When using nodal analysis of a circuit involving CCCS, how do you know which currents are entering and which are leaving?

Question

I am trying to solve the following circuit:

I believe the answer I'm getting for \$i_b\$ is wrong because I put it into LTSpice and I'm getting that \$i_b = -3.63636\$

This is my LTSpice diagram:

I found \$i_b = 1\$mA by doing a loop voltage analysis on the left loop; for the voltage drop across the \$200\Omega\$ resistor I assumed that it would be \$i_b + 29i_b\$, which works out to be a nice number and in fact all of the numbers are nice in this case--usually when the numbers are nice, you know you're doing it right.

At this point, I'm not sure if I incorrectly modeled this in LTSpice, or if I incorrectly assumed which way the current was flowing.

Instead of giving me the answer directly, I would just like to know how to determine whether the current at a node is entering or leaving a branch.

Answer 1

Your paper analysis is correct, but your LTspice simulation is incorrect. I get the same (incorrect) result as you if I use a gain of \$+29\$ for the F device (your \$I_1\$). But the gain should be \$-29\$ since \$i_b\$ flows from the negative to positive terminal of \$V_{\text{ib}}\$. Changing the gain gives you the correct result.

Circuit:

F device attributes:

Result:

If I change the gain to \$+29\$ the result is:

Note that the simulation result is \$v_y = v_{y1} - v_{y2} \approx 98\$V when using a gain of \$+29\$, which is clearly wrong.

The two simulations highlight the importance of maintaining consistency in the direction of currents. The problem statement defines \$i_b\$ and \$29i_b\$ as both flowing toward the middle "T" node. LTspice defines \$i_b\$ as flowing away from it since it defines the current through \$V_{\text{ib}}\$ as flowing from positive to negative terminal. That means you also have to define the CCCS \$29i_b\$ as flowing away from the middle "T" node. In the incorrect simulation (with gain of \$+29\$), \$29i_b\$ is still flowing toward the "T" node while \$i_b\$ is flowing away from it. The correct simulation defines them both as flowing away from the "T" node. Alternatively, you could just switch the direction of the "F" device and use a positive current gain -- it would then also be defined as flowing away from the "T" node.

Answer 2

While doing these type of problems don't worry about current directions. First covert \$i_b\$ in terms of the principle node, then apply nodal analysis thereafter and find all the currents in the branch. Then you will know the direction of currents.