In this section, we will examine two power switching examples, starting with the simulation of the power dissipation of a single diode circuit, as well as a transistor circuit, and then looking at the power dissipation in a boost converter. Here I have a rectification circuit with an AC source, 120 volt RMS at 60 hertz, which I have implemented in SPICE by identifying the peak voltage of a 173 volts. The source is connected in series with the diode, and the diode model is shown on top, as well as a load resistance of 100 ohms. As we then perform the simulation, we see the voltage that has been applied as a sinusoidal voltage with a peak value of 173 volts, but then also the current going through the diode, as well as the power dissipation in the diode. The power dissipation is calculated by taking the product of the voltage across the diode, meaning the voltage between node 1 and node 2, multiply it with the current that is going through that diode. Next, we can use one of the SPICE features to come up with the average power dissipation by hitting the "Ctrl" key and then selecting the particular label, in this case, the 140 instantaneous power dissipation. That then gives us a window containing the average power dissipation, which here is found to be about 470 milliwatts. We can do the same thing for the dissipation in the resistor, taking the average of the product of the current through the resistor R2, multiply it with the voltage at node number 2, which gives us an average value around 74 watts. Now, we can then compare these simulated values with the first diode loss estimate by assuming a certain on-voltage, I've picked here 0.8 volt, multiplied with the RMS current going through the diode, 1.2 amps, and then recognizing that only during half the period, the diode is going to be dissipating power. Then multiplying all three numbers, I end up with an estimated power dissipation of 480 milliwatts, which compares favorably with the 470 milliwatts from the simulation. Now, you could ask why I used an on-voltage of 0.8 volts, whereas typically one would quote 0.7 volt. But if you look at the series resistance in the model of 0.1 ohm and multiply it with the RMS current of 1.2 amp, that would be an additional 0.12 volt that you would have, and therefore, I came up with an estimate of 0.8 volts across the diode. The second example is that of a MOSFET that it's switching. I'm using here a pulse-width modulation and a switching frequency, 250 kilohertz, with a duty cycle of 50 percent. Corresponding circuit is shown here in the lower right of the slide. I have a power supply voltage, V1, which is ramped up in 1 microsecond to a voltage of a 1,000 volts. That power supply is then connected to a load resistance of 20 ohms, and then the actual MOSFET. For the MOSFET, I'm using a randomly picked MOSFET model from the SPICE library, and then I'm applying a gate voltage and I'm simulating a driver as being an ideal voltage source with still a series resistance of 5 ohm at the gate. Looking at the corresponding values for the voltage and the current as a function of time, what we see is that there is a very rapid transition to the extent that we don't really see on this timescale the detail during the switching itself. But the device is being turned on at 1.5 microseconds and then being turned off at 3.5 microseconds. The range I've shown here is a little larger than the period corresponding to the 250 kilohertz, which is 4 microseconds. In the analysis, we'll be then looking at the interval from 1 microsecond to 5 microsecond because that would be a full period. Here I'm then showing in the table, individual values that were extracted from the simulation. For the whole on-off cycle, I find that there is a total energy loss of 580 microjoule, corresponding to a total power dissipation of 105 watts. But then I can look at the individual components and I'm starting off with the range where the device is turned on from 1 to 2 microseconds, and I find the total energy of 258 microjoules. Next, I look at the power dissipation in the on-state from 2 to 3 microseconds. I find the corresponding switching energy of 16.7 microjoules, corresponding to a voltage across the transistor of 334 millivolts and a current going through of 50 amps, and combined that translates into a power dissipation of 16.7 watts. Looking at the turn-off cycle, I find total energy dissipation of 307 microjoules; and in the off-state from 4 to 5 microseconds, I find that there's only a very small dissipation energy 2.05 picojoules which corresponds to having a high voltage across the device. But the device is turned off so it only has a very small current, a leakage current going through, giving then steady-state power dissipation in the off-state of 2 microwatts, which is quite a bit smaller than the power dissipation when the device is turned on, as expected. In terms of the ratio between the voltage and the current, that is directly linked to the on-resistance of the device, which I can extract from this also, as being 6.7 milliohm. Now, zooming in even more into detail of the transient behavior, I've expanded the scale going only from 1.5 to 1.6 microseconds and I can then see that the voltage changes almost linearly as I turn on the device, whereas the current increases linearly. That means the maximum power is going to occur at the point where the product is the highest, and therefore, I'd half the voltage and half the current, or one-quarter of the peak power. The peak power for 1,000 volt and 50 watt, the total product is 50 kilowatts and the peak power is therefore one-quarter of that, 12.5 kilowatts. As I then look at the full width of half max of 20 nanoseconds of the instantaneous power dissipation, which is calculated as a product of voltage across the device and the current going through, I end up with a value of 250 microjoules, which is very close to the measured value in the simulation of 258 microjoules. Then I can do the same thing as the device turns off. That maximum power is the same, whereas the full-width half max in this case is a little larger, 25 nanoseconds, but the product compares well to the 305 microjoules that I've identified from the simulation. These are slight overestimate because in this range, the device is partially turned on as well in each of these ranges. But given that this is only over a short period of time, the total energy is relatively small compared to the switching energy. Now, that I've extracted the power dissipation in the on and the off state, as well as the switching energy, I can then come up with a chart that shows the total power dissipation as a function of frequency for a variable duty cycle. The power dissipation increases linearly with duty cycle, it also increases linearly with the switching frequency. Hence, we end up with a set of straight lines. Total power dissipation equation is shown here, where I assumed that the power in the off-state is negligible and the total power dissipation is then the power dissipation in the on-state times the duty cycle plus the switching energy of turning the device on and off, multiplied with the switching frequency. I've transcribed from the previous chart these individual values, which then led to this graph. Now, in this particular example, the power in the off-state is negligible, but it could actually become more significant if you have a higher leakage current and then especially at very low duty cycle and low switching frequencies. Then finally, I also have a numeric example here that goes back to the actual simulation I showed you earlier, looking at the dissipation, add a switching frequency of 250 kilohertz and a 50 percent duty cycle, and I find that I end up, based on these numbers, with an estimated total power dissipation of 151 watts, which you'll find this is a little larger than what I had on the table earlier on as 145 watts because the switching energies are slightly overestimated because of the range that I chose to identify the total energy.
