Transistor Safe Operating Area

Transistors differ in many aspects. One of them is their ”Safe Operating Area” (SOA). This area determines how much current can run through the transistor at a certain voltage. If you don't respect these limits, the transistor will surely fail, which is inconvenient at least. One good explanation on the importance of transistor SOA can be found at Rod Elliot sound products. However, his page doesn't go into how to interpret the graphs that can be found in manufacturers datasheets. And that is what I will try to do here.
To determine which transistors, and with which voltages, can be used in my 8 channel amplifier I have created a spreadsheet. I will use this as an example on how to read the SOA and temperature derating graphs in transistor datasheets.

SOA graphThis is a SOA graph.
As you can see, there are 4 types of limits.
The first, marked with a long/short dashed line is the current limit (usually of the actual wires used inside the transistor).
The second limit, marked with a dashed line is the thermal limit. This is caused by the fact that there is more heat generated inside the transistor package than it can actually transport to the outside world.
The third limit, marked with the solid line is the secondary breakdown. As the voltage grows higher, current hot spots appear in non-uniform parts of chip junctions and in defects within the chip. And because they become hotter, they will become more conductive, thus getting even hotter. This usually causes this part of the chip to melt and self-destruct.
The fourth limit, marked by the vertical line is the maximum collector-emitter voltage, which is dictated by the design of the transistor. This maximum collector-emitter voltage should exceed the total voltage of the powersupply, which is the sum of the + and - rails

Temp DeratingThis is a temperature derating graph.
This graph shows what the maximum power dissipation at a certain temperature is. This usually begins to drop from 25ºC.

My spreadsheet looks like this:

Spreadsheet

This is how it works:
The small table at the top-left contains 5 important variables.
The par devices is the number of transistors that will be used in the output (per supply-side). In this example, it says 1, which is the number of transistors per side that are used in my 8 channel amplifier. The safety factor determines how close you want to operate the transistors to their limits. If the planned amplifier is only going to drive pure resistances and you like living on the edge, enter 1. If the amplifier will be driving real loudspeakers and it is supposed to last some time, 2 is a better choice. The derate factor is the factor with which the power dissipation has been decreased at the expected operating temperature. A safe assumption for this temperature when using a properly chosen heatsink is 80ºC. So when you look at the power derating graph above, the maximum power dissipation at 80ºC is about 65 watts. The maximum at 25ºC is 125 watts. Calculating the derate factor is simply done by dividing these two: 65/125=0.52
The minimal load is up to the designer to decide. I chose 4ohms.
The maximum output voltage is the voltage of one of the rails of the split power supply (positive and negative PSU). This is also up to the designer to decide. In this example, it is 25V (use positive values).

The next column to fill in is the ”Max Ic (SOA)” column. These values can be found in the SOA graph, using the DC curve. For a collector-emitter voltage (Vceo) of 50V, the maximum collector current according to the DC curve in the SOA graph is 1A. For a Vceo of 30V, it is 4A. You need to fill in the whole column.

And that's it! The spreadsheet does the rest.
The derated Ic column calculates the maximum current that is allowed per transistor at the operating temperature (80ºC in this case). The Vout column shows the output voltage at a certain Vceo, and is calculated from what you gave as the max Vout. The 3 Iout columns show the current that flows through each transistor at this output voltage with different load-resistances. These values are divided by the safety factor you entered, 2 in this case.
The safe column shows what it's all about. It divides the derated Ic by the load current. This load current is taken from the column right next to it, which in this case is the 2ohm column. This 2ohm reflects the chosen load resistance (4ohm) divided by the safety factor (2). If the actual load current is higher than the maximum safe current (Derated Ic), the cells turn red. If it is safe, the cell remains white. The dark gray cells are not applicable (if you know of a way to let non-used cells magically disappear in excel, let me know!)
This column is also represented in the graph below the table.
In this example, when the output voltage is between 10 and 15 volts, the SOA of the transistor is exceeded and it will fail. This means that these transistors can't be used with a supply voltage of 25V and a 4 ohm load.

Only the cells that need to be filled in by the user, can be edited. The rest of the spreadsheet is locked. This prevents that I try to fill in the wrong column, when working at 2am. There is no password, so if you want to change anything, it can be easily done.
And special thanks go to Lukas Louw. This spreadsheet is based on his and he explained this concept to me :)