Introduction
This experiment is about different methods of solving sinusoidal steady-state voltage magnitude and phase. The different methods are as follows: (1) MULTISIM, (2) MATLAB, and (3) theory.
Results
1.-2. For MULTISIM, the component values of the inductor and capacitor at 1 kHz are computed as follows:
-j1=1jωC→-j1=-jωC→1=1ωC→C=1ω=12π1000=0.15915 mF
2j=jωL→2=ωL→L=2ω=22π1000=0.31831 mH
MULTISIM VALUE: V0=6.654 ∠33.69° V
3. Theoretical Values:
The effective impedance at the right of the 12VRMS source is:
Z=-j+j2||3=-j+j63+j2=1.0 ∠22.62°
Thus, the current coming from the 12 VRMS source to the right circuit is:
I=12∠0°1.0∠22.62°=12∠-22.62°
IR=Ij2j2+2+1=12∠-22.62°j2j2+3=6.66 ∠33.69°
The voltage is (theoretical value):
V0=IRR=6.66 ∠33.69° 1=6.66 ∠33.69° V
4. MATLAB Code:
% MATLAB Code to solve for V0
% Current from 12<0 to RLC Network
I = 12/(-j+(2j*3)/(2j+3));
% Current through 2-ohm and 1-ohm using Current Division
IR = I*2j/(3+2j);
% V0 by Ohm's Law
V0 = IR*1;
abs(V0)
angle(V0)*180/pi
The output is:
V0=6.6564 ∠33.69° V
5. Table of V0 Values:
6. AC Sweep:
7.-8. For MULTISIM, the component values of the inductor and capacitor at 1 kHz are computed as follows:
-j1=1jωC→-j1=-jωC→1=1ωC→C=1ω=12π1000=0.15915 mF
3j=jωL→3=ωL→L=3ω=32π1000=0.47746 mH
MULTISIM VALUE: V0=6.418 ∠19.84° V
9. Theoretical Values:
The Y-network of 2Ω resistors on the left can be converted into a delta network:
RΔ=3RY2RY=3∙222=6Ω
The effective impedance on the left of the current source is:
Z=666+j36=63+1.2+2.4j=6||4.2+2.4j=2.6557+j0.7869 Ω
IRC=12∠0Z1-j+Z=12∠0 2.6557+j0.78691-j+2.6557+j0.7869=9.08∠19.84°
The voltage output is:
V0=9.08∠19.84° V
10. MATLAB Code:
% Impedance of the RL Network ZRL
ZRL1 = 3j*Rd/(3j+Rd);
ZRR = 6*Rd/(6+Rd);
ZRL = (ZRL1+ZRR)*Rd/((ZRL1+ZRR)+Rd);
% Current through RC Network by Current Division
IRC = 12*ZRL/(ZRL+1-j);
% Voltage V0
V0 = IRC * 1;
abs(V0)
angle(V0)*180/pi
The output is:
V0=9.0767∠19.84° V
11. Table of V0 Values:
12. AC Sweep:
