PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

Alternating Current Analysis 247

and

 2 2

2

2

1

2

1

2

1

2

114

R 


RC RC C R R

C

L



















 

The BW is then given by

BW

RC Q

R

P








21

1

2

^1







R.3.54 A parallel RLC circuit presents the following characteristics at resonance:

a. ZT is at a maximum.

b. ZT = R, since the angle between I and V is zero.

c. Current is at a minimum.

d. The effective power is at its minimum.

R.3.55 Practical resonant circuits are constructed by placing a capacitor and an inductor

in parallel as shown in Figure 3.20, where R 1 and R 2 are the internal resistances

of L and C, respectively. Recall that the condition at resonance is that the complex

admittance Y is a real number, then

X

RX

X

RX

C

C

L

2 L

2 2

1


^22 

and the resonant frequency is given by

R

LC

RLC

RLC





1 12

2

2

()

()

Since ωR is real, R^21 > L/C and R^22 > L/C.

R.3.56 Recall that the process used in the mesh or loop equations techniques was presented

and discussed in Chapter 2, for the purely resistive DC case. The theory developed

L C

R 1 R 2

Y

FIGURE 3.20

Network of R.3.55.