So much ladened with confused theory, I just wonder how you are going to do troubleshooting field measurements when the point you want to probe at is of "unknown" impedance?
Theories sounded like textbook I must say, yeah!
Practically dumpfounded - How much voltage drop will you encounter if DG1022U is at high impedance, 10Vpp, sine wave at 25Mhz, and the oscilloscope is set to 1Megohm input impedance over the RG58 - BNC to BNC cable of length 2m? [knowing that the characteristic impedance of the RG58 cable is 50 ohms]. ?
With that findings, you build onto your foundation only to move forward.
Cheers;
It seems that you have confused a little. Here are discussed only simple and practical things.
To answer your question, I will try to explain some simple things:
- The output amplifier, of a typical function generator, has a very low output impedance. For practical reasons there is a resistor connected in series from it to the output connector. This resistor, almost always, has a value of 50 Ohms. This means that when any load is connected at the connector it is created a voltage divider with the upper resistor having this 50 Ohms value. The setting of the load impedance, on the generator, simply adjusts the amplitude of the amplifier to have on the load the "requested" value. It does nothing else.
- To simplify things about the transmission line (the RG58 cable): when it is terminated with a "pure resistance" equal to its characteristic value, then this resistance is "reflected" to the input. Anything else produces disturbances that need a little physics and mathematics to analyze them... (search for forward/reflected/standing waves on transmission lines). Also, have a look at the other specifications of the RG58, such as capacitance/resistance/inductance per length unit.
- It is already described a little the voltage divider of the probe...
- It is also proposed an experiment by sweeping the frequency... (even if the mentioned length of the line seems that is short relative to the wavelength, around 1/8, it can reveal some disturbances)
If you separate each one of the above, you will see that they are not a "mountain" but simple things...
In conclusion: you have to transfer the signal with a transmission line, up to a point and then measure it with a high-impedance probe. In accordance with the above, terminate the line with a suitable resistor and connect the properly adjusted probe on this resistance.