Eleaf Istick - Easy Mean to RMS Conversion Formulas

[donf99]

Hi, All...

My first post - I've been vaping since last Spring. I haven't touched a cigarette since my first puff.

I started with a fixed-voltage EGO-C pass-through battery with a few Aspire BDC tanks. The setup has been OK for me, until last week when the battery refused to shut off - likely due to a failed button.

As I was leaving on a business trip the next day, I made a quick stop to the local vape shop. They had no EGO-C style pass-through batteries, but had just gotten in a shipment of the Eleaf Istick full kits in all the color choices. I picked one up along with a Nautilus Mini tank with the BVC coils. What a great combo!

Like others, I noticed that the unit seemed to vape very hot on a voltage setting equivalent to the old EGO-C battery. After watching a few videos and reading some posts, I think I have a good grasp of the issue - the unit uses unfiltered PWM to down-convert the voltage, and is calibrated in mean voltage versus RMS voltage.

Being an engineer, I wanted to come up with an easy way to convert the displayed settings (based on PWM mean voltage) to the more conventional RMS-based settings so I could better evaluate power settings mentioned in various reviews and recommended power charts.

After playing with the Vrms and Vmean square wave formula, I came up with a very simple formula that allows converting the power setting as displayed on the Istick to an equivalent RMS-based power figure.

The formula is simply: Vmean * Vmax / Rcoil = Prms

No square roots to calculate - you can do the calculation in your head!

For example, you are running the Istick in vw mode and it displays 8.0 Watts, 4.0 Volts, and 2.0 Ohms of coil resistance. The voltage and wattage calculations are based upon mean PWM voltage, so are significantly less than the equivalent RMS values.

In this case the RMS power is the displayed voltage (4.0) times the battery voltage (5.5 for a full charge) divided by the coil resistance (2.0 ohms displayed) or:

4.0 * 5.5 / 2.0 = 11 Watts RMS

Easy and no square root calculations!

Here are the intermediate calculations:

Vrms = squrrt(Vmean * Vmax)
Prms = sqr(Vrms) / Rcoil

Substituting.......

Prms = sqr(sqrrt(Vmean * Vmax)) / Rcoil

The square cancels the square root operation so.....

Prms = Vmean * Vmax / Rcoil

For the curious, here are some other relevant formulas:

Determine mean voltage from battery voltage and the PWM duty cycle: Vmean = Vmax * DutyCycle% / 100
Determine mean power from mean voltage and coil resistance: Pmean = sqr(Vmean) / Rcoil
Determine mean current from mean voltage and coil resistance: Imean = Vmean / Rcoil

Determine RMS voltage from mean voltage and battery voltage: Vrms = sqrrt(Vmean * Vmax)
Determine RMS wattage from mean voltage, battery voltage and coil resistance: Prms = Vmean * Vmax / Rcoil
Determine RMS current from mean voltage, battery voltage and coil resistance: Irms = sqrrt(Vmean * Vmax) / Rcoil
Determine RMS wattage from mean wattage, coil resistance and battery voltage: Prms = squrt(Pmean) * sqrrt(Rcoil) * Vmax / Rcoil


I am puzzled by those who claim the Istick cannot regulate the voltage below the actual battery voltage (Vmax in the above formulas). It can, but it does so using PWM techniques - it does not use an analog regulator to down-regulate the battery voltage before further down-converting with PWM. There is no need for analog regulation and would add additional power losses in the linear regulator if it did so.

Best regards,

Don

 

[Woofer]

A PBusardo Review & Contest - The Eleaf iStick - YouTube

As I recall the measurements are around 22 mins in.

 

[readeuler]

Killer first post, friend! I will be sure to digest it all later, but I'll just say - you're going to do quite well here!

 

[donf99]

Here's a quick graph using my simple Mean to RMS power conversion formula. I show RMS and Mean power plots for 5 coil resistance values. You can see the difference in power between Mean (Istick) and RMS is worse the lower the coil resistance and the greater the difference between the voltage displayed on the Istick and the actual battery voltage. As voltage in the Istick is turned to the maximum, the difference vanishes.

Sorry the image is so small...I can't post a link to the full-size image, as I am a new user.

Best,

Don


This might work:


"projectmf.homelinux.com/ecig/Eleaf_Istick_Mean_vs_RMS_Power.jpg"

 

[DavidOck]

Nicely done, and welcome to ECF.

