[Radio Wrangler]

Bipolar LS TTL isn't ideal. It can pull down strongly, but up only weakly, so its output impedance is different in each state. Later CMOS logic has a better output stage and gives a better defined output voltage in the logic 1 state. So it's worth trying 74HC family.

As for the filtered sine output, the RC RC RC network is looking for a much higher load Z than 50 Ohm cable. It will see 50 Ohm coax as yet more capacitance added to that final 1000pF. and if the cable goes into a genuine 50 Ohm load, then the amplitude will fall dramatically.

Yes, it can be calculated by hand by traditional means, but it's a lot easier to just put it into LTspice and then you'll see. You can easily play around with loading values and see their effects.

RC filtering is cheap and easy in some respects but it ain't half lossy, and offers a poor amount of filtering per dB of insertion loss. An LC filter is much less compromised, but then inductors cost a bit more.

You can design filters with unequal input and output impedances, but the load you'd need to put on the LS TTL driving the input of the buffers above and the RC filter makes it a bit extreme. Filters are also transparent, so changes in loading will affect the load it applies to whatever drives it... but here the large loss of the RCRCRC fixes that problem.

It's a compromise, in other words.

David