Electronic – Glitch filter implementation

It's used when a low-pass filter is required. They are often used to filter noise from power supplies and in radio transmitters and receivers. In the latter applications it needs to be designed to match the impedances on the input and output.

I use this software for LC filter design, it's very good. The ARRL Handbook has design tables for the amateur radio bands.

A simulator (I use SPICE) is useful for checking a filter's characteristics.

Tunable filters over this sort of range are really, really difficult to do. For reals.

In high end network analysers you will find a special type of filter called a YIG filter (low end ones often don't use them because of their price) or a sweep oscillator based on a YIG VCO. Your best bet would be to just make 10 lowpass filters and switch them in with relays (or use relays to change the capacitance). You'll note that older signal generators do a lot of clicking when you crank the frequency up. If all of the HP RF boffins couldn't work out a good way of making tunable filters then I think you may struggle.

But to be honest, I am not sure why you are doing this to generate a sine wave. Just go DDS! Any modern signal and/or function gen will use DDS for this frequency range. You can buy off the shelf chips that go way above what you need; the AD9914 does <0Hz to 1.4GHz sine waves.