Measuring Impedance
I saw a video today from one of the Youtube members that I subscribe to: Kevin Loughin KB9RLW. In the video he was demonstrating how to use an oscilloscope and a signal generator to measure the impedance of a circuit ( in this case, it was simply a toroid coil). The process made sense, but I was a little confused by his results. He found that by decreasing the test frequency by half (10 Mhz down to 5 Mhz), his impedance went UP from 533 ohms to 2395 ohms! I believe that is not reasonable, in that the impedance (inductive reactance, in this case) should have dropped by about half, to about 267 ohms. Inductive reactance varies directly with frequency, not inversely, and not by 6 times with a simple halving of the test frequency.
So after checking all of the math, which seemed to be fine, I set up an experiment in my shop to check the results using the method Kevin was using. Follow after the break to see my results…
Kevin’s video is here:
I started by checking other sources for a similar procedure. I found a source at http://www.zen22142.zen.co.uk/Theory/inzoz.htm
The premise is that you can place a resistor that is in series with the rest of the circuit, then take AC voltage measurements on each side of the resistor (V1 & V2). That allows you to calculate the current flow through the resistor (I). Once you know the current flow in the circuit, you can use the voltage measurement on the circuit side of the resistor (V2) to calculate the impedance of the circuit.
So first, find the current through the resistor:
I_{in} =  V1 – V2

R1 
Since the resistor and the circuit under test are in series, the current must be the same through both. So Now use the V2 measurement and the current to determine the impedance of the circuit:
Z =  V2

I_{in} 
The math appears to work out as I would expect it to. So the basic procedure appears to be valid.
I built a spreadsheet and used Kevin’s measurements as input, and got the same results that he did. But they still didn’t make sense.
So I set about duplicating the experiment here. Since Kevin’s work pointed to a coil with 533 ohms of reactance at 10 mhz.
Let’s see, the formula for inductive reactance is Xl = 2*PI*F*L. So dividing XL by (2*PI*F) should give us the inductance of the toroid.
L = 533/(2*PI*F)
L = 533/(6.28 * 10,000000)
L = 533/62,800,000
L = 0.000008487 henry, or 8.5 uh. I looked through my stash for something close. And I found an 8 uh coil.
Next, I measured the reactance of the coil with my MFJ259B antenna analyzer at 5 mhz. I found the coil to measure 246 ohms at that frequency. That is pretty close to the calculated 240 ohms from the XL=2*PI*F*L formula.
I also checked the reactance at 4 Mhz = 193 ohms, 3 Mhz = 142 ohms and 2 Mhz = 93 ohms, and found them all to be close to the calculated values for that inductor.
(Note that the impedance reading fluctuated a couple of counts, and I took an average of the reads as I read them, so the pictures may be off by a couple of counts)
My MFJ analyzer could not read the reactance at 10 mhz for this coil, because it exceeded the 650 ohms limit of the analyzer.
So that confirmed for me that the impedance should go down as frequency goes down. Notice that the 2 Mhz reading is about half of the 4 Mhz reading.
Next, I built a jig to duplicate Kevin’s experiment. I used a 1000 ohm resistor in series with the coil and took readings with my oscilloscope, duplicating Kevin’s test.
Coil measured  Frequency  Calculated Xl  Measured Xl  R Reference  V1  V2  Z Calculated  Error Percent  
7.65 uh  2 Mhz  96.132  93  1005  1.215  0.123  113.200  17.75%  
7.65 uh  3 Mhz  144.199  142  1005  1.215  0.183  178.212  23.59%  
7.65 uh  4 Mhz  192.265  193  1005  1.217  0.25  259.824  35.14%  
7.65 uh  5 Mhz  240.331  246  1005  1.217  0.323  363.104  51.08%  
7.65 uh  10 Mhz  480.663  N/A  1005  1.233  0.812  1938.384  303.27% 
You can see that the Z calculated starts off with a bit of an error at lower frequencies, and increases as the frequency is raised. At 10 Mhz, the method is useless for this coil. But in all cases, you can see that the impedance rises as frequency rises.
So why such a great error at higher frequencies? I decided to continue the experiment, but using my Hewlett Packard 8640B signal generator as the source, rather than the antenna analyzer. The results were nearly identical. So it had nothing to do with the source.
Next, I thought that maybe the coil itself was flawed. It’s possible that the capacitance between the windings, or core saturation, or something was contributing to the error.
I made a few more Xl calculations, and determined that a smaller coil of about 0.8 uh would result in measurements within the limits of my antenna analyzer.
So here is my new coil, wound on a T506 toroid core:
With this coil, the readings were more reasonable at the higher frequencies, good from 4 to 10 Mhz.
Coil Marked  Coil measured  Frequency  Calculated Xl  Measured Xl  R Ref  V1  V2  Z Calculated  Error Percent 
12t T506  0.727 uh  2 Mhz  9.135  9  1005  4.51  N/A  
12t T506  0.727 uh  3 Mhz  13.703  14  1005  4.48  0.042  9.511  30.59% 
12t T506  0.727 uh  4 Mhz  18.271  18  1005  2.43  0.045  18.962  3.78% 
12t T506  0.727 uh  5 Mhz  22.839  23  1005  2.525  0.059  24.045  5.28% 
12t T506  0.727 uh  10 Mhz  45.67  46  1005  3.6  0.166  48.581  6.36% 
12t T506  0.727 uh  12 Mhz  54.814  55  1005  3.46  0.2  61.656  12.48% 
12t T506  0.727 uh  14 Mhz  63.950  65  1005  3.53  0.25  76.600  19.78% 
12t T506  0.727 uh  16 Mhz  73.086  76  1005  3.12  0.26  91.363  25.01% 
12t T506  0.727 uh  18 Mhz  82.221  86  1005  3.08  0.29  104.462  27.05% 
12t T506  0.727 uh  20 Mhz  91.357  96  1005  2.84  0.305  120.917  32.36% 
So what did I learn from all of this? The method of using an oscilloscope and signal generator may be useful for finding the input impedance to a circuit or device, but try to make certain that you are testing at frequencies that are reasonable for the device. For instance, it is probably not reasonable to use an 8 uh coil in a 10 Mhz circuit. Stray capacitances, core saturation and maybe other effects may cause unexpected results.
January 1st, 2018 at 10:08 am
Randy,
That is a wonderful example of a well thought out experiment! It goes to prove what one of my old math instructors used to tell us and that is that you should have some idea of what the answer should be before you start solving the problem. Otherwise, how would you know if the answer you got was anywhere near what it should be. Also, once the answers you were getting still didn’t make all that much sense you went on to design a further experiment to investigate this. Very impressive!
One must know the limitations of his instruments and tools before he can place a lot of faith in their results. Good job!
73, Lynn, KJ3V
January 1st, 2018 at 12:27 pm
Thanks, Lynn! I learn more from failures than successes…
August 27th, 2018 at 2:28 am
I wonder Kevin if reading was influence by his system / component Parasitic Capacitance properties which lead to that high impedance at low freq.