Two linear transformers are cascaded as shown in Fig. 13.101. Show that Z in = ω 2 R ( L a 2 + L a L b − M a 2 ) + j ω 3 ( L a 2 L b + L a L b 2 − L a M b 2 − L b M a 2 ) ω 2 ( L a L b + L b 2 − M b 2 ) − j ω R ( L a + L b )
Two linear transformers are cascaded as shown in Fig. 13.101. Show that Z in = ω 2 R ( L a 2 + L a L b − M a 2 ) + j ω 3 ( L a 2 L b + L a L b 2 − L a M b 2 − L b M a 2 ) ω 2 ( L a L b + L b 2 − M b 2 ) − j ω R ( L a + L b )
Solution Summary: The author explains the input impedance expression for the cascaded linear transformers in Figure 13.101.
Two linear transformers are cascaded as shown in Fig. 13.101. Show that
Z
in
=
ω
2
R
(
L
a
2
+
L
a
L
b
−
M
a
2
)
+
j
ω
3
(
L
a
2
L
b
+
L
a
L
b
2
−
L
a
M
b
2
−
L
b
M
a
2
)
ω
2
(
L
a
L
b
+
L
b
2
−
M
b
2
)
−
j
ω
R
(
L
a
+
L
b
)
A linear transformer couples a load consisting of a 360 Ω resistor inseries with a 0.25 H inductor to a sinusoidal voltage source, as shown.The voltage source has an internal impedance of 184+j0 Ω and amaximum voltage of 245.20 V, and it is operating at 800 rad/s. Thetransformer parameters are R1=100 Ω, L1=0.5 H, R2=40 Ω,L2=0.125 H, and k=0.4. Calculate (a) the reflected impedance; (b) theprimary current; and (c) the secondary current
The diagram shown below is a typical tuning circuit. Considering this circuit comprises a transformer (with a coil ratio of 20:1 and an HV side voltage of 240V ), a capacitor of impedance -j20Ω, an inductor of impedance j40Ω, and a 50Ω resistor, determine:
the current supplied by the source
the impedance seen at the supply (HV side)
the power dissipated by the resistor
the operating power factor of the fitting
If the capacitor is now removed from the above circuit and is placed in parallel with the secondary of the transformer, redraw the circuit diagram and recalculate parts a. to d. in question (i).
Draw the phasor diagram for both series and parallel RLC circuits in parts (i) and (ii). Discuss the effects of changing the capacitor connection in parallel on the power factor of the circuit.
State the benefits of using the transformer in the above circuit. Explain the operating principle of the transformer with particular reference to electro-magnetic…
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