# Spice modelling of back EMF

Started by March 22, 2016
```On Wed, 23 Mar 2016 14:57:21 -0500, "Tim Williams"
<tiwill@seventransistorlabs.com> wrote:

>"John Larkin" <jjlarkin@highlandtechnology.com> wrote in message
>news:tgu3fb53rh5a5pb60qqkuvumnm276rtghg@4ax.com...
>> Not to be too pickey, but we don't consider inductors to have "back
>> emf". That term is usually reserved for motors.
>
>In the fundamental inductor equation:
>V = L * dI/dt
>
>V is defined as the EMF.

We call it "voltage". Voltage isn't a force.

>
>(I don't have a curly 'E' so I put 'V' there.)
>
>Faraday's law says it doesn't matter if the dPhi/dt is from relative motion
>(as in a motor) or varying magnitude (as in a transformer); indeed,
>Relativity itself says the two are perfectly equivalent.
>
>A motor is just a spinning transformer!

With one winding?

--

John Larkin         Highland Technology, Inc
picosecond timing   precision measurement

jlarkin att highlandtechnology dott com
http://www.highlandtechnology.com

```
```On 24.3.16 19:39, John Larkin wrote:
> On Wed, 23 Mar 2016 14:57:21 -0500, "Tim Williams"
> <tiwill@seventransistorlabs.com> wrote:
>
>> "John Larkin" <jjlarkin@highlandtechnology.com> wrote in message
>> news:tgu3fb53rh5a5pb60qqkuvumnm276rtghg@4ax.com...
>>> Not to be too pickey, but we don't consider inductors to have "back
>>> emf". That term is usually reserved for motors.
>>
>> In the fundamental inductor equation:
>> V = L * dI/dt
>>
>> V is defined as the EMF.
>
> We call it "voltage". Voltage isn't a force.
>
>>
>> (I don't have a curly 'E' so I put 'V' there.)
>>
>> Faraday's law says it doesn't matter if the dPhi/dt is from relative motion
>> (as in a motor) or varying magnitude (as in a transformer); indeed,
>> Relativity itself says the two are perfectly equivalent.
>>
>> A motor is just a spinning transformer!
>
> With one winding?

There is a shorted secondary in the rotor of squirrel-cage motors.

The current in the rotor is what makes the rotor to chase the
rotating magnetic field of the stator.

--

-TV

```
```John Larkin <jjlarkin@highlandtechnology.com> writes:

> On Wed, 23 Mar 2016 14:57:21 -0500, "Tim Williams"
> <tiwill@seventransistorlabs.com> wrote:
>
>>"John Larkin" <jjlarkin@highlandtechnology.com> wrote in message
>>news:tgu3fb53rh5a5pb60qqkuvumnm276rtghg@4ax.com...
>>> Not to be too pickey, but we don't consider inductors to have "back
>>> emf". That term is usually reserved for motors.
>>
>>In the fundamental inductor equation:
>>V = L * dI/dt
>>
>>V is defined as the EMF.
>
> We call it "voltage". Voltage isn't a force.
>
>>
>>(I don't have a curly 'E' so I put 'V' there.)
>>
>>Faraday's law says it doesn't matter if the dPhi/dt is from relative motion
>>(as in a motor) or varying magnitude (as in a transformer); indeed,
>>Relativity itself says the two are perfectly equivalent.
>>
>>A motor is just a spinning transformer!
>
> With one winding?

I think it's something like this

2.65Ohm  12,000uF    340uH
o------/\/\-----||--------//////----o
'        '
`--/\/\--'
~ 3-260Ohm

I was trying to model a 6V Maxon F2140 motor

Voltage on the C is proportional to speed. Current proportional to
torque.

--

John Devereux
```
```John Larkin <jjlarkin@highlandtechnology.com> writes:

> On Thu, 24 Mar 2016 18:00:32 +0000, John Devereux
> <john@devereux.me.uk> wrote:
>
>>John Larkin <jjlarkin@highlandtechnology.com> writes:
>>
>>> On Wed, 23 Mar 2016 14:57:21 -0500, "Tim Williams"
>>> <tiwill@seventransistorlabs.com> wrote:
>>>
>>>>"John Larkin" <jjlarkin@highlandtechnology.com> wrote in message
>>>>news:tgu3fb53rh5a5pb60qqkuvumnm276rtghg@4ax.com...
>>>>> Not to be too pickey, but we don't consider inductors to have "back
>>>>> emf". That term is usually reserved for motors.
>>>>
>>>>In the fundamental inductor equation:
>>>>V = L * dI/dt
>>>>
>>>>V is defined as the EMF.
>>>
>>> We call it "voltage". Voltage isn't a force.
