I am laying out an ESC - VESC design - and I came across a few papers from TI, ST, and ADI talking about running the sense lines from the phase shunt resistors to the amplifiers/CSAs as a differential pair on the PCB. The issue I'm having is with calculating the impedance of the differential pairs - this is a little out of my wheelhouse. Where I can create differential pair trace sets in Altium based on given impedance, I'm uncertain of how to calculate the impedance of the differential pair I need to bring to the amplifier. Can someone shed some light?
The issue I'm having is with calculating the impedance of the differential pairs [between the motor current sense resistor and the amplifier]
You can safely ignore transmission line effects in the motor current sensing resistor differential lines. You don't have to match impedances.
When should one consider transmission line effects? When can one ignore them? If the length of the connection is shorter than 1/6 of the length¹ of the raising edge, then transmission line effects should be considered.
\$ l_r = t_r c \$
\$ l_r \$ is the length of the raising edge [m]
\$ t_r \$ is the raise from 10% to 90% in [ns]
\$ c \$ is propagation speed in [m/ns].
Notice that the PWM frequency doesn't appear here. We're dealing only with the raise time of the edge.
Let's plug in some numbers. I'll guess that the raise time for the PWM drive² voltage is 20 ns. Propagation speed for FR4 PCB material³ c = 0.15 m/ns . The length of the raising edge is 3 m. If the current sense resistor is no further than 0.5 m from the current sensing amplifier, then you can ignore transmission line effects.
¹ The fraction varies from one text to another. I saw values between 1/4 and 1/10.
² I'll also guess that the PWM frequency is somewhere brtween 30 kHz and 100 kHz. You have room for raise time loner than 20 ns. Consider slowing down the raise time.
³ Value obtained from here.