Lets say you are looking to measure the ripple (AC) on your 12V DC supply. You can set the 12V somewhere on the screen and try to see mV of ripple. If you increase the gain the 12V line goes off the top of the screen. So you wind up trying to see mV of ripple while the gain is set to 2V/division.
Set the input to AC and the 12V (or DC) is removed and you only see the AC part of the signal. Set the line in the center of the screen and increase the gain as much as you want the line is still still in the center of the screen.
Picture of power supply noise. (might be only 2mV) Can not be seen unless you remove the supply voltage (dc) and increase the gain to max.
Set the input to AC and the 12V (or DC) is removed and you only see the AC part of the signal. Set the line in the center of the screen and increase the gain as much as you want the line is still still in the center of the screen.
The last figure shows a 100 nF capacitor. They get the -3db frequency from fc=1/2*PI*1M*100nF)
fc is known as the -3db point or the corner frequency. It's the frequency where the output is down 70.7%or (sqrt(2).
A typical scope has in input Z of 1M shunted by 22pf, Why 22pf? When you add a x10 probe, it has an RC network in it too. C is variable and the coax has a capacitance per foot. The variable capacitor allows you to adjust the compensation so the divider is purely resistive. The bandwidth can actually increase using a probe.
The adjustable capacitor in the cable can be at the probe or at the connector. The probe tip have a x1, x10 and gnd switch.
What's compensation? Usually there is a 1kHz square wave signal available. The Forier series of a square wave says it's made of the sum of an infinate number of odd harmonics of the fundamental. In the limit, it needs an infinate bandwidth to display. So, you adjust the compensation capacitor so the square wave signal is square.
The DC/AC capacitor can also be after the attenuator where the impeadances are well known.