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# Method to Calculate Response Due to an Arbitrary Number of Noise Sources Using One Frequency in a CAD Program

IP.com Disclosure Number: IPCOM000045255D
Original Publication Date: 1983-Feb-01
Included in the Prior Art Database: 2005-Feb-06
Document File: 3 page(s) / 46K

IBM

## Related People

Chang, CS: AUTHOR [+2]

## Abstract

An efficient technique is implemented in a general purpose CAD (Computer Assisted Design) program to compute noise in electronic circuits. In this method, a pre-ordered sparsely stored circuit matrix is transposed in an easy but subtle manner. And as a consequence, one frequency domain (AC) analysis is needed to compute noise at an output regardless of the number of noise sources. Furthermore, unlike other programs that compute noise, the Interactive Circuit Design program used allows arbitrary types of noise expressions Which could be functions of an arbitrary set of parameters, voltages, currents and frequency, and, therefore, the most common noise sources are covered. 1. Theoretical Consideration.

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Method to Calculate Response Due to an Arbitrary Number of Noise Sources Using One Frequency in a CAD Program

An efficient technique is implemented in a general purpose CAD (Computer Assisted Design) program to compute noise in electronic circuits. In this method, a pre-ordered sparsely stored circuit matrix is transposed in an easy but subtle manner. And as a consequence, one frequency domain (AC) analysis is needed to compute noise at an output regardless of the number of noise sources. Furthermore, unlike other programs that compute noise, the Interactive Circuit Design program used allows arbitrary types of noise expressions Which could be functions of an arbitrary set of parameters, voltages, currents and frequency, and, therefore, the most common noise sources are covered. 1. Theoretical Consideration.

To compute the rms value, R, at the jth output due to m noise sources, where
R equals E/i=1/m X(ji)/2/ (1) the linearized circuit equations in a frequency-domain (AC) analysis are of the form
A-x=b (2) x, b Epsilon C/n/, the n-dimensional Euclidean space over the complex the complex field, and a A:C/n/ approaches C/n/ mapping.

For the ith noise source the equations are A x(i)=b(i) (i=1, 2...m) (3)

Combining Eqs. (3) into one matrix equation there results A-X=B (4) and

X=A/-1/ B (5) where X is an nxm matrix of response vectors. The jth row of X, which is X(j)., is obtained from (5),
X(j).=(X(j1),X(j2)...X(jm))=Epsilon/j/T/ A/-1/ B=y/T/B (6) where y is the solution of the following equation A/T/ .y= Epsilon(j) (7) and Epsilon(j) is an n-dimensional unit vector, and the jth coordinate is one, the rest are zeros. In Equation (6), X(ij) (i=1...m) is the response at the jth output due to the ith noise source. Thus, to get the effect of m noise sources at the jth output, one solves Eq. (7) for y and multiplies y/T/ by B, using Equation (6). The rms value, R, follows directly from Eq. (1).
2. Implementation in an Interactive Circuit Design Program.

The method described above has been implemented in an APL Interactive Circuit Design program.

Fig. 1A shows the structure of the matrix after...