Enunciado

Calcule os parâmetros h e g da rede do Ex. 14.8.1

Passo 1

Iae, meus queridos! Td certinho??

Antes de tudo, vamos nos lembrar das equações das malhas do circuito.

{[[V_1 (s) = 6 I_1 (s) + 4 I_2 (s)],[V_2 (s) = 4 I_1 (s) + 10 I_2 (s)]])

Primeiro vamos calcular os parâmetros h da rede.

{[[V_1 (s) = h_11 I_1 (s) + h_12 V_2 (s)],[I_2 (s) = h_2 1 I_1 (s) + h_2 2 V_2 (s)]])

h_11 :

h_11 = (V_1 (s))/(I_1 (s)) (​|_V_2 (s) = 0

Pra chegar a essa razão, vamos manipular as equações de malhas.

V_2 (s) = 4 I_1 (s) + 10 I_2 (s) = 0 *fazendo V_2 (s) = 0

I_2 (s) = - (4)/(10) I_1 (s) *substituindo em V_1

V_1 (s) = 6 I_1 (s) + 4 (- (4)/(10) I_1 (s))

V_1 (s) = (6 0)/(10) I_1 (s) - (16)/(10) I_1 (s)

V_1 (s) = (44)/(10) I_1 (s)

(V_1 (s))/(I_1 (s)) = h_11 = (44)/(10)

h_12 :

h_12 = (V_1 (s))/(V_2 (s)) (​|_I_1 (s) = 0

(V_1 (s))/(V_2 (s)) = (6 I_1 (s) + 4 I_2 (s))/(4 I_1 (s) + 10 I_2 (s)) (​|_I_1 (s) = 0

(V_1 (s))/(V_2 (s)) = (0 + 4 I_2 (s))/(0 + 10 I_2 (s))

(V_1 (s))/(V_2 (s)) = h_12 = (4)/(10)

h_21 :

h_2 1 = (I_2 (s))/(I_1 (s)) (​|_V_2 (s) = 0

V_2 (s) = 4 I_1 (s) + 10 I_2 (s) = 0

10 I_2 (s) = - 4 I_1 (s)

(I_2 (s))/(I_1 (s)) = h_21 = - (4)/(10)

h_22 :

h_22 = (V_2 (s))/(I_2 (s)) (​|_I_1 (s) = 0

V_2 (s) = 4 I_1 (s) + 10 I_2 (s) (​|_I_1 (s) = 0

V_2 (s) = 0 + 10 I_2 (s)

(V_2 (s))/(I_2 (s)) = h_22 = (1)/(10)

Passo 2

Por fim, calculando os parâmetros g da rede.

{[[I_1 (s) = g_1 1 V_1 (s) + g_1 2 I_2 (s)],[V_2 (s) = g_2 1 V_1 (s) + g_2 2 I_2 (s)]])

g_11 :

g_11 = (I_1 (s))/(V_1 (s)) (​|_I_2 (s) = 0

V_1 (s) = 6 I_1 (s) + 4 I_2 (s) (​|_I_2 (s) = 0

V_1 (s) = 6 I_1 (s) + 0

(I_1 (s))/(V_1 (s)) = g_11 = (1)/(6)

g_12 :

g_1 2 = (I_1 (s))/(I_2 (s)) (​|_V_1 (s) = 0

V_1 (s) = 6 I_1 (s) + 4 I_2 (s) (​|_V_1 (s) = 0

0 = 6 I_1 (s) + 4 I_2 (s)

6 I_1 (s) = - 4 I_2 (s)

(I_1 (s))/(I_2 (s)) = g_12 = - (4)/(6)

g_21 :

g_21 = (V_2 (s))/(V_1 (s)) (​|_I_2 (s) = 0

g_21 = (V_2 (s))/(V_1 (s)) = (4 I_1 (s) + 10 I_2 (s))/(6 I_1 (s) + 4 I_2 (s)) (​|_I_2 (s) = 0

g_21 = (V_2 (s))/(V_1 (s)) = (4 I_1 (s) + 0)/(6 I_1 (s) + 0)

(V_2 (s))/(V_1 (s)) = g_21 = (4)/(6)

g_22 :

g_22 = (V_2 (s))/(I_2 (s)) (​|_V_1 (s) = 0

0 = 6 I_1 (s) + 4 I_2 (s)

I_1 (s) = - (4)/(6) I_2 (s) *substituindo em V_2

V_2 (s) = 4 (- (4)/(6) I_2 (s)) + 10 I_2 (s)

V_2 (s) = - (16)/(6) I_2 (s) + (6 0)/(6) I_2 (s)

V_2 (s) = (44)/(6) I_2 (s)

(V_2 (s))/(I_2 (s)) = g_22 = (44)/(6)

Um pouco trabalhoso só, mas bem simples de resolver, oq vc achou?

Resposta

Parâmetros h: h_11 = (44)/(10) , h_12 = (4)/(10) , h_21 = - (4)/(10) , h_22 = (1)/(10) .

Parâmetros g: g_11 = (1)/(6) , g_12 = - (4)/(6) , g_21 = (4)/(6) , g_22 = (44)/(6) .