Calculation of electromagnetic field intensity by moment method

A computer implemented method of calculating an electromagnetic field intensity, comprising:

• a) inputting geometric data of an electric circuit device located outside of the computer;
• b) calculating, from the geometric data, approximation coefficients for each of approximate equations that respectively yield approximate values of electromagnetic characteristic values, between a plurality of elements constituting the electric circuit device and of the elements themselves, at an arbitrary frequency;
• c) calculating approximate values of the electromagnetic characteristic values between the elements and of the elements themselves at a designated frequency in accordance with the approximate equations having the approximation coefficients calculated in b), making it possible to evaluate the electromagnetic field intensity for the designated frequency,
• wherein the b) includes
• i) calculating the electromagnetic characteristic values between the elements and of the elements themselves from geometric data of the elements at each of a plurality of sample frequencies;
• ii) calculating the approximation coefficients by solving simultaneous equations obtained by substituting the electromagnetic characteristic values calculated at the plurality of sample frequencies into each of the approximate equations
• wherein the bii) includes,
• calculating matrix elements in a lower triangular matrix and an upper triangular matrix from the sample frequencies, said lower triangular matrix and upper triangular matrix being derived from a matrix containing powers of the sample frequencies as matrix elements by being decomposed as a product of a lower triangular matrix, with diagonal elements of 1, and an upper triangular matrix;
• calculating the approximation coefficient from the electromagnetic characteristic values and the matrix elements in the lower triangular matrix and the upper triangular matrix;
• and
• determining, using the calculating in c), proper shielding required for the electric circuit device.

A computer implemented method of calculating an electromagnetic field intensity, comprising:

• a) inputting geometric data of an electric circuit device located outside of the computer:
• b) calculating, from the geometric data, approximation coefficients for each of approximate equations that respectively yield approximate values of electromagnetic characteristic values, between a plurality of elements constituting the electric circuit device and of the elements themselves, at an arbitrary frequency:
• c) calculating approximate values of the electromagnetic characteristic values between the elements and of the elements themselves at a designated frequency in accordance with the approximate equations having the approximation coefficients calculated in b), making it possible to evaluate the electromagnetic field intensity for the designated frequency,
• wherein the electromagnetic characteristic values include mutual impedances between the elements constituting the electric circuit device and of the elements themselves,
• wherein the elements constituting the electric circuit device include conductor elements and dielectric elements,
• wherein the electromagnetic characteristic values further include mutual admittances between the dielectric elements and of the dielectric elements themselves, mutual reactions between the conductor and dielectric elements, and mutual reactions between the dielectric elements and of the dielectric elements themselves;
• and
• determining, using the calculating in c), proper shielding required for the electric circuit device.

A computer implemented method of calculating an electromagnetic field intensity, comprising:

• a) inputting geometric data of an electric circuit device located outside of the computer;
• b) calculating, from the geometric data, approximation coefficients for each of approximate equations that respectively yield approximate values of electromagnetic characteristic values, between a plurality of elements constituting the electric circuit device and of the elements themselves, at an arbitrary frequency;
• c) calculating approximate values of the electromagnetic characteristic values between the elements and of the elements themselves at a designated frequency in accordance with the approximate equations having the approximation coefficients calculated in b), making it possible to evaluate the electromagnetic field intensity for the designated frequency,
• wherein the electromagnetic characteristic values include mutual impedances between the elements constituting the electric circuit device and of the elements themselves,
• wherein the approximate equations for the mutual impedances zij are zij=exp(−jkr) {a0+a1f2+a2f4+a3f6+a4f8+ . . . j(b0/f+b1f+b2f3+b3f5+b4f7+ . . . )}, where f is the frequency, k is a wavenumber where k=2πf/c and c is the velocity of light, r is an element-to-element distance, j is an imaginary unit, and a0, a1, . . . and b0, b1, . . . are the approximation coefficients;
• and
• determining, using the calculating in c), proper shielding required for the electric circuit device.

A computer implemented method of calculating an electromagnetic field intensity, comprising:

• a) inputting geometric data of an electric circuit device located outside of the computer;
• b) calculating, from the geometric data, approximation coefficients for each of approximate equations that respectively yield approximate values of electromagnetic characteristic values, between a plurality of elements constituting the electric circuit device and of the elements themselves, at an arbitrary frequency, each of said approximation equations including a real part which is a sum of terms with frequencies raised to an even numbered power and an imaginary part which is a sum of terms with frequencies raised to an odd numbered power;
• c) calculating approximate values of the electromagnetic characteristic values between the elements and of the elements themselves at a designated frequency in accordance with the approximate equations having the approximation coefficients calculated in b), making it possible to evaluate the electromagnetic field intensity for the designated frequency, wherein the b) includes:
• i) calculating the electromagnetic characteristic values between the elements and of the elements themselves from geometric data of the elements at each of a plurality of sample frequencies;
• ii) calculating the approximation coefficients by solving simultaneous equations obtained by substituting the electromagnetic characteristic values calculated at the plurality of sample frequencies into each of the approximate equations,
• wherein the number of sample frequencies is equal to the number of terms in a real part and in an imaginary part of each of the approximate equations;
• and
• determining, using the calculating in c), proper shielding required for the electric circuit device.

