# abcd

Construct state-space matrices from rational object

Since R2020a

## Description

example

[A,B,C,D,sharedpoles] = abcd(fit) constructs real diagonal form A, B, C, and D state-space matrices from input fit, a rational object. This function also indicates whether or not each element of fit has the same poles using sharedpoles output argument.

## Examples

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Create S-Parameters from the file named passive.s2p.

S = sparameters('passive.s2p');

Perform rational fitting of the S-parameters.

fit = rational(S);

Construct state-space matrices from rational object, fit.

[A,B,C,D,sharedpoles] = abcd(fit)
A =
1.0e+11 *

(1,1)      -0.0008
(2,1)      -0.0011
(1,2)       0.0011
(2,2)      -0.0008
(3,3)      -4.0560
(4,4)      -0.8359
(5,5)      -0.5389
(6,6)      -0.1148
(7,7)      -0.0173
(8,8)      -0.0008
(9,9)      -0.0008
(10,9)      -0.0011
(9,10)      0.0011
(10,10)     -0.0008
(11,11)     -4.0560
(12,12)     -0.8359
(13,13)     -0.5389
(14,14)     -0.1148
(15,15)     -0.0173
(16,16)     -0.0008

B =
(1,1)       1.4142
(3,1)       1.0000
(4,1)       1.0000
(5,1)       1.0000
(6,1)       1.0000
(7,1)       1.0000
(8,1)       1.0000
(9,2)       1.4142
(11,2)       1.0000
(12,2)       1.0000
(13,2)       1.0000
(14,2)       1.0000
(15,2)       1.0000
(16,2)       1.0000

C = 2×16
1011 ×

0.0001    0.0001   -2.8008    0.6205    0.0907    0.0831   -0.0015   -0.0006   -0.0001   -0.0001   -3.1065    2.4562   -0.7797   -0.0750    0.0010    0.0007
-0.0001   -0.0001   -3.1236    2.4641   -0.7827   -0.0750    0.0010    0.0007    0.0001    0.0001   -2.6254    0.4517    0.1564    0.0878   -0.0015   -0.0006

D = 2×2

0     0
0     0

sharedpoles = logical
1

## Input Arguments

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Rational fit, specified as a rational or rfmodel.rational object.

## Output Arguments

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State-space matrices, returned as an array of scalar numbers. The size of the state-space matrix elements are

• AM-by-M array.

• BM-by-NumPorts array.

• CNumPorts-by-M array.

• DNumPorts-by-NumPorts array.

where, M is NumPoles × NumPorts and NumPoles and NumPorts are number of poles and ports, respectively, derived from fit.

Shared poles indicating whether or not each element of fit has the same poles, returned as 1 or 0 of data type logical.

Data Types: logical

## Version History

Introduced in R2020a