Difference between revisions of "Noise Analysis"
Jump to navigation
Jump to search
(Created page with "Once we have our device models with the appropriate noise generators, we can determine the effects of these individual noise sources on the behavior of larger circuits.") |
|||
| Line 1: | Line 1: | ||
| − | Once we have our device models with the appropriate noise generators, we can determine the effects of these individual noise sources on the behavior of larger circuits. | + | Once we have our device models with the appropriate noise generators, we can determine the effects of these individual noise sources on the behavior of larger circuits. Consider the linear and time invariant (LTI) system with transfer function <math>H\left(f\right)</math> shown in Fig. 1. If we inject noise <math>S_i\left(f\right)</math>, we would get: |
| + | |||
| + | {{NumBlk|::|<math>S_o\left(f\right)=\left|H\left(f\right)\right|^2\cdot S_i\left(f\right)</math>|{{EquationRef|1}}}} | ||
| + | |||
| + | Thus, the output noise spectrum is shaped or "filtered" by the magnitude of the transfer function. Note that the phase is random and cannot be determined. The total integrated noise at the output of the LTI system is: | ||
| + | |||
| + | {{NumBlk|::|<math>\overline{v^2_{o,T}}=\int_{-\infty}^{\infty}\left|H\left(f\right)\right|^2\cdot S_i\left(f\right) \,\df</math>|{{EquationRef|2}}}} | ||
Revision as of 19:11, 6 October 2020
Once we have our device models with the appropriate noise generators, we can determine the effects of these individual noise sources on the behavior of larger circuits. Consider the linear and time invariant (LTI) system with transfer function shown in Fig. 1. If we inject noise , we would get:
-
(1)
-
Thus, the output noise spectrum is shaped or "filtered" by the magnitude of the transfer function. Note that the phase is random and cannot be determined. The total integrated noise at the output of the LTI system is:
-
(2)
-