A computer implemented apparatus for calculating an electromagnetic field intensity, comprising:

• means for inputting geometric data of an electric circuit device located outside of the computer;
• means for calculating from the geometric data approximation coefficients for each of approximate equations that respectively yield approximate values of electromagnetic characteristic values, between a plurality of elements constituting the electric circuit device and of the elements themselves, at an arbitrary frequency;
• means for calculating approximate values of electromagnetic characteristic values between the elements and of the elements themselves at a designated frequency in accordance with the approximate equations having the approximation coefficients calculated by the approximation coefficient calculating means, making it possible to evaluate the electromagnetic field intensity for the designated frequency, each of said approximation equations including a real part which is a sum of terms with frequencies raised to an even numbered power and an imaginary part which is a sum of terms with frequencies raised to an odd numbered power;
• means for calculating an electric current flowing on each element by solving simultaneous equations obtained by substituting the approximate values of the electromagnetic characteristic values calculated by the approximate value calculating means into equations respectively describing boundary conditions for the elements;
• means for calculating the electromagnetic field intensity for the designated frequency from the electric currents respectively flowing on the elements, calculated by the electric current calculating means;
• and
• means for outputting the calculated electromagnetic field intensity, wherein the approximation coefficient calculating means comprises:
• means for calculating the electromagnetic characteristic values between the elements and of the elements themselves from geometric data of the elements at each of a plurality of sample frequencies;
• and
• means for calculating the approximation coefficients by solving simultaneous equations obtained by substituting the electromagnetic characteristic values calculated at the plurality of sample frequencies into each of the approximate equations.

A computer implemented apparatus for calculating an electromagnetic field intensity, comprising:

• means for inputting geometric data or an electric circuit device located outside of the computer;
• means for calculating from the geometric data approximation coefficients for each of approximate equations that respectively yield approximate values of electromagnetic characteristic values, between a plurality of elements constituting the electric circuit device and of the elements themselves, at an arbitrary frequency;
• means for calculating approximate values of electromagnetic characteristic values between the elements and of the elements themselves at a designated frequency in accordance with the approximate equations having the approximation coefficients calculated by the approximation coefficient calculating means, making it possible to evaluate the electromagnetic field intensity for the designated frequency;
• means for calculating the electromagnetic characteristic values between the elements and of the elements themselves from geometric data of the elements at each of a plurality of sample frequencies;
• means for calculating the approximation coefficients by solving simultaneous equations obtained by substituting the electromagnetic characteristic values calculated at the plurality of sample frequencies into each of the approximate equations;
• means for calculating matrix elements in a lower triangular matrix and an upper triangular matrix from the sample frequencies, said lower triangular matrix and upper triangular matrix being derived from a matrix containing powers of the sample frequencies as matrix elements by being decomposed as a product of a lower triangular matrix, with diagonal elements of 1 and an upper triangular matrix;
• means for calculating the approximation coefficient from the electromagnetic characteristic values and the matrix elements in the lower triangular matrix and the upper triangular matrix;
• and
• means for outputting the calculated approximation coefficient.

A computer implemented apparatus for calculating an electromagnetic field intensity, comprising:

• means for inputting geometric data of an electric circuit device located outside of the computer;
• means for calculating from the geometric data approximation coefficients for each of approximate equations that respectively yield approximate values of electromagnetic characteristic values, between a plurality of elements constituting the electric circuit device and of the elements themselves, at an arbitrary frequency;
• means for calculating approximate values of electromagnetic characteristic values between the elements and of the elements themselves at a designated frequency in accordance with the approximate equations having the approximation coefficients calculated by the approximation coefficient calculating means, making it possible to evaluate the electromagnetic field intensity for the designated frequency;
• and
• means for outputting the calculated approximate values of electromagnetic characteristic values,
• wherein the electromagnetic characteristic values include mutual impedances between the elements constituting the electric circuit device and of the elements themselves,
• wherein the elements constituting the electric circuit device include conductor elements and dielectric elements,
• wherein the electromagnetic characteristic values further include mutual admittances between the dielectric elements and of the dielectric elements themselves, mutual reactions between the conductor and dielectric elements, and mutual reactions between the dielectric elements and of the dielectric elements themselves.

A computer implemented apparatus for calculating an electromagnetic field intensity, comprising:

• means for inputting geometric data of an electric circuit device located outside of the computer;
• means for calculating from the geometric data approximation coefficients for each of approximate equations that respectively yield approximate values of electromagnetic characteristic values, between a plurality of elements constituting the electric circuit device and of the elements themselves, at an arbitrary frequency;
• means for calculating approximate values of electromagnetic characteristic values between the elements and of the elements themselves at a designated frequency in accordance with the approximate equations having the approximation coefficients calculated by the approximation coefficient calculating means, making it possible to evaluate the electromagnetic field intensity for the designated frequency;
• and
• means for outputting the calculated approximate values,
• wherein the electromagnetic characteristic values include mutual impedances between the elements constituting the electric circuit device and of the elements themselves,
• wherein the approximate equations for the mutual impedances zij are zij=exp(−jkr) {a0+a1f2+a2f4+a3f6+a4f8+ . . . j(b0/f+b2f3+b3f5+b4f7+ . . . )}, where f is the frequency, k is a wavenumber where k=2πf/c and c is the velocity of light, r is an element-to-element distance, j is an imaginary unit, and a0, a1, . . . and b0, b1, . . . are the approximation coefficients.

A computer implemented apparatus for calculating an electromagnetic field intensity, comprising:

• means for inputting geometric data of an electric circuit device located outside of the computer;
• means for calculating from the geometric data approximation coefficients for each of approximate equations that respectively yield approximate values of electromagnetic characteristic values, between a plurality of elements constituting the electric circuit device and of the elements themselves, at an arbitrary frequency;
• means for calculating approximate values of electromagnetic characteristic values between the elements and of the elements themselves at a designated frequency in accordance with the approximate equations having the approximation coefficients calculated by the approximation coefficient calculating means, making it possible to evaluate the electromagnetic field intensity for the designated frequency;
• means for outputting the calculated approximate values, wherein the approximation coefficient calculating means includes:
• means for calculating the electromagnetic characteristic values between the elements and of the elements themselves from geometric data of the elements at each of a plurality or sample frequencies;
• and
• means for calculating the approximation coefficients by solving simultaneous equations obtained by substituting the electromagnetic characteristic values calculated at the plurality of sample frequencies into each of the approximate equations,
• wherein the number of sample frequencies is equal to the number of terms in a real part and in an imaginary part of each of the approximate equations.

A program storage device readable by a machine, tangibly embodying a program of instructions executable by the machine to perform a method for calculating an electromagnetic field intensity, the method comprising:

• a) inputting geometric data of an electric circuit device located outside of the computer;
• b) calculating, from the geometric data, approximation coefficients for each of approximate equations that respectively yield approximate values of electromagnetic characteristic values, between a plurality of elements constituting the electric circuit device and of the elements themselves, at an arbitrary frequency, each of said approximation equations including a real part which is a sum of terms with frequencies raised to an even numbered power and an imaginary part which is a sum of terms with frequencies raised to an odd numbered power;
• c) calculating approximate values of the electromagnetic characteristic values between the elements and of the elements themselves at a designated frequency in accordance with the approximate equations having the approximation coefficients calculated in b), making it possible to evaluate the electromagnetic field intensity for the designated frequency;
• d) calculating an electric current flowing on each element by solving simultaneous equations obtained by substituting the approximate values of the electromagnetic characteristic values calculated in c) into equations respectively describing boundary conditions for the elements;
• e) calculating the electromagnetic field intensity for the designated frequency from the electric currents respectively flowing on the elements calculated in d);
• and
• determining, using the calculating in e), proper shielding required for the electric circuit device,
• wherein the b) comprises:
• i) calculating the electromagnetic characteristic values between the elements and of the elements themselves from geometric data of the elements at each of a plurality of sample frequencies;
• and
• ii) calculating the approximation coefficients by solving simultaneous equations obtained by substituting the electromagnetic characteristic values calculated at the plurality of sample frequencies into each of the approximate equations.

