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Author Topic: Trying to understand battery power (math)  (Read 354 times)

W9IQ

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Re: Trying to understand battery power (math)
« Reply #15 on: December 16, 2019, 05:46:42 PM »

First thing you need to understand is just what an AMP-HOUR is. 
simple version is if a battery is rated for 1 AH (amp-hour) and its fully charged that you can draw 1 amp for one hour and the battery will be depleted.

That is too simple to be correct. Most lead acid type batteries rate their capacity over a 20 hour period. So your 1 Ah battery would be rated for a 0.05 amp draw over 20 hours.

If you draw more amps than 0.05 in this example, the Ah capacity will be less according to Peukert's law. The exact capacity depends upon the battery's construction.

Lithium ion batteries on the other hand will provide about twice the usable capacity.

- Glenn W9IQ
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- Glenn W9IQ

God runs electromagnetics on Monday, Wednesday and Friday by the wave theory and the devil runs it on Tuesday, Thursday and Saturday by the Quantum theory.

KA9OFN

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Re: Trying to understand battery power (math)
« Reply #16 on: December 16, 2019, 05:48:23 PM »

This article gives a straightforward explanation without getting too deep:

https://offgridham.com/2018/08/how-much-battery/

The Off Grid Ham blog in general is a good source for information. It's very user friendly!
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W9IQ

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Re: Trying to understand battery power (math)
« Reply #17 on: December 17, 2019, 01:28:35 AM »

This article gives a straightforward explanation without getting too deep:

https://offgridham.com/2018/08/how-much-battery/

The Off Grid Ham blog in general is a good source for information. It's very user friendly!

While that site makes some good points, the article contains a critical error. The author states:

Quote
A 35 amp hour battery can provide 35 amps for one hour.

This is completely incorrect in the context of the AGM battery discussed in the article. A 35 Ah AGM battery is rated for 1.75 amps over 20 hours before it reaches its terminal voltage. If you attempted to draw 35 amps, it would probably last less than 30 minutes. This would be an effective capacity of ~17 Ah or less. Peurkert's law predicts this and many of the larger AGM battery manufacturers publish data or charts to support this analysis.

I have written to the author of the web site to point out his error.

- Glenn W9IQ
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- Glenn W9IQ

God runs electromagnetics on Monday, Wednesday and Friday by the wave theory and the devil runs it on Tuesday, Thursday and Saturday by the Quantum theory.

W9IQ

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Re: Trying to understand battery power (math)
« Reply #18 on: December 17, 2019, 03:54:10 AM »

John KC3EDP,

We now return to our regularly scheduled program...

Are you OK with the math so far using your data? I am happy to discuss anything that isn't clear.

If there are no issues, the next section will deal with applying that information to batteries to get the needed operating hours or to figure out how long a battery would last.

- Glenn W9IQ
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- Glenn W9IQ

God runs electromagnetics on Monday, Wednesday and Friday by the wave theory and the devil runs it on Tuesday, Thursday and Saturday by the Quantum theory.

KC3EDP

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Re: Trying to understand battery power (math)
« Reply #19 on: December 17, 2019, 09:40:37 AM »

    No, please continue. I'm copy/pasting your formulas.

  I haven't vested into batteries yet, but am considering a lithium type.
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KC3EDP

WB6BYU

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Re: Trying to understand battery power (math)
« Reply #20 on: December 19, 2019, 07:58:27 PM »

The hardest part may be figuring out how much current your rig draws
on transmit, especially if you are using SSB.

Its easy with FM, as the transmit current is constant for each power setting
whenever the mic is keyed.  So let's start with that as an example.

Say your 2m FM rig draws 8 amps on transmit, and 1 amp on receive.  Then
you need to consider how much of each hour you plan to be doing each of
those.  In a normal QSO you might figure 50% duty cycle.  Listening to a
net you might transmit less than 10% of the time and listen the rest.  Let's
use 20% transmit as an example.

