Revision of Circuits and Electronics - Incremental Analysis (Lecture 7)

Video:- http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-002-circuits-and-electronics-spring-2007/video-lectures/lecture-7/

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

A small region of the transfer characteristic curve looks linear so we have to use this region for the circuit to work. The way to implement this is to boost and shrink the signal - shrink the signal of interest and add a dc offset to it. Here is where signal notation becomes important. The response i_d to small signal v_d is approximately linear.

What does this mean mathematically? The total variable i_D is a function of v_D. (Let delta v_D be equal to v_d.) Taylor's expansion  is used to expand this function. The higher order terms of delta v_D  are neglected.

Why is the small signal response linear? If we equate the DC component and the time varying component of the current with the expanded function, there will be a constant part for the time varying one. This constant part is the the slope of the transfer characteristic. The other constant part for the DC component  is the the operating point.

From the circuit view of the small signal model, where the original elements are replaced by their small signal models,  the LED behaves like a resistor.

To summarise, there are 3 steps for the small signal method:-

(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.

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

For a voltage source containing both dc and small signal, the small signal model is the small signal part of the source.

For a resistor , the small signal model is the resistor itself.

For a non linear device , the small signal model is a resistor.

In the small circuit analysis example, i_d needs to be found.  For step  1,  with the large signal circuit model, nodal  analysis is  used to find V_D and I_D.  For step 2,   with the small signal circuit model,  R_D of the non-linear device needs to be found.  For step 3, i_d can be obtained from the linearized circuit.