I am calculating parameters of the Thevenin's equivalent circuit as seen from the terminals A and B, for this circuit:
So I am following two steps.
Calculate Thevenin's equivalent impedance Z_AB. Remove load, short all voltage sources and open circuit current sources. We get simplified circuit whith R3 removed and R1 and R2 connected in series. Therefore:
Z_AB = (R1 + R2) = 12
Calculate Thevenin's equivalent voltage across A and B terminals using original circuit. Here's where I have some questions. I can calculate the voltage using KCL for center node (blue pixel, the only node in fact) and get
Step 2 : solution 1
Mark the voltage at the center node (blue pixel) by V1 and voltage source as E = 12. Applying KCL for this node gives:
(E - V1) / R1 + I1 = 0
(12 - V1) / 6 + 2 = 0
V1 = 24
Which seems to be the right result, confirmed by simulating this circuit in LTSpice:
Based on that voltage at terminal A can be calculated as V1 * R3 / (Z_AB + R3) = 24 * 4 / (12 + 4) = 6
Step 2 : solution 2
But if I try to apply complete Node analysis I cannot get correct result. I know it must work, so apparently I am doing something wrong. I would like to know where do I fail in my node analysis. My calculation:
YV = I
V = voltage at nodes matrix = [ V1 ]
Y = admittance matrix = [ 1/R1 + 1/(R2 + R3) ]
I = [ (E - V1) / R1 + I1 - V1 / (R2 + R3) ]
V1/R1 + V1 / (R2 + R3) = (E - V1) / R1 + I1 - V1 / (R2 + R3)
Which would agree with previous result only if
V1/R1 + V1 / (R2 + R3) = 0
which is not the case.
Where is an error in my proper node analysis? I can see that I would get right answer if Y = 0 but why should I set admittance matrix to be 0?
Found it (think so...). We need to include only independent current sources in I matrix, so the equation system is:
Y = [ 1/R1 ]
V = [ V1 ]
I = [ I1 + E/R1 ]
Then it gives the same:
YV = I so V1/R1 = I1 + E/R1
But I would be very thankful to anyone for confirming that or providing different explanation.