Tribhuvan University • IOE

Official ENEE 154 Syllabus

Electrical Circuits and Machines (ENEE 154) — Complete curriculum, lecture breakdown, laboratory modules, and evaluation criteria for Bachelor in Computer Engineering (BCT) and Electronics, Information & Communication Engineering (BEI).

Year / Part
Year I / Part II
Teaching Hours
L: 4 | T: 1 | P: 1.5
Final Theory Exam
60 Marks (3 Hours)
Pass Marks
24 Marks

Course Objectives

To develop a comprehensive understanding of electric circuit theory and analysis techniques, alongside the operating principles, mathematical models, and operational characteristics of electric machinery including transformers, DC machines, and AC machines.

Detailed Course Content (60 Hours)

Chapter 1 • 7 Hours • 7 Marks

Transients in Electric Circuit

  • 1.1 Characteristics of various network elements: Linear, non-linear, bilateral, unilateral, passive (R, L, C), and active elements.
  • 1.2 Nodal analysis with dependent and independent sources: Application of KCL, supernode formation when ideal voltage sources exist between non-reference nodes.
  • 1.3 Mesh analysis with dependent and independent sources: Application of KVL, supermesh formation when current sources are shared between meshes.
  • 1.4 Application of matrix method in network analysis: Setting up \([Z][I] = [V]\) and \([Y][V] = [I]\) and solving via Cramer's rule / matrix inversion.
  • 1.5 Procedure of evaluating initial conditions: Behavior of circuit elements at \(t = 0^-\), \(t = 0^+\), and \(t = \infty\). Invariance of inductor current \(i_L(0^+) = i_L(0^-)\) and capacitor voltage \(v_C(0^+) = v_C(0^-)\).
  • 1.6 Initial values of derivatives: Determining \(\frac{di_L}{dt}(0^+)\), \(\frac{dv_C}{dt}(0^+)\), and higher-order derivatives \(\frac{d^2 i}{dt^2}(0^+)\).
  • 1.7 Initial condition in the case of R-L-C network: Systematic multi-loop transient analysis at the switching instant.
Chapter 2 • 10 Hours • 10 Marks

Transient Analysis R-L-C Circuit by Classical Method

  • 2.1 Introduction: Concept of transient vs steady-state responses in dynamic networks.
  • 2.2 First order differential equation with constant coefficient: Form \(a_1 \frac{dx}{dt} + a_0 x = f(t)\). Time constant \(\tau = L/R\) or \(\tau = RC\).
  • 2.3 Higher order homogeneous and non-homogeneous differential equation with constant coefficient: Complementary function \(x_c(t)\) and characteristic equation roots.
  • 2.4 Particular integral by method of undetermined coefficient: Determination of steady-state response \(x_p(t)\) for step, exponential, and sinusoidal forcings.
  • 2.5 Response of R-L and R-C circuits:
    • 2.5.1 DC excitation (step response)
    • 2.5.2 Exponential excitation \(v(t) = V_0 e^{-at}\)
    • 2.5.3 Sinusoidal excitation \(v(t) = V_m \sin(\omega t + \theta)\)
  • 2.6 Response of Series R-L-C circuits: Overdamped (\(\zeta > 1\)), critically damped (\(\zeta = 1\)), and underdamped (\(\zeta < 1\)) responses with:
    • 2.6.1 DC excitation
    • 2.6.2 Exponential excitation
    • 2.6.3 Sinusoidal excitation
  • 2.7 Response of Parallel R-L-C circuits:
    • 2.7.1 DC excitation
    • 2.7.2 Exponential excitation
Chapter 3 • 7 Hours • 7 Marks

Transient Analysis Using Laplace Transform

  • 3.1 Introduction: Definition of unilateral Laplace transform, operational properties (linearity, differentiation, integration, shifting theorems).
  • s-Domain Transformed Circuit Models: Resistor \(R\), Inductor \(sL\) with initial condition series voltage generator \(L i_L(0^-)\) or parallel current generator \(i_L(0^-)/s\), Capacitor \(1/sC\) with initial voltage generator \(v_C(0^-)/s\) or parallel current generator \(C v_C(0^-)\).
  • 3.2 Response of R-L and R-C circuits:
    • 3.2.1 DC excitation
    • 3.2.2 Exponential excitation
    • 3.2.3 Sinusoidal excitation
  • 3.3 Response of series R-L-C circuits with:
    • 3.3.1 DC excitation
    • 3.3.2 Exponential excitation
    • 3.3.3 Sinusoidal excitation
  • 3.4 Response of parallel R-L-C circuits with:
    • 3.4.1 DC excitation
    • 3.4.2 Exponential excitation
Chapter 4 • 8 Hours • 8 Marks