But curious about your given max voltage for fully charged. You state "the battery voltage (5.5 for a full charge)" - and while the IStick may be different, all the Lions I've used have a full charge voltage of 4.2?

 

[donf99]

The Istick allows setting the voltage up to 5.5volts. Looking on the scope, the duty cycle is near 100% at that setting, with a peak voltage of 5.5v on the square wave. If the battery is not running at 5.5vdc itself, the circuitry in the Istick is outputing a 5.5 volt input to the PWM chopper circuit.

Best,

Don

 

[Auxx]

iStick always boosts the voltage. Otherwise it would be impossible to use PWM method to lower down the voltage. It works in two stages:

1. Increases the voltage to 5.5V in boost circuit.
2. Decrease the voltage to a desired value in PWM circuit.

 

[Wow1420]

Thanks for the post donf99!

I hope we'll be seeing you on the long istick thread as soon as you get your 5 posts in! http://www.e-cigarette-forum.com/forum/variable-voltage-apv-discussion/601111-eleaf-istick.html

 

[donf99]

Yes, the voltage boost explains it. Vmax is the voltage from the boost circuit (not the raw battery voltage) which is then chopped by the PWM circuit at different duty cycles to result in the Istick displayed voltage, calibrated as mean voltage.

Thanks for the clarification!

Best,

Don

 

[DavidOck]

Thanks - makes sense that way. Battery voltage max is (probably) 4.2 / 4.1, but device output max is the 5.5.

 

[donf99]

iStick always boosts the voltage. Otherwise it would be impossible to use PWM method to lower down the voltage. It works in two stages:

1. Increases the voltage to 5.5V in boost circuit.
2. Decrease the voltage to a desired value in PWM circuit.

I'm thinking the boost circuit likely does regulate to 5.5 volts so that as the battery voltage sags with use, the boost circuit compensates and holds the Vmax value to a more or less constant 5,5v, at least until the battery is near the Istick's cutoff value.

Don

 

[donf99]

Here is an abbreviated link to the full size chart using the simple Pmean to Prms formula I mentioned earlier.

"projectmf.homelinux.com/ecig/Eleaf_Istick_Mean_vs_RMS_Power.jpg"

Best regards,

Don

 

[EBates]

Welcome aboard

 

[tiburonfirst]

Here is an abbreviated link to the full size chart using the simple Pmean to Prms formula I mentioned earlier.

"projectmf.homelinux.com/ecig/Eleaf_Istick_Mean_vs_RMS_Power.jpg"

Best regards,

Don

no problem posting larger pictures as long as you don't have them hosted on ecf just use the image icon, add your link at 'from url' make sure you do not click 'reference locally'

 

[donf99]

Ahhh...thanks!

And nice avatar!

Don

 

[tiburonfirst]

Ahhh...thanks!

And nice avatar!

Don

............................

 

[donf99]

I was informed by another member that the actual peak value of the PWM square wave is nominally 5.8 volts rather than the 5.5 volts I used in my calculation.

I have had hints that Istick's boost circuit drops the amplitude of the PWM square wave lower after the battery discharges below 2/3 when the Istick sets the voltage below a certain value. If true, that throws off these charts and tables when operating under those conditions.

Here are the updated charts and graphs, All assume a constant PWM square wave constant peak value of 5.8 volts.

The first chart is the interesting one - It shows the actual RMS watts output by the Istick for a given displayed mean voltage and coil resistance. It allows converting the displayed Istick voltage and resistance to the RMS wattage. Again, a Vmax (peak voltage of the PWM square wave) is assumed to always be 5.8 volts.

The second table just matches what the Istick already does for you. The mean watts shown on the second chart should match what is displayed on the Istick.

The last graph shows the difference between the mean watts and the RMS watts for a given displayed voltage and coil resistance.

 

[BigEgo]

I just bought one of these tonight. This graph is very helpful, as I noticed immediately it vaped hot. It's just unfortunate that we have to do these calculations manually when the engineers could have just used RMS values from the outset (which is the default in e-cigs nowadays).

I'm looking forward to a version 2. Hopefully they ditch PWM all together and implement a retractable spring loaded pin. Also wouldn't mind seeing it go to 30+ watts, but that might be asking too much.

 

[Auxx]

I have made an online converter based on your math. Will add credits later, need to start doing my work finally, lol. Enjoy anyways!

 

[Rsunderl]

I have made an online converter based on your math. Will add credits later, need to start doing my work finally, lol. Enjoy anyways!

Thanks for doing that - already have it bookmarked.