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W(jω), W(p) p jω. (ω) φ(ω), :

 

W(jω) = (ω)∙(ω) = N(ω) + jM(ω). (1)

 

: (ω) , ;

φ(ω) , ;

N(ω) = (ω)∙cosφ(ω) ;

M(ω) = (ω)∙sinφ(ω) ;

ω , .

.

 

.

 

W(jω) = K/(1 + jωT) = = .

 

(ω) = ; φ(ω) = arctg(ωT);

 

N(ω) = K/[1 + (ω∙T)2]; M(ω) = K∙ ω∙T/[1 + (ω∙T)2]. (2)

 

φ(0) = 0o; (0) = K; N(0) = K; M(0) = 0;

 

φ(ω = 1/T) = 45o; (T) = K/√2; N(T) = K/2; M(T) = K/2;

 

φ(ω → ∞) = 90o; (∞) = N(∞) = M(∞) = 0.

 

.

 

W(jω) = K/jω = K∙e /ω;

 

(ω) = K/ω; φ(ω) = 90o;

 

N(ω) = 0; M(ω) = K/ω; (3)

 

φ(0) = 90o; (0) = ∞; N(0) = 0; M(0) = ∞;

 

φ(ω → ∞) = 90o; (∞) = N(∞) = M(∞) = 0.

 

.

 

W(jω) = K/[ (ω∙T)2 + j2ξ∙T∙ω + 1] = =

 

= = ;

 

(ω) = ; φ(ω) = arctg{2ξ∙T∙ω/[1 (ω∙T)2]};

 

N(ω) = K∙[1 (ω∙T)2]/{[1 (ω∙T)2]2 + 4(ξ∙T∙ω)2};

 

M(ω) = 2K∙ξ∙T∙ω/{[1 (ω∙T)2]2 + 4(ξ∙T∙ω)2}; (4)

φ(0) = 0o; (0) = K; N(0) = K; M(0) = 0;

 

φ(ω) = 1/T) = 90o; (T) = K/(2ξ); N(T) = 0; M(T) = K/(2ξ);

 

φ(ω → ∞) = 180o; (∞) = N(∞) = M(∞) = 0.

 

.

 

 

W(jω) = jK∙ω = K∙ω∙e ;

 

(ω) = K∙ω; φ(ω) = 90o;

 

N(ω) = 0; M(ω) = K∙ω; (5)

 

φ(0) = 90o; (0) = 0; N(0) = 0; M(0) = 0;

 

φ(ω → ∞) = 90o; (∞) = M(∞) = ∞; N(∞) = 0.

 

, :

- ;

.

L(ω) = 20lg[H(ω)] lg(ω). , L(ω). L(ω) (), . L(ω) = 20 , 10 .

φ(ω) lg(ω). , φ(ω) .

, 10 . (ω = 1) lg(1) = 0.

, (), , .

.

 

. (2) :

L(ω) = 20lg[H(ω)] = 20lg - 20lg . (6)

 

ω<ωc = 1/T, , ωc, L(ω) = 20lg. , 20lg.

ω>ωcL(ω) = 20lg - 20lg(ω∙). , 20 .

, ωc = 1/T.

 

 

. (3) :

L(ω) = 20lg[H(ω)] = 20lg - 20lgω. (7)

 

ω = 1 (7) L(ω) = 20lg, 20 ω = ωc = 1.

 

 

. (4) :

L(ω) = 20lg[H(ω)] = 20lgK 20lg . (8)

 

ω<ωc = 1/T, , ωc, L(ω) = 20lg, ω>ωc 4(ξ∙ω∙T)2. :

 

L(ω) = . (9)

 

(9) ω<ωc = 1/T, ωc , , ωc 40 .

 

. (5) :

L(ω) = 20lg[H(ω)] = 20lg + 20lgω. (10)

 

, 20lgK ωc = 1 20/.

 

, , .

. 1932 . . , , W(jω) (- 1; j0).

( ), ω = 0 N(0) = H(0) = K, . ω = ∞ .

( ), ω = 0 , W(jω) (jω)r, r . , r = 1 ω = 0 W(jω) , r = 2 , r = 3 .

 

 

. . , φ(ω) = - 180 : L(ω) = 20lg[H(ω)] < 0, .. , , , -180. , ω, L(ω) = 20lg[H(ω)] = 0, φ(ω) > - 180o.

, .. . h(ω) ψ(ω).

h(ω) ω, φ(ω) = - 180: h(ω) = - L(ω) , . .

ψ(ω) ω, : ψ(ω) = φ(ω) + 180 , ω, .

 

 

ψ(ω) ≥ 30, h(ω) ≥ 6 , .

 





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