That means that, in each hour, you would draw 20% * 8 amps or 1.6 amp-hours
on transmit and 80% * 1 amp or 0.8 amp-hours on receive, for a total consumption
of 2.6 amp-hours of battery capacity for each hour of operation.

That is:

     Transmit power required per hour = % transmit time * transmit current
     Receive power required per hour = % receive time * receive current
     Total required power per hour = transmit power/hour + receive power/hour


Now, here's the problem with calculating the transmit current:  it varies with the
mode, output power, and other factors.  On CW, the rig draws full current when
it is keyed (and this can be measured at different power levels) but the output
is interrupted by the spaces between the dits and dahs.  So I generally figure
about 50% duty cycle during the time I'm transmitting (though it might be more
like 40%).  In my case, the rig draws receive current when the key is up, so I
can just cut my transmit cycle percentage in half and get reasonably close.  If you
are running VOX or manual switching, then the rig may draw more current when
the key is up than in receive mode, but not as much as in full transmit.

SSB is even more difficult, because the current varies with the voice waveform.
When  you press the mic button, the rig switches to transmit mode, which, with
a typical 100W radio might draw 4 or 5 amps.  Then, the louder your talk, the
higher the current goes from there up to a maximum of, say, 20 amps.  As a
rough guess, the average current is probably around 1/3 to 1/2 of the maximum
value, so with a radio rated for 20 amps on transmit you might figure only 10 amps
in the equation (more if you are using speech compression).

And if you reduce the power of an SSB rig, the current doesn't drop linearly as
one might expect.  Even if you turn the power down to zero, there is still that
minimum 4 - 5 amps of current.  So if you turn a 100W radio down to 40W output
or so, it might still draw 12 amps rather than 8.  You really have to measure that
with your own rig, and such numbers are not often included in the specifications.


The result of that formula is how many amp-hours of capacity you need to operate
the station for an hour.  Multiply that by the number of hours you want to work and
it gives you the required battery capacity.  Or divide the battery capacity by that
number and it gives you the number of hours of operation the battery will support.

Well, it isn't quite that simple, either.  Batteries have a maximum current rating
that you don't want to exceed, so you can't draw 120A for 1 minute out of a
2 amp-hour battery and expect it to survive.  And often (depending on the rig) the
battery voltage will drop below the minimum required by the radio before it is
depleted to the specified limit.  With lead gel batteries I allow a 50% capacity margin
(especially with used batteries).  With lithium types you probably run them much
closer to full depletion, as long as you don't totally drain them.


So the math is pretty simple, but there are a number of design choices (like how
much of the time you are transmitting) that will vary depending on your specific
application and operating style, and some that you really need to measure with
your rig if possible in the configuration / mode / power level you plan to use.

W9IQ

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Re: Trying to understand battery power (math)
« Reply #21 on: December 20, 2019, 08:33:36 AM »

John,

Since you said you are interested in using a lithium ion battery, here are the pertinent factors. First a bit of background information on the lithium ion technology:

Background Information

A secondary (rechargeable) lithium ion cell has a nominal voltage of 3.6 volts. There are variations in chemistry that can take this from about 3.25 volts up to 3.8 volts but the 3.6 volt version is the most widely available to consumers. The nominal voltage is the point half way point between charged and discharged. A lithium ion cell is considered fully discharged when it reaches 3.0 volts. So its usable range for most applications is from 4.2 volts down to 3 volts.

Lithium ion cells are rated by their amp hour (Ah) capacity. This rating is generally considered the "1C" rating. The 1C rating is its normal discharge rating - meaning that a cell rated for 3 Ah, for example, can deliver 3 amps continuous over a one hour period.  The 1C rating is always for 1 hour. During this time, the voltage will go from 3.6 volts down to 3 volts. If the current draw is less than the 1C rating, the cell will simply last proportionately longer. So for the 3 Ah cell, if you drew 1.5 amps continuously, the cell would last for a bit longer than 2 hours. Since the 1.5 amps is 1/2 of the rated 3 amp capacity, this is considered a 0.5C rating. The 0.5C rate is the profile that is used to find the nominal voltage of a cell.

