--- title: "Double field revolving theory" subject: "Electric Machines II" chapter: 3 key: "semester_5/electric_machines_ii:double-field-revolving-theory" source: https://www.bctengineer.com/q/semester_5/electric_machines_ii/double-field-revolving-theory site: BCT Engineering --- # Double field revolving theory Electric Machines II · Chapter 3: Fractional Kilowatt Motors - Asked in: 2074 Chaitra, 6 marks; 2074 Asoj, 8 marks; 2073 Shrawan, 6 marks; 2069 Chaitra, 8 marks (asked 4 times) - Video: [IM31 Double Field Revolving Theory](https://www.youtube.com/watch?v=LQDBRhNO-9Y) — Lectures in Electrical Engineering - Answer checked by Claude Sonnet 5.5 on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_5/electric_machines_ii/double-field-revolving-theory - Whole chapter: https://www.bctengineer.com/md/semester_5/electric_machines_ii/chapter-3 ## Question State and explain the double field revolving theory of single phase induction motor with detailed diagram (and expressions). ## Short answer A pulsating field equals two constant-magnitude fields rotating oppositely at synchronous speed. At standstill torques cancel, so starting torque is zero. When running, forward torque dominates, giving net torque; motor not self-starting but runs if started. ## Answer **Double field revolving theory** states that a pulsating (alternating) magnetic field of maximum value $\phi_m$ can be replaced by **two fields, each of constant magnitude $\phi_m/2$, rotating in opposite directions at synchronous speed** $N_s = 120f/P$. #### Pulsating field resolved The single-phase stator winding produces a flux that only alternates along its axis: $$ \phi = \phi_m \cos\omega t $$ This is equal to the sum of two rotating phasors $\phi_f$ (forward) and $\phi_b$ (backward), each $\phi_m/2$, turning at $\omega$ in opposite directions: $$ \phi = \frac{\phi_m}{2}e^{j\omega t} + \frac{\phi_m}{2}e^{-j\omega t} = \phi_m\cos\omega t $$ ```text wt = 0 wt = 90 deg wt = 180 deg ^ ^ <-- --> v v | | phi_f phi_b | | sum = phi_m sum = 0 sum = -phi_m (both along (cancel) (both reversed) the axis) phi_f turns anticlockwise, phi_b clockwise ``` At every instant the vertical components add and the horizontal components cancel, so the resultant is the pulsating field. #### Torque at standstill - not self-starting - At standstill each rotating field induces equal rotor currents (slip = 1 for both), so the forward torque $T_f$ and backward torque $T_b$ are equal and opposite. - Net starting torque $T = T_f - T_b = 0$. Hence a single-phase induction motor is **not self-starting**. #### Torque when running If the rotor turns at speed $N$ in the forward direction: $$ s_f = \frac{N_s - N}{N_s} = s, \qquad s_b = \frac{N_s + N}{N_s} = 2 - s $$ Using the induction motor torque expression for each field: $$ T_f = \frac{K s R_2}{R_2^2 + (sX_2)^2}, \qquad T_b = -\frac{K (2-s) R_2}{R_2^2 + \left((2-s)X_2\right)^2} $$ $$ T = T_f + T_b $$ - Near normal speed $s$ is small, $2 - s \approx 2$: the backward rotor current sees a large frequency $(2-s)f$ and high reactance, so $T_b$ is small and $T_f \gg |T_b|$. The motor keeps running in whichever direction it was started. ```text T | _ | .-' \ forward run | .-' | (Tf > Tb) -Ns ---+----.'--------+---> speed | | .' 0 Ns \_|.' reverse run net T = 0 at N = 0 (mirror image) ``` The resultant torque-speed curve passes through **zero at standstill** and is symmetrical: positive in the forward direction, negative in the reverse direction. #### Equivalent circuit (based on DFRT) The rotor is split into two halves, one for each field: forward half with $0.5R_2'/s$ and $0.5X_2'$, backward half with $0.5R_2'/(2-s)$ and $0.5X_2'$, each with $0.5X_m$ in parallel, in series with the stator $R_1 + jX_1$. ```text o--R1--X1--+--0.5X2'--0.5R2'/s ------+ V | (0.5Xm parallel) forward +--0.5X2'--0.5R2'/(2-s)---+ | (0.5Xm parallel) backward o----------+-------------------------+ ``` Hence, an auxiliary means (split phase, capacitor, shaded pole) is needed only to start the motor; once running, the forward field dominates. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. According to the double field revolving theory, a pulsating field of maximum value phi_m is equivalent to: A. One rotating field of magnitude phi_m at synchronous speed B. Two fields of phi_m/2 rotating in opposite directions at synchronous speed C. Two fields of phi_m rotating in the same direction at Ns/2 D. Two fields of phi_m/2 rotating in opposite directions at half synchronous speed Answer: B. The pulsating flux phi_m cos(wt) is the sum of a forward and a backward phasor, each phi_m/2, turning at synchronous speed in opposite directions. (Key point: Statement of the theory) 2. Why is the net torque zero at standstill? A. The rotor current is zero at standstill B. The forward and backward fields have slip 1 and give equal and opposite torques C. The backward field is much weaker than the forward field D. The two fields rotate in the same direction and cancel the rotor flux Answer: B. At standstill both fields have slip 1, so T_f = T_b in magnitude but opposite in direction, and T = 0. (Key point: Why no starting torque) 3. If the rotor runs forward with slip s, the slip with respect to the backward field is: A. s B. 1 - s C. 2 - s D. s - 2 Answer: C. s_b = (Ns + N)/Ns = 2 - s, which is close to 2 near normal speed. (Key point: Slips when running) 4. Near normal speed, why is the backward torque T_b small compared with T_f? A. The backward rotor current has a high frequency (2-s)f and high reactance, so it is small B. The backward field has a much smaller flux than the forward field C. The backward rotor current is at zero frequency D. The centrifugal switch removes the backward field Answer: A. The backward rotor frequency is about 2f, so the large rotor reactance limits the current and torque, and T_f >> |T_b|. (Key point: Why the motor keeps running) ## Close variants set in other exams - [Double field revolving theory and a starting method](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machines_ii%3Adfrt-one-starting-method) — Electric Machines II, chapter 3, asked 5× ## Related in Electric Machines II - [DFRT and equivalent circuit of single phase IM](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machines_ii%3Adfrt-equivalent-circuit) — Electric Machines II, chapter 3 - [DFRT, starting methods and capacitor start-run motor](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machines_ii%3Adfrt-starting-methods-csr) — Electric Machines II, chapter 3 ## Related in other subjects - [Double revolving field theory](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machine%3Adouble-field-revolving-theory) — Electrical Machine, chapter 7, asked 3× - [Double field revolving theory](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Adfrt-single-phase-motor) — Electrical Machines, chapter 7, asked 3× - [Double field theory; not self-starting](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machine%3Adfrt-not-self-starting-proof) — Electrical Machine, chapter 7, asked 2× - [Double field theory; starting methods](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machine%3Adfrt-two-starting-methods) — Electrical Machine, chapter 7