2018 Solution 01

An oscilloscope-probe of (-f3dB = ) 20 GHz bandwidth is paired with an oscilloscope of 20 GHz bandwidth. What is the approximate highest bandwidth you can measure with reasonable confidence?
We know that the answer we are looking for the -f3dB point of the combined system. This allows us to work with the signal amplitude. Let the gain of each stage be g1 and g2. In real life the total gain will be the product of the two gains. We can write,
​
20*log(g1*g2) = 20*log(g1) + 20*log(g2)
The composite system will have a -3 dB loss; implying that each may lose an equal -1.5 dB. Assuming a reasonable -20 dB/decade, we can calculate the decades (of frequency) lost for each -1.5 dB.
decades (Hz) = (1/(-20 dB)) * (-1.5 dB) = 0.075 decades
A decade is 10 times some frequency. Here the "some frequency" is the basic bandwidth of each system. Therefore 0.075 decades is 0.75*20 GHz = 15 GHz.