Does anyone here know how various high-integration tuners achieve more-or-less continuously-variable corner low-pass frequency on the baseband
 outputs?

I'm aware of switched-capacitor filters, but my understanding is that due to the high branch ratios, you need a clock with a very high ratio relative to the corner frequency (like 50:1 or 100:1), and so doing these for RF/IF filters isn't that practical.

Another approach is to have a little matrix of Ls and Cs and Rs, and switch different ones in to get a tailored response. But again, CMOS chips
  aren't that good at producing Ls and Cs of significant value.

Inquiring minds want to know....

-Marcus



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