How about using a PLL with a mixer, to tune in? Would that work? How would I go about designing it?
Yep, it's possible.
A Superheterodyne structure will work but the operating bandwidth is very large.That's why a simple Mix+Osc configuration wil not be sufficient.
-First, a very wideband ( nearly DC to 4GHz) LNA should be used ( design is very tough but possible !! There are also some products from Minicircuits )
-A verywideband Mixer can be used ( err.. There are some diode or passive FET solutions, it's OK let say mostly possible )
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Local oscillator can not cover this bandwidth.That's the problem...
And all of them won't be low power design.
Another solution for Local Osciallator is to use a Fractional PLL+VCO from Hittite or Maxim
https://www.maximintegrated.com/en/products/comms/wireless-rf/MAX2871.html
https://www.analog.com/en/rfif-components/pll-synthesizersvcos/adf4351/products/product.html
As you see, Min. synthesizable frequency is starting from 25-30MHz, that's not proper for you...
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Another solution is to use a programmable divider with a fixed oscillator circuit in order to desired mixing signal.
http://www.centellax.com/sites/centellax.com/files/UXN14M32K.pdf
For instance, you design a 4GHz fixed ( by another PLL) oscillator and then you divide this signal to mix-down the input signal.Programmation ratio will be 1 and 4,294,967,295 so min. frequency
1Hz and max. frequency will be 4GHz.It seems pretty brillant.
So, theoritically it's possible to down/up convert the signals between 1Hz to 4Ghz to a fixed IF frequency.This IF frequency must be lower than the min. input freqeuncy.
For instance, if the min. input signal is 50kHz, the IF frequency may be 20kHz ( NZIF ).Then this IF signal can be processed by a seperate RSSI circuit to obtain signal strength in dBm.There will also be very carefully designed calibration routines...
It's a typical frequency synthesized signal generator design...