A program storage device readable by a machine, tangibly embodying a program of instructions executable by the machine to perform a method for calculating an electromagnetic field intensity, the method comprising:

• a) inputting geometric data of an electric circuit device located outside of the computer;
• b) calculating, from the geometric data, approximation coefficients for each of approximate equations that respectively yield approximate values of electromagnetic characteristic values, between a plurality of elements constituting the electric circuit device and of the elements themselves, at an arbitrary frequency;
• c) calculating approximate values of the electromagnetic characteristic values between the elements and of the elements themselves at a designated frequency in accordance with the approximate equations having the approximation coefficients calculated in b), making it possible to evaluate the electromagnetic field intensity for the designated frequency,
• wherein the b) includes
• i) calculating the electromagnetic characteristic values between the elements and of the elements themselves from geometric data of the elements at each of a plurality of sample frequencies;
• ii) calculating the approximation coefficients by solving simultaneous equations obtained by substituting the electromagnetic characteristic values calculated at the plurality of sample frequencies into each of the approximate equations,
• wherein the substep b) ii) includes:
• calculating matrix elements in a lower triangular matrix and an upper triangular matrix from the sample frequencies, said tower triangular matrix and upper triangular matrix being derived from a matrix containing powers of the sample frequencies as matrix elements by being decomposed as a product of a lower triangular matrix, with diagonal elements of 1, and an upper triangular matrix;
• calculating the approximation coefficient from the electromagnetic characteristic values and the matrix elements in the lower triangular matrix and the upper triangular matrix;
• and
• determining, using the calculating in c), proper shielding required for the electric circuit device.

A program storage device readable by a machine, tangibly embodying a program of instructions executable by the machine to perform a method for calculating an electromagnetic field intensity, the method comprising:

• a) inputting geometric data of an electric circuit device located outside of the computer;
• b) calculating, from the geometric data, approximation coefficients for each of approximate equations that respectively yield approximate values of electromagnetic characteristic values, between a plurality of elements constituting the electric circuit device and of the elements themselves, at an arbitrary frequency;
• c) calculating approximate values of the electromagnetic characteristic values between the elements and of the elements themselves at a designated frequency in accordance with the approximate equations having the approximation coefficients calculated in b), making it possible to evaluate the electromagnetic yield intensity for the designated frequency,
• wherein the electromagnetic characteristic values include mutual impedances between the elements constituting the electric circuit device and of the elements themselves,
• wherein the elements constituting the electric circuit device include conductor elements and dielectric elements,
• wherein the electromagnetic characteristic values further include mutual admittances between the dielectric elements and of the dielectric elements themselves, mutual reactions between the conductor and dielectric elements, and mutual reactions between the dielectric elements and of the dielectric elements themselves;
• and
• determining, using the calculating in c), proper shielding required for the electric circuit device.

A program storage device readable by a machine, tangibly embodying a program of instructions executable by the machine to perform a method for calculating an electromagnetic field intensity, the method comprising:

• a) inputting geometric data of an electric circuit device located outside of the computer;
• b) calculating, from the geometric data, approximation coefficients for each of approximate equations that respectively yield approximate values of electromagnetic characteristic values, between a plurality of elements constituting the electric circuit device and of the elements themselves, at an arbitrary frequency, each of said approximation equations including a real part which is a sum of terms with frequencies raised to an even numbered power and an imaginary part which is a sum of terms with frequencies raised to an odd numbered power;
• c) calculating approximate values of the electromagnetic characteristic values between the elements and of the elements themselves at a designated frequency in accordance with the approximate equations having the approximation coefficients calculated in b), making it possible to evaluate the electromagnetic field intensity for the designated frequency,
• wherein the approximate equations for the mutual impedances zij are zij=exp(−jkr) {a0+a1f2+a2f4+a3f6+a4f8+ . . . j(b0/f+b1f+b2f3+b3f5+b4f7+ . . . )}, where f is the frequency, k is a wavenumber where k=2πf/c and c is the velocity of light, r is an element-to-element distance, j is an imaginary unit, and a0, a1, . . . and b0, b1, . . . are the approximation coefficients;
• and
• determining, using the calculating in c), proper shielding required for the electric circuit device.

A program storage device readable by a machine, tangibly embodying a program of instructions executable by the machine to perform a method for calculating an electromagnetic field intensity, the method comprising:

• a) inputting geometric data of an electric circuit device located outside of the computer;
• b) calculating, from the geometric data, approximation coefficients for each of approximate equations that respectively yield approximate values of electromagnetic characteristic values, between a plurality of elements constituting the electric circuit device and of the elements themselves, at an arbitrary frequency, each of said approximation equations including a real part which is a sum of terms with frequencies raised to an even numbered power and an imaginary part which is a sum of terms with frequencies raised to an odd numbered power;
• c) calculating approximate values of the electromagnetic characteristic values between the elements and of the elements themselves at a designated frequency in accordance with the approximate equations having the approximation coefficients calculated in b), making it possible to evaluate the electromagnetic field intensity for the designated frequency,
• wherein the b) includes
• i) calculating the electromagnetic characteristic values between the elements and of the elements themselves from geometric data of the elements at each of a plurality of sample frequencies;
• ii) calculating the approximation coefficients by solving simultaneous equations obtained by substituting the electromagnetic characteristic values calculated at the plurality of sample frequencies into each of the approximate equations,
• wherein the number or sample frequencies is equal to the number of terms in a real part and in an imaginary part of each of the approximate equations;
• and
• determining, using the calculating in c), proper shielding required for the electric circuit device.

