--- title: "DFRT and making single phase motor self-starting" subject: "Electrical Machines" chapter: 7 key: "semester_4/electrical_machines:dfrt-self-starting-explain" source: https://www.bctengineer.com/q/semester_4/electrical_machines/dfrt-self-starting-explain site: BCT Engineering --- # DFRT and making single phase motor self-starting Electrical Machines · Chapter 7: Fractional Kilowatt Motors - Asked in: 2077 Chaitra, 8 marks; 2069 Bhadra (asked 2 times) - Video: [double revolving field theory of single phase induction motor | double revolving theory](https://www.youtube.com/watch?v=pXmPCSc9di0) — 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-self-starting-explain - Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machines/chapter-7 ## Question Explain double field revolving theory. How do we make single phase induction motor self-starting? ## Short answer A pulsating flux equals two oppositely rotating fluxes; at standstill their torques cancel. To self-start, a second winding displaced 90° with phase difference (split-phase, capacitor, or shaded pole) creates a rotating field. ## Answer #### Double field revolving theory 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**. $$ \phi_m\cos\omega t = \frac{\phi_m}{2}e^{j\omega t} + \frac{\phi_m}{2}e^{-j\omega t} $$ - $\phi_f$: forward-rotating component (in the direction of the rotor). - $\phi_b$: backward-rotating component (opposite). ```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 vertical components cancel and the horizontal components add up, giving the pulsating flux $\phi_m\cos\omega t$. #### Rotor behaviour Each field induces rotor currents and produces its own torque. For 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 forward and backward torques become unequal. The backward field induces rotor currents of frequency $(2-s)f$; at this high frequency the rotor reactance is large, so these currents are small and lag heavily, and the backward torque falls. So $T_f > T_b$ in the direction of rotation, and the motor keeps accelerating towards $N_s$. - 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 therefore 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 the reverse for negative speeds). #### Making a single-phase induction motor self-starting Since a single-phase winding gives no starting torque, a **rotating field must be created at starting**. This is done by adding an auxiliary (starting) winding displaced $90^\circ$ electrically from the main winding and making its current differ in phase from the main winding current. The methods are: 1. **Resistance split-phase:** the auxiliary winding has higher resistance and lower reactance than the main winding. The currents differ in phase by about $30^\circ$, giving a weak rotating field and a moderate starting torque. A centrifugal switch cuts the auxiliary winding out at about 75 % speed. 2. **Capacitor-start:** a capacitor in series with the auxiliary winding gives a phase difference near $90^\circ$ and a high starting torque (3 to 4.5 times full load). 3. **Capacitor-start, capacitor-run:** a capacitor stays in the circuit while running (a smaller one than at starting), giving good torque and power factor. 4. **Permanent split capacitor:** the same capacitor is used for starting and running. Starting torque is low, but running is smooth and quiet. 5. **Shaded pole:** copper rings around part of each pole delay the flux in the shaded part, giving a small rotating-field effect. Used for very small motors (fans, toys). ```text Main winding ------+ +---- supply Aux. winding --[C]-+-(centrifugal switch) ``` ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. In DFRT, how is the pulsating flux represented? A. Two rotating fluxes of phi_m/2 in opposite directions at Ns B. One rotating flux of phi_m C. Two rotating fluxes of phi_m in the same direction D. Two fluxes at 2Ns Answer: A. The pulsating flux phi_m cos(wt) equals two phi_m/2 fields rotating in opposite directions. (Key point: DFRT statement) 2. Why does a single-phase induction motor not self-start? A. The rotor has too high resistance B. At standstill the forward and backward torques are equal and opposite C. The supply frequency is too low D. The stator has no poles Answer: B. At s = 1, Tf = Tb so net torque is zero. (Key point: Zero starting torque) 3. What is needed to make it self-starting? A. A larger air gap B. A DC supply C. A rotating field at start, produced by an auxiliary winding displaced 90 degrees electrically with a phase difference D. A smaller rotor Answer: C. An auxiliary winding 90 degrees away, with phase-shifted current, creates a rotating field. (Key point: Self-starting principle) 4. Which method gives the highest starting torque (3 to 4.5 times full-load)? A. Capacitor-start B. Resistance split-phase C. Shaded pole D. Permanent split capacitor Answer: A. A series capacitor makes the auxiliary current lead by nearly 90 degrees, giving a near-circular field and high torque. (Key point: Starting methods) ## Close variants set in other exams - [Single phase motor not self-starting; DFRT](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Aspim-not-self-starting-dfrt) — Electrical Machines, chapter 7, asked 3× ## Related in Electrical Machines - [Single phase motor not self-starting; two starting methods](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Aspim-not-self-starting-starting-methods) — Electrical Machines, chapter 7 - [Reason: single phase motor not self-starting](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Aspim-not-self-starting-reason) — Electrical Machines, chapter 7 - [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× - [Need of starter and induction motor starting methods](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Ainduction-motor-starter-methods) — Electrical Machines I, chapter 5 - [Synchronous motor not self-starting; starting methods](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Async-motor-not-self-starting-methods) — Electrical Machines, chapter 6, asked 2× ## Related in other subjects - [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× - [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 revolving theory](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machines_ii%3Adouble-field-revolving-theory) — Electric Machines II, chapter 3, asked 5× - [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×