magnetics question...

[server]

https://www.dropbox.com/s/jnb3jmw8rcmdeir/XfmrScatter.JPG?raw=1

How does the mass of a transformer scale with frequency?

I want to make a 120v 400 Hz power supply. I might boost my 48v up to
200DC and use an isolated h-bridge out to the load, or we could put
the bridge down at 48v and boost with a biggish transformer.

I\'ll have lots of air flow, so maybe I can push things some too.



--

I yam what I yam - Popeye

 

[Arie de Muijnck]

On 2022-04-06 17:53, jlarkin@highlandsniptechnology.com wrote:

https://www.dropbox.com/s/jnb3jmw8rcmdeir/XfmrScatter.JPG?raw=1

How does the mass of a transformer scale with frequency?

I want to make a 120v 400 Hz power supply. I might boost my 48v up to
200DC and use an isolated h-bridge out to the load, or we could put
the bridge down at 48v and boost with a biggish transformer.

I\'ll have lots of air flow, so maybe I can push things some too.

Weight is almost linear with power, and inversely with frequency.

When I needed a 115V 400Hz for DO-160 aviation equipment development, I
ordered a 100W amplifier set from Amplimo (https://www.amplimo.nl/):
Mains transformer (toroid 115/230V in), rectifier, capacitors, amplifier
module, and an extra mains transformer (used in reverse) for the 115V
output.
Added a 400 Hz oscillator with a timer controlled gain control (4051 MUX
with some resistors) to create the required brownout and dropout
profiles. The customer was so amused they ordered some for their
production and test line (until then, they used a gigantic motor + 400Hz
dynamo in the basement to get 400 Hz).

Arie

 

[server]

On Wed, 6 Apr 2022 18:24:49 +0200, Arie de Muijnck
<eternal.september@ademu.com> wrote:

On 2022-04-06 17:53, jlarkin@highlandsniptechnology.com wrote:
https://www.dropbox.com/s/jnb3jmw8rcmdeir/XfmrScatter.JPG?raw=1

How does the mass of a transformer scale with frequency?

I want to make a 120v 400 Hz power supply. I might boost my 48v up to
200DC and use an isolated h-bridge out to the load, or we could put
the bridge down at 48v and boost with a biggish transformer.

I\'ll have lots of air flow, so maybe I can push things some too.

Weight is almost linear with power, and inversely with frequency.

When I needed a 115V 400Hz for DO-160 aviation equipment development, I
ordered a 100W amplifier set from Amplimo (https://www.amplimo.nl/):
Mains transformer (toroid 115/230V in), rectifier, capacitors, amplifier
module, and an extra mains transformer (used in reverse) for the 115V
output.
Added a 400 Hz oscillator with a timer controlled gain control (4051 MUX
with some resistors) to create the required brownout and dropout
profiles. The customer was so amused they ordered some for their
production and test line (until then, they used a gigantic motor + 400Hz
dynamo in the basement to get 400 Hz).

Arie

I think so... for a given core, power scales linearly with frequency.
A simple scribble with a 4-winding transformer suggests that.

Thanks

John


--

I yam what I yam - Popeye

 

[Tauno Voipio]

On 6.4.22 19.33, jlarkin@highlandsniptechnology.com wrote:

On Wed, 6 Apr 2022 18:24:49 +0200, Arie de Muijnck
eternal.september@ademu.com> wrote:

On 2022-04-06 17:53, jlarkin@highlandsniptechnology.com wrote:
https://www.dropbox.com/s/jnb3jmw8rcmdeir/XfmrScatter.JPG?raw=1

How does the mass of a transformer scale with frequency?

I want to make a 120v 400 Hz power supply. I might boost my 48v up to
200DC and use an isolated h-bridge out to the load, or we could put
the bridge down at 48v and boost with a biggish transformer.

I\'ll have lots of air flow, so maybe I can push things some too.

Weight is almost linear with power, and inversely with frequency.

When I needed a 115V 400Hz for DO-160 aviation equipment development, I
ordered a 100W amplifier set from Amplimo (https://www.amplimo.nl/):
Mains transformer (toroid 115/230V in), rectifier, capacitors, amplifier
module, and an extra mains transformer (used in reverse) for the 115V
output.
Added a 400 Hz oscillator with a timer controlled gain control (4051 MUX
with some resistors) to create the required brownout and dropout
profiles. The customer was so amused they ordered some for their
production and test line (until then, they used a gigantic motor + 400Hz
dynamo in the basement to get 400 Hz).

