Banda passante di un sistema
Con³i¤e² iamo u® ³i³´em¡ ¤ © ¦ unº io®e ¤ © tras¦ ² ie® to G(s) . I¬ ¤ iagramm¡ ¤ © Bo¤e ¤e¬ mo¤ ulo ¤ © G(s) e' pa² ´ ©- colare® ´e µ ´ i¬e °erc¨e' e¶i¤enº i¡ ime¤ i¡ tae® ´e ± ua¬ ©
f²± µenºe ¶ ngono a p¬ i¦ ic¡ ´e e ± ua¬ © in¶ £e ¶ ngono ¡ ´-
´e® µ ´e da¬ ³i³´em¡.
I® pa² ´ icola², i® p² im¡ ¡ ° pros³imaº io®e, pos³iamo co®-
³i¤era² c¨e i® us£ © t¡ ¤e¬ ³i³´em¡ ar² i¶ino solo ¬e co po-
®e® ´ © f²± µenº ia¬ © ¤el¬'ing²sso c¨e ³© trovano al¬'i® ´erno
¤ell¡ co³id¤e ´ t¡ banda passante ¤ © G(s). µe³t¡ e' ¤e¦ i® © t¡
coe ¬'in³©ee ¤el¬e ° ulsaº io® © ω ta¬ © c¨e i¬ mo¤ ulo G(jω) no® s£en¤e ¤ © ° © µ' ¤ © 3 dB a¬ ¤ © s¯´ to ¤e¬ mas³imo mo¤ ulo.
I® ´er i® © ° © µ' forma¬ ©, ¤e ´ to M := sup
ω≥0
|G(jω)| dB
i¬ mas³imo mo¤ ulo ¤ © G(jω) (°er amo² ¤ © §®era¬ © t¡'
³© p²n¤e i¬ sup in¶ £e c¨e i¬ mas³imo c¨e p¯t²b¢ no®
e³i³´e²), l¡ band¡ passa® ´e ¤e¬ ³i³´em¡ ¤ © ¦ unº io®e ¤ ©
1
tras¦ ² ie® to G (c¨e in¤ ic¨ iamo co® B G ) e' d¡ t¡ d¡
B G = {ω : |G(jω)| dB ≥ M − 3}.
¬ caso ´ © ° ico, © ³i³´e © ¡ c¡ ´en¡ c¨ © us¡ sono ¤ © ´ © po passa-basso , os³i¡ i¬ mas³imo mo¤ ulo e' rag§ © u® to i®
co® ´ i® u¡ £ i¯ ' all¡ f²± µenz¡ ® ull¡. ² ta® to M = |G(0)| dB e ³ , coe ³°esso acca¤e, i¬ ¤ iagramm¡ ¤ © Bo¤e ¤e¬ mo¤ ulo
¤ © G e' ³ p² ¤ec²s£e® ´e, l¡ band¡ passa® ´e e' d¡ t¡
dal¬'i® ´ervallo
B G = [0, B max ]
do¶ B max , ¤e ´ t¡ pulsazione di taglio , e' i¬ valo² ¤ell¡
° ulsaº io®e ta¬e c¨e
|G(jB max )| dB = |G(0)| dB − 3.
ualc¨e vo¬ t¡, co® ¬eg§ro a¢uso ¤ © n¯taº io®e, ³© ¤ i£e c¨e l¡
band¡ passa® ´e ¤ © u® ³i³´em¡ pass¡-basso e' B max in¶ £e
c¨e ¬'i® ´ervallo [0, B max ] .
L¡ ¦ i§ ur¡ ³ § µe® ´e r¡ ° p²³ ® t¡ l¡ band¡ passa® ´e ¤ © u®
2
³i³´em¡ pass¡-basso.
Bmax 15
16 17 18 19 20 21
Magnitude (dB)
Bode Diagram
Frequency (rad/s)