Network Transfer Function and Frequency Response

  • 4.1 Concept of complex frequency: \(s = \sigma + j\omega\), physical interpretation of real attenuation \(\sigma\) and oscillation frequency \(\omega\).
  • 4.2 Transfer functions of two-port networks: Driving-point impedance \(Z_{in}(s)\), admittance \(Y_{in}(s)\), voltage transfer ratio \(G_{21}(s) = V_2(s)/V_1(s)\), current transfer ratio \(\alpha_{21}(s) = I_2(s)/I_1(s)\), transfer impedance \(Z_{21}(s)\).
  • 4.3 Poles and zeros of networks: Definition, s-plane mapping, pole-zero constellation, stability implications (poles must lie in left half of s-plane for BIBO stability).
  • 4.4 Magnitude and phase response: Graphical evaluation from pole-zero vectors along \(s = j\omega\).
  • 4.5 Bode diagrams: Asymptotic magnitude plot (dB vs \(\log \omega\)) and phase plot (degrees vs \(\log \omega\)). Standard factors: constant \(K\), origin poles/zeros \((s)^{\pm n}\), simple poles/zeros \((1 + s/\omega_c)^{\pm 1}\), quadratic poles/zeros \([1 + 2\zeta(s/\omega_n) + (s/\omega_n)^2]^{\pm 1}\).
  • 4.6 Bandwidth, high-Q and low-Q circuits: Series and parallel resonance, half-power frequencies \(\omega_1, \omega_2\), bandwidth \(BW = \omega_2 - \omega_1 = \omega_0 / Q\). Differences between high-Q (\(Q \ge 10\)) and low-Q approximations.
  • 4.7 Basic concept of filters: Ideal vs practical frequency characteristics of High-pass (HPF), Low-pass (LPF), Band-stop (BSF/notch), and Band-pass (BPF) filters.
Chapter 5 • 8 Hours • 8 Marks

Two-Port Parameters of Network

  • 5.1 Definitions of two-port networks: Terminal pairs, port condition (\(I_1 = I_1', I_2 = I_2'\)).
  • 5.2 Parameters of two-port networks:
    • 5.2.1 Open circuit impedance parameters (\(Z\)-parameters): \(V_1 = Z_{11} I_1 + Z_{12} I_2\), \(V_2 = Z_{21} I_1 + Z_{22} I_2\)
    • 5.2.2 Short circuit admittance parameters (\(Y\)-parameters): \(I_1 = Y_{11} V_1 + Y_{12} V_2\), \(I_2 = Y_{21} V_1 + Y_{22} V_2\)
    • 5.2.3 Transmission line parameters (\(T\) or \(ABCD\)-parameters): \(V_1 = A V_2 - B I_2\), \(I_1 = C V_2 - D I_2\)
    • 5.2.4 Inverse transmission line parameters (\(T'\) or \(A'B'C'D'\)-parameters)
    • 5.2.5 Hybrid parameters (\(h\)-parameters): \(V_1 = h_{11} I_1 + h_{12} V_2\), \(I_2 = h_{21} I_1 + h_{22} V_2\)
    • 5.2.6 Inverse hybrid parameters (\(g\)-parameters)
  • 5.3 Relationship and transformation between sets of parameters: Inter-conversion formulas (e.g. \(h\) in terms of \(Z\), \(Z\) in terms of \(ABCD\)).
  • 5.4 Interconnection of two-port networks: Series-series (\([Z] = [Z_A] + [Z_B]\)), parallel-parallel (\([Y] = [Y_A] + [Y_B]\)), and cascade connection (\([T] = [T_A] \times [T_B]\)). Validity checks (Brune's test).
  • 5.5 Condition for reciprocity and symmetry: Reciprocity: \(Z_{12} = Z_{21}\), \(Y_{12} = Y_{21}\), \(AD - BC = 1\), \(h_{12} = -h_{21}\). Symmetry: \(Z_{11} = Z_{22}\), \(Y_{11} = Y_{22}\), \(A = D\), \(\Delta h = 1\).
Chapter 6 • 3 Hours • 3 Marks

