# DC motors, AC motors, and Kv

As I understand it, DC motors have Kv values because their speed is determined by the applied voltage. AC motors don't have Kv values because their speed is determined by the frequency of the AC input.

The structure of a brushless DC motor (BLDC) is essentially similar to that of a permanent-magnet synchronous motor (PMSM). The main difference is the input voltage, which produces a different BEMF (trapezoidal for BLDC, sinusoidal for PMSM). So I've been wondering why BLDCs have Kv and PMSMs don't.

My theory is that BLDCs have Kv values because their speed is increased by increasing voltage, and not by changing the input voltage more quickly. PMSMs don't have Kv values because their speed is increased by increasing the frequency. Does this sound accurate? Or am I completely mistaken?

• The speed of a synchronous AC motor is determined by the frequency of the AC input. Some motors that run on AC are not synchronous (the "universal" motor, for instance). Nov 6, 2014 at 15:21
• ...and induction motors are only sort-of synchronous. Their torque comes from "slipping", or running slower than the synchronous speed. Nov 6, 2014 at 15:32

In both PMSM and BLDC motors, the speed and frequency are indeed locked to each other. However:

• The PMSM has a fixed input frequency in the sense that it's not affected by the motor itself and therefore a fixed speed in relation to that frequency. Speed is controlled directly by frequency; the voltage and current limits are simply high enough to provide some headroom so that it doesn't stall under load. (but not so high as to fry the motor) It's also designed to run directly from AC power, which is sinusoidal, so it needs a sinewave inverter to control the speed well.
• The BLDC has a controller/inverter that varies the frequency to match whatever the motor is doing at the time. Think of a brushed motor that uses transistors instead of brushes, and you're really close. Therefore, the BLDC has a Kv. It's designed to run exclusively from an inverter, so the flat-topped trapezoid is more transistor-friendly and allows the inverter to be cheaper yet still just as effective.

These two kinds of motors are actually interchangeable in a pinch; they just won't work as well. Higher noise, less efficient, etc., unless the inverter can drive both and you tell it about the change.

There are two other things to know about motors in general:

• All motors have inductance that increases their impedance with higher speed. AC impedance is somewhat analogous to DC resistance, except that there's now a phase angle involved that makes things more complicated. (There's also a phase angle between a PMSM's rotor and the driving voltage that varies with load and contributes to the impedance.) The increased impedance lowers the current for a given voltage, which reduces the torque. This is why a stalled motor draws maximum current and produces maximum torque.
• All motors generate a voltage while they're running that is proportional to their speed and locked in frequency. This back EMF works against the voltage being applied to further reduce the current. Kv is theoretically the rate of back EMF vs. speed. (it would require a mythical free-energy source to go beyond that)
• There are some issues with this answer: 1) The only difference between PMSM and BLDC is the bEMF shape. PMSMs have sinusoidal bEMF, BLDCs have trapezoidal bEMF. 2) Higher velocity does not increase resistance but reactive impedance. Nov 6, 2014 at 16:06
• @SunnyBoyNY Yes, I know about the reactive impedance vs. resistance distinction, but I was keeping it simple because of what I read from the original question. And yes, the only difference is the bEMF; the different shape makes each one better suited for its power source: transistors like to be on/off only, hence the trapezoid, and raw AC tends to be sinusoidal. Nov 6, 2014 at 16:13
• Furthermore, PMSMs do not have a fixed input frequency as this answer states -- saying so is simply wrong. PMSMs are often controlled with variable-frequency drives which allow them to operate at arbitrary speeds. Very similar to BLDCs. Nov 7, 2014 at 6:30
• @Jay Fixed in the sense that it's not affected by the motor itself like it is for a BLDC. I know what VFD's are; I used to work with them a lot. Please ask to clarify before downvoting. Nov 7, 2014 at 6:36