Thus becoming equal short circuit

772	C H A P T E R				s t e a d y
772	C H A P T E R		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	C

Z	C2	L	+	+	+	+	+
Z		R		v1	v2	+	+
						v1	v2
			-			v1	v2
				-	-	-	-
	C1			-	-	-	-

	L1 = 2.5 H, L2 = 0.025 H, M = k√L1L2 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( 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
	R		L
	Vo	+ -	R1
			L1
			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( jω) (magnitude and phase) versus. log ω for the values of R and L found

previously.

I1		M	I2			I1		+
I1		M	I2	switch		I1
+				+		+
+ -				V2	Door bell	+	M
+ -				V2	Door bell	V1	M	V2
-						-		-
	Bell transformer
	Bell transformer						bell transformer
120 V AC, 60 Hz							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