1. Analog Filters: Sensitivity Franco Maloberti

2. Analog Filters: Sensitivity2 Introduction A very large number of networks realize a certain transfer function. How can we choose the “best” one? Volume? Power consumption? Cost? Hardware complexity? Sensitivity?

3. Franco MalobertiAnalog Filters: Sensitivity3 Example Consider the band-pass filter (two transmission zeros) Assume to change one element of the circuit the transmission zeros are affected by the tank pole at zero and infinite changes with other elements

4. Franco MalobertiAnalog Filters: Sensitivity4 Example (ii) Change the 7/9 F to 7/10 F 20Log(k/f)=20Log k -20Log f f 

5. Franco MalobertiAnalog Filters: Sensitivity5 Definition of Sensitivity A change of the value of a parameter of the network, x, affects a performance y If the performance y depends on several parameters

6. Franco MalobertiAnalog Filters: Sensitivity6 Properties of Sensitivity

7. Franco MalobertiAnalog Filters: Sensitivity7 Biquad Filters A biquad band-pass response can be written as Q represents the sharpness of the response around  0 (half-power bandwidth BW=Q/  0 ) Q and  0 sensitivities are important parameters. The Q and  0 concepts are extended to any second order network function

8. Franco MalobertiAnalog Filters: Sensitivity8 Minimum Sensitivity Any network function implementation normally aims at minimum sensitivity Minimum sensitivity means operate at the maximum (or minimum) of y(x) Doubly terminated LC two-port has maximum power transfer in the band-pass

9. Franco MalobertiAnalog Filters: Sensitivity9 High-order Filters Cascade of bi-quad or multi-feedback loops? How to do the pole-zero pairing in a cascade of biquad? Active or passive filter design? ALL THE ANSWERS DEPENDS ON THE SENSITIVITY