Magnetic Circuit and Induction

  • 6.1 Magnetic circuit and its types: MMF (\(\mathcal{F} = N I\)), magnetic flux (\(\Phi\)), reluctance (\(\mathcal{R} = l / (\mu_0 \mu_r A)\)), permeance (\(\mathcal{P} = 1/\mathcal{R}\)). Series and parallel magnetic circuits with composite cores and air gaps. Leakage flux and fringing effect.
  • 6.2 B-H relationship and hysteresis with DC excitation: Magnetization curve, magnetic saturation, retentivity (residual magnetism), coercivity (coercive force).
  • 6.3 Hysteresis with AC excitation: Dynamic cycling through the B-H loop under alternating current excitation.
  • 6.4 Hysteresis loss and Eddy current loss: Steinmetz's empirical formula \(P_h = \eta B_{max}^{1.6} f V\). Eddy current loss \(P_e = K_e B_{max}^2 f^2 t^2 V\). Reduction methods: silicon steel alloy and thin core laminations insulated by varnish.
  • 6.5 Faraday’s law of electromagnetic induction: Statically induced EMF (self-induced \(e = -L \frac{di}{dt}\) and mutually induced \(e = -M \frac{di_1}{dt}\)) vs Dynamically induced EMF (\(e = B l v \sin\theta\)). Fleming's right-hand rule and Lenz's law.
  • 6.6 Force on current-carrying conductor: \(F = B I l \sin\theta\), direction given by Fleming's left-hand rule.
Chapter 7 • 6 Hours • 6 Marks

Transformers

  • 7.1 Construction, operating principle and EMF equation of single-phase transformer: Core-type vs shell-type construction. Derivation of EMF equation: \(E_1 = 4.44 f N_1 \Phi_m\), \(E_2 = 4.44 f N_2 \Phi_m\). Features of ideal transformer. Constancy of main magnetic core flux under varying load currents.
  • 7.2 No-load and load operation: No-load current \(I_0\) components (working component \(I_w\) and magnetizing component \(I_\mu\)). Phasor diagrams for lagging, unity, and leading power factor loads.
  • 7.3 Equivalent circuit diagram of transformer: Exact and approximate equivalent circuits referred to primary and secondary windings. Impedance transformation ratio \(K = N_2 / N_1\), \(R_1' = R_1 / K^2\), \(R_2' = K^2 R_2\).
  • 7.4 Transformer testing (Open circuit and Short circuit):
    • Open Circuit (OC) test: Conducted on LV side at rated voltage to determine core losses (\(P_i\)), shunt branch parameters (\(R_0, X_0\)).
    • Short Circuit (SC) test: Conducted on HV side at rated current to determine full-load copper losses (\(P_{cu,FL}\)), series equivalent parameters (\(R_{eq}, X_{eq}\)).
  • 7.5 Voltage regulation, losses, efficiency and maximum-efficiency condition: Definition of voltage regulation \(\%VR = \frac{V_0 - V_L}{V_0} \times 100\). Efficiency expression \(\eta = \frac{x S \cos\phi}{x S \cos\phi + P_i + x^2 P_{cu,FL}}\). Derivation of condition for maximum efficiency (\(x^2 P_{cu,FL} = P_i\)). All-day efficiency for distribution transformers.
  • 7.6 Auto-transformer and Isolation transformer: Operating principle of single-winding autotransformer, copper saving formula \(\frac{\text{Weight of Cu in Auto}}{\text{Weight of Cu in 2-Wdg}} = (1 - K)\), power transferred inductively vs conductively. Functions and applications of isolation transformers.
Chapter 8 • 5 Hours • 5 Marks

DC Machine

  • 8.1 Constructional details of DC machine: Magnetic frame (yoke), pole core and shoes, field coils, armature core and windings (lap vs wave), commutator segments, and carbon brushes.
  • 8.2 DC generator operating principle and EMF equation: Elementary generator action. Derivation of EMF equation: \(E_g = \frac{P \Phi Z N}{60 A}\), where \(A = P\) for lap winding, \(A = 2\) for wave winding.
  • 8.3 DC motor operating principle and torque equation: Elementary motor action. Derivation of electromagnetic torque: \(T = \frac{P \Phi Z I_a}{2\pi A} \propto \Phi I_a\).
  • 8.4 Types of DC machine: Separately excited, Shunt, Series, and Compound (Cumulative & Differential) machines with schematic circuit diagrams and terminal voltage-current equations.
  • 8.5 Back EMF and its role in DC motor: \(E_b = V - I_a R_a\). Role as self-regulating governor of armature current and power developer (\(P_m = E_b I_a\)).
  • 8.6 Performance characteristics of DC motor: Torque vs Armature current (\(T\) vs \(I_a\)), Speed vs Armature current (\(N\) vs \(I_a\)), and Speed vs Torque (\(N\) vs \(T\)) characteristics for shunt, series, and compound motors.
  • 8.7 Starting of DC motor using 3-point starter: Why direct starting causes dangerous inrush currents (\(I_{start} = V/R_a\)). Operation of 3-point starter with No-Volt Coil (NVC) and Overload Release (OLR) coil.
  • 8.8 Speed control of DC motor: Derived from \(N = \frac{V - I_a R_a}{k \Phi}\).
    • Armature resistance control: Variable resistor in series with armature (controls speed below base speed).
    • Field flux control: Field rheostat in series with shunt winding (controls speed above base speed).
  • 8.9 Losses and efficiency: Copper losses (\(I_a^2 R_a, I_{sh}^2 R_{sh}\)), magnetic core losses (hysteresis + eddy current), mechanical losses (friction + windage). Commercial, electrical, and mechanical efficiency definitions.
Chapter 9 • 6 Hours • 6 Marks

