Circuits with Resistor Combinations (2.6, 7.7) - Y Transformation (2.7)

Circuits with Resistor Combinations (2.6, 7.7)-Y Transformation (2.7) Dr. S. M. Goodnick September 22, 2003 ECE201 Lect-12

Using MATLAB to Solve Circuits • MATLAB can perform computations with complex numbers. • You can use it as a calculator to compute phasors and impedances for AC steady-state analysis. • You can also use it to automate computations of frequency responses. ECE201 Lect-12

Using MATLAB • Entering a complex number: >> 1+2j ans = 1.0000 + 2.0000i • Multiplying complex numbers: >> (1+2j)*(3+4j) ans = -5.0000 +10.0000i ECE201 Lect-12

Example: Notch Filter 70.4mH 0.1W Find Vout Use w = 1500 100W + + – 10V  0 1kW Vout 100mF – ECE201 Lect-12

Compute Impedances >> omega = 377 omega = 377 >> xl = j*omega*70.4e-3 xl = 0 +26.5408i >> xc = 1/(j*omega*100e-6) xc = 0 -26.5252i ECE201 Lect-12

Equivalent Capacitor/Inductor Impedance >> zeq = (0.1+xl)*xc /(0.1+xl+xc) zeq = 6.8687e+03 - 1.0981e+03i ECE201 Lect-12

Voltage Divider >> vin = 10 vin = 10 >> vout = vin*1e3 /(100+zeq+1e3) vout = 1.2315 + 0.1697i ECE201 Lect-12

Magnitude and Angle >> abs(vout) ans = 1.2432 >> angle(vout) ans = 0.1369 >> angle(vout)*180/pi ans = 7.8461 ECE201 Lect-12

-Y Transformation • A particular configuration of resistors (or impedances) that does not lend itself to the using series and parallel combination techniques is that of a delta () connection • In such cases the delta () connection is converted to a wye (Y) configuration • The reverse transformation can also be performed ECE201 Lect-12

-Y Transformation a a Ra R1 R2 Rc Rb c b R3 c b ECE201 Lect-12

-Y Transformation • To compute the new Y resistance values • For the balanced case (RY= Ra= Rb= Rc) RΔ = 3 RY ECE201 Lect-12

Class Example • Learning Example 2.22 ECE201 Lect-12

Circuits with Resistor Combinations (2.6, 7.7) - Y Transformation (2.7)