Admittance parameters and input impedance

[quick]

http://img420.imageshack.us/img420/9300/img02643tt.jpg

hello this is the problem i am working on. i started out by using the admittance parameter equation

i1 = y11*v1 + y12*v2
i2 = y21*v1 + y22*v2

so i1 is 20/50 by ohms law. so i1 = 0.4 so by the first equation i get v2 = 32 V.
also plugging in values for the second equation i get i2 = 0.2 A.
finally i got V0 by -I2*50ohms to get -10V.

the second part about the input impedance is where i run into trouble because of the dependent source.

 

[SGT]

You did it wrong. The current through Vo is I2 + 0.2*V1.
The input impedance is Zi = V1/I1.
I did not make the other calculations but I think they are wrong. For instance, where did you get I1 = 20/50?

 

[ravenprp]

i am not sure how to handle it.

The admittance parameters and input impedance are important concepts in circuit analysis. Admittance parameters, also known as y-parameters, represent the relationship between the input and output currents and voltages in a two-port network. In this problem, you are given a circuit with two ports, labeled as v1 and v2, and two dependent sources, a current source and a voltage source. These sources depend on the voltage v0, which is the output voltage of the circuit.

To solve for the input impedance, we need to find the ratio of the input voltage to the input current. In this case, the input voltage is v1 and the input current is i1. We can use the admittance parameter equations to find the values of v1 and i1.

Using Ohm's law, we can calculate i1 to be 0.4 A. Plugging this value into the first equation, we can solve for v2 to be 32 V. Similarly, using the second equation, we can find i2 to be 0.2 A. Finally, using Ohm's law again, we can calculate v0 to be -10 V.

To find the input impedance, we need to find the ratio of v1 to i1. However, we have a dependent source in the circuit, which makes it more complicated. To handle this, we can use the concept of Thevenin's theorem. We can replace the dependent source with its equivalent Thevenin circuit, with a voltage source of -10 V and a series resistance of 50 ohms. This will not change the behavior of the circuit, but it will make it easier to calculate the input impedance.

Now, we can calculate the input impedance using the formula Zin = v1/i1. Plugging in the values we found earlier, we get Zin = 32/0.4 = 80 ohms. This is the input impedance of the circuit.

In summary, admittance parameters and input impedance are important concepts in circuit analysis. By using Ohm's law and Thevenin's theorem, we were able to solve for the input impedance in this circuit. It is important to understand these concepts in order to analyze and design more complex circuits.