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# Thus becoming equal short circuit     772

C H A P T E R

s t e a d y
b)

You may use either linear or log-log coordinates, but it is recommended that you

Z R C

learn to use both kinds of axes.

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

i1

L1-M L2-M +
Z R v1

v2

v1 v2
-
- - - -
C1

L1 = 2.5 H, L2 = 0.025 H, M = kL1L2 where k < 1, R1 = 1 k, R2 = 10 .

a) Determine an expression for the sinusoidal steady-state transfer function V2/Vs.
b) In the tight-coupling 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 log-log scales.

p r o b l e m 13.3
H( ) =Y( ) X( ) = 105(10 + )(1000 + )
(1 + )(100 + )(10000 + )
a) Plot the magnitude of H( ) in decibels versus the logarithm of frequency, labeling

c) For what values of ω does the magnitude of H( ) equal 0db? What is the relationship between the magnitudes of X( ) and Y( ) at these frequencies?

d) List the frequencies at which the phase of H( ) equals −45 degrees.

b) 13.8 Summary

T H I R T E E N

773
R

L

Vo +
-
R1
L1

Find R so that the DC gain is 1/10.

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

previously.

I1 M I2
I1
L2-M I2 +
switch
+

+

+

+
-

V2 Door
bell
M
V1 V2
-
-
-

Bell transformer

bell transformer

120 V AC, 60 Hz

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

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