So I was measuring the induced voltage in a solenoid (air-core) with the primary solenoid being on the outside (parameters:$N_p=100$, $l_p=12.6cm$, $d_p=5.1 cm$, $N_s=50$, $l_s=6.3 cm$ and $d_s=3.1 cm$). We were using the ideal transformer equation with a small modification ($V_s = V_p \frac{d_s^2}{d_p^2}\frac{N_s}{N_p}$) to account for the smaller radius of our secondary coil. Our circuit was a function generator connected to an amplifier and the voltage across the amplifier was put through a $17 \Omega$ resistor and the primary coil. We were measuring directly on the terminals of the primary coil as well as the secondary coil using an oscilloscope.

All was well until we noticed that we are getting strange results only a few pairs were having. We were advised to measure the potential difference not only on the primary coil but to measure it directly on the terminals of the amp. Here comes the problem. As soon as the ground of the coax cable is disconnected from the circuit (The one measuring the primary coil) the output of the secondary coil changed significantly (Up until this point the phase difference in the sine wave between primary and secondary was negligible, but this caused it to jump to ~$\pi /2$). The weird thing was that the output measured on the primary coil/circuit was unaffected, while the secondary coil's voltage changed to the values that we should be getting according to simulation.

My question is twofold. One is whether someone can explain the phenomenon or give an idea as to what this might be, where to start looking and how to rule out specifics. Second is how do I find the voltage across the primary coil and only the primary coil without biasing my measurements.

A bit of further info: Oscilloscope is Rhode Schwartz RTB 2004 input impedance: $R=1M\Omega$ and $C=9pF$

EDIT: Both coils were connected using a coax cable, and although I do not know the exact capacitance I modeled them using $C=100pF$, which I inferred from a previous experiment.

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    $\begingroup$ Were you connecting your oscilloscope to the circuit using a probe or using a coax cable with no matching circuit between the circuit and the coax? (A schematic showing the setup would help make it clear). If you had no probe, then start by figuring out what's the capacitance of the coax cable and what's its effect at your operating frequency (which you should also probably tell us, if you want us to check your work). $\endgroup$ – The Photon Feb 14 '19 at 17:57

At frequencies significantly above the audio range, the stray capacitance and inductance of the O-scope leads themselves will present a load to the device being measured, and cause a voltage drop and/or a phase shift in the signal being measured. Avoiding this requires the use of a scope probe that has a miniature trimming capacitor built into it. Adjusting that trimmer cap nulls out this effect and prevents the scope from loading the source.

The other thing that might be happening is related to the ground connections in your circuit and the scope. It's possible to have stray currents running around on the ground lines if they are unartfully connected. This is too long a topic to dive into here, but most scopes have a ground lift switch which "floats" the signal ground off the chassis ground of the scope. Flipping this might make things better for you.

  • $\begingroup$ Both are things I considered but I don't see how the first would change the measurement in the secondary coil while leaving the measurement in the primary intact. The first I even modelled with LTSpice IV, but I could not reproduce the result. It seemed as if the resistor was replaced by one with tenth of the resistance. Fortunately the scope could be replaced by a multimeter for this experiment. $\endgroup$ – Lala5th Feb 15 '19 at 14:58
  • $\begingroup$ I have no answer to that, except to remark that weirder things than that have happened to me while making O-scope measurements. Checking the result with a multimeter is a good idea. $\endgroup$ – niels nielsen Feb 15 '19 at 18:22
  • $\begingroup$ Sorry man for dismissing your comment so early I have looked into it and I have not considered that the coax cable might have an inductance that would change anything, but now I thought, why not and added 1nH parallel inductor and the phenomenon appeared on the simulation. Still weird that the primary scope reading was unchanged $\endgroup$ – Lala5th Feb 15 '19 at 21:10
  • $\begingroup$ just another grain of sand in the Sahara of the inexplicable... O-scopes are mysterious devices... $\endgroup$ – niels nielsen Feb 15 '19 at 23:04

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