BNC Cables and their impedances

V1=10 V(peak to peak), frequency of voltage source = 1kHz, D1 is a standard 1N4007 Silicon Diode, R1=10 kilo ohm (the load resistor)

In our electrical lab, we were given the circuit shown in the diagram. I haven't been able to perform this lab due to the pandemic. So I don't have a clear idea of the equipment and what the question means. The question is:

Assume that a BNC cable is connected across the resistor(R1) and fed into the DSO. To get the best possible bandwidth (limited by the scope), we should pick an impedance of 10 k Ohm for the BNC cable? Yes or No

Could you explain the terms used and what the answer would be?

What I know: In practice, there are 50 ohm and 75 ohm BNC cables. DSO is an instrument that is used for continuous measurement of properties of signal like voltage and current(unlike the multimeter which reports average values of AC currents). It has a certain range of frequency of input signal that it can measure.

• I really think you should ask your instructor about this. You want to make sure that you understand the specific issues that the instructor expects you to understand, because this kind of question will likely come up again in an exam. You may get answers here that are technically correct but won't help you get a good grade. Commented May 5, 2021 at 12:25
• @ElliotAlderson could you explain the terms used like the bandwidth and how that is limited by the scope? I would appreciate it. Commented May 5, 2021 at 12:31
• Oscilloscope probe cables, although they use BNC connectors are typically NOT standard 50 or 75 Ohm coax. (Some scopes have an option to use 50 or 75 Ohm coax, but the standard probe cables are not.) I will see if I can track down a reference, and post it here. Commented May 5, 2021 at 13:16
• As promised, here is an article which digs deep into secrets of oscilloscope probe cables. By digging deep, I mean the author actually dissects his probe cable. :-) as well as discussing the problems of reflections caused by impedance mis-matches. Commented May 5, 2021 at 14:01
• I agree with the first comment about asking the instructor. One thing I would ask about is how you can analyze the characteristic impedance of the BNC without knowing the input impedance of the DSO. Most DSO's have a setting to choose either 50Ω and high-Z (something like 10MegΩ). Commented May 5, 2021 at 18:33

The characteristic impedance of coaxial cable is given by the equation $$Z =\frac{60 \Omega}{\sqrt{\varepsilon_r}} ln{\frac{D} {d}}$$

Setting $$\varepsilon_r = 1$$

and

$$Z = 10000\Omega$$ we get D/d = 2.4e72.

So if we set the diameter of the central conductor to 1 mm we get an outer diameter far beyond the diameter of the known universe. I think that such a coaxial cable is not available in your lab.

You also should keep in mind that your instructor is intentionally misleading you by introducing the resistor R1 with the same resistance as characteristic resistance of the coaxial cable he is writing about. The intrinsic resistance of your source is given by your ideal voltagesource (when neglecting the diode) and is therefore zero. It is not 10 kOhm.

Firstly, I will assume that by "BNC cable" the question means a traditional scope probe with a BNC connector at the other end of a short cable. The DSO is a digital sampling oscilloscope (i.e. anything not out of the ark). These are not shown in the diagram.

The probe impedance does not arise from the cable's transmission-line characteristics; the cable is far too short at the given signal frequency. So don't worry about 50 ohm vs 75 ohm. Scope probes typically have a series resistor and maybe some other components in there. The question is effectively asking if it should present a 10k input impedance.

The answer is no. The 10k argument would only apply if you were seeking maximum power transfer. In the present situation, as in most, the higher the probe impedance, the less it will draw additional load and distort the signal.

I wouldn't normally suggest the answer, but the problem is so badly worded as to deserve it. For example in my world, a "BNC cable" is a coax cable with a BNC connector at each end, and the connector and cable impedances are matched. But it is not sensible to require that such a thing be connected across a resistor in an existing circuit!

NO, The connector has a 50 Ω impedance and operates best in the 0–11 GHz frequency spectrum. It has better performance than the BNC connector at microwave frequencies.