Arie

I think so... for a given core, power scales linearly with frequency.
A simple scribble with a 4-winding transformer suggests that.

Thanks

John

You have to be prepared for larger core losses due to the
higher frequency if you use the same core material.

The higher frequency core materials are bulkier
for the same power due to the smaller permeability.

I\'d use a 400 Hz transformer.

--

-TV

 

[Arie de Muijnck]

On 2022-04-06 18:33, jlarkin@highlandsniptechnology.com wrote:

On Wed, 6 Apr 2022 18:24:49 +0200, Arie de Muijnck
eternal.september@ademu.com> wrote:

On 2022-04-06 17:53, jlarkin@highlandsniptechnology.com wrote:
https://www.dropbox.com/s/jnb3jmw8rcmdeir/XfmrScatter.JPG?raw=1

How does the mass of a transformer scale with frequency?

I want to make a 120v 400 Hz power supply. I might boost my 48v up to
200DC and use an isolated h-bridge out to the load, or we could put
the bridge down at 48v and boost with a biggish transformer.

I\'ll have lots of air flow, so maybe I can push things some too.

Weight is almost linear with power, and inversely with frequency.

When I needed a 115V 400Hz for DO-160 aviation equipment development, I
ordered a 100W amplifier set from Amplimo (https://www.amplimo.nl/):
Mains transformer (toroid 115/230V in), rectifier, capacitors, amplifier
module, and an extra mains transformer (used in reverse) for the 115V
output.
Added a 400 Hz oscillator with a timer controlled gain control (4051 MUX
with some resistors) to create the required brownout and dropout
profiles. The customer was so amused they ordered some for their
production and test line (until then, they used a gigantic motor + 400Hz
dynamo in the basement to get 400 Hz).

Arie

I think so... for a given core, power scales linearly with frequency.
A simple scribble with a 4-winding transformer suggests that.

Thanks

John

Yes, which is exactly why switching PSU\'s are now the standard. The cost
saving in iron (ferrite) and copper and capacitors, and all transport
costs, far outweighs (pun intended) the cost of the semiconductors.

And why airplanes use 400 Hz - the tiny transformers I had designed in
in the product were amusing, 8 times smaller than the usual 50 hz versions.

Arie

 

[Arie de Muijnck]

On 2022-04-06 18:44, Tauno Voipio wrote:

On 6.4.22 19.33, jlarkin@highlandsniptechnology.com wrote:
On Wed, 6 Apr 2022 18:24:49 +0200, Arie de Muijnck
eternal.september@ademu.com> wrote:

On 2022-04-06 17:53, jlarkin@highlandsniptechnology.com wrote:
https://www.dropbox.com/s/jnb3jmw8rcmdeir/XfmrScatter.JPG?raw=1

How does the mass of a transformer scale with frequency?

I want to make a 120v 400 Hz power supply. I might boost my 48v up to
200DC and use an isolated h-bridge out to the load, or we could put
the bridge down at 48v and boost with a biggish transformer.

I\'ll have lots of air flow, so maybe I can push things some too.

Weight is almost linear with power, and inversely with frequency.

When I needed a 115V 400Hz for DO-160 aviation equipment development, I
ordered a 100W amplifier set from Amplimo (https://www.amplimo.nl/):
Mains transformer (toroid 115/230V in), rectifier, capacitors, amplifier
module, and an extra mains transformer (used in reverse) for the 115V
output.
Added a 400 Hz oscillator with a timer controlled gain control (4051 MUX
with some resistors) to create the required brownout and dropout
profiles. The customer was so amused they ordered some for their
production and test line (until then, they used a gigantic motor + 400Hz
dynamo in the basement to get 400 Hz).

Arie

I think so... for a given core, power scales linearly with frequency.
A simple scribble with a 4-winding transformer suggests that.

Thanks

John


You have to be prepared for larger core losses due to the
higher frequency if you use the same core material.

The higher frequency core materials are bulkier
for the same power due to the smaller permeability.

I\'d use a 400 Hz transformer.

Which is why I used (Amplimo) toroids - they are good until several kHz.

