Why is this signal stronger on 50 Ohm input impedance ?

[MathWizard]

I have a 20ft wire strung up to try and measure AM radio strength, and test a tapped, air coil  inductor I made. 1 end of the wire goes to the 495uH tapped inductor, and scope gnd is on the other end.

The strongest station is 800kHz, looking at it with FFT on a SDS2204x-plus, when using cheap coax w/ alligator leads, and the scope on 50R input, the strongest signal I can get is -13dB. And it's also on the center tap . It measures ~200uH on either side. And the amplitude increases as I move up or down towards the center tap.

But with a probe and scope set to 10x, and 1M input on the scope, I get -23.5dB on the middle tap. And it's not the strongest signal tap I can measure with the 10x probe. The voltage increases as I move up the coil taps, like a voltage divider.


I'm just studying a chapter on transformers and mutual inductance, but what's going on there, how can I measure a stronger signal, with a 50R resistance in parallel to that tap ? The coil resistance is only 4.5R total, so the 50R barely makes a difference anyways, and 10M certainly doesn't. Was is something to do with the input capacitance ?

What am I seeing ?

[vk6zgo]

I have a 20ft wire strung up to try and measure AM radio strength, and test a tapped, air coil  inductor I made. 1 end of the wire goes to the 495uH tapped inductor, and scope gnd is on the other end.

The strongest station is 800kHz, looking at it with FFT on a SDS2204x-plus, when using cheap coax w/ alligator leads, and the scope on 50R input, the strongest signal I can get is -13dB. And it's also on the center tap . It measures ~200uH on either side. And the amplitude increases as I move up or down towards the center tap.

But with a probe and scope set to 10x, and 1M input on the scope, I get -23.5dB on the middle tap. And it's not the strongest signal tap I can measure with the 10x probe. The voltage increases as I move up the coil taps, like a voltage divider.


I'm just studying a chapter on transformers and mutual inductance, but what's going on there, how can I measure a stronger signal, with a 50R resistance in parallel to that tap ? The coil resistance is only 4.5R total, so the 50R barely makes a difference anyways, and 10M certainly doesn't. Was is something to do with the input capacitance ?

What am I seeing ?

The 20ft wire has significant capacitance to earth, so you aren't looking at a simple inductive or resistive circuit.
It might be fun to look at your setup with a NanoVna.

[T3sl4co1l]

What is the antenna capacitance? Is it tuning with the coil as you vary the impedance on it (namely where the 50R tap connects)?

Tim

[MathWizard]

Ok thanks, I'll try an equation I just saw for wire capacitance, in a sim. On the outer taps of either end, it did measure around -25dB with the basic cable. The probe measured around -30 and -18dB iirc, on the end taps, it seemed fairly linear across the taps, so I'll use it's values for making models of the radio front-end.

I forgot how strong these local signals are.

[T3sl4co1l]

That's not a great plan: capacitance depends on everything nearby.  You can't just measure it (e.g. DMM with capacitance range)?

Tim

[Bud]

Look up the "Maximum power transfer theorem".

Your tapped coil has different RF impedance at different taps (forget about DC resistance, it is irrelevant). The coil has higher impedance at its top end, so it matches the x10 impedance of your scope probe better then x1 probe. When you use x1 50 Ohm probe , ypu adjust the match by switching to a coil tap down the coil that is closer to 50 Ohm impedance.

[DaJMasta]

Your antenna is better matched to the 50 ohm impedance than the 10M impedance, so you're getting better power transfer into the lower load.  You don't have the units in your post, but your dB are normally dBm, decibels relative to a milliwatt, so it's not that the voltage appearing at the input probe tip is lower on the 10M impedance, it's that the power through it is, and this depends on matching the source to the load.

You could adjust or resimulate the antenna, but at 800kHz, you could probably just put an external load in series with the scope and leave it on 1M input.  So your circuit would be Antenna -> scope with 1M input and no probe, but with an external resistor in parallel to the scope, between the antenna and ground.  If this resistor is 50 Ohms, it should look just like leaving the scope on 50 ohm input and connecting the antenna directly, but you can vary your resistor choice (maybe try 40 Ohms or 75 ohms) and see if the power transfer is better.  I don't know if a low value trimpot is in your stash, but maybe that would be interesting to play with and optimize to find where your power transfer is highest (then you can adjust the antenna or loading to optimize that for 50 ohms or some other standard).

