School of Engineering & Information Technology
UNSW Canberra
ZEIT 1206 Design of Electronic Circuits 1
Tutorial Week 9: Sinusoidal Steady-State Circuit Analysis; Source
Transformations, Nodal & Mesh Analysis
Friday 24th September 2021
1. Find I0 in the circuit of Fig. 1 using the source transformation method.
2Ω j1 Ω
I0
4Ω
1Ω
12∠90 Ao j5 Ω
−j3 Ω
−j2 Ω
Figure 1: Circuit for Q1.
2. Obtain the Norton equivalent of the circuit shown in Fig. 2 at terminals a − b.
5 µF
a
4 cos(200t + 30o ) A 10 H 2 kΩ
b
Figure 2: Circuit for Q2.
,3. Figure 3 illustrates a circuit with a sinusoidal voltage source,
vs (t) = 20 cos(1000t + 10◦ ).
Using the node-voltage method, calculate the phasor of the output voltage vo .
R1 20 Ω R2 70 Ω
+
L 80 mH R3 30 Ω
+
vs (t) − R4 40 Ω vo
C1 10 µF C2 30 µF
−
Figure 3: RLC circuit with a sinusoidal voltage source.
4. Use mesh analysis to find v0 in the circuit in Fig. 4. Here, vs1 = 120 cos (100t + 90o ) V, vs2 = 80 cos (100t) V.
R1 20 Ω L3 200 mH
L2 400 mH
+ R2 10 Ω
+
vs1 (t) − L1 300 mH C1 50 µF vo
+
− − vs2 (t)
Figure 4: RLC circuit with a sinusoidal voltage source.
Quick answers
1. I0 = 10
−20+j40
10 A ≈ 9.863∠99.46o A
3 +j 3 +1−j2
2. iN = 5.6569 cos(200t + 75o ) A, ZN = 1 kΩ.
◦
3. Vo = 2.6492 e−j42.53 V.
4. v0 (t) = 56.26 cos(100t + 33.93o ).
, School of Engineering & Information Technology
UNSW Canberra
ZEIT 1206 Design of Electronic Circuits 1
Tutorial Week 10: Transformers
Friday 1st October 2021
1. Figure 1 illustrates a transformer driving a load consisting of a resistor and a capacitor, excited by a
voltage source
vg (t) = 560 cos(2 × 105 t) V
with a source resistance of 150 Ω.
[Based on Problem 9.77, Nilsson & Riedel Electric Circuits, Pearson 2015]
(a) Derive the (algebraic) mesh current equations
√ for I1 and I2 (use the phasor representations). Note
that the mutual inductance is M = k L1 L2 where k is a coupling coefficient.
(b) Find I1 and I2 for k = 0.2.
Rs 150Ω R1 50Ω R2 100Ω R3 200Ω
k
+
+
vg − L1 1 mH L2 4 mH vL C 12.5 nF
−
i1 i2
Figure 1: Linear transformer connecting a voltage source to a load.
2. Figure 2 shows an ideal transformer with a winding ratio of N2 = 4N1 . This transformer drives a load
with a resistor and a capacitor. Find i1 and i2 .
−j40 Ω
2Ω
i1 1:4 i2
+ +
+
30 − j10 V − V1 V2 8Ω
- -
Figure 2: Ideal transformer connecting a voltage source to a load.
Quick answers
1. (a) Vg = (R
s + R1 + jωL1 ) I1 − 1jωM
I2 .
jωM I1 = R2 + R3 + j ωL2 − ωC I2 .
(b) I1 = 1.991∠ − 42.42o A, I2 = 0.3186∠ − 5.55o A
2. I1 = 8 + j4 A, I2 = 2 + j A
UNSW Canberra
ZEIT 1206 Design of Electronic Circuits 1
Tutorial Week 9: Sinusoidal Steady-State Circuit Analysis; Source
Transformations, Nodal & Mesh Analysis
Friday 24th September 2021
1. Find I0 in the circuit of Fig. 1 using the source transformation method.
2Ω j1 Ω
I0
4Ω
1Ω
12∠90 Ao j5 Ω
−j3 Ω
−j2 Ω
Figure 1: Circuit for Q1.
2. Obtain the Norton equivalent of the circuit shown in Fig. 2 at terminals a − b.
5 µF
a
4 cos(200t + 30o ) A 10 H 2 kΩ
b
Figure 2: Circuit for Q2.
,3. Figure 3 illustrates a circuit with a sinusoidal voltage source,
vs (t) = 20 cos(1000t + 10◦ ).
Using the node-voltage method, calculate the phasor of the output voltage vo .
R1 20 Ω R2 70 Ω
+
L 80 mH R3 30 Ω
+
vs (t) − R4 40 Ω vo
C1 10 µF C2 30 µF
−
Figure 3: RLC circuit with a sinusoidal voltage source.
4. Use mesh analysis to find v0 in the circuit in Fig. 4. Here, vs1 = 120 cos (100t + 90o ) V, vs2 = 80 cos (100t) V.
R1 20 Ω L3 200 mH
L2 400 mH
+ R2 10 Ω
+
vs1 (t) − L1 300 mH C1 50 µF vo
+
− − vs2 (t)
Figure 4: RLC circuit with a sinusoidal voltage source.
Quick answers
1. I0 = 10
−20+j40
10 A ≈ 9.863∠99.46o A
3 +j 3 +1−j2
2. iN = 5.6569 cos(200t + 75o ) A, ZN = 1 kΩ.
◦
3. Vo = 2.6492 e−j42.53 V.
4. v0 (t) = 56.26 cos(100t + 33.93o ).
, School of Engineering & Information Technology
UNSW Canberra
ZEIT 1206 Design of Electronic Circuits 1
Tutorial Week 10: Transformers
Friday 1st October 2021
1. Figure 1 illustrates a transformer driving a load consisting of a resistor and a capacitor, excited by a
voltage source
vg (t) = 560 cos(2 × 105 t) V
with a source resistance of 150 Ω.
[Based on Problem 9.77, Nilsson & Riedel Electric Circuits, Pearson 2015]
(a) Derive the (algebraic) mesh current equations
√ for I1 and I2 (use the phasor representations). Note
that the mutual inductance is M = k L1 L2 where k is a coupling coefficient.
(b) Find I1 and I2 for k = 0.2.
Rs 150Ω R1 50Ω R2 100Ω R3 200Ω
k
+
+
vg − L1 1 mH L2 4 mH vL C 12.5 nF
−
i1 i2
Figure 1: Linear transformer connecting a voltage source to a load.
2. Figure 2 shows an ideal transformer with a winding ratio of N2 = 4N1 . This transformer drives a load
with a resistor and a capacitor. Find i1 and i2 .
−j40 Ω
2Ω
i1 1:4 i2
+ +
+
30 − j10 V − V1 V2 8Ω
- -
Figure 2: Ideal transformer connecting a voltage source to a load.
Quick answers
1. (a) Vg = (R
s + R1 + jωL1 ) I1 − 1jωM
I2 .
jωM I1 = R2 + R3 + j ωL2 − ωC I2 .
(b) I1 = 1.991∠ − 42.42o A, I2 = 0.3186∠ − 5.55o A
2. I1 = 8 + j4 A, I2 = 2 + j A
