Hello members,
There have been several queries regarding using Class-D amplifiers for driving AC turntable motors, often of the synchronous type. I would therefore like to show a few simple methods for obtaining decent results using a 3-phase motor. These methods, starting from a square waveform, use Selective Harmonic Elimination (SHE) and other cancellation techniques that, along with an LC filter, provide low distortion sinusoidal waveforms with lesser electromagnetic interference (EMI) compared to the high frequency PWM used by class-D amplifiers. The techniques used here are very well understood, and in use by the power industry for decades. I shall also share some of the significant published literature on the topic for those interested in the 'details'.
Some of the features of the presented methods are:
Thanks.
There have been several queries regarding using Class-D amplifiers for driving AC turntable motors, often of the synchronous type. I would therefore like to show a few simple methods for obtaining decent results using a 3-phase motor. These methods, starting from a square waveform, use Selective Harmonic Elimination (SHE) and other cancellation techniques that, along with an LC filter, provide low distortion sinusoidal waveforms with lesser electromagnetic interference (EMI) compared to the high frequency PWM used by class-D amplifiers. The techniques used here are very well understood, and in use by the power industry for decades. I shall also share some of the significant published literature on the topic for those interested in the 'details'.
Some of the features of the presented methods are:
- Open-loop drive for all kinds of sinusoidal flux synchronous motors - wound-field / separately excited, permanent magnet or reluctance types.
- Suitable for large / small motors with no changes to underlying philosophies.
- Suitable for star, delta and open-ended winding motors.
- Only two level inverters are used in these methods (though the final phase voltages may have multiple levels). These could be implemented using half-bridge / Class-D modules available in the market.
- Minimal switching transitions give reduced EMI and switching losses when compared to high frequency PWM.
- Guaranteed elimination of all selected harmonics (according to the method), for lower acoustic noise and torque ripple necessary for turntables.
- A single DC bus voltage is used wherever possible.
- MCU implementation requires only counters and GPIOs, without the need for DAC or PWM modules.
- Accurate timing / speed control is obtained using a MHz crystal with the possibility for storing the timing information for various record speeds when implemented on MCUs.
Thanks.
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Background Information (for the interested):
The Fourier series expansion for the above waveform is such that each term of the expansion is given by:
The plus / minus sign depends on whether the harmonic under consideration is odd (negative) or even (positive). Thus, by equating the coefficient of the sinusoidal component to zero, we're able to completely eliminate a particular harmonic. For example, eliminating the 7th harmonic (only) implies:
(degrees)
The Fourier series expansion for the above waveform is such that each term of the expansion is given by:
The plus / minus sign depends on whether the harmonic under consideration is odd (negative) or even (positive). Thus, by equating the coefficient of the sinusoidal component to zero, we're able to completely eliminate a particular harmonic. For example, eliminating the 7th harmonic (only) implies:
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And, when we look at the pulse waveform and its FFT, the seventh harmonic is eliminated as expected. The extra switching for eliminating the harmonic occurs at 8.5 degrees and 180 - 8.5 degrees, as calculated above.
Note that the switching position is in degrees and is therefore applicable to a waveform of any frequency though the example shown below is that of 50Hz, with the 7th harmonic occuring at 350Hz.
Now, it is fairly easy to see that eliminating one harmonic (7th in this case) required an extra switching transition in the waveform, which also implies that eliminating every single harmonic into the kHz would require as many switching transitions. This is why this method is suitable for eliminating only a "selected set harmonics", so that the switchings / losses / EMI are also minimised.
Fortunately, this fact also suits the case of a 3-phase motor drive in which many triplen (3n) harmonics are already eliminated, and the only the remaining energy concentrated in the 5th and 7th harmonics need to be removed.
Note that the switching position is in degrees and is therefore applicable to a waveform of any frequency though the example shown below is that of 50Hz, with the 7th harmonic occuring at 350Hz.
Now, it is fairly easy to see that eliminating one harmonic (7th in this case) required an extra switching transition in the waveform, which also implies that eliminating every single harmonic into the kHz would require as many switching transitions. This is why this method is suitable for eliminating only a "selected set harmonics", so that the switchings / losses / EMI are also minimised.
Fortunately, this fact also suits the case of a 3-phase motor drive in which many triplen (3n) harmonics are already eliminated, and the only the remaining energy concentrated in the 5th and 7th harmonics need to be removed.
Modifying the equation in post #2 to eliminate two harmonics (5th and 7th) gives a system of trigonometric equations known as transcendental equations
that are more conveniently solved using computers. The mathematics for the same, being beyond the scope of this thread (and forum), is therefore omitted. Highly interested members may refer to the following paper:
J. Chiasson, L. M. Tolbert, K. McKenzie, and Z. Du, “A complete solution to the harmonic elimination problem,” IEEE Trans. Power Electron.,vol. 19, no. 2, pp. 491–499, Mar. 2004.
