Signals.and.Systems.with.MATLAB.Computing.and.Simulink.Modeling.4th_Part81

# Signals.and.Systems.with.MATLAB.Computing.and.Simulink.Modeling.4th_Part81

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Unformatted text preview: Signals and Systems with MATLAB Computing and Simulink Modeling, Fourth Edition D − 29 Copyright © Orchard Publications Solution of Simultaneous Equations with Matrices the current can be found from the relation (D.59) and the voltages and can be computed from the nodal equations (D.60) and (D.61) Compute, and express the current in both rectangular and polar forms by first simplifying like terms, collecting, and then writing the above relations in matrix form as , where , , and Solution: The matrix elements are the coefficients of and . Simplifying and rearranging the nodal equations of (D.60) and (D.61), we obtain (D.62) Next, we write (D.62) in matrix form as (D.63) where the matrices , , and are as indicated. We will use MATLAB to compute the voltages and , and to do all other computations. The script is shown below. Y=[0.0218 − 0.005j − 0.01; − 0.01 0.03+0.01j]; I=[2; 1.7j]; V=Y\I; % Define Y, I, and find V fprintf('\n'); % Insert a line disp('V1 = '); disp(V(1)); disp('V2 = '); disp(V(2)); % Display values of V1 and V2 V1 = 1.0490e+002 + 4.9448e+001i I X I X V 1 V 2 – R 3------------------ = V 1 V 2 V 1 170 0 ° ∠ – 85------------------------------- V 1 V 2 – 100------------------ V 1 – j200--------------- + + = V 2 170 0 ° ∠ – j100 –------------------------------- V 2 V 1 – 100------------------ V 2 – 50--------------- + + = I x YV I = Y A d m i t c e tan = V Voltage = I Current = Y V 1 V 2 0.0218 j0.005 – ( ) V 1 0.01V 2 – 2 = 0.01 – V 1 0.03 j0.01 + ( ) V 2 + j1.7 = 0.0218 j0.005 – 0.01 – 0.01 – 0.03 j0.01 + Y V 1 V 2 V 2 j1.7 I = Y V I V 1 V 2 Appendix D Matrices and Determinants D − 30 Signals and Systems with MATLAB Computing and Simulink Modeling, Fourth Edition Copyright © Orchard Publications V2 = 53.4162 + 55.3439i Next, we find from R3=100; IX=(V(1) − V(2))/R3 % Compute the value of I X IX = 0.5149 - 0.0590i This is the rectangular form of . For the polar form we use the MATLAB script magIX=abs(IX), thetaIX=angle(IX)*180/pi % Compute the magnitude and the angle in degrees magIX = 0.5183 thetaIX =-6.5326 Therefore, in polar form Spreadsheets have limited capabilities with complex numbers, and thus we cannot use them to compute matrices that include complex numbers in their elements as in Example D.18....
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Signals.and.Systems.with.MATLAB.Computing.and.Simulink.Modeling.4th_Part81

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