0195136047.pdf

38 CIRCUIT CONCEPTS

−

+

N 1

Ideal transformer

(a)

N 2

v 1

i 1 i 2

v 2

+

−

+

−

RL

−

+

N 1 N 2

(b)

v 1

i 1 i 2

+

−

−

+

(c)

v 1

i 1

+

−

RL = RL

N 1

N 2

2

()

RL = RL

N 1

N 2

2

()= a

(^2) RL
′
′
Figure 1.2.13Equivalent circuits viewed from source
terminals when the transformer is ideal.
EXAMPLE 1.2.6
Consider a source of voltagev(t)= 10
√
2 sin 2tV, with an internal resistance of 1800.A
transformer that can be considered ideal is used to couple a 50-resistive load to the source.
(a) Determine the primary to secondary turns ratio of the transformer required to ensure
maximum power transfer by matching the load and source resistances.
(b) Find the average power delivered to the load.
Solution
By considering a constant voltage source (with a given internal resistanceRS) connected to a
variable-load resistanceRL, as shown in Figure E1.2.6(a), for a value ofRLequal toRSgiven
by Equation (1.2.13), the maximum power transfer to the load resistance would occur when the
load resistance is matched with the source resistance.
(a) For maximum power transfer to the load,R′L(i.e.,RLreferred to the primary side of the
transformer) should be equal toRS, which is given to be 1800. Hence,
R′L=a^2 RL= 50 a^2 = 1800 or a^2 = 36 ,ora= 6.
ThusN 1 /N 2 =6 [see Figure E1.2.6(b)].