If you own osciloscope/spectrum analyzer that has max sampling
frequency of 20MHz and I would like to analyze spectrum of higher
frequency band(also 20Mhz wide) for example 90-110MHZ.
If the oscilloscope or analyser is well designed then it will no-doubt have anti-alias filters built in that restricts the maximum analogue spectrum to somewhat less than 10 MHz.
This means you can't rely on directly under-sampling in that device.
Is there a way(some analog circuit) that can convert that higher F
signal into lower F one, and keep some proportion / ratio ? So I could
determine original F? Basically I would like to "move signal down" the
Given that it is unlikely that the device can under-sample effectively, you should try and use "radio methods" such as mixing and filtering to lower the 90 MHz to 110 MHz band down to near base-band. Note that you are going to be limited to something a little less than 10 MHz base-band-width so, I would recommend a tight filter after the mixer that takes the relevant portion of the down converted signal into base-band. Then use the local oscillator (associated with down-converting) connected to a frequency counter so you know what part of the upper spectrum you are dealing with when you view the signals on your device.
Another term to look for is super-heterodyning (as per fairly standard radio receivers). You also might be able to use a standard FM radio receiver with some modifications: -
The original block diagram is from the superhet link above. I've marked it in red. This will likely get you a band from 88 MHz to 108 MHz (the standard FM broadcast band) with a detector output bandwidth of between 100 kHz and 200 kHz (something you'll need to measure). Good luck.