Available online at: https://web.eecs.utk.edu/~tolbert/publications/apec_2003_complete.pdf
The resulting waveform for eliminating 5th and 7th harmonics and its FFT spectrum are shown below.
We see that:
As we see above in the FFT of the phase voltage, the first dominant harmonic is the 11th.
that are more conveniently solved using computers. The mathematics for the same, being beyond the scope of this thread (and forum), is therefore omitted. Highly interested members may refer to the following paper:
J. Chiasson, L. M. Tolbert, K. McKenzie, and Z. Du, “A complete solution to the harmonic elimination problem,” IEEE Trans. Power Electron.,vol. 19, no. 2, pp. 491–499, Mar. 2004.
Available online at: https://web.eecs.utk.edu/~tolbert/publications/apec_2003_complete.pdf
The resulting waveform for eliminating 5th and 7th harmonics and its FFT spectrum are shown below.
We see that:
- Orders 2, 4, 6, 8,... etc. are already eliminated using half-wave symmetry of the waveform.
- 5th & 7th are eliminated using SHE modulation.
- The triplen (3rd, 9th, 15th) would be removed by the 3-phase system and as a result, they wouldn't appear in the motor phase voltage, as shown below.
As we see above in the FFT of the phase voltage, the first dominant harmonic is the 11th.
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The switching angles used in the above-mentioned method (5th & 7th elimination) are:
To implement the above modulation, simply include these switching timings into the basic waveform in post#2.
Note that these angles are fixed and may therefore be "burnt" into the program memory of a simple MCU and then be directly put out through GPIOs as the gate-drive signals for the inverter.
To implement the above modulation, simply include these switching timings into the basic waveform in post#2.
Note that these angles are fixed and may therefore be "burnt" into the program memory of a simple MCU and then be directly put out through GPIOs as the gate-drive signals for the inverter.
The preferred circuit diagram for Method 1 above (5 & 7th harmonic elimination) uses the floating star-connection as shown below. However, a delta-connected motor maybe used if desired. An open-end winding motor is capable of being reconnected as star or delta and should not be a problem in any case.
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Method 2 - Non-SHE method for eliminating all harmonics of order 6n±1 (for n = odd).
- For open-end winding motors.
- Only 50% square-waveforms are used with no extra switchings as in SHE.
- Requires two inverters and two separate (isolated) DC voltages in the ratio 1: 0.268.
- More sophisticated and higher performance when compared to the single supply SHE methods.
Look, with all do respect, who is interested in 3-phase PWM systems for dummies? Specifically in turn table with sub millivolt signal sources?
It's plain inappropriate. Those waveforms were widely used in 70-s for fans and such and are a part of power electronics basic course.
What about speed/torque control and vector modulation for better DC bus voltage utilization? Let's call it poor joke... Who need a second hand account of a textbook anyway
It's plain inappropriate. Those waveforms were widely used in 70-s for fans and such and are a part of power electronics basic course.
What about speed/torque control and vector modulation for better DC bus voltage utilization? Let's call it poor joke... Who need a second hand account of a textbook anyway
Modulation of the dual-inverter circuit in post #7
The main inverter (powered by Vdc) is fed with a three-phase square-wave of fundamental frequency while the auxiliary inverter (powered by 0.268Vdc) is fed with a suitable waveform so as to cancel all unwanted harmonic components upto the 11th, according to the following expressions:
The main inverter (powered by Vdc) is fed with a three-phase square-wave of fundamental frequency while the auxiliary inverter (powered by 0.268Vdc) is fed with a suitable waveform so as to cancel all unwanted harmonic components upto the 11th, according to the following expressions:
The waveforms for Method 2 are shown below with the FFT of the final motor phase voltage:
As seen above, all harmonic pairs around 6n for n = odd i.e. 6n±1 have been eliminated, as opposed to only 5th &,7th for the SHE method above.
As seen above, all harmonic pairs around 6n for n = odd i.e. 6n±1 have been eliminated, as opposed to only 5th &,7th for the SHE method above.
We don't know who is interested, and I'd therefore say that we keep an open mind. Besides, if a 2-phase motor can be used that way, a 3-phase motor which is electrically and mechanically superior is a certain candidate, and it may not be necessary to run these using ROM-driven DACs and linear amplifiers like many are, hence this thread.
Yes, and so were turntables ! However, these 70s techniques are effective even today and many are still not aware of these simple but elegant techniques that have existed for a long time !!
i just use a nice quiet BLDC 3 phase motor, an Arduino, a BLDC motor shield, and the SimpleFOC software running Open Loop. and it outputs nice clean SpaceVector or Sinusoidal waves.
super easy.
super easy.
