A microcontroller drives a cable of characteristic impedance to a CMOS logic input
PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Electronics, Instrumentation & Communication · Digital electronics, embedded systems and data acquisition
Electronics for Measurement, Ch Digital logic and its physical realisation
Problem
A microcontroller drives a 2m cable of characteristic impedance Z0=50Ω to a CMOS logic input. The cable is long enough, relative to the driver's rise time, that it must be treated as a transmission line with reflections rather than as a lumped node. The driver's output resistance is Rs=10Ω; the CMOS input, presenting only a few picofarads and negligible input current, behaves as an open circuit at the far end of the cable.
((a)) Compute the voltage reflection coefficient at the source end of the cable, Γs=(Rs−Z0)/(Rs+Z0), before any termination is added.
((b)) Find the value of a resistor to add in series with the driver so that the source end is matched to Z0 (so that any wave reflected back from the open far end is fully absorbed and does not re-reflect).
((c)) Without the added resistor, ringing on the unterminated line corrupts bit 3 (the bit worth 8, counting bit 0 as the least significant) of one transmitted byte, flipping it from 0 to 1. The byte sent was 101000112 (hexadecimal A3; decimal 163 read as an unsigned byte, −93 read as two's complement). Give the byte actually latched, in binary, and its value as an unsigned decimal number and as a two's complement signed decimal number.