I'd like to view the phase shift between currents and voltages testing various combinations of inductor, resistor and capacitor networks. The voltages should be no problem, but how can I display the currents? Do I have to have some kind of special probe?
The simplest method is to put a small resistor in series with it, and measure the voltage drop. This is how a multimeter does it. This perturbs the circuit, of course--the voltage drop in the meter is called the "burden voltage", which is an apt name.
The second simplest is to use a current probe. I have a classic Tektronix P6042 that cost me $175 a few years back. It uses a combination of a current transformer and a Hall sensor to cover DC-50 MHz. Interestingly, clamping the probe over your signal wire adds series inductance. That causes a voltage drop at AC, almost like the DMM's burden voltage.
The most complicated is to build a transimpedance amplifier. This is basically an op amp inverter with the input resistor left off, so that you dump current straight into the inverting input. Ideally the op amp will force the voltage swing at its input to be small, so there's effectively much less burden voltage.
The circuit itself is conceptually simple--the parlour trick is getting it to work fast enough without oscillating when you hang a cable on its input.
Yes, or, just put a R in series with your circuit and measure it with a secondary channel on the scope. Make sure the commons of your probes (BNC) are isolated on the scope. I know My cheap hand held Owen is. Not sure about the Rigol etc..
The other tool is to get yourself a low current DC clamp meter with a BNC or adapter to plug into your scope, I have 2 60 amps and 1 650 amp. Thinking of getting a much larger one, soon.
If it's a current to ground, you can use an inverting op amp to generate a voltage signal (sometimes called 'transimpedance amp'). For some situations, a diamond transistor is a good sensor (and it'll be faster than most op amps); ground the 'base', current sense pin is the 'emitter', and output from 'collector' to ground through a resistor generates the voltage output.
If it is a current NOT to a midlevel power point (ground), the amplifier situation gets tricky, of course. Usually that means a sense resistor and an instrumentation amplifier are required. Sometimes, though, you can just connect two o'scope probes to the sense resistor and display the difference.
What's the highest frequency you are hoping to look at. If you are staying well away from ~1MHz, and are good at making your own circuits. Then I took the TIA at the bottom of your post to be a sign that you should make a TIA (Trans Impedance Amp.) I made a little one of these on some copper clad to look at I-V curves of diodes and things. One opamp, bypass caps, some R's and a switch. I was going to post a picture, but it's "on loan" to someone.
Here's how I learned to do it, with a current sense resistor. The pcb* was built to accept scope probes and will work reasonably well up to 2 MHz.
Current and voltage waveform
You can add a few extra solder points for you resistor, as you see in green, I have add connections for a capacitor.
If you have more questions about the pcb or use, ask.
*The pcb was designed to plug in a piezo ceramic transducer, a variable inductor was adjusted until the current and voltage were in phase. Used for measuring specs of our transducers to then calculate drive inductor and transformer ratio. Mikek
If you pull one apart you will see that it is a very tiny coil on a ferrite former. If you want to detect the current flowing in a pcb trace or wire you just align it with the trace and look at the output with a scope. A times 10 op amp helps since the output voltage is quite small.
I was just thinking that there must be current sensing circuitry in many SMPSs - the newer ones that provide for power factor correction anyway - so I guess it should be possible to obtain a suitable current sensing element for free from, say an old scrap computer for example?