Me preguntaba si alguien puede confirmar si esto es correcto o no, o si estoy en el camino correcto
El estado ON:
NodoVL:\$-\int\frac{V_{IN}}{L}=0\$
NodoVC:\$C\dotV_C+\frac{V_C}{R}=0\$
-
Nodo VC: \ $ \ frac {V_C-V_ {IN}} {L} + C \ ddot V_C + \ frac {\ dot V_C} {R} = 0 \ $
-
MODELO SSA: \ $ \ frac {V_C} {L} - \ frac {V_C * d} {L} \ frac {-V_ {IN}} {L} + C \ punto V_C * d + C \ ddot V_C-C \ ddot V_C * d + \ frac {\ dot V_C} {R} - \ frac {\ dot V_C * d} {R} + \ frac {V_C * d} {R} = 0 \ $
donde (variables)
- \ $ V_c = Capacitor \ Voltage \ $
- \ $ D = Duty \ Cycle \ $
Suponiendo que es correcto, necesito linealizarlo debido a que \ $ V_C * d \ $ no es lineal.
* \ $ V_ {CE} \ $ como en Voltaje del capacitor en equilibrio, no VCE de BJT.
Buscando puntos de equilibrio, quiero linealizarlo alrededor de \ $ V_ {CE} = 5V \ $ para encontrar De y suponiendo que todas las condiciones iniciales son = 0
Donde
\ $ C = 0.000272F \ $
\ $ L = 0.000047242H \ $
\ $ R = 2 \ Omega \ $
\ $ \ frac {5} {0.000047242} - \ frac {5 * d_e} {0.000047242} - \ frac {3.3} {0.000047242} + \ frac {5 * d_e} {2} = 0 \ $
Resolviendo \ $ D_e = 0.34 \ $
Puntos de equilibrio
\ $ V_ {CE} = 5V \ $
\ $ D_E = 0.34 \ $
Linealización:
\ $ (\ frac {\ partial \ frac {V_C} {L}} {\ partial V_c} * \ sigma V_C \ Bigr | _ {\ substack {V_ {CE} = 5V \\ D_E = 0.34}} + \ frac {\ partial \ frac {V_C} {L}} {\ partial d} * \ sigma d \ Bigr | _ {\ substack {V_ {CE} = 5V \\ D_E = 0.34}})) (\ frac {\ partial \ frac {V_C * d} {L}} {\ partial V_c} * \ sigma V_C \ Bigr | _ {\ substack {V_ {CE} = 5V \\ D_E = 0.34}} + \ frac {\ partial \ frac {V_C * d} {L}} {\ partial d} * \ sigma d \ Bigr | _ {\ substack {V_ {CE} = 5V \\ D_E = 0.34}})) (\ frac {\ partial \ frac {V_ {IN}} {L}} {\ partial V_c} * \ sigma V_C \ Bigr | _ {\ substack {V_ {CE} = 5V \\ D_E = 0.34}} + \ frac {\ partial \ frac {V_ {IN}} {L}} {\ partial d} * \ sigma d \ Bigr | _ {\ substack {V_ {CE} = 5V \\ D_E = 0.34}}) + (\ frac {\ partial C \ dot V_C * d} {\ partial \ dot V_c} * \ sigma V_C \ Bigr | _ {\ substack {V_ {CE} = 5V \\ D_E = 0.34}} + \ frac {\ parcial C \ punto V_C * d} {\ parcial d} * \ sigma d \ Bigr | _ {\ substack {V_ {CE} = 5V \\ D_E = 0.34}}) + (\ frac {\ partial C \ ddot V_C} {\ partial \ ddot V_c} * \ sigma V_C \ Bigr | _ {\ substack {V_ {CE} = 5V \\ D_E = 0.34}} + \ frac {\ parcial C \ ddot V_C} {\ partial d} * \ sigma d \ Bigr | _ {\ substack {V_ {CE} = 5V \\ D_E = 0.34}})) (\ frac {\ partial C \ ddot V_C * d} {\ partial \ ddot V_c} * \ sigma V_C \ Bigr | _ {\ substack {V_ {CE} = 5V \\ D_E = 0.34}} + \ frac {\ parcial C \ ddot V_C * d} {\ parcial d} * \ sigma d \ Bigr | _ {\ substack {V_ {CE} = 5V \\ D_E = 0.34}}) + (\ frac {\ partial \ frac {\ dot V_C} {R}} {\ partial \ dot V_c} * \ sigma V_C \ Bigr | _ {\ substack {V_ {CE} = 5V \\ D_E = 0.34}} + \ frac {\ partial \ frac {\ dot V_C} {R}} {\ partial d} * \ sigma d \ Bigr | _ {\ substack {V_ {CE} = 5V \\ D_E = 0.34}}) - (\ frac {\ partial \ frac {\ dot V_C * d} {R}} {\ partial \ dot V_c} * \ sigma V_C \ Bigr | _ {\ substack {V_ {CE} = 5V \\ D_E = 0.34} } + \ frac {\ partial \ frac {\ dot V_C * d} {R}} {\ partial d} * \ sigma d \ Bigr | _ {\ substack {V_ {CE} = 5V \\ D_E = 0.34}} ) + (\ frac {\ partial \ frac {V_C * d} {R}} {\ partial \ dot V_c} * \ sigma V_C \ Bigr | _ {\ substack {V_ {CE} = 5V \\ D_E = 0.34}} + \ frac {\ partial \ frac {V_C * d} {R}} {\ partial d} * \ sigma d \ Bigr | _ {\ substack {V_ {CE} = 5V \\ D_E = 0.34}} = 0 \ $