I'm looking for double-checking my math/assumptions, and if possible, a physical explanation of the "rising corner frequency" phenomenon.
When controlling a DC brushed motor with PWM, typically by switching MOSFETs in a bridge configuration (or a single MOSFET plus reverse diode when driving in only one direction,) it is possible to limit the maximum amount of current seen by the MOSFET by measuring resistance and inductance of the motor, and setting the PWM on-time to be no more than an appropriate time.
For example, for a 16V drive of a 20 uH motor with internal resistance of 2 Ohm, the time constant is (0.000020 / 2.0) or 10 microseconds, and the current achieved after that time is 16V * (1 - 1/e) / 2.0 Ohm = 5.06A. Alternatively, if I have a fixed PWM frequency, the duty cycle has to be set appropriately to make the on-time be at the given length. For example, with a duty cycle of 20%, the total cycle time is 50 microseconds and the frequency is 20 kHz.
I want to reduce the risk of overloading the output MOSFET in the case of a short, so I add a 1 Ohm series resistor (rated for appropriate wattage at the expected duty cycle -- this is an example!) The time constant now shifts to (0.000020 / 3.0) or 6.7 microseconds. In effect, the corner frequency of the low-pass filter of the RL circuit has gone up; it now passes more high-frequency signal. This means that at the same 10 microseconds as before, the circuit has reached a higher percentage of its "final" current.
First: Am I missing something, or is this correct? (to the first order -- motors seem tricky when you want to model everything!)
Second: It seems unintuitive to me that adding resistance increases the passband of the filter. Is it correct to say that the reason for this is that the time constant measures "time to 1-1/e of final current," and the additional resistance makes "final current" lower? I e, the actual current growth / voltage drop "speed" in the inductor doesn't change; instead it's the "goal" that changes? The math is very clear that this change in time constant (and thus frequency response) happens, so I'm trying to find the right "hook" to anchor my physical understanding to.