# Kirchhoff's voltage law in a two-port network

In a tutorial about h parameters of a two port network, I find the below snippet in the image unable to grasp.

According to KVL, the total voltage in a loop is the algebraic sum of the individual voltages. But why in this tutorial (equation 1 in below image) it's given like that? It should be something like V1 = h11 I1 + V2 according to KVL. What does this h12 V2 mean?

The whole tutorial is here.

the total voltage in a loop is the algebraic sum of the individual voltages.

This is KVL, not KCL.

It should be something like V1 = h11 I1 + V2 according to KCL.

The voltage across the resistor is $$\h_{11}I_1\$$ and the voltage across the controlled voltage source is $$\h_{12}V_2\$$.

Therefore the KVL equation for this subcircuit is

$$V_1 = h_{11}I_1 + h_{12}V_2$$

as shown in the quoted text.

What is this h12 V2 mean?

$$\h_{12}V_2\$$ is the voltage across the VCVS shown in the diagram.

$$\h_{12}\$$ is the gain of the VCVS.

$$\V_2\$$ is the voltage across the other port of the 2-port. This is shown in the very next diagram in the linked tutorial.

• I made some mistakes in my actual question. Now I have edited the question. Can you tell me how the equation 1 represents the circuit diagram? How did the author conclude that KVL applicable there? May 25, 2019 at 17:17
• Why do you think KVL wouldn't be applicable? So long as we don't violate the lumped circuit approximation, KVL can be applied to any path we like around a network. May 25, 2019 at 18:13

The two port parameters are given by the equation: $$\begin{gather} \begin{bmatrix} V_1\\ I_2 \end{bmatrix} = \begin{bmatrix} h_{11} & h_{12}\\ h_{21} & h_{22} \end{bmatrix} \begin{bmatrix} I_1\\ V_2 \end{bmatrix} \end{gather}$$

It is from here that we get the two equations mentioned in the question. $$V_1 = h_{11} I_1 + h_{12}V_2$$ $$I_2 = h_{21} I_1 + h_{22}V_2$$ Then an equivalent circuit is drawn for the first equation. If we consider the first equation as a KVL analysis of a network, then the network has to be the one given in the question.

It should be something like V1 = h11 I1 + V2 according to KVL. What is this h12 V2 mean?

$$\h_{12} V_2\$$ comes from the matrix equation. To represent it in the diagram, a VCVS is used with voltage as $$\h_{12}V_2\$$. The equations are not written by KVL analysis of a network, rather a network has been drawn which, when analysed using KVL, will give you the equations.