A computer implemented apparatus for calculating an electromagnetic field intensity, comprising:

• an input unit inputting geometric data of an electric circuit device located outside of the computer;
• a first unit calculating from the geometric data approximation coefficients for approximate equations that yield approximate values of electromagnetic characteristic values, each of said approximation equations including a real part which is a sum of terms with frequencies raised to an even numbered power and an imaginary part which is a sum of terms with frequencies raised to an odd numbered power;
• a second unit calculating the approximate values of the electromagnetic characteristic values between elements comprising the electric circuit device and of the elements themselves;
• a third unit calculating an electric current by solving simultaneous equations obtained by substituting the approximate values of the electromagnetic characteristic values into equations describing boundary conditions for the elements;
• a fourth unit calculating the electromagnetic field intensity for a designated frequency from the calculated electric current;
• and
• a fifth unit outputting the calculated electromagnetic field intensity
• wherein the first unit further comprises:
• a sixth unit calculating electromagnetic characteristic values between the elements and of elements themselves from geometric data of elements at each of a plurality of sample frequencies;
• and
• a seventh unit calculating the approximation coefficients by solving simultaneous equations obtained by substituting the electromagnetic characteristic values calculated at the plurality of sample frequencies into each of the approximate equations.

A computer implemented method of calculating an electromagnetic field intensity, comprising:

• inputting geometric data of an electric circuit device located outside of the computer;
• calculating from the geometric data approximation coefficients for approximate to equations that yield approximate values of electromagnetic characteristic values, each of said approximation equations including a real part which is a sum of terms with frequencies raised to an even numbered power and an imaginary part which is a sum of terms with frequencies raised to an odd numbered power;
• calculating the approximate values of the electromagnetic characteristic values between elements comprising the electric circuit device and of the elements themselves;
• calculating an electric current by solving simultaneous equations obtained by substituting the approximate values of the electromagnetic characteristic values into equations describing boundary conditions for the elements;
• calculating the electromagnetic field intensity for a designated frequency from the calculated electric current;
• and
• outputting the calculated electromagnetic field intensity,
• wherein the calculating from the geometric data approximation coefficients further comprises:
• i) calculating electromagnetic characteristic values between the elements and of elements themselves from geometric data of elements at each of a plurality of sample frequencies;
• and
• ii) calculating the approximation coefficients by solving simultaneous equations obtained by substituting the electromagnetic characteristic values calculated at the plurality of sample frequencies into each of the approximate equations.

A computer implemented apparatus calculating an electromagnetic field intensity, comprising:

• a first unit inputting geometric data of an electric circuit device located outside of the computer;
• a second unit calculating from the geometric data approximation coefficients for each of approximate equations that respectively yield approximate values of electromagnetic characteristic values, between a plurally of elements constituting the electric circuit device and of the elements themselves, at an arbitrary frequency, each of said approximation equations including a real part which is a sum of terms with frequencies raised to an even numbered power and an imaginary part which is a sum of terms with frequencies raised to an odd numbered power;
• a third unit calculating approximate values of the electromagnetic characteristic values between the elements and of the elements themselves at a designated frequency in accordance with the approximate equations having the approximation coefficients calculated by the approximation coefficient calculating unit, thereby making it possible to evaluate the electromagnetic field intensity for the designated frequency;
• a fourth unit calculating an electric current by solving simultaneous equations obtained by substituting the approximate values of the electromagnetic characteristic values into equations describing boundary conditions for the elements;
• a fifth unit calculating the electromagnetic field intensity for a designated frequency from the calculated electric current;
• and
• a sixth unit outputting the calculated electromagnetic field intensity,
• wherein the second unit further comprises:
• a seventh unit calculating electromagnetic characteristic values between the elements and of elements themselves from geometric data of elements at each of a plurality or sample frequencies;
• and
• an eighth unit calculating the approximation coefficients by solving simultaneous equations obtained by substituting the electromagnetic characteristic values calculated at the plurality of sample frequencies into each of the approximate equations.