**Local Bias Thermal Stability**
Hi minek123,

Bo Cordell covers this from p405 (2nd Ed). Thermal runaway without source degeneration resistors can occur if the thermal loop gain is greater than unity. The thermal loop gain is the product of 4 terms:

The temp-co of the MOSFET eg -6mV/C for an IRFP240

The Gm of the MOSFET bias current (eg at the turn on)

The thermal resistance from junction up to the bias sense point

The rail voltage (for a split rail amp).

Looking at the IRF640 Gm vs Id plot (no data for the IRFP240 but is usually the same die) we see the Gm is about 3A/V at 1 amp and we can interpolate for lower bias current of say 0.3A to get 1A/V.

The thermal resistance of an IRFP240 from junction to case is around 1.1C/W and then add around 0.5C/W for the thermal washer giving around 1.6C/W to the heatsink. To the bias sensor assume a bit extra say total now 2C/W. For an IRF640 TO-220 it is closer to 3C/W.

Now multiply all these and we get 6mV/C * 1A/V * Vrail * 2C/W <=1

Solve for Vrail <= 1/12m or

**Vrail <83 Volts for the IRFP240 with no source resistors**.

For the IRF640 <= 56 Volts with no source resistors.

If you use less bias the maximum thermally stable rail voltage increases. If you use more bias the rail voltage decreases!

If you have the SPICE model Kp then you can use that since Gm vs Id plots are not always available. The Gm vs Id for a MOSFET at lower currents is approximately

. Gm=Sqrt(2*Kp) * Sqrt(Id)

EG the IRFP240 has a KP of around 6-9A/V^2 giving a Gm of around 1A/V at 0.3A (like as from the Gm plot).

Now for your amp with a single pair of vertical MOSFET's like the IRFP240/9240.

Since a single pair cannot do much more than 50W for SOA reasons you should not use rail voltages over 35V in which case no source resistors will not lead to thermal runaway if your bias sensor is working properly and is reliable (bolted to the heatsink for peace of mind).

You can use the IRF640 TO-220 without source resistors as well.

For other MOSFETs you can do the sums and find out whether it is safe to use no source resistors in your Class-AB amp. For parallel MOSFET's the calculation applies to one of the group and as Elvee pointed out above you

**must match** the threshold voltages closely so they share currents reasonably well without source resistors. EG 30% match in Id at 0.3A idle is a 100mA and the Gm is 1A/V there so +/-100mV matching is need for the gate voltages.

BTW the more recent trench FETs with their much higher Gm and Kp values are not generally thermally stable with no source resistors in linear mode like power amplifiers and need source degeneration resistors to get the thermal loop gain below unit for stability.

Lastly, I have found not using source resistors in MOSFET Class-AB stages does make a big difference to the distortion at the lower power levels like up to 1W where it matters the most. I note Nelson Pass has recently found not using source resistors in Class-A has real benefits, including better sound quality, particularly for low feedback vertical power MOSFET amps

Nelson Pass BAF 2019.

Cheers,