eqn 3: } s C_1 \left(V_1 - V_{out}\right) + s C_2 \left(V_x - V_{out}\right) = g_{m_2} V_x + \dfrac{V_{out}}{r_{o_2}}##

Thank you!
 
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e_jane said:
For clarity's sake, is the following an accurate statement of the three equations?

##\qquad \textrm{Eqn 1: } V_1 = \dfrac{-g_{m_1} V_{in} + sC_1V_{out}}{g_{m_c} + sC_1}##

##\qquad \textrm{Eqn 2: } g_{m_c} V_1 + s C_2 V_{out} = V_x \dfrac{s r_b C_2 + 1}{r_b}##

##\qquad \textrm{Eqn 3: } s C_1 \left(V_1 - V_{out}\right) + s C_2 \left(V_x - V_{out}\right) = g_{m_2} V_x + \dfrac{V_{out}}{r_{o_2}}##

Thank you!
Yes, these are the equations. Thank you very much.
 
ckt.png


I am sorry for not elaborating. The equations are obtained by KCL of the above image.
Here ##V_1##, ##V_x##, ##V_{in}## and ##V_{out}## are variables and all else are constants. I need to find the relation between ##V_{in}## and ##V_{out}##.
 
Hi, I found the solution using the method of determinants. It was not difficult. Thanks.
 
Debdut said:
Hi, I found the solution using the method of determinants. It was not difficult. Thanks.
If not overly long, why not write it here so others can benefit from it?
 
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