You will often find two types of cells advertised: energy cells and power cells. The energy cell is designed to provide maximum performance at a discharge rate of 1C or less (some rate the capacity at 0.5C). The power cell is designed to allow a discharge rate of much greater than 1C, often to 10C. This means that if a power cell is rated for 3 Ah and it is permitted to be used at a 10C rate, that the cell can deliver 30 amps but only for a 6 minute or less period. When you exceed the 1C rate, the amp hour capacity will go down but generally only to about 90% or so of its 1C rating - so maybe in this example it would last for about 5 minutes. Extra care must be taken when discharging a cell near or above its 1C rate as this can generate excessive heat. This heat should be vented so as to not overheat the cell and possibly start a fire.

The temperature of the cell also affects its capacity. Most cells are rated at room temperature (25° C). If the cell becomes colder, its capacity reduces. For example, a typical cell at freezing (0° C) will have about 70% of its capacity. As the cell becomes warmer than room temperature, it gains a small bit of capacity but as the temperature continues to climb, the danger of overheating the cell grows. So always think through the temperature conditions under which your cell will be utilized.

To make a battery, multiple cells are combined. A 12 volt battery can be approximated with 4 cells in series. At full charge the standard chemistry battery would supply 16.8 volts (4.2 volts * 4 cells) and at full discharge it would supply 12 volts(3.0 volts * 4 cells). Always check to see if your radio will work within this voltage range. This represents 13.8 volts +21%/-13% radio rating, for example.

Lithium ion cells should not simply be hooked in series. They require a battery management circuit so as to properly balance the cells during charging, monitor the temperature of the cells during charge and discharge, manage the charging profile and limit the maximum current that can be drawn during discharge. Failure to use a properly engineered battery management circuit with quality cells can lead to a fire (remember the hover board fires of a few Christmases ago?). Check to make sure that any lithium ion battery you are using includes a battery management circuit and consult the datasheet for proper operation.

Also make sure that in use, you don't draw the cells down to less than their 3 volt limit unless otherwise indicated by the manufacturer as this will greatly reduce the overall life of the battery.

Your Application

Keep in mind that all of the following calculations are approximations that will get you in the ballpark for a solution. You should always test the final design to ensure it meets the minimum requirements.

We previously calculated that your average current draw will be 7.3 amps. This is based on a receive current of 1 amp and a transmit current of 22 amps. For the rest of this example, let's assume you wish to supply your radio for 10 hours with the lithium ion battery. The required battery amp hour capacity is then 73 amp hours (7.3 amps * 10 hours) - this would be the minimum required 1C rating. But it is always good to check on the "C" ratings based on the actual currents. On the average, the battery would be discharged at 0.1C (7.3 amps /73 amps), on receive it would discharge at  0.01C (1 amp / 73 amps) and at peak transmit current it would discharge at 0.3C (22 amps / 73 amps). Because all current drawn is less than the 1C rating, you would get a little more than the 10 predicted hours of use. Because all currents drawn are below the 1C rating, an "energy" style battery could be utilized to save cost.

Before settling on a particular lithium ion battery, it is wise to check the specifications to determine what cut off voltage was used for the 1C rating. Normally this should be 3.0 volts per cell but if the manufacturer specifies a lower voltage, you may find that your radio cannot operate at the lower voltage. This reduces the effective capacity of the battery for your application.

When you shop for a 75 amp hour lithium ion battery from this example, you will quickly find that a lead acid AGM battery is a much more economical purchase. But this does not tell the full story. A lithium ion battery will hold a higher voltage during its discharge cycle. A properly managed lithium ion battery will often last for 3 to 4 times the number of discharge cycles. And a lithium ion battery will be much lighter in weight.

Let me know if you have questions or comments.