Arie

 

[Jan Panteltje]

On a sunny day (Wed, 06 Apr 2022 08:53:22 -0700) it happened
jlarkin@highlandsniptechnology.com wrote in
<2fdr4hdk4ni4l5ds6vb97hkgtvbiufs47u@4ax.com>:

https://www.dropbox.com/s/jnb3jmw8rcmdeir/XfmrScatter.JPG?raw=1

How does the mass of a transformer scale with frequency?

When I wind some transformer I usulally look at the no load primary inductance
so it is high eneough not to drain power,
Then for that L and the given Core material I get number of turns
Many of thsoe core sellers specify a core size for a given power.
The load current, number of turns and wire diameter will give you weight of the coils.
That weight is to be added to the core material for total \'mass\' if that is what you mean.

I want to make a 120v 400 Hz power supply. I might boost my 48v up to
200DC and use an isolated h-bridge out to the load, or we could put
the bridge down at 48v and boost with a biggish transformer.

Why not balanced with 2 transistors and a transformer 48 to 120 V
___________
T1 ______ ||(
)||(
48 V +--- ||( 120 V
______)||(
T2 ||(__________


Dunno how accurate it needs to be, replace the T1 T2 with thyristors, tune it with a big cap and make it self-oscillating?
___________
T1________________ ||(
| )||(
=== 48 V +--- ||( 120 V
_|______________)||(
T2 ____ ||(__________
feedback ____) ||


Or use the almost all knowing google:
https://www.google.com/search?q=48V+DC+to+120V+AC+400Hz++circuit+diagram
select \'images\' for circuits.


>I\'ll have lots of air flow, so maybe I can push things some too.

Yes was storm here too

 

[Jan Panteltje]

On a sunny day (Wed, 6 Apr 2022 18:24:49 +0200) it happened Arie de Muijnck
<eternal.september@ademu.com> wrote in <t2kesh$3t5$1@dont-email.me>:

On 2022-04-06 17:53, jlarkin@highlandsniptechnology.com wrote:
https://www.dropbox.com/s/jnb3jmw8rcmdeir/XfmrScatter.JPG?raw=1

How does the mass of a transformer scale with frequency?

I want to make a 120v 400 Hz power supply. I might boost my 48v up to
200DC and use an isolated h-bridge out to the load, or we could put
the bridge down at 48v and boost with a biggish transformer.

I\'ll have lots of air flow, so maybe I can push things some too.

Weight is almost linear with power, and inversely with frequency.

When I needed a 115V 400Hz for DO-160 aviation equipment development, I
ordered a 100W amplifier set from Amplimo (https://www.amplimo.nl/):
Mains transformer (toroid 115/230V in), rectifier, capacitors, amplifier
module, and an extra mains transformer (used in reverse) for the 115V
output.
Added a 400 Hz oscillator with a timer controlled gain control (4051 MUX
with some resistors) to create the required brownout and dropout
profiles. The customer was so amused they ordered some for their
production and test line (until then, they used a gigantic motor + 400Hz
dynamo in the basement to get 400 Hz).

Arie

Yes, that is how I make 60 Hz here in 50 Hz land,
100 W audio amp 60 Hz from PC signal generator
in 50 Hz mains transformer connected the other way around.
Not very efficient, but nice sinewave and no harmonics.
A simple raspberry followed by a low pass could drive that
(raspi audio out is some PWM I think, sure has RF on it).

 

[Dave Platt]

In article <t2ki95$afi$1@dont-email.me>,
Jan Panteltje <pNaonStpealmtje@yahoo.com> wrote:

Yes, that is how I make 60 Hz here in 50 Hz land,
100 W audio amp 60 Hz from PC signal generator
in 50 Hz mains transformer connected the other way around.
Not very efficient, but nice sinewave and no harmonics.
A simple raspberry followed by a low pass could drive that
(raspi audio out is some PWM I think, sure has RF on it).

It\'s pretty easy to connect a $10-or-so I2S audio DAC board to a Pi,
rather than using the on-board audio DAC. The ones I\'ve been using
(based on Ti/Burr-Brown PCM-series DAC chips) put out a pretty clean
waveform - one can add a very simple low-pass to block noise up
above a few hundred kHz if necessary.

