# Calculating gate resistor value for enhanced active-region stability

I'm working on an electronic load design driving an n-channel MOSFET with an op-amp.

I'd like to consider adding a gate resistor (R3 in the schematic) to improve the stability. I've searched quite a bit, but have been unable to find any hard description of just how to analyze that portion of the circuit. I understand the gate resistor forms a low-pass filter with the gate capacitance and that limits the bandwidth of the signal applied to the MOSFET, improving the phase margin and making the circuit less susceptible to oscillation.

I've also found some heuristics that the value ought to be somewhere between 10R and 1K, but I'd like to understand the design choice better.

I suspect I'm calculating a Bode plot pole for the RC filter formed by the resistor and the gate capacitance. However I'm not sure which capacitance value from the MOSFET datasheet to use (guessing Ciss = 2.4nF) and whether it's just a case of applying 1/(2πRC) to locate the pole or whether it's more complicated in this case. That works out to roughly 650kHz with a 100Ω value for R3, which makes me think maybe I'm on the right track.

Also I'd love any advice of where to reasonably locate the pole to maximize stability without negatively impacting the circuit performance. Just guessing, I would expect that bandwidth of 100kHz would be plenty, but not sure if there would be reasons to place the pole either lower or higher.

## 1 Answer

The pole formed by the gate resistor and the input capacitance would actually make the circuit less stable. This is because there will already be a pole in the opamp giving a 20db/decade gain change (up to 90 deg phase shift). If you add another pole in the loop you now potentially have 40dB/decade gain change with the phase shift being asymptotic to 180 deg.

I would add a resistor in the connection from the sense resistor to the opamp negative input and then add a capacitor from the output of the opamp to the negative input of the opamp. This can then give you a dominant pole that rolls off the gain before the phase shift in the output stage gives significant phase shift. It cane useful to put resistor in series with the feedback capacitor to give better gain at higher frequencies.

The resistor in the gate of the MOSFET can be useful for stopping high-frequency instability - a value of 22-100 ohms is appropriate there.

• Any advice on how to choose values for the feedback resistor and capacitor you mention? – scanny Jun 15 '15 at 4:17
• I would probably start with 1K and 1000pF and then simulate. – Kevin White Jun 15 '15 at 4:25
• Regarding the stability impact of adding the gate resistor (R3), that's not going to add a pole, is it? Wouldn't it just move a pole that was already there? As I understand it, the pole comes from the reactance of the gate capacitance interacting with Ro (the op amp output resistance) and R3 just moves that pole by adding to Ro, doesn't it? – scanny Jun 17 '15 at 5:16
• True, but it will move it down in frequency - probably to a region where it causes more trouble. After all the main pole in a dominant pole compensated opamp is going to be around 10Hz. – Kevin White Jun 17 '15 at 16:54
• After getting further in my learning, I realized that @Kevin is quite right about this, and that adding a so-called "gate isolating" resistor between the op-amp output and MOSFET gate is only useful when the feedback loop is connected to the op-amp output (the left side of the resistor). In the case above, it just moves the problematic pole downward in frequency (by perhaps a factor of two), which would certainly aggravate any stability problem. – scanny Aug 22 '15 at 19:20