This is a case where the standard explanation people reach for is actually wrong in a way that matters — the formula “output voltage = input voltage × (output frequency ÷ input frequency)” gets repeated in a lot of introductory content, and it doesn’t describe how a VFD actually works. Worth correcting properly, because the real relationship (V/Hz control) is genuinely simple once it’s explained right.
Why that formula doesn’t hold up
A VFD doesn’t take the incoming 50 Hz mains frequency as a reference point for scaling voltage — it rectifies the incoming AC to DC, then synthesizes a new AC waveform of whatever frequency and voltage the application needs, up to a ceiling set by the DC bus voltage (roughly proportional to the input voltage, not the input frequency). Mains frequency (50 Hz in Europe) isn’t an input to this calculation at all — it’s just the frequency of the fixed supply the drive rectifies. Using it as “input frequency” in a voltage-scaling formula conflates two unrelated things and, worse, implies the drive can output more voltage than it received just by commanding a higher frequency, which it can’t — the inverter stage is limited by the DC bus voltage it has to work with, full stop.
What actually determines output voltage: the V/Hz ratio
The real relationship is defined by the motor’s own nameplate: rated voltage ÷ rated frequency, giving a volts-per-hertz ratio. For a standard 400V/50Hz three-phase motor, that’s 400 ÷ 50 = 8 V/Hz. For a 230V/50Hz motor, it’s 230 ÷ 50 = 4.6 V/Hz.
Below the motor’s rated (base) frequency, the drive maintains this ratio as output frequency changes — this is the constant torque region, and it’s why it’s called V/Hz or “volts per hertz” control. At 25 Hz on that 400V/50Hz motor: 25 × 8 = 200 V. At 40 Hz: 40 × 8 = 320 V. The relationship is genuinely linear across this range, and this is the part the original formula happened to loosely resemble — but only up to the motor’s base frequency, and only because European mains happens to be 50 Hz, the same as most motors’ rated frequency, which is a coincidence, not the actual mechanism.
What happens at and above base frequency — this is where the wrong formula really breaks
Once output frequency reaches the motor’s rated frequency, output voltage hits its ceiling — the drive cannot keep increasing voltage proportionally beyond this point because it’s already at the maximum the DC bus can supply (which is set by the input voltage, not by how high you set the output frequency). Push the output frequency higher than base frequency — a common technique for applications wanting more speed than the motor’s nameplate implies — and the drive holds voltage flat at its maximum while frequency keeps climbing. This is the field-weakening region: the effective V/Hz ratio drops as frequency rises past base, and torque capability falls off roughly in proportion, while output power stays roughly constant. This is exactly the mechanism covered in more depth in our piece on VFDs and drilling machines, where it matters directly for spindle speed selection.
The wrong formula, if you actually followed it past base frequency, would suggest voltage keeps climbing indefinitely with frequency — which would require the drive to output more voltage than its DC bus has available. It can’t, and any drive that appeared to do this would be a serious safety and equipment problem, not a feature.
Low-frequency voltage boost — the other place linear V/Hz falls short
At very low output frequencies, a motor’s own winding resistance causes a voltage drop that a pure linear V/Hz calculation doesn’t account for, meaning the motor gets less actual torque-producing voltage than the simple ratio suggests — this shows up as poor low-speed torque or stalling on starting under load. Most drives offer a torque boost or voltage boost parameter that adds extra voltage at low frequency specifically to compensate for this, at the cost of some extra motor heating. This is a genuinely useful parameter to know about if an application is struggling with torque at startup or low speed on basic V/F control — it’s a much smaller, more targeted fix than jumping straight to vector control, and worth trying first on applications where vector control isn’t otherwise needed.
What to actually check on your drive
- Confirm the motor’s rated voltage and base frequency are correctly entered — this is the actual reference the drive’s V/Hz curve is built from, and it’s the same nameplate data commissioning depends on (see our piece on commissioning).
- If running above base frequency, understand you’re in field weakening and torque capability is reduced — check this is acceptable for the application before relying on it.
- If torque is weak at low speed on V/F control, check the boost parameter before assuming you need vector control or a bigger motor.
The short version
Output voltage tracks output frequency in a straight line up to the motor’s base frequency, at a ratio set by the motor’s own rated voltage and frequency — not by any relationship to the incoming mains frequency. Above base frequency, voltage is capped and torque falls off in field weakening. At very low frequency, a boost parameter compensates for voltage drop the linear ratio doesn’t capture. None of this depends on “input frequency” the way the commonly repeated formula implies — get the V/Hz curve concept right and the rest of VFD speed/torque behavior falls into place logically.
If you’re working out where a specific application sits relative to base frequency and field weakening, that’s worth checking against your actual motor’s nameplate data rather than assuming.
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