What would be the simplest BJT based *linear* ramp generator?
Replace Q1 with a PNP transistor (collector down) and you'll have a constant(-ish) current source.



simulate this circuit &ndash; Schematic created using CircuitLab

It would be better to use something like a 74HC123 to generate the reset pulse if you can't generate it digitally, but something like what you show would work.
Of course you can make the constant current source temperature compensated and do other things to make it better, but this is the simplest. For best results have a volt or two across my R2, however that limits how high the Vramp can go.