>>>
>>>>
>>>>(I don't have a curly 'E' so I put 'V' there.)
>>>>
>>>>Faraday's law says it doesn't matter if the dPhi/dt is from relative motion
>>>>(as in a motor) or varying magnitude (as in a transformer); indeed,
>>>>Relativity itself says the two are perfectly equivalent.
>>>>
>>>>A motor is just a spinning transformer!
>>>
>>> With one winding?
>>
>>
>>I think it's something like this
>>
>>     2.65Ohm  12,000uF    340uH
>>o------/\/\-----||--------//////----o
>>            '        '
>>            `--/\/\--'
>>            ~ 3-260Ohm
>>
>>I was trying to model a 6V Maxon F2140 motor
>>
>>Voltage on the C is proportional to speed. Current proportional to
>>torque.
>
> Right. The voltage in the cap is "back EMF" which decays slowly as the
> motor spins down.

That's the 260Ohms, when the motor is just free-spinning. It's 3Ohms at
full load so it stops quickly then.

--

John Devereux
```
```On Thu, 24 Mar 2016 19:30:14 +0000, John Devereux
<john@devereux.me.uk> wrote:

>John Larkin <jjlarkin@highlandtechnology.com> writes:
>
>> On Thu, 24 Mar 2016 18:00:32 +0000, John Devereux
>> <john@devereux.me.uk> wrote:
>>
>>>John Larkin <jjlarkin@highlandtechnology.com> writes:
>>>
>>>> On Wed, 23 Mar 2016 14:57:21 -0500, "Tim Williams"
>>>> <tiwill@seventransistorlabs.com> wrote:
>>>>
>>>>>"John Larkin" <jjlarkin@highlandtechnology.com> wrote in message
>>>>>news:tgu3fb53rh5a5pb60qqkuvumnm276rtghg@4ax.com...
>>>>>> Not to be too pickey, but we don't consider inductors to have "back
>>>>>> emf". That term is usually reserved for motors.
>>>>>
>>>>>In the fundamental inductor equation:
>>>>>V = L * dI/dt
>>>>>
>>>>>V is defined as the EMF.
>>>>
>>>> We call it "voltage". Voltage isn't a force.
>>>>
>>>>>
>>>>>(I don't have a curly 'E' so I put 'V' there.)
>>>>>
>>>>>Faraday's law says it doesn't matter if the dPhi/dt is from relative motion
>>>>>(as in a motor) or varying magnitude (as in a transformer); indeed,
>>>>>Relativity itself says the two are perfectly equivalent.
>>>>>
>>>>>A motor is just a spinning transformer!
>>>>
>>>> With one winding?
>>>
>>>
>>>I think it's something like this
>>>
>>>     2.65Ohm  12,000uF    340uH
>>>o------/\/\-----||--------//////----o
>>>            '        '
>>>            `--/\/\--'
>>>            ~ 3-260Ohm
>>>
>>>I was trying to model a 6V Maxon F2140 motor
>>>
>>>Voltage on the C is proportional to speed. Current proportional to
>>>torque.
>>
>> Right. The voltage in the cap is "back EMF" which decays slowly as the
>> motor spins down.
>
>That's the 260Ohms, when the motor is just free-spinning. It's 3Ohms at
>full load so it stops quickly then.

It's fun to spin up a really good PM motor and then short the leads.

--

John Larkin         Highland Technology, Inc
picosecond timing   precision measurement

jlarkin att highlandtechnology dott com
http://www.highlandtechnology.com

```
```John Larkin <jjlarkin@highlandtechnology.com> writes:

> On Thu, 24 Mar 2016 19:30:14 +0000, John Devereux
> <john@devereux.me.uk> wrote:
>
>>John Larkin <jjlarkin@highlandtechnology.com> writes:
>>
>>> On Thu, 24 Mar 2016 18:00:32 +0000, John Devereux
>>> <john@devereux.me.uk> wrote:
>>>
>>>>John Larkin <jjlarkin@highlandtechnology.com> writes:
>>>>
>>>>> On Wed, 23 Mar 2016 14:57:21 -0500, "Tim Williams"
>>>>> <tiwill@seventransistorlabs.com> wrote:
>>>>>
>>>>>>"John Larkin" <jjlarkin@highlandtechnology.com> wrote in message
>>>>>>news:tgu3fb53rh5a5pb60qqkuvumnm276rtghg@4ax.com...
>>>>>>> Not to be too pickey, but we don't consider inductors to have "back
>>>>>>> emf". That term is usually reserved for motors.
>>>>>>
>>>>>>In the fundamental inductor equation:
>>>>>>V = L * dI/dt
>>>>>>
>>>>>>V is defined as the EMF.
>>>>>
>>>>> We call it "voltage". Voltage isn't a force.