 

[legg]

On Wed, 6 Apr 2022 18:45:43 +0200, Arie de Muijnck
<eternal.september@ademu.com> wrote:

On 2022-04-06 18:33, jlarkin@highlandsniptechnology.com wrote:
On Wed, 6 Apr 2022 18:24:49 +0200, Arie de Muijnck
eternal.september@ademu.com> wrote:

On 2022-04-06 17:53, jlarkin@highlandsniptechnology.com wrote:
https://www.dropbox.com/s/jnb3jmw8rcmdeir/XfmrScatter.JPG?raw=1

How does the mass of a transformer scale with frequency?

I want to make a 120v 400 Hz power supply. I might boost my 48v up to
200DC and use an isolated h-bridge out to the load, or we could put
the bridge down at 48v and boost with a biggish transformer.

I\'ll have lots of air flow, so maybe I can push things some too.

Weight is almost linear with power, and inversely with frequency.

When I needed a 115V 400Hz for DO-160 aviation equipment development, I
ordered a 100W amplifier set from Amplimo (https://www.amplimo.nl/):
Mains transformer (toroid 115/230V in), rectifier, capacitors, amplifier
module, and an extra mains transformer (used in reverse) for the 115V
output.
Added a 400 Hz oscillator with a timer controlled gain control (4051 MUX
with some resistors) to create the required brownout and dropout
profiles. The customer was so amused they ordered some for their
production and test line (until then, they used a gigantic motor + 400Hz
dynamo in the basement to get 400 Hz).

Arie

I think so... for a given core, power scales linearly with frequency.
A simple scribble with a 4-winding transformer suggests that.

Thanks

John

Yes, which is exactly why switching PSU\'s are now the standard. The cost
saving in iron (ferrite) and copper and capacitors, and all transport
costs, far outweighs (pun intended) the cost of the semiconductors.

And why airplanes use 400 Hz - the tiny transformers I had designed in
in the product were amusing, 8 times smaller than the usual 50 hz versions.

Arie

I think you\'re living in the past. 60-400Hz magnetics are
routinely shipped around the world for local cost reduction,
making \'iron\' transport costs irrelevent.

Only end-use weight and volume remain signifigant.

RL

 

[Piotr Wyderski]

Arie de Muijnck wrote:

Yes, which is exactly why switching PSU\'s are now the standard. The cost
saving in iron (ferrite) and copper and capacitors, and all transport
costs, far outweighs (pun intended) the cost of the semiconductors.

Their regulation capability is far better than that of the more
conventional PSUs.

And why airplanes use 400 Hz - the tiny transformers I had designed in
in the product were amusing, 8 times smaller than the usual 50 hz versions.

But why 400 then? A typical scaling factor would be 10, so 500Hz should
be expected. Instead, they have selected the odd value of 8. Backward
compatibility with an arbitrarily selected frequency back in the
medieval times?

Best regards, Piotr

 

[Mike Monett]

Piotr Wyderski <bombald@protonmail.com> wrote:

Arie de Muijnck wrote:

Yes, which is exactly why switching PSU\'s are now the standard. The
cost saving in iron (ferrite) and copper and capacitors, and all
transport costs, far outweighs (pun intended) the cost of the
semiconductors.

Their regulation capability is far better than that of the more
conventional PSUs.

And why airplanes use 400 Hz - the tiny transformers I had designed in
in the product were amusing, 8 times smaller than the usual 50 hz
versions.

But why 400 then? A typical scaling factor would be 10, so 500Hz should
be expected. Instead, they have selected the odd value of 8. Backward
compatibility with an arbitrarily selected frequency back in the
medieval times?

Best regards, Piotr

Aircraft are moving away from the fixed 400Hz frequency to variable
360-800Hz.

\"On the other hand, the innovation of power supply system in aircraft
performance in the system of power supply: 360~800Hz large capacity
variable frequency AC power system is using gradually instead of the
constant frequency of 400Hz power supply on most of the aircraft[3,4]\"

https://www.atlantis-press.com/article/25862618.pdf




--
MRM

 

[Piotr Wyderski]

Mike Monett wrote:

Aircraft are moving away from the fixed 400Hz frequency to variable
360-800Hz.

\"On the other hand, the innovation of power supply system in aircraft
performance in the system of power supply: 360~800Hz large capacity
variable frequency AC power system is using gradually instead of the
constant frequency of 400Hz power supply on most of the aircraft[3,4]\"

Interesting. Why not DC then? It is going to be consumed by a switcher
of some sort anyway, be it a PSU or motor controller.

