Analyzing circuit sensitivity for analog circuit design

Mark Fortunato, Texas Instruments

April 16, 2008

Mark Fortunato, Texas Instruments

Sensitivity analysis with filters
As stated earlier, all circuits have characteristics that are functions of the component values of the circuit. Filter characteristics are dependent upon these component values. Some filters are more sensitive to these component value variations than others. Knowing how much a circuit's behavior changes with a component variation, the sensitivity of the circuit to the component, is important for proper selection of components, as well as choice of circuit topology. These sensitivities should be evaluated in the paper-and-simulation design phase to ensure an adequate filter topology is used and that the components are chosen with the proper specifications.

There are many ways to look at the filter's sensitivity to the variations in its components. One way is to evaluate how the overall AC transfer function behaves as a component value is varied. Similarly, you can evaluate individual pole and zero sensitivities. A common way, especially when working with filters split into second order sections, is to look at the sensitivity of the natural frequency (w_n) and of the quality factory (Q) for the pole-pairs, and zero-pairs for each second order section.

A second-order lowpass function with two poles has a generic transfer function (Equation 5).

(5)

Some designers use the "damping factor," ζ, rather than Q. These are directly related by Equation 6:

(6)

Simple passive filter
Consider a basic L-C lowpass filter as a starting point shown in Figure 2.

Equations 7 through 9 give the transfer function, natural frequency, and Q:

(7)

(8)

(9)

By inspection we see that the natural frequency is independent of the resistor value. Therefore, use the resistor to independently vary the Q, resulting in a family of curves shown in Figure 3. These will be familiar to anyone who has studied second-order systems.