Do not hesitate to specify in what exactly:
Wide band harmonic source? Textbook pictures with IGBT? Please suggest an appropriate IGBT part number, just for heck of it.
It's leading to nowere... today it takes 3 pcs of off the shelf class D amps having no harmonics per say.
P.S. This was used when transistors were crap and every switching instance did matter.
And eggheads came up with ingenious solution to generate harmonics in the opposite phase to cancel existing ones.
It's eased filter design making ones lighter, which did matter... in avionics... and in other "movable assets."
Then yet another eggheads bettered switches rendering it obsolete.
Method 3 - SHE of 5th, 7th, 11th and 13th harmonics - circuit diagram from post #6
Switching pattern (A phase)
Phase voltage (A phase)
FFT (phase voltage)
The phase voltage spectrum is missing all harmonics up to order 17. Many harmonics of order between 20 and 30 have also been suppressed by the modulation. The switching angles used above were:
- Single DC supply
- Regular 3-phase inverter.
- Standard star or delta motor.
Switching pattern (A phase)
Phase voltage (A phase)
FFT (phase voltage)
The phase voltage spectrum is missing all harmonics up to order 17. Many harmonics of order between 20 and 30 have also been suppressed by the modulation. The switching angles used above were:
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Method 4 - Non-SHE method for eliminating several lower and higher order harmonics - circuit diagram of post #7 with aux DC bus changed to 0.29Vdc.
The inverter is modulated as in Method 2, but using slightly different expressions given below:
Waveforms
FFT (phase voltage)
The FFT shows that several lower and higher order ones are eliminated. However, the 7th harmonic is present and therefore needs to be suppressed using the LC filter.
- Open-end winding motors only.
- Square-waveform based harmonic cancellation.
- Two inverters and two isolated DC sources in the ratio 1: 0.29.
- Eliminates more harmonics when compared to the non-SHE method from post #7, 8, but does not eliminate the 7th that needs to be suppressed using additional means.
The inverter is modulated as in Method 2, but using slightly different expressions given below:
Waveforms
FFT (phase voltage)
The FFT shows that several lower and higher order ones are eliminated. However, the 7th harmonic is present and therefore needs to be suppressed using the LC filter.
Why do you want to aggressively silence this thread?
Simply don't read it.
Obtaining sinusoidal output from the above methods
As already mentioned in post #1, an LC filter maybe added to any of the above methods to order to obtain a sinusoidal output much like in any Class-D amplifier, and with the benefits of lower EMI and losses.
Now, let us add a second order filter to each of the phase voltages from each of the above methods and inspect the spectral purity of the sinusoidal outputs by taking the THD and weighted THD (WTHD, more relevant to inductive loads) values.
Method 1 (SHE of 5th & 7th harmonics)
Method 2 - 12-step output that eliminates harmonics of order 6n±1 (n = odd) for open-end winding motor
Method 3 - SHE of 5th, 7th, 11th and 13th harmonics
Method 4 - Elimination of several higher and lower order harmonics (except 7th and 17th) for open-end winding motor
As seen from the above, all the methods (with reduced switching transitions) are capable of sinusoidal output with THD figures comparable to those of modern Class-D amplifiers,
It is worth noting however that this result is achieved along with the advantages of lower EMI (less pickup noise in nearby analogue circuits) and higher efficiency (negligible switching losses and less heatsinking).
As already mentioned in post #1, an LC filter maybe added to any of the above methods to order to obtain a sinusoidal output much like in any Class-D amplifier, and with the benefits of lower EMI and losses.
- It is not recommended to connect the filter ground to the inverter ground i.e. minus of the DC supply.
- For star motors, the filter ground maybe returned to the neutral point of the motor if available or else left floating, as shown below.
- Since delta motors do not have a neutral, the filter ground is simply left floating.
Now, let us add a second order filter to each of the phase voltages from each of the above methods and inspect the spectral purity of the sinusoidal outputs by taking the THD and weighted THD (WTHD, more relevant to inductive loads) values.
Method 1 (SHE of 5th & 7th harmonics)
Method 2 - 12-step output that eliminates harmonics of order 6n±1 (n = odd) for open-end winding motor
Method 3 - SHE of 5th, 7th, 11th and 13th harmonics
Method 4 - Elimination of several higher and lower order harmonics (except 7th and 17th) for open-end winding motor
As seen from the above, all the methods (with reduced switching transitions) are capable of sinusoidal output with THD figures comparable to those of modern Class-D amplifiers,
It is worth noting however that this result is achieved along with the advantages of lower EMI (less pickup noise in nearby analogue circuits) and higher efficiency (negligible switching losses and less heatsinking).
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