drawing small signal model
it works like this.....
1) We first set the VDS and ID or VCE and IC at a fixed value to ensure that our devices(mos or bjt) will first of all act as a linear VCVS or CCCS respectively....hope u understand this first point correctly.
2) Next once the "Q" points have been set correctly, now we "send in" or "inject" a very "small signal".....I mean we impose alternating voltages or currents onto our device. These are btw the RF or biomedical or some signals...that we want to boost up in power(either thru Vgain(CB) or Igain(CC) or thru both Vgain and Igain(CE)).
3) So now if u see the ID vs VDS for different VGS and IC vs VCE for different IB u "must" observe that the curves are somewhat like IC=mVCE+c and ID=mVDS+c for bjt and mosfet for a small range or ID/IC and VDS/VCE around the bias point(provided u biased the mos/bjt in such a region in the ID/IC vs VDS/VCE graph)
4) so essentially u can now analyze the entire circuit first by writing down a complete ID=f(VGS,VDS) form.
now we take partial derivatives on both sides
=> d(ID) = (df/dVGS) d(VGS) + (df/dVDS) d(VDS) + higher derivatives....these higher derivatives are zero or near zero by our statement in point 3
so hence these 3 signals d(ID) and d(VGS) and d(VDS) are the "small signals"....they are just
"pertubations or deviatons which are injected or caused by us"
PLEASE UNDERSTAND THIS CLEARLY...I DONT KNOW IF I HAVE CONVEYED THE FULL IDEA SO FAR....BUT I AM GOING ON....
5) now these sort of "math" can be carried out purely on paper alone for any electronic circuit....but it is a bit tedious.....and not a general method which can be used very easily...so we understand these equations by drawing what are called "small signal circuits"...or rather circuit in which the voltages and currents are the dID or dIC and dVGS or dIB and dVDS or VCE....and so are all the other V and I also at other points....go on below..
6) so we "represent" the "differential equation" in terms of circuit connections using L,C,R and controlled sources......this representation is called the "small signal circuit representation".........it is not a physical circuit....but just a way in which we humans can understand and more easily perform analysis...or rather atleast have a general first step for analysing the circuits wrt small signals.....PLEASE KEEP IN MIND THAT WE ARE DEALING WITH A DIFFERENTIAL EQUATION...SO ALL OUR CURVES....ANYTHING FOR THAT MATTER ARE ALL LINEAR around Q point or bias point...AND HENCE WE CAN DRAW SMALL SIGNAL CIRCUIT ...IN TERMS OF LINEAR COMPONENTS LIKE L,C,R AND CONTROLLED SOURCES....
IT IS A VERY VERY IMPORTANT QUESTION THAT HAS BEEN RAISED....I HAVE ALSO MENTIONED IN A PREVIOUS POST
PLEASE REFER TO CHAPTER 1 OF THE BOOK
Electronic Principles: Physics, Models and Circuits
by paul e. gray and campbell l. searle
in fact this book is really the best book for starting electronic circuit design mainly for analog....it is quite a dense book like grey and meyer for analog ic design.....i would say the former is the grey and meyer equivalent for discrete circuits or something....anyway....
hope I have been able to direct you in the right directions at least?
best of luck
p.s:- just found out...go here hxxp://ocw.mit.edu/NR/rdonlyres/Electrical-Engineering-and-Computer-Science/6-002Circuits-and-ElectronicsFall2000/3C831A49-1BB2-4403-B201-27BE302EA6B5/0/6002L7.pdf