Revision of Circuits and Electronics - Small signal circuits (Lecture 11)

Video:- http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-002-circuits-and-electronics-spring-2007/video-lectures/lecture-11/

Lecture Notes:- http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-002-circuits-and-electronics-spring-2007/lecture-notes/


How to choose a bias point aka operating point? If you want a symetric  input swing, choose an operating point in the middle of the input operating range but  this does not necessarily produce a symetric output swing.

(1) Gain and (2) input swing are the two points for selecting a bias point. From  v_o=- (k*R_L(V_I - V_T))*v_i,  higher V_I gives higher gain but input swing may not be symetric.



Recall the 3 steps for the small signal analysis:-

(1) Find the operating point using DC bias inputs from large signal circuit

(2) Develop small signal models for each of the elements around the operating point.

(3) Analyze the linearized circuit to get the small signal response.

In lecture 7, it can be seen how small signal models can be derived from non linear components.

The DC voltage source  behaves as a short to small signals.  The DC current source  behaves as an open to small signals.


The  large signal model of the MOSFET makes use of the equation i_DS=k/2 ( v_GS - V_T)^2 .

What is the small signal model for the MOSFET?  i_ds is found by differentiating I_DS=k/2 ( v_GS - V_T)^2 w.r.t. v_GS taking v_GS=V_GS and then multiply this value  by v_gs.  Notice that this is similar to what was done in lecture 7 and end of lecture 10 but in this case i_ds and v_gs are used instead.
 The equation i_ds=k ( V_GS - V_T)*v_gs is obtained. What  is this device?

 g_m is equal to k ( V_GS - V_T) and it is a  transconductance as the  current through the drain source terminals is controlled  by the voltage between the gate source terminals.

Node analysis is used for developing the large signal and small signal model equations. For large signal models, the equations used are  i_DS=k/2 ( v_I - V_T)^2 and v_O=V_S - (k/2(v_I - V_T)^2)*R_L    (i_DS, v_I, v_O being replaced by I_DS, V_I and V_O respectively) while in the small signal model, the equations are i_ds=k ( V_I - V_T)*v_i  and v_o=- (k(V_I - V_T)R_L*v_i)

v_i is not always equal to v_gs as seen from the last example.