AC Motor

  • 9.1 Construction, production of rotating magnetic field and operating principle of three-phase induction motor: Stator, squirrel-cage vs slip-ring (wound) rotor. Mathematical proof showing that a 3-phase balanced supply produces a magnetic field of constant magnitude \(1.5 \Phi_m\) rotating at synchronous speed \(N_s = 120f/P\). Slip definition \(s = (N_s - N)/N_s\). Why rotor speed can never equal synchronous speed.
  • 9.2 Torque equation of three-phase induction motor: Standstill torque \(T_{st} \propto \frac{E_2^2 R_2}{R_2^2 + X_2^2}\) and running torque \(T \propto \frac{s E_2^2 R_2}{R_2^2 + (s X_2)^2}\).
  • 9.3 Torque-slip characteristics: Low slip region (stable, linear), high slip region (unstable). Derivation of maximum breakdown torque \(T_{max} = \frac{k E_2^2}{2 X_2}\) and slip at maximum torque \(s_{mT} = R_2 / X_2\). Effect of adding external rotor resistance in slip-ring motor on starting torque and maximum torque.
  • 9.4 Single-phase induction motor: Non-self-starting nature explained by pulsating stator field.
  • 9.5 Double revolving field theory: Resolution of pulsating field into forward rotating field \(\Phi_f = \frac{1}{2}\Phi_m\) (slip \(s\)) and backward rotating field \(\Phi_b = \frac{1}{2}\Phi_m\) (slip \(2-s\)). Resultant torque at standstill is zero.
  • 9.6 Starting of single-phase induction motor: Auxiliary winding with phase-split mechanism:
    • Capacitor-start induction motor (centrifugal switch disconnects capacitor at 75% speed)
    • Capacitor-run / permanent-split capacitor motor (higher running power factor and quiet operation)
    • Shaded-pole motor (copper shading band delays flux, producing weak rotating field for low-power fans)
  • 9.7 Introduction to special AC/DC motors:
    • Permanent Magnet Brushless DC (BLDC) motor (electronic commutation, Hall-effect sensors)
    • Hysteresis motor (smooth rotor, hysteresis loss torque, perfectly constant synchronous speed)
    • Stepper motor (variable reluctance and permanent magnet types, step angle \(\beta = \frac{N_s - N_r}{N_s N_r} \times 360^\circ\))
    • Servo motor (AC and DC servomotors for closed-loop position control)
    • Universal motor (series motor operating on both AC and DC, high speed portable power tools)

Laboratory Experiments (Practical: 22.5 Hours)

  1. Transient response in first order passive circuit: Measure step and impulse response of series RL and RC circuits using oscilloscope; relate time response to analytical time constants \(\tau = L/R\) and \(\tau = RC\).
  2. Transient response in second order passive circuit: Measure step response of series and parallel RLC circuits on DSO; observe underdamped oscillation, critical damping, and overdamped exponential decay; correlate damping ratio \(\zeta\) with pole-zero configuration.
  3. Two port network: Calculate, measure, and verify \(ABCD\) parameters of resistive T and \(\pi\) networks; determine equivalent parameters of parallel-connected two-port networks.
  4. Two winding transformers: Measure amplitude and phase frequency response and plot Bode diagram for RLC circuits; perform Open Circuit (OC) and Short Circuit (SC) tests on a single-phase transformer to determine core loss, copper loss, equivalent resistance \(R_{eq}\), equivalent reactance \(X_{eq}\), and efficiency.
  5. DC motor: Speed control of DC shunt motor by (a) armature resistance control method and (b) field flux control method; observe the effect of mechanical loading on speed, armature current \(I_a\), and shunt field current \(I_{sh}\).
  6. Single phase AC motors: Study the effect of starting and running capacitors on torque and vibration of a single-phase induction motor; demonstrate reversing the direction of rotation by interchanging starting winding connections.

Standard Reference Books

  • Van Valkenburg, M. E. (2019). Network Analysis. Pearson Education.
  • Hayt, W. H., Kemmerly, J. E., Phillips, J. D., & Durbin, S. M. (2019). Engineering Circuit Analysis. McGraw-Hill Education.
  • Nagrath, I. J., & Kothari, D. P. (2017). Electric Machines. McGraw-Hill Education.
  • Fitzgerald, A. E., Kingsley, C., & Umans, S. D. (2017). Electric Machinery. McGraw-Hill Education.
  • Soni, K. M. (2013). Circuits and Systems. S. K. Kataria & Sons.
  • Sahdev, S. K. (2018). Electrical Machines. Cambridge University Press.