Patent US6072947A successfully refreshed from Google Patents.
US6072947A
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Method of making an integrated circuit including noise modeling and prediction
Assignee: Nokia of America Corp
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Filing: 1997-09-23
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Granted: 2000-06-06
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Expires: 2017-09-23
Abstract
Abstract A frequency-domain analysis method computes noise power spectral densities (PSDs) in nonlinear circuits. The method uses harmonic components of the periodic time-varying PSD of cyclostationary noise, i.e., harmonic power spectral densities which are deterministic functions that describe the time-varying second-order statistics of cyclostationary noise. A block-structured matrix equation is used which relates output noise statistics to input noise statistics. By exploiting Toeplitz block structure, an efficient noise calculation method requires O(nN log N) computation time and O(nN) memory, where n is the circuit size and N is the number of significant harmonics in the circuit's steady state. The method successfully treats device noise sources with arbitrarily shaped PSDs (including thermal, shot, and flicker noises), handles noise input correlations and computes correlations between different outputs.
Inventors
- 👤 Jaijeet Roychowdhury
- 👤 Peter Feldmann
- 👤 David Esley Long
Bibliographic Details
Application Number
—
Jurisdiction
US
Data Source
google_patents
Last Synchronized
2026-11-08 15:03
CPC Classifications
G; G06; G06F; G06F30/00; G06F30/30; G06F30/36; G06F30/367
Claims Analysis
Total Claims: 12
Claim 1
Independent Claim
213 words
A method of analyzing a circuit, comprising the steps of: a) writing the equations characterizing the circuit, in terms of the time-domain circuit variables x(t), a vector of large-signal excitations b(t), the resistive elements of the circuit f(x(t)), the dynamic elements of the circuit q(x(t)), and the small perturbations of the system Au(t); b) solving the equations from step (a) for a nonlinear steady state; c) performing a time-varying linearization of the circuit equations from step (a), giving the linearized small signal differential equation, in terms of the derivative matrices of resistive and dynamic elements of the circuit, giving the equation C(t)x+G(t)x+Au(t)=0, where x(t) represents the small-signal deviations of the perturbed solution of the equations of step (a), C(t) is the derivative matrix of f(•), and G(t) is the derivative matrix of q(•); d) obtain C i and G i using the equations ##EQU28## e) selecting a frequency ω for which noise is to be evaluated; f) evaluate the equation S.sup.t.sub.xx(•,0).sbsb.(•,p) (ω)=H(ω)S.sup.T.sub.uu (ω)H.sup.t (ω)E.sub.0 e.sub.p applying block matrix functions H T , S T uu and H analyzing the propagation of noise through the circuit using the linearized small signal differential equations; g) if a noise characteristic of the circuit is not within predetermined limits, modifying the circuit in accordance with the evaluation.
Claim 2
Independent Claim
213 words
A method of analyzing a circuit, comprising the steps of: a) writing the equations characterizing the circuit, in terms of the time-domain circuit variables x(t), a vector of large-signal excitations b(t), the resistive elements of the circuit f(x(t)), the dynamic elements of the circuit q(x(t)), and the small perturbations of the system Au(t); b) solving the equations from step (a) for a nonlinear steady state; c) performing a time-varying linearization of the circuit equations from step (a), giving the linearized small signal differential equation, in terms of the derivative matrices of resistive and dynamic elements of the circuit, giving the equation C(t)x+G(t)x+Au(t)=0, where x(t) represents the small-signal deviations of the perturbed solution of the equations of step (a), C(t) is the derivative matrix of f(•), and G(t) is the derivative matrix of q(•); d) obtain C i and G i using the equations ##EQU28## e) selecting a frequency ω for which noise is to be evaluated; f) evaluate the equation S.sup.t.sub.xx(•,0).sbsb.(•,p) (ω)=H(ω)S.sup.T.sub.uu (ω)H.sup.t (ω)E.sub.0 e.sub.p applying block matrix functions H T , S T uu and H analyzing the propagation of noise through the circuit using the linearized small signal differential equations; g) if a noise characteristic of the circuit is not within predetermined limits, modifying the circuit in accordance with the evaluation.
Claim 3
Dependent Claim
17 words
The method of claim 1, in which the equations of step (a) are in the form: q(x(t))+f(x(t))+b(t)+Au(t)=0.
Claim 4
Dependent Claim
24 words
The method of claim 1, in which ##EQU29## is the large signal solution of the equation of step (a) with u(t) set to 0.
Claim 5
Dependent Claim
191 words
The method of claim 1, in which the evaluation of step 1(e) comprises the steps of: a) defining the input/output relationship of the circuit using the formula ##EQU30## where h(t 2 ,t 1 ) is a matrix representing the time-varying impulse response of the circuit; b) defining R xx and R uu , the covariance matricies of x(t) and u(t), R xx and R uu being termed the harmonic covariances of the output and input noise, respectively; c) relating R xx and R uu in one equation; d) expanding h(t 2 ,t 1 ) in a Fourier series, giving the harmonic transfer functions; e) converting the equation of step 3(c) to the frequency domain by relating the two-dimensional Fourier transforms of R xx and R uu ; f) deriving the two-dimensional power spectral densities S xx and S uu from the Fourier transforms of the harmonic covariances, assuming a cyclostationary noise; g) relating the two-dimensional spectral densities derived in step (f) and rewriting in terms of the one-dimensional harmonic power spectral densities, giving the relationship, in block matrix form: S.sub.xx (ω))=H(ω)S.sub.uu (ω)H*(ω), where H* denotes the Hermitian of H, S.sub.xx, S.sub.uu.