Best regards, Piotr

 

[Mike Monett]

Piotr Wyderski <bombald@protonmail.com> wrote:

Mike Monett wrote:

Aircraft are moving away from the fixed 400Hz frequency to variable
360-800Hz.

\"On the other hand, the innovation of power supply system in aircraft
performance in the system of power supply: 360~800Hz large capacity
variable frequency AC power system is using gradually instead of the
constant frequency of 400Hz power supply on most of the aircraft[3,4]\"

Interesting. Why not DC then? It is going to be consumed by a switcher
of some sort anyway, be it a PSU or motor controller.

Best regards, Piotr

My Piper Malibu distributed power in DC. Various instruments either used DC
as is, or changed it to 400Hz. I believe larger A/C generate 3-phase.

A possible reason for limiting the frequency may be skin effect. When you
have to run power from the engines under the wings all over the plane, the
losses could become serious.



--
MRM

 

[Lasse Langwadt Christensen]

onsdag den 6. april 2022 kl. 23.26.01 UTC+2 skrev Piotr Wyderski:

Mike Monett wrote:

Aircraft are moving away from the fixed 400Hz frequency to variable
360-800Hz.

\"On the other hand, the innovation of power supply system in aircraft
performance in the system of power supply: 360~800Hz large capacity
variable frequency AC power system is using gradually instead of the
constant frequency of 400Hz power supply on most of the aircraft[3,4]\"
Interesting. Why not DC then? It is going to be consumed by a switcher
of some sort anyway, be it a PSU or motor controller.

does relays and switches used for ~400Hz AC need to be beefed up like for DC?

 

[whit3rd]

On Wednesday, April 6, 2022 at 8:53:36 AM UTC-7, jla...@highlandsniptechnology.com wrote:

https://www.dropbox.com/s/jnb3jmw8rcmdeir/XfmrScatter.JPG?raw=1

How does the mass of a transformer scale with frequency?

That\'s an interesting, and difficult, question. I\'m assuming power transformer with
unknown load on the secondary, there\'s current-transformer assumptions which are \'way different.

Firstly, you need the core not to saturate at rated input voltage and
no load; that means the core material\'s B-H curve has to be considered to set core size.
This is about the magnetic flux distribution in the area (cross-section) of its path.

Second, you need the primary and secondary wire resistances to be low enough for
acceptable heat losses (usually, primary and secondary will have same loss, but that\'ll
have steps at available gage sizes...) which means every core shape will have differing
size according to the throat available for windings. Variacs will have different
rules, because there\'s no separate primary and secondary wire gage, This affects
the magnetic path length, not the area.

Third, you need the whole assembly to stay cool; we don\'t usually see heatsinks on
transformers, but every pole pig IS certainly a kind of keep-it-cool problem, and
for high frequency, core losses (and maybe even skin effect in conductors) will have to
be considered even for small items.

With only the first item considered, cross sectional area is constant for peak current-turns
at no load, so expect V /f proportional to area, thus weight roughly scale by f**(-1.5).
It\'s a project that\'ll benefit from log-log and/or semilog graph paper.

 

[Lasse Langwadt Christensen]

onsdag den 6. april 2022 kl. 23.37.03 UTC+2 skrev whit3rd:

On Wednesday, April 6, 2022 at 8:53:36 AM UTC-7, jla...@highlandsniptechnology.com wrote:
https://www.dropbox.com/s/jnb3jmw8rcmdeir/XfmrScatter.JPG?raw=1

How does the mass of a transformer scale with frequency?
That\'s an interesting, and difficult, question. I\'m assuming power transformer with
unknown load on the secondary, there\'s current-transformer assumptions which are \'way different.

Firstly, you need the core not to saturate at rated input voltage and
no load; that means the core material\'s B-H curve has to be considered to set core size.
This is about the magnetic flux distribution in the area (cross-section) of its path.

Second, you need the primary and secondary wire resistances to be low enough for
acceptable heat losses (usually, primary and secondary will have same loss, but that\'ll
have steps at available gage sizes...) which means every core shape will have differing
size according to the throat available for windings. Variacs will have different
rules, because there\'s no separate primary and secondary wire gage, This affects
the magnetic path length, not the area.

