--- title: "Double field revolving theory" subject: "Electrical Machines" chapter: 7 key: "semester_4/electrical_machines:dfrt-single-phase-motor" source: https://www.bctengineer.com/q/semester_4/electrical_machines/dfrt-single-phase-motor site: BCT Engineering --- # Double field revolving theory Electrical Machines · Chapter 7: Fractional Kilowatt Motors - Asked in: 2078 Baisakh, 8 marks; 2072 Asoj; 2070 Magh, 8 marks (asked 3 times) - Video: [Double revolving theory | double revolving field theory of single phase induction motor | lecture -2](https://www.youtube.com/watch?v=PQgC2N-RE04) — Mind of Engineer - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/electrical_machines/dfrt-single-phase-motor - Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machines/chapter-7 ## Question What do you understand by double field revolving theory? Explain it with the help of a neat diagram. ## Short answer A pulsating flux is resolved into two equal rotating fluxes of half amplitude, rotating oppositely at synchronous speed. At standstill, their torques cancel, so the motor is not self-starting; once rotating, forward torque exceeds backward torque. ## Answer #### Double field revolving theory (DFRT) A single-phase winding carrying alternating current produces a **pulsating** (alternating) flux along a fixed axis: $\phi = \phi_m\cos\omega t$. According to the **double field revolving theory**, this pulsating flux is equivalent to two rotating fluxes, each of constant magnitude $\phi_m/2$, rotating at synchronous speed $N_s = \frac{120f}{P}$ in **opposite directions**. $$ \phi_m\cos\omega t = \frac{\phi_m}{2}e^{j\omega t} + \frac{\phi_m}{2}e^{-j\omega t} $$ - $\phi_f$: the forward-rotating component (in the direction of the rotor). - $\phi_b$: the backward-rotating component (in the opposite direction). ```text phi_f = phi_m/2 --> (anticlockwise) \ / phi_b \ / resultant = phi_m cos(wt) = phi_m/2 X along fixed axis (pulsating) (clockwise) ``` At every instant the components perpendicular to the winding axis cancel, and the components along the axis add, giving the pulsating flux $\phi_m\cos\omega t$. #### Rotor behaviour Each field induces rotor currents and produces its own torque. For a rotor speed $N_r$ in the forward direction: - Slip with respect to the forward field: $s_f = s = \frac{N_s - N_r}{N_s}$ - Slip with respect to the backward field: $s_b = 2 - s$ The net torque is $T = T_f - T_b$. - **At standstill** ($s = 1$): $s_f = s_b = 1$, so $T_f = T_b$ and the net torque is **zero**. The motor is not self-starting. - If the rotor is started in either direction, the two torques become unequal. The backward field acts on the rotor at a high slip ($2 - s$), so the rotor current it induces has a high frequency, is limited mainly by reactance and has a low power factor; the backward torque is therefore small. So $T_f > T_b$ in the direction of rotation, and the motor keeps accelerating to near $N_s$. - At $N_s$ ($s=0$): $T_f = 0$, but $T_b$ is not zero (slip 2), so the net torque is slightly negative; the motor runs at a speed a little below $N_s$. ```text T | Tf net T = Tf - Tb | .--. _.-'-._ | / \ / \ +-/------\--------/---------\---> N -Ns Tb 0 (start) Ns ``` The net torque curve passes through zero at standstill and is positive at positive speeds (and negative at negative speeds). ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What does the double field revolving theory state? A. A pulsating flux equals two rotating fluxes of phi_m/2 turning at Ns in opposite directions B. A pulsating flux equals one rotating flux of phi_m C. A pulsating flux equals two rotating fluxes of phi_m turning at Ns/2 D. A pulsating flux equals two stationary fluxes Answer: A. phi_m cos(wt) is the sum of two constant-magnitude phi_m/2 fields rotating at synchronous speed in opposite directions. (Key point: Statement of DFRT) 2. If the rotor slip with respect to the forward field is s, what is the slip with respect to the backward field? A. s B. 1 - s C. 2 - s D. 2s Answer: C. The backward field turns in the opposite direction, so its slip is 2 - s. (Key point: Slips) 3. Why is the starting torque zero? A. The rotor has no winding B. At s = 1 both slips are 1, so Tf = Tb and the net torque is zero C. The forward field is zero at standstill D. The backward field has twice the speed Answer: B. The two fields have equal magnitude and slip at standstill, so the equal and opposite torques cancel. (Key point: Torque at standstill) 4. Once the rotor is turning forward, why does the motor keep accelerating? A. The backward field vanishes B. Tb increases with speed C. The forward field torque exceeds the backward field torque, whose torque falls D. The supply frequency changes Answer: C. The backward-field rotor reactance is high and its torque falls, so Tf > Tb and net torque is positive in the direction of rotation. 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