Thus becoming equal short circuit
772 

s t e a d y  

b) 
You may use either linear or loglog coordinates, but it is recommended that you
Z  R  C 



Z  R  C2  L  vS  +  R1  +  i2  +  R2  + 

L1M  L2M  +  

Z  R  v1 


v1  v2  
  
        
C1 



a)  Determine an expression for the sinusoidal steadystate transfer function V2/Vs.  
b)  In the tightcoupling limit, k → 1, the two natural frequencies are far apart. (See Problem 12.3 in the previous chapter.) For this specific case, sketch the magnitude 
and angle of the transfer function on loglog scales.
p r o b l e m 13.3  

H( jω) =Y( jω) X( jω)  =  105(10 + jω)(1000 + jω) (1 + jω)(100 + jω)(10000 + jω) 

a)  Plot the magnitude of H( jω) in decibels versus the logarithm of frequency, labeling 
c) For what values of ω does the magnitude of H( jω) equal 0db? What is the relationship between the magnitudes of X( jω) and Y( jω) at these frequencies?
d) List the frequencies at which the phase of H( jω) equals −45 degrees.
b)  13.8 Summary 

773  

R 


Vo  +  
R1  
L1  


c)  Find a value of L so that the response at high frequencies is equal to response at DC.  
d)  Plot H( jω) (magnitude and phase) versus. log ω for the values of R and L found 
previously.
I1  M  I2  I1  L2M  I2  +  

switch  
+ 

+  

V2  Door bell 
M  
V1  V2  
      


bell transformer  

a) 

c) An important safety issue in such circuits is the prevention of fire in the event that the doorbell should accidently stick with its contact closed, thus becoming equal to a short circuit. This can be accomplished by adjusting the value of k. Find the value