Third, you need the whole assembly to stay cool; we don\'t usually see heatsinks on
transformers, but every pole pig IS certainly a kind of keep-it-cool problem, and
for high frequency, core losses (and maybe even skin effect in conductors) will have to
be considered even for small items.

With only the first item considered, cross sectional area is constant for peak current-turns
at no load, so expect V /f proportional to area, thus weight roughly scale by f**(-1.5).
It\'s a project that\'ll benefit from log-log and/or semilog graph paper.

can\'t it be more or less simplified to:
if you take a suitable transformer and run it at 8 times the frequency you can also
increase the voltage 8 times, and thus get 8 times the power

 

[Clifford Heath]

On 7/4/22 7:00 am, Piotr Wyderski wrote:

Arie de Muijnck wrote:
And why airplanes use 400 Hz - the tiny transformers I had designed in
in the product were amusing, 8 times smaller than the usual 50 hz
versions.

But why 400 then?

Probably to do with still using rotating converters and other
synchronous things. 24000RPM is feasible in 1950s technology, but much
more gets hard.

 

[John Larkin]

On Wed, 6 Apr 2022 21:19:49 -0000 (UTC), Mike Monett <spamme@not.com>
wrote:

Piotr Wyderski <bombald@protonmail.com> wrote:

Arie de Muijnck wrote:

Yes, which is exactly why switching PSU\'s are now the standard. The
cost saving in iron (ferrite) and copper and capacitors, and all
transport costs, far outweighs (pun intended) the cost of the
semiconductors.

Their regulation capability is far better than that of the more
conventional PSUs.

And why airplanes use 400 Hz - the tiny transformers I had designed in
in the product were amusing, 8 times smaller than the usual 50 hz
versions.

But why 400 then? A typical scaling factor would be 10, so 500Hz should
be expected. Instead, they have selected the odd value of 8. Backward
compatibility with an arbitrarily selected frequency back in the
medieval times?

Best regards, Piotr

Aircraft are moving away from the fixed 400Hz frequency to variable
360-800Hz.

\"On the other hand, the innovation of power supply system in aircraft
performance in the system of power supply: 360~800Hz large capacity
variable frequency AC power system is using gradually instead of the
constant frequency of 400Hz power supply on most of the aircraft[3,4]\"

https://www.atlantis-press.com/article/25862618.pdf

There are constant-frequency generators that always make 400 Hz. I
don\'t know how they work.

360 (sometimes 250) to 800 Hz is \"Wild power\", what you can get from
anywhere to stay alive. A ram air turbine is \"the thing you never want
to see used.\"

--

If a man will begin with certainties, he shall end with doubts,
but if he will be content to begin with doubts he shall end in certainties.
Francis Bacon

 

[whit3rd]

On Wednesday, April 6, 2022 at 2:51:50 PM UTC-7, lang...@fonz.dk wrote:

onsdag den 6. april 2022 kl. 23.37.03 UTC+2 skrev whit3rd:
On Wednesday, April 6, 2022 at 8:53:36 AM UTC-7, jla...@highlandsniptechnology.com wrote:
https://www.dropbox.com/s/jnb3jmw8rcmdeir/XfmrScatter.JPG?raw=1

How does the mass of a transformer scale with frequency?
That\'s an interesting, and difficult, question. I\'m assuming power transformer with
unknown load on the secondary, there\'s current-transformer assumptions which are \'way different.

Firstly, you need the core not to saturate at rated input voltage and
no load; that means...

With only the first item considered, cross sectional area is constant for peak current-turns
at no load, so expect V /f proportional to area, thus weight roughly scale by f**(-1.5).
It\'s a project that\'ll benefit from log-log and/or semilog graph paper.

can\'t it be more or less simplified to:
if you take a suitable transformer and run it at 8 times the frequency you can also
increase the voltage 8 times, and thus get 8 times the power

Yes, that\'s correct. I was thinking, though, of resizing the core which would shorten
the wire length required, thus allow thinner wire with similar resistance; a redesign of
the transformer for the higher frequency is different from using the same transformer.
So, my scaling assumes a transformer reconfiguration in shape. It doesn\'t get into
the correct way to do that wire re-dimensioning, because that includes dissipation of heat
changing with size... and heat can be shed by conduction, or convection, with different
power laws.