>>>>>
>>>>>>
>>>>>>(I don't have a curly 'E' so I put 'V' there.)
>>>>>>
>>>>>>Faraday's law says it doesn't matter if the dPhi/dt is from relative motion
>>>>>>(as in a motor) or varying magnitude (as in a transformer); indeed,
>>>>>>Relativity itself says the two are perfectly equivalent.
>>>>>>
>>>>>>A motor is just a spinning transformer!
>>>>>
>>>>> With one winding?
>>>>
>>>>
>>>>I think it's something like this
>>>>
>>>>     2.65Ohm  12,000uF    340uH
>>>>o------/\/\-----||--------//////----o
>>>>            '        '
>>>>            `--/\/\--'
>>>>            ~ 3-260Ohm
>>>>
>>>>I was trying to model a 6V Maxon F2140 motor
>>>>
>>>>Voltage on the C is proportional to speed. Current proportional to
>>>>torque.
>>>
>>> Right. The voltage in the cap is "back EMF" which decays slowly as the
>>> motor spins down.
>>
>>That's the 260Ohms, when the motor is just free-spinning. It's 3Ohms at
>>full load so it stops quickly then.
>
> It's fun to spin up a really good PM motor and then short the leads.

Yes I have done that. In the ideal case of zero winding resistance and
inductance, there would be an infinite torque (current), and the speed
(voltage on the "C") goes instantly to zero.

Similarly when open circuit it spins forever (the "C" above stays
charged up) if there is no friction.

--

John Devereux
```
```On Thu, 24 Mar 2016 20:15:13 +0000, John Devereux
<john@devereux.me.uk> wrote:

>John Larkin <jjlarkin@highlandtechnology.com> writes:
>
>> On Thu, 24 Mar 2016 19:30:14 +0000, John Devereux
>> <john@devereux.me.uk> wrote:
>>
>>>John Larkin <jjlarkin@highlandtechnology.com> writes:
>>>
>>>> On Thu, 24 Mar 2016 18:00:32 +0000, John Devereux
>>>> <john@devereux.me.uk> wrote:
>>>>
>>>>>John Larkin <jjlarkin@highlandtechnology.com> writes:
>>>>>
>>>>>> On Wed, 23 Mar 2016 14:57:21 -0500, "Tim Williams"
>>>>>> <tiwill@seventransistorlabs.com> wrote:
>>>>>>
>>>>>>>"John Larkin" <jjlarkin@highlandtechnology.com> wrote in message
>>>>>>>news:tgu3fb53rh5a5pb60qqkuvumnm276rtghg@4ax.com...
>>>>>>>> Not to be too pickey, but we don't consider inductors to have "back
>>>>>>>> emf". That term is usually reserved for motors.
>>>>>>>
>>>>>>>In the fundamental inductor equation:
>>>>>>>V = L * dI/dt
>>>>>>>
>>>>>>>V is defined as the EMF.
>>>>>>
>>>>>> We call it "voltage". Voltage isn't a force.
>>>>>>
>>>>>>>
>>>>>>>(I don't have a curly 'E' so I put 'V' there.)
>>>>>>>
>>>>>>>Faraday's law says it doesn't matter if the dPhi/dt is from relative motion
>>>>>>>(as in a motor) or varying magnitude (as in a transformer); indeed,
>>>>>>>Relativity itself says the two are perfectly equivalent.
>>>>>>>
>>>>>>>A motor is just a spinning transformer!
>>>>>>
>>>>>> With one winding?
>>>>>
>>>>>
>>>>>I think it's something like this
>>>>>
>>>>>     2.65Ohm  12,000uF    340uH
>>>>>o------/\/\-----||--------//////----o
>>>>>            '        '
>>>>>            `--/\/\--'
>>>>>            ~ 3-260Ohm
>>>>>
>>>>>I was trying to model a 6V Maxon F2140 motor
>>>>>
>>>>>Voltage on the C is proportional to speed. Current proportional to
>>>>>torque.
>>>>
>>>> Right. The voltage in the cap is "back EMF" which decays slowly as the
>>>> motor spins down.
>>>
>>>That's the 260Ohms, when the motor is just free-spinning. It's 3Ohms at
>>>full load so it stops quickly then.
>>
>> It's fun to spin up a really good PM motor and then short the leads.
>
>Yes I have done that. In the ideal case of zero winding resistance and
>inductance, there would be an infinite torque (current), and the speed
>(voltage on the "C") goes instantly to zero.

And the motor jumps off the table.

--

John Larkin         Highland Technology, Inc
picosecond timing   precision measurement

jlarkin att highlandtechnology dott com
http://www.highlandtechnology.com

```
```<bill.sloman@ieee.org> wrote in message
On Thursday, March 24, 2016 at 9:28:48 AM UTC+11, Bill Bowden wrote:
>> Interwinding-capacitance causes eddy currents in the wire and lowers the
>> Q
>> of the inductor.

