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Hopefully this helps to explain why the number of servos that you can run decreases as the battery cell count goes up.
The BEC circuit in a standard speed controller consists of several linear typ voltage regulator IC chips, usually 3 or 4 of them. These voltage regulators take the input voltage and reduce it to a fixed level, usually 5.0 volts, and drop the rest of the voltage across an internal solid state load. This excess voltage gets converted into heat energy which is dissipated out the metal tab that is on the back of the voltage regulator chip. The amount of heat that gets generated is proportional to the excess voltage that that is being dropped and the amount of current running through the regulators.
Let's take a look at a couple scenarios to see how this load changes with different voltages. For this example I will assume that we have a 35 amp ESC that has 3 voltage regulator chips in the BEC circuit, providing a maximum of 3 amps of BEC current at 5.0 volts.
First, if you run the ESC on a 2-cell Li-Po, you have 8.4 volts on a fully charged battery. Since the output of the BEC circuit is usually 5.0 volts, the BEC has to get rid of 8.4 - 5.0 or 3.4 volts. Most of the voltage regulators used in our ESC's can provide 1 amp of current, and dissipate about 5 watts of electrical energy without overheating. Since the power being dissipated by a part is equal to the voltage drop across the part multiplied by the current through it, the power dissipated by each voltage regulator can be easily calculated.
Let's assume that we want to pull the full 3 amps of current from the BEC circuit to drive 6 servos that pull 1/2 amp each. In the above example, there is 3.4 volts being dropped across the BEC circuit. Since the 3 voltage regulators share the load equally, each one will provide 1 amp for the total of 3 amps. Now, since the power that is dissipated in the voltage regulator chips is equal to the current times the voltage, we have 1 amp x 3.4 volts for 3.4 watts. You may remember that earlier I said that each of these voltage can dissipate 5 watts safely, so we are are OK with each regulator dissipating 3.4 watts.
Now let's up the voltage to a 3-cell pack, or 12.6 volts. Now the BEC circuit has to get rid of more voltage, 12.6 - 5.0 is 7.6 volts that the BEC regulators have to get rid of. If we try to pull the full 1 amp of current through each voltage regulator chip, for a total of 3 amps, we now run into a bit of a problem. If we take the 1 amp of current and multiply it by the 7.6 volts that we are trying to drop, we get 7.6 watts of heat energy. This exceeds the maximum capacity of 5 watts for each regulator, so it is too much.
To calculate how much current we can actually pull through the regulators, you take 5 watts, and divide it by 7.6 volts to get 0.658 amps. This is the maximum current we can pull through each regulator without exceeding its maximum power rating. Since there are 3 of them in this ESC, the total current available is now 0.658 x 3 or 1.97 amps. So if our servos pull .5 amps each, now we can just barely get by with 4 servos, where we could easily run 6 before.
Taking it one step further, if we go to a 4-cell Li-po battery, we now have 16.8 volts to drop down to 5.0 volts. This means that we have to get rid of 11.8 volts now. Just like we did before, since each regulator can dissipate 5 watts of heat, since we are dropping 11.8 volts, the maximum current available is 5 divided by 11.8 or only .424 amps. With 3 regulators you have a total of 1.27 amps available. This would only be enough current to run 2 servos now.
Hopefully this helps to explain why the number of servos that you can run decreases as the battery cell count goes up.
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