Go to w2aew youtube videos to see all videos by w2aew.
NOTE: I'm just calling the author of this videos w2aew because this is his username on youtube, and also on several forums where he has answered questions about the videos. I don't remember whether he has mentioned his real name anywhere, but in any case, I'm sure that w2aew is more widely known in the electronics community. Actually, if you follow the link above you will not only find videos about analog scopes, but I will restrict my review to them.
You can get a very good introduction to analog scopes by watching these videos. Though normally I prefer written tutorials, in this case I must say that watching the videos is much better. However, if you would like to have a written tutorial (maybe so that you can keep it next to your scope) the Oscilloscope Applications Guidebook by BK Precision is a good one. If you are more interested in digital scopes, take a look at the XYZs of Oscilloscopes primer by Tektronix instead.
Before you decide which scope you buy, you might watch the video Analog Oscilloscope bandwidth considerations: It demonstrates why it is a good idea to have a scope with as much bandwidth as you can get. Even if your scope has sufficient bandwidth to watch all signals that you want to generate or amplify, there might be some parasitic oscillations at a much higher frequency. If you cannot see these oscillations on your scope and take the appropriate measures to eliminate them, the performance of your circuit might be degraded. Sadly, scopes with high bandwidths are also expensive (but if you are lucky you might find a secondhand analog scope with a high bandwidth for a decent price).
If you are new to scopes, start with AC / DC Coupling on an Oscilloscope. Using measurements on an example circuit, w2aew offers a good explanation of this important basics. Also very important is the Basic 1X and 10X Oscilloscope Probe tutorial, showing you examples of when you should use what probe. Later in the video he shows how you can properly compensate the 10X probes - you should watch this very carefully. In Oscilloscope AUTO Triggering explained is a good explanation of auto triggering for analog and digital scopes. Tektronix Oscilloscope Triggering controls and their usage is a detailed explanation of the triggering controls of analog scopes, a Tektronix scope is used as an example but the explanations are applicable to analog scopes in general. Analog oscilloscope ALT, CHOP, ADD, INVERT vertical controls shows when to use ALT and CHOP to switch between the channels. The example of a little transistor amplifier circuit shows how to use ADD and INVERT to make voltage measurements between two points. More details are covered in Using the ADD/INVERT mode on an analog scope to view differential voltages.
Another very basic video that you should watch (especially if you are new to scopes) is How to Measure Frequency with an Analog Scope - after a short fundamental explanation of frequency and period, w2aew explains how you can measure the period on an analog scope with the best possible accuracy.
The next videos cover some more advanced topics: Using Analog scope to view two signals of wildly different frequencies, How to get a stable scope display with two signals very close in frequency (for analog and digital scopes) and Tektronix delayed timebase operation.
You may also be interested in some other Recommendations for Introductions to Oscilloscopes (and probes).
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