>The current that charges the inter-winding capacitances runs through the
>windings. If you bank wound an inductor, so it had lower interwinding
>capacitance it >would be self-resonant at a higher frequency, so the
>inductive reactance would be higher and the winding resistance less
>important.

>> This is why Litz wire is used to wind antenna
>> loopsticks.for higher Qs and narrower bandwidths.

>Wrong. Litz wire is better because at higher frequencies, current tends to
>flow on the surface of a wire. Litz wire has a lot more surface area spread
>over a >number of parallel windings. If you look at the manufacturers notes
>on Litz wire, you will find that progessively finer-filament Litz wire is
>recommended for >progressively higher frequency applications.

>Interwinding capacitance doesn't come into it.

Apparently, interwinding capacitance determines the upper frequency limit
5 MHz.

http://www.kerrigan-lewis.com/use-litz-wire/

"At frequencies > 5 Mhz, Litz wire becomes less practical. The capacitance
effects between the strands are the reasons for this high-frequency limit on
the use of Litz wire."

<snip>

--- news://freenews.netfront.net/ - complaints: news@netfront.net ---
```
```On Friday, March 25, 2016 at 10:15:31 AM UTC+11, Bill Bowden wrote:
> <bill.sloman@ieee.org> wrote in message
> On Thursday, March 24, 2016 at 9:28:48 AM UTC+11, Bill Bowden wrote:
> >> Interwinding-capacitance causes eddy currents in the wire and lowers the
> >> Q
> >> of the inductor.
>
> >The current that charges the inter-winding capacitances runs through the
> >windings. If you bank wound an inductor, so it had lower interwinding
> >capacitance it >would be self-resonant at a higher frequency, so the
> >inductive reactance would be higher and the winding resistance less
> >important.
>
> >> This is why Litz wire is used to wind antenna
> >> loopsticks.for higher Qs and narrower bandwidths.
>
> >Wrong. Litz wire is better because at higher frequencies, current tends to
> >flow on the surface of a wire. Litz wire has a lot more surface area spread
> >over a >number of parallel windings. If you look at the manufacturers notes
> >on Litz wire, you will find that progessively finer-filament Litz wire is
> >recommended for >progressively higher frequency applications.
>
> >Interwinding capacitance doesn't come into it.
>
> Apparently, interwinding capacitance determines the upper frequency limit
> 5 MHz.
>
> http://www.kerrigan-lewis.com/use-litz-wire/
>
> "At frequencies > 5 MHz, Litz wire becomes less practical. The capacitance
> effects between the strands are the reasons for this high-frequency limit on
> the use of Litz wire."
>
> <snip>

This sounds like total nonsense. The skin depth for copper at 1MHz is 66 micron, and 21 micron at 10MHz. You can't make wire strands  that fine, which is why Litz wire stops making things better at around 5MHz.

The whole point about Litz wire is that there is no voltage difference between the strands in a bundle (and the strands have to be distributed rather carefully to make sure that this is true) so the capacitance between the strands should be a non-issue.

--
Bill Sloman, Sydney
```
```"Tauno Voipio" <tauno.voipio@notused.fi.invalid> wrote in message
news:nd19e5\$vtd\$1@dont-email.me...
> There is a shorted secondary in the rotor of squirrel-cage motors.
>
> The current in the rotor is what makes the rotor to chase the
> rotating magnetic field of the stator.

Yup, or if it's just a fixed magnet (permanent or otherwise), it works just
as well. :)

Of course, with an electromagnet, if it's not rotating, it's just a regular
transformer.

Indeed, a motor is even more rich than the earlier simplification!  It is a
multiplying device, between mechanical motion and magnetic field.  There
exists no linear circuit which can convert, say, 50Hz to 60Hz mains power,
but a motor-generator (with suitable gearing) can do the job with lockstep
precision.

The reason a "universal" motor is, well, as its name suggests, is because it
mixes the input with itself, giving a square-law response.  The applied
voltage becomes DC and even harmonics; the harmonics become torque ripple,
while the DC makes it spin in a consistent direction.

Likewise, torque is proportional to current squared, and is inverse with
RPM, making universal / series-wound motors extremely effective for high
impact and high power density applications.

(Traction applications tend to favor induction motors because of their
simplicity and efficiency, absorbing the complexity into a VFD instead.  Or
PM AC (synchronous) motors, because of their low-end torque and synchronous
operation, without wasting the power of an electromagnet winding.)

Tim

--
Seven Transistor Labs, LLC
Electrical Engineering Consultation and Contract Design
Website: http://seventransistorlabs.com

```