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Capacitor size

I am running a 20V DC battery power source with a resistance heater load. My switch is a PWM three position switch. On the high setting the power is constant 19.4V. Medium setting, one second on, one off. Low setting, one second on, three off.
What capacitor size would be needed to even out the lowest setting?
 
To answer your question: Likely huge, also likely not a good idea without circuit changes.

Take a look at
https://www.electronics-tutorials.ws/rc/rc_1.html
or similar. Google capacitor charging or similar.

But, other questions are probably better asked first.
Why?
Often heaters have significant thermal inertia, meaning that they heat up slowly and cool down slowly. This means that their temperature tends to be a smoothed version of the power going in anyway. Is there a strong motivation to smooth the input?
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If the PWM ran faster, it would give the heater less time to heat & cool beteween changes, be smoother in that the heating and cooling times would be shorter, so the heater instantaneous temperature would vary less.
If you put a capacitor directly on the output of a PWN, then the PWM circuit is seeing a quite different load: it may need changes if it is not to expire.
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So, a few more details?
What sort of heater, PWM supply, powers?
 
Energy in Joules is power in Watts times time in seconds and is also equal to half capacity in Farads times voltage squared.

E = Pt = 1/2 C V^2
 
To answer your question: Likely huge, also likely not a good idea without circuit changes.

Take a look at
https://www.electronics-tutorials.ws/rc/rc_1.html
or similar. Google capacitor charging or similar.

But, other questions are probably better asked first.
Why?
Often heaters have significant thermal inertia, meaning that they heat up slowly and cool down slowly. This means that their temperature tends to be a smoothed version of the power going in anyway. Is there a strong motivation to smooth the input?
.
If the PWM ran faster, it would give the heater less time to heat & cool beteween changes, be smoother in that the heating and cooling times would be shorter, so the heater instantaneous temperature would vary less.
If you put a capacitor directly on the output of a PWN, then the PWM circuit is seeing a quite different load: it may need changes if it is not to expire.
.
So, a few more details?
What sort of heater, PWM supply, powers?
 
I am using a standard car seat heater as the load. When I put my hand directly on it I can feel the pulses. My expectation is that smoothing out the current would save energy in the long run. I want to test it for battery longevity and that would answer that question.
I have used other PWM switches and they heat up. This one does not.
Energy in Joules is power in Watts times time in seconds and is also equal to half capacity in Farads times voltage squared.
External, thank you for the equation. I will give it my best shot. Great to see an explanation of equations with symbols a layman cannot understand.

E = Pt = 1/2 C V^2
 
The energy delivered to a heater is basically all turned into heat.
Smoothing the current will not save any energy.
.
If you want to get away from a perception pulses of hot & cooler, probbably better yo look to a PWM controller with a faster cycle time.
.
Again, if you want to experiment with a capacitor load, which is unlikely a good option, it will need a few more details, like a combination of the power involved, the current peak, the element resistance &c. These being related by Ohm's law one missing, would allow others to be calculated.
Sorry, never seen a seat heater, so no idea of typical values.
Between the two references, provided, you can likely calulate the ballpark value required as a feasibility test.
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Again, a acapacitor on the output of a PWM is likely to take it out of it's intended operating area, as it is seen as the load on the PWM drive. Also a capacitor discharging into a heater load with a time constant in the order of seconds, would be very large. Also assuming thatthe PWM controller cycle goes from powered to unpowered, rather than form powered 20 volts to powered zero volts.
.
All this suggests that doing this differently is probbably worth considering.
 
The energy delivered to a heater is basically all turned into heat.
Smoothing the current will not save any energy.
.
If you want to get away from a perception pulses of hot & cooler, probbably better yo look to a PWM controller with a faster cycle time.
.
Again, if you want to experiment with a capacitor load, which is unlikely a good option, it will need a few more details, like a combination of the power involved, the current peak, the element resistance &c. These being related by Ohm's law one missing, would allow others to be calculated.
Sorry, never seen a seat heater, so no idea of typical values.
Between the two references, provided, you can likely calulate the ballpark value required as a feasibility test.
.
Again, a acapacitor on the output of a PWM is likely to take it out of it's intended operating area, as it is seen as the load on the PWM drive. Also a capacitor discharging into a heater load with a time constant in the order of seconds, would be very large. Also assuming thatthe PWM controller cycle goes from powered to unpowered, rather than form powered 20 volts to powered zero volts.
.
All this suggests that doing this differently is probbably worth considering.
So why would a v capacitor reduce power consumption when running a motor. Is that just for a smooth start?
 
You can google and look for something to check what I say, as you wish.
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Of loads that need power, such as motors, inductive loads and heaters, heaters are the simplest; they look resistors. No substantial phase shifts.
Motors are a bit more complicated. They have inductors and the load depends on the mechanical load and the current is not necessarily in phase with the voltage, so changing the phase with capaicance can affect the power in the motor & the drive.
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Heaters are generally pretty simple. V*I = P.
For a resistive load, a well-deisgned PWM drive is a really efficient way to drive at less than full power.
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Smoothing the power consumption over time won't change the power consumption. Power is power.
If you don't like the pulses of hot & cooler, then that can be treated as above.
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