- Glenn W9IQ





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- Glenn W9IQ

God runs electromagnetics on Monday, Wednesday and Friday by the wave theory and the devil runs it on Tuesday, Thursday and Saturday by the Quantum theory.

W9IQ

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Re: Trying to understand battery power (math)
« Reply #22 on: December 20, 2019, 09:20:10 AM »

Quote
During this time, the voltage will go from 3.6 volts down to 3 volts.

should be "...4.2 volts down to 3 volts"

- Glenn W9IQ
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- Glenn W9IQ

God runs electromagnetics on Monday, Wednesday and Friday by the wave theory and the devil runs it on Tuesday, Thursday and Saturday by the Quantum theory.

W9WQA

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Re: Trying to understand battery power (math)
« Reply #23 on: December 20, 2019, 09:56:23 AM »

i cant read it all, wow. "wall of words". simple solution:get 2 batteries. use one till it quits. make a note of how long it lasts.
thats pretty much what to expect next time...
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G4AON

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Re: Trying to understand battery power (math)
« Reply #24 on: December 21, 2019, 10:32:39 AM »

    No, please continue. I'm copy/pasting your formulas.

  I haven't vested into batteries yet, but am considering a lithium type.
I moved from using an AGM lead acid battery to a lithium iron phosphate type this year. They are hugely expensive but having hurt my back it was an easy choice. Check out the technology on Wikipedia, but don’t get too carried away unless you want to spend 3 or 4 times the cost of a premium AGM battery!

I have a page on battery choice for use with a 100 Watt transceiver, it may (or may not) help as there has already been a lot of useful info posted:
https://www.qsl.net/g4aon/batteries/

73 Dave
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KC3EDP

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  • Posts: 71
Re: Trying to understand battery power (math)
« Reply #25 on: December 21, 2019, 01:11:13 PM »

John,

Since you said you are interested in using a lithium ion battery, here are the pertinent factors. First a bit of background information on the lithium ion technology:

Background Information

A secondary (rechargeable) lithium ion cell has a nominal voltage of 3.6 volts. There are variations in chemistry that can take this from about 3.25 volts up to 3.8 volts but the 3.6 volt version is the most widely available to consumers. The nominal voltage is the point half way point between charged and discharged. A lithium ion cell is considered fully discharged when it reaches 3.0 volts. So its usable range for most applications is from 4.2 volts down to 3 volts.

Lithium ion cells are rated by their amp hour (Ah) capacity. This rating is generally considered the "1C" rating. The 1C rating is its normal discharge rating - meaning that a cell rated for 3 Ah, for example, can deliver 3 amps continuous over a one hour period.  The 1C rating is always for 1 hour. During this time, the voltage will go from 3.6 volts down to 3 volts. If the current draw is less than the 1C rating, the cell will simply last proportionately longer. So for the 3 Ah cell, if you drew 1.5 amps continuously, the cell would last for a bit longer than 2 hours. Since the 1.5 amps is 1/2 of the rated 3 amp capacity, this is considered a 0.5C rating. The 0.5C rate is the profile that is used to find the nominal voltage of a cell.

You will often find two types of cells advertised: energy cells and power cells. The energy cell is designed to provide maximum performance at a discharge rate of 1C or less (some rate the capacity at 0.5C). The power cell is designed to allow a discharge rate of much greater than 1C, often to 10C. This means that if a power cell is rated for 3 Ah and it is permitted to be used at a 10C rate, that the cell can deliver 30 amps but only for a 6 minute or less period. When you exceed the 1C rate, the amp hour capacity will go down but generally only to about 90% or so of its 1C rating - so maybe in this example it would last for about 5 minutes. Extra care must be taken when discharging a cell near or above its 1C rate as this can generate excessive heat. This heat should be vented so as to not overheat the cell and possibly start a fire.

