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para_Y.jpg
Figure 32-01
    eq.   32-02

    The terms Y are known as Admitting Parameters, and its unit of measure is the SIEMENS.

    The parameters values can be calculated by making V1 = 0, that is, short-circuited input port or V2 = 0, which means short-circuited output port. Therefore, these parameters are known as Short Circuit Admittance Parameters.

    We can define the parameters as:

    a) Y11 ⇒ Short-circuit input admittance.

    b) Y12 ⇒ Short-circuit transfer admittance from Port 2 to Port 1.

    c) Y21 ⇒ Short-circuit transfer admittance from Port 1 to Port 2.

    d) Y22 ⇒ Admittance of short-circuit output.



    2.   Calculation of Parameters Y

    Therefore, if we want to calculate Y11 and Y21 we should connect a current source I1to port 1 and short-circuit port 2. Thus, determining the values of V1 e I2, together with the value of I1 which we already know, we calculate the parameters.

    Y11 = I1 / V1        and       Y21 = I2 / V1
    eq.   32-03

    And to calculate Y22 and Y12, we use the same reasoning, connecting a current source I2 to port 2 and short-circuiting port 1. As we know the value of I2 and calculating V1 and I2, we can determine the parameters.

    Y22 = I2 / V2        and       Y12 = I1 / V2
    eq.   32-04

    Similar to the Parameters Z , if Y12 = Y21 we say that the circuit is PASSIVE or RECIPROCAL.

    Thus, when a circuit is of this type, we can represent it by the circuit in the Figure 32-02.

quad32-1J.jpg
Figure 32-02

    If the circuit is not Reciprocal or Passive, that is, have dependent sources, then we have to modify the model. See the Figure 32-03 an equivalent circuit model for general cases.

quad32-1K.jpg
Figure 32-03

    Note that this circuit is derived directly from the equations of the Parameters Y , given at the beginning of the page.



    3.   Equivalence between Z and Y Parameters

    There is a relation between the parameters Y and Z given by the equations:


    Δ Z = Z11 Z22 - Z12 Z21
    eq.   32-05
    Y11 =  Z22 / Δ Z
    eq.   32-06
    Y12 = - Z12 / Δ Z
    eq.   32-07
    Y21 = - Z21 / Δ Z
    eq.   32-08
    Y22 =  Z11 / Δ Z
    eq.   32-09