Power and Energy Dissipated in Precharge Resistors
- Micah Black
The energy dissipated in the precharge resistors is important to manage so that we don’t destroy them through overheating.
Resistors are typically rated for an amount of power dissipation in steady state. Precharge, however is definitely not a steady state. As can be seen from the graphs below, the power dissipated in the precharge resistors is exponentially decaying - this should be an intuitive observation, as the voltage drop across them decreases, the current decreases. Since P = I2R, the power exponentially decays as the current linearly decays.
1.2k total resistance
300 Ohms total resistance
Because of this non steady-state condition, we do not need resistors that can sustain the full instantaneous power during steady state, nor does our cooling solution need to accommodate that amount of power.
Instead of steady state thermal analysis with thermal resistance, we need to ensure that there is enough thermal mass to absorb the spikes of power in the resistors, and then slowly dissipate it over time.
The resistor datasheets can help us here:
The energy of an individual pulse cannot be so high that the heat does not have time to escape the resistor. Hence for longer pulse times, there are larger amounts of energy that can be transferred outside of the resistor, so more total energy in the pulse is allowed.
For a 6J pulse, and a time constant of t = 0.162s, we can figure out if these resistors will work. Currently, we are planning to use 3 resistors in series, each of the MP915 15W variety to share the power load. This calculation is done with each resistor being 100Ohms, for a total of 300Ohms, according to the graph above.
Across the 3 resistors, we will have 2J each dissipated. For the pulse of 0.162s, which extends past the graph, we can extrapolate and each resistor will be able to handle roughly 4J? For the momentary overload condition that applies for these longer pulses, at 1.5x rated power:
1.5 x 15W x 5s = 112.5J. So we are well within the momentary overload maximum.
Keep in mind that the momentary overload mentioned is with heat sinking and the single pulse events ““Qualified” single event pulses determined from the chart do not require additional heat sinking.”
So, we should not need additional heatsinking.
One other interesting observation from the graphs is that the energy dissipated in the resistors is not affected by the value of the resistor (notice it is 6J in each). This is confirmed by mathematics here:
The energy dissipated in the resistors is the same as the energy stored in the capacitors.