[MathWizard]

I've done a chapter on AC power just lately, that's fun, for simple circuits anyways. I worked out a big transfer function for the whole tank+CE amp circuit I'm just building now, but I got stuck on finding the poles, by reducing a 6th degree denominator, which should be 3, 2nd degree polynomials, with conjugate pair roots.

I've heard there's supposed to be a way using complex numbers, to factor any arbitrary degree polynomial, but I can't find it so far. And I haven't tried to find a root, by like Newton's method. I starting dividing the whole transfer function out, maybe I should finish that part. I guess I should drop the resistances, that would simplify.

I haven't tried it for just my input tank circuit, because IDK the right way to model or measure the antenna. Using an LCR meter, at 100kHz I measured 456pF between the antenna alone, and the ground of my scope, with an ESR of 402. Any lower frequencies, and it didn't really settle, so IDK if that should work or not.

The meter said there's 2.55mH between the GND and the wire, IDK what to make of that, with a Q of 8.7.

With the 20-30ft wire wrapped back in loop to measure, I got some double digit nH, so say 50nH, iirc.



Using the calculation for an infinite wire above a ground plane, I calculated 579 ohms, so if at 100kHz, thats 275pF. IDK if that's per meter tho, or if that's about what I measured ?

IDK about the impedance of EM waves, or what source impedance to use as the Vin, if I put a 456pF cap in parallel with the source to GND, well that won't do anything with a perfect Vsource.

All I did was go by my probe measurements, and the measured inductance of the 2 halves of the coil, and get about 16mVp as Vin. I forgot to mention above all the dB numbers are in dBVrms too.

For my amp tho, I used the Miller model to get an input capacitance of ~930pF with a gain of -80V/V. Then I've been using LTSpice to get the tank  section centred on the frequency I want.

[T3sl4co1l]

Ok, so let's say 456pF.  That seems the most likely of the available numbers.  (And your meter is lying, it can't be both inductance and capacitance at a given frequency; 2.55mH at 100kHz would be +1600j ohm reactance, while 456pF would be -3490j.  If it's inferring from |Z| instead, clearly the two checks were not at the same frequency.  It might not even be a single frequency, but harmonics included as well.)

At 800kHz, 456pF is 436 ohms.  The antenna is electrically short, so if we resonate this with a series inductance of 69.4uH, we get a remaining ESR of losses plus radiation resistance.  Radiation is likely a few ohms worth.  This can be matched with a transformer, or a fairly low tap on the coil, to give a more reasonable 50 ohms, or whatever else you might need for the circuit (a BJT CE amplifier for example might have an input impedance of low kohms).

"Radiation resistance" means the Thevenin equivalent (for series, or Norton for parallel) resistance that's coupled to radiating fields, i.e. the source resistance for received signals, and the load resistance for transmitted signals.  These are of course perfectly reciprocal so we can use both directions interchangeably for analysis purposes, and make our word choice based on context more or less (which, we're only receiving here, so that's fine).

If the resistance is say 2 ohms, then that can be matched to 50 ohms with a 1:25 impedance ratio, or 1:5 turns ratio.  Connect this transformer in series with the ground return of the inductor, and there's your matching.  A ferrite toroid >6mm would be a fine choice, and a couple turns primary will do.

For parallel resonance, the same inductance is used, but the parallel equivalent resistance is Q times higher instead of lower; that is, for Zo = sqrt(L/C) = 390 ohms, a 2 ohm ESR gives a Q factor of 195, so the EPR is 195 times higher or 76kohm.  This will be as good of a match to the scope probe as you can get, without extending it as a transformer of course (and even then, 100s of kohms are hard to construct in general, with stray capacitance and losses tending to limit things).  Or for an amplifier, most op-amps will be fine with that, or a JFET (common source).

Which since this isn't a two-terminal capacitor but one antenna to space, we are limited to one side being common-ground (which, we need an earth return wire somewhere; an earthed scope will do), and then the only meaningful difference between series and parallel is whether we connect the load in parallel or series with the inductor.

Parallel includes a tapped inductor, by the way.  Or, mostly does, if the coupling factor between halves is good.  A 39:1 tapping would match parallel resonance to 50 ohms, but somewhat higher might be needed for tapping a single-layer solenoid (which will also need to be re-tuned as the 50 ohms shunts out part of the inductance).

Tim