Claim 6
Dependent Claim
19 words
The method of claim 1, further comprising the step of repeating steps (e), (f) and (g) for additional frequencies.
Claim 7
Independent Claim
295 words
A method of making a circuit, comprising the steps of: a) providing a first circuit design; b) determining a noise characteristic of the first circuit design by mathematical analysis; c) comparing the noise characteristic of the first circuit design to a desired noise characteristic, with the noise characteristic of the first circuit design being within predetermined limits of the desired noise characteristic; and d) making the circuit in accordance with said first circuit design; wherein step b) comprises the steps of: i) writing the equations characterizing the circuit, in terms of the time-domain circuit variables x(t), a vector of large-signal excitations b(t), the resistive elements of the circuit f(x(t)), the dynamic elements of the circuit q(x(t)), and the small perturbations of the system Au(t); ii) solving the equations from step (a) for a nonlinear steady state; iii) performing a time-varying linearization of the circuit equations from step (d)(i), giving the linearized small signal differential equation, in terms of the derivative matrices of resistive and dynamic elements of the circuit giving the linearized small signal differential equation, in terms of the derivative matrices of resistive and dynamic elements of the circuit, giving the equation C(t)x+G(t)x+Au(t)=0, where x(t) represents the small-signal deviations of the perturbed solution of the equations of step (a), C(t) is the derivative matrix of f(•), and G(t) is the derivative matrix of q(•); iv) obtain C i and G i using the equations ##EQU31## v) selecting a frequency ω for which noise is to be evaluated; vi) evaluate the equation S.sup.t.sub.xx(•,0).sbsb.(•,p) (ω)=H(ω)S.sup.T.sub.uu (ω)H.sup.t (ω)E.sub.0 e.sub.p applying block matrix functions H T , S T uu and H analyzing the propagation of noise through the circuit using the linearized small signal differential equations; vii) outputting a graphical plot of the noise at frequency ω.
Claim 8
Independent Claim
295 words
A method of making a circuit, comprising the steps of: a) providing a first circuit design; b) determining a noise characteristic of the first circuit design by mathematical analysis; c) comparing the noise characteristic of the first circuit design to a desired noise characteristic, with the noise characteristic of the first circuit design being within predetermined limits of the desired noise characteristic; and d) making the circuit in accordance with said first circuit design; wherein step b) comprises the steps of: i) writing the equations characterizing the circuit, in terms of the time-domain circuit variables x(t), a vector of large-signal excitations b(t), the resistive elements of the circuit f(x(t)), the dynamic elements of the circuit q(x(t)), and the small perturbations of the system Au(t); ii) solving the equations from step (a) for a nonlinear steady state; iii) performing a time-varying linearization of the circuit equations from step (d)(i), giving the linearized small signal differential equation, in terms of the derivative matrices of resistive and dynamic elements of the circuit giving the linearized small signal differential equation, in terms of the derivative matrices of resistive and dynamic elements of the circuit, giving the equation C(t)x+G(t)x+Au(t)=0, where x(t) represents the small-signal deviations of the perturbed solution of the equations of step (a), C(t) is the derivative matrix of f(•), and G(t) is the derivative matrix of q(•); iv) obtain C i and G i using the equations ##EQU31## v) selecting a frequency ω for which noise is to be evaluated; vi) evaluate the equation S.sup.t.sub.xx(•,0).sbsb.(•,p) (ω)=H(ω)S.sup.T.sub.uu (ω)H.sup.t (ω)E.sub.0 e.sub.p applying block matrix functions H T , S T uu and H analyzing the propagation of noise through the circuit using the linearized small signal differential equations; vii) outputting a graphical plot of the noise at frequency ω.
Claim 9
Dependent Claim
94 words
The method of claim 6, further comprising: providing, prior to steps a)-c), a second circuit design that differs from said first circuit design, determining the noise characteristic of the second circuit design by said mathematical analysis, comparing the noise characteristic of the second circuit design to said desired noise characteristic, if the noise characteristic of the second circuit design is not within said predetermined limits of the desired noise characteristic, changing the second circuit design in response to the result of the comparing step, the changed second circuit design being said first circuit design.
Claim 10
Dependent Claim
17 words
The method of claim 6, in which the equations of step 6(d)(i) are in the form: q(x(t))+f(x(t))+b(t)+Au(t)=0.
Claim 11
Dependent Claim
26 words
The method of claim 6, in which ##EQU32## where x* is the large signal solution of the equation of step (a) with u(t) set to 0.
Claim 12
Dependent Claim
192 words
The method of claim 6, in which the analysis of step 6(d)(iv) comprises the steps of: a) defining the input/output relationship of the circuit using the formula ##EQU33## where h(t 2 ,t 1 ) is a matrix representing the time-varying impulse response of the circuit; b) defining R xx and R uu , the covariance matricies of x(t) and u(t), R xx and R uu being termed the harmonic covariances of the output and input noise, respectively; c) relating R xx and R uu in one equation; d) expanding h(t 2 ,t 1 ) in a Fourier series, giving the harmonic transfer functions; e) convert the equation of step 3(c) to the frequency domain by relating the two-dimensional Fourier transforms of R xx and R uu ; f) deriving the two-dimensional power spectral densities S xx and S uu from the Fourier transforms of the harmonic covariances, assuming a cyclostationary noise; g) relating the two-dimensional spectral densities derived in step (f) and rewriting in terms of the one-dimensional harmonic power spectral densities, giving the relationship, in block matrix form: S.sub.xx (ω)=H(ω)S.sub.uu (ω)H*(ω), where H * denotes the Hermitian of H, S.sub.xx, S.sub.uu.
References Cited (Backward Citations)
US5537329A
Cited
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