Hello!
I am trying to find a space state model for the following circuit. My approach was to try to divide the circuit in various blocks and then
find the output expression for those blocks.
So i have defined the voltages V1,V2 and Vo has shown in the circuit.
Then i have calculated the ouput expressions for the blocks i have considered and i got:
Note that for representing V1(dotted)i used small case letters that is in this case, v1
[tex]
Equation 1
[plain][tex]
(Vi0)=C1*(d)/(dt)*(0V1)+(0V1)/(R2)
(Vi)/(R1)=C1*v1(V1)/(R2)
C1*v1=(V1)/(R2)(Vi)/(R1)
v1=(V1)/(C2*R2)+(Vi)/(C2*R1)
[/tex]
[tex]
Equation 2:
(Vi0)/(R4)+(V10)/(R3)=C2*(d)/(dt)*(0V2)+(0V2)/(R5)
(Vi)/(R4)+(V1)/(R3)=C2*v2(V2)/(R5)
C1*v2=(V2)/(R5)(Vi)/(R4)(v1)/(R3)
v2=(V2)/(C2*R5)+(Vi)/(C2*R4)+(V1)/(C2R3)
[/tex]
[tex]
Equation 3:
(V20)/(R7)+(V10)/(R4)=(0Vo)/(R6)
(V2)/(R7)+(V1)/(R4)=(Vo)/(R6)
(Vo)/(R6)=(V2)/(R7)(V1)/(R4)
[/tex]
So the matrix that represent the space state model of the circuit are
[tex]
[v1;v2]=[(1)/(C2*R2) 0 ; (1)/(C2*R3) (1)/(C2*R5)] [V1;V2] +[(1)/(C2*R1); (1)/(C2*R4)] *Vi
Vo=[1 1] [V1;V2] + 0*Vi [/tex]
Is this correct? Thanks
I am trying to find a space state model for the following circuit. My approach was to try to divide the circuit in various blocks and then
find the output expression for those blocks.
So i have defined the voltages V1,V2 and Vo has shown in the circuit.
Then i have calculated the ouput expressions for the blocks i have considered and i got:
Note that for representing V1(dotted)i used small case letters that is in this case, v1
[tex]
Equation 1
[plain][tex]
(Vi0)=C1*(d)/(dt)*(0V1)+(0V1)/(R2)
(Vi)/(R1)=C1*v1(V1)/(R2)
C1*v1=(V1)/(R2)(Vi)/(R1)
v1=(V1)/(C2*R2)+(Vi)/(C2*R1)
[/tex]
[tex]
Equation 2:
(Vi0)/(R4)+(V10)/(R3)=C2*(d)/(dt)*(0V2)+(0V2)/(R5)
(Vi)/(R4)+(V1)/(R3)=C2*v2(V2)/(R5)
C1*v2=(V2)/(R5)(Vi)/(R4)(v1)/(R3)
v2=(V2)/(C2*R5)+(Vi)/(C2*R4)+(V1)/(C2R3)
[/tex]
[tex]
Equation 3:
(V20)/(R7)+(V10)/(R4)=(0Vo)/(R6)
(V2)/(R7)+(V1)/(R4)=(Vo)/(R6)
(Vo)/(R6)=(V2)/(R7)(V1)/(R4)
[/tex]
So the matrix that represent the space state model of the circuit are
[tex]
[v1;v2]=[(1)/(C2*R2) 0 ; (1)/(C2*R3) (1)/(C2*R5)] [V1;V2] +[(1)/(C2*R1); (1)/(C2*R4)] *Vi
Vo=[1 1] [V1;V2] + 0*Vi [/tex]
Is this correct? Thanks
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