Math guyz, please help with an equation

Thread Starter

Skfir

Joined Aug 19, 2010
137
Hello everybody, I have been currently reading the MOSFET chapter from Dr Sedra's book "Microelectronic circuits". There is an equation there that describes the voltage gain Av.
It is derived like that: first of all - output voltage vo=(i-gm*vgs)Rl (signal current - transcunductance*signal voltage at the gate)*load resistance
Next, there is an equation to describe the signal current i=(vgs-vo)/Rg (signal voltage-output voltage)/input resistance

And now is the problem, the author says that if we substitute for signal current i from the second equation into the first equation, then the voltage gain vo/vgs will be -gmRl*[(1-(1/gmRg))/(1+(Rl/Rg))]
So he arrives from here: vo=[((vgs-vo)/Rg)-gm*vgs]Rl to here vo/vgs=-gmRl*[(1-(1/gmRg))/(1+(Rl/Rg))]

I fail to understand which transformations does he do to arrive there, please guyz help me out!! In the 6th edition it is page 286 top.
 

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WBahn

Joined Mar 31, 2012
30,016
It's doesn't involve any transformations at all. It's pure algebra.

First, collect terms so that you have the terms involving vo on one side and those involving vgs on the other. Then factor out vo and vgs from their respective sides. Then divide both sides by vgs. Now on the right side factor out -gmRl. Finally, divide both sides by the coefficient of (vo/vgs) and you are done.

For more detailed assistance, I need to see YOUR best attempt to work through it so that I can see where you get stuck.
 

Thread Starter

Skfir

Joined Aug 19, 2010
137
Yes! I did it! Thank you so much mate! For some reason I didn't collect vo and vgs on different sides... Well, art school major, stupid musician, no brains...
Thank you again bro!!
 

WBahn

Joined Mar 31, 2012
30,016
Good! I'm glad you got it.

It sounds like you are going down a technical path starting from a very non-technical background. That's going to be a problem for you, but one that you can overcome with enough effort and determination. The biggest hurdle will likely from weak foundational math skills (algebra, trig, and calculus in particular), so you might put together a personal course of study to address those. If you don't do that (or something along those lines) this you will just be digging yourself a deeper and deeper hole and, in the process, miss out on understanding the material you are studying because you are struggling too much with the math.
 

Thread Starter

Skfir

Joined Aug 19, 2010
137
Yes, sure. I study algebra along with electronics. I needs time, but I am quite diligent and it is really great to have around people like yourself, who really do help. I even invented a device for the blind, which may really help them a bit.
 

Russmax

Joined Sep 3, 2015
82
Don't sell yourself short, Skfir. You were able to get on the right track with just Wbahn's gentle nudge, so you've got the ability.
You likely hated math growing up, but now you find it easier, especially since the question of "What is this good for?" has been answered.

Regards
 

Thread Starter

Skfir

Joined Aug 19, 2010
137
Thank you really for the support. The thing is not only I didn't like math, but also in my art school even teachers for some reason believed that musicians didn't need natural science at all and thought us correspondingly. So I had to start everything anew myself. Thank you people for helping me out, this site is really a treasure.
 

Russmax

Joined Sep 3, 2015
82
Which is the greater tragedy, artists that disdain math and science, or mathematicians, scientists, and engineers that disdain the arts?
Or as Heinlein once said, "Specialization is for insects."
 

WBahn

Joined Mar 31, 2012
30,016
Which is the greater tragedy, artists that disdain math and science, or mathematicians, scientists, and engineers that disdain the arts?
Or as Heinlein once said, "Specialization is for insects."
Interestingly, I have found a great many scientists, particularly physicists, are accomplished artists (usually musicians).

While I have seen the opposite, it has been my experience that it is quite rare.
 

Russmax

Joined Sep 3, 2015
82
I worked for an audio company for a dozen years, and for a dozen years after that in the audio division of a Tier 1 IC manufacturer. My experience therefore a little skewed. Most of us were also musicians. I, unfortunately, am not good at playing music. I'm pretty good with a sword and a dirt bike, though, but not at the same time.
 
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