It is a classic problem when designing with op amps: you need the output to go to zero, but — for most op amps — you can’t quite get down to the supply rail. If your power options are a positive voltage and ground, you can’t get down to zero without a special kind of op amp which might not meet your needs. The best thing to do is provide a negative supply to the chip. Don’t have one? [Peter Demchenko] can help. He uses a simple two-transistor multivibrator along with some diodes and capacitors to generate a minimal negative voltage for this purpose.
The circuit is simple and only produces a small negative voltage. He mentions that into a 910 ohm load, he sees about -0.3V. Not much, but enough to get that op amp down to zero with a reasonable load. Unlike other circuits he’s used in the past, this one is efficient. With a 5-volt input, it draws less than 1.5 mA.