Express the following frequency ranges in decades. a. 0.1 Hz to 100 Hz b. 0.1 rad/s to 100 rad/s c....

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Express the following frequency ranges in decades. a. 0.1 Hz to 100 Hz b. 0.1 rad/s to 100 rad/s c. 10 Hz to 100 KHz d. 2.5 Hz to 15 KHz 4. What are the lowest and highest frequencies that can be plotted on the Wowing frequency response plots? a. Bode plot b. Polar plot 5. Express the following quantities in decibels. a. 100 b. 120 c. 0.25 d XXXXXXXXXXe XXXXXXXXXXExpress the following decibel values as standard numbers. a. 6 dB b. —6 dB c. 20 dB d. —40 dB e. 120 dB
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Robert · Accepted Answer

7.(a) Sol.
 ( )  
  
   
 
Putting     , we get 
 (  )  
  
    
 
Gain of this system is given by, 
      | (  )|       
  
√    
 
              √     
At      gain is  
         √
At      , gain is (since   >>1)  
         √
Magnitude at     is given as,
√    
  
  
√ 
       
And at       (    ), magnitude is
√    

√  
 
  
   
     
Phase angle at     is given by, 
      ( )        ( )        
Phase angle at       is (      (  )  
  
  
) 
       (simple pole at origin) 
(b). Sol 
 ( )        
    (  )         
Gain of this system is given by, 
      | (  )|             
At       gain is
At      , gain is
Magnitude at     is given as,
And at       magnitude is
Phase angle at               is,
(Simple zero at origin) 
© Sol.
 ( )  
 
        
 
Putting     , we get 
 (  )  
  
         
 
Gain of this system is given by, 
      | (  )|       
 
√(     )    
 
             √(     )     
At      gain is  
       √
At      , gain is  
               √(       )
Magnitude at     is given as,
√(     )    

√  
        
And at      , magnitude is
√(     )    

      
      
Phase angle at     is given by, 
     ( )       (
  
     
) 
      ( )       (
 
 
)
= 32.47    
Phase angle at       is  
      (   )       (
   
        
)
         (        )
(d). Sol.  
 ( )  
(    )
 (   )(   )
 
    (  )  
(     )
  (    )(    )
 
Gain of this system is given by,

Express the following frequency ranges in decades. a. 0.1 Hz to 100 Hz b. 0.1 rad/s to 100 rad/s c. 10 Hz to 100 KHz d. 2.5 Hz to 15 KHz 4. What are the lowest and highest frequencies that can be...

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