The temperature of the cell also affects its capacity. Most cells are rated at room temperature (25° C). If the cell becomes colder, its capacity reduces. For example, a typical cell at freezing (0° C) will have about 70% of its capacity. As the cell becomes warmer than room temperature, it gains a small bit of capacity but as the temperature continues to climb, the danger of overheating the cell grows. So always think through the temperature conditions under which your cell will be utilized.

To make a battery, multiple cells are combined. A 12 volt battery can be approximated with 4 cells in series. At full charge the standard chemistry battery would supply 16.8 volts (4.2 volts * 4 cells) and at full discharge it would supply 12 volts(3.0 volts * 4 cells). Always check to see if your radio will work within this voltage range. This represents 13.8 volts +21%/-13% radio rating, for example.

Lithium ion cells should not simply be hooked in series. They require a battery management circuit so as to properly balance the cells during charging, monitor the temperature of the cells during charge and discharge, manage the charging profile and limit the maximum current that can be drawn during discharge. Failure to use a properly engineered battery management circuit with quality cells can lead to a fire (remember the hover board fires of a few Christmases ago?). Check to make sure that any lithium ion battery you are using includes a battery management circuit and consult the datasheet for proper operation.

Also make sure that in use, you don't draw the cells down to less than their 3 volt limit unless otherwise indicated by the manufacturer as this will greatly reduce the overall life of the battery.

Your Application

Keep in mind that all of the following calculations are approximations that will get you in the ballpark for a solution. You should always test the final design to ensure it meets the minimum requirements.

We previously calculated that your average current draw will be 7.3 amps. This is based on a receive current of 1 amp and a transmit current of 22 amps. For the rest of this example, let's assume you wish to supply your radio for 10 hours with the lithium ion battery. The required battery amp hour capacity is then 73 amp hours (7.3 amps * 10 hours) - this would be the minimum required 1C rating. But it is always good to check on the "C" ratings based on the actual currents. On the average, the battery would be discharged at 0.1C (7.3 amps /73 amps), on receive it would discharge at  0.01C (1 amp / 73 amps) and at peak transmit current it would discharge at 0.3C (22 amps / 73 amps). Because all current drawn is less than the 1C rating, you would get a little more than the 10 predicted hours of use. Because all currents drawn are below the 1C rating, an "energy" style battery could be utilized to save cost.

Before settling on a particular lithium ion battery, it is wise to check the specifications to determine what cut off voltage was used for the 1C rating. Normally this should be 3.0 volts per cell but if the manufacturer specifies a lower voltage, you may find that your radio cannot operate at the lower voltage. This reduces the effective capacity of the battery for your application.

When you shop for a 75 amp hour lithium ion battery from this example, you will quickly find that a lead acid AGM battery is a much more economical purchase. But this does not tell the full story. A lithium ion battery will hold a higher voltage during its discharge cycle. A properly managed lithium ion battery will often last for 3 to 4 times the number of discharge cycles. And a lithium ion battery will be much lighter in weight.

Let me know if you have questions or comments.

- Glenn W9IQ

   Thanks so much! Is there one you have experience with?
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KC3EDP

KC3EDP

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Re: Trying to understand battery power (math)
« Reply #26 on: January 18, 2020, 05:29:24 AM »

  Glenn is there a  lithium ion battery you may recommend?
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KC3EDP

W9IQ

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Re: Trying to understand battery power (math)
« Reply #27 on: January 18, 2020, 06:16:27 AM »

One brand that has targeted the ham radio marketplace and seems to get good reviews is Bioenno (https://www.bioennopower.com/pages/comm-equipment-ham-radio) although I have no personal experience with them.

Most major lead acid battery manufacturers are offering a lithium ion lineup. The market is dipping below $750 for a 100 Ah version as competition mounts. But watch the weight and the charge management requirements as you compare.

- Glenn W9IQ
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- Glenn W9IQ

God runs electromagnetics on Monday, Wednesday and Friday by the wave theory and the devil runs it on Tuesday, Thursday and Saturday by the Quantum theory.
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