Radio Frequency

                                                                    Transistors:

All FETs can be called UNIPOLAR devices because the charge carriers that carry the current through the device are all of the same type i.e. either holes or electrons, but not both. This distinguishes FETs from the bipolar devices in which both holes and electrons are responsible for current flow in any one device.

                                                             

                                                                      AMPLIFIERS :

Amplifiers do not have the same gain at all frequencies. 

For example, an amplifier designed for audio frequency amplification will amplify signals with a frequency of less than about 20kHz but will not amplify signals having higher frequencies.

LINEAR ALGEBRA :

                                  CALCULATING INVERSE OF A MATRIX

IMP : Check for the determinant. if det =0, then det does not exist AND that matrix is called as SINGULAR MATRIX.

Inverse of 2*2 matrix A :

Inverse of a 3*3 matrix 

SOLVING LINEAR EQUATIONS USING MATRICES :

SPAN of vectors:

Span of vector a : (constant=c)*a(vector) = c*a

scale (vector a) up an down. all the resulting vectors will be span of (vector) a.

For vectors to be represented as linear combinations of all of the 'n' other vectors in R(sub)n, then it is only possible if these n vectors are not collinear (ie these n vectors must not lie in the same line (graphically)).

IF the n vectors are collinear, then not all vectors in R(sub)n can be represented as linear combinations of these n vectors.  

[refer : https://www.youtube.com/watch?v=Qm_OS-8COwU&index=15&list=PLFD0EB975BA0CC1E0 ]

SPAN of vectors {v1, v2, v3, ........, v(sub)n } is the linear combinations of {v1, v2, ......, v(sub)n}

 that is : span = c1v1 + c2v2 + ......... + c(sub)n v(sub)n = any vector in R.