What is the significance of input and output load lines in microelectronics?

[Ahmad Kishki]

Homework Statement

I am not sure i know what is meant by the input load line and the output load line in parts b and c. I tried looking it up in my book (fundamentals of microelectronics by razavi) but to no avail. Any help is appreciated.

 

[NascentOxygen]

To derive the output load line imagine removing everything from the circuit except the R_D and R_S resistors, then plotting I vs. V where I is the current in those resistors and V is the voltage across the "empty gap" between them. It is immaterial what element you insert into that gap, the current through it and voltage across it are fully constrained by that pair of resistors together with the supply voltage, and this gap's I vs. V plot is known as the output DC load line.

 

[LvW]

* Input load line:
V_GS=V_G-V_S=V_G-I_DS*R_S.
From this: I_DS=V_G/R_S-V_GS/R_S.
This gives a straight line crossing the I_DS=f(V_GS) graph in one point.

* Output load line
V_DS=V_D-V_S=V_DD-I_DS*R_D-I_DS*R_S=V_DD-I_DS*(R_D+R_S).
From this: I_DS=(V_DD-V_DS)/(R_D+R_S)=V_DD/(R_D+R_S)-V_DS/(R_D+R_S).
This load line has a negative slope.