# Increasing the 50 Ohm bandwidth of an impedance-matched system

• decaf14
In summary: I think I need to go lower in frequency and increase the size of the matching network.In summary, you are looking for a way to increase the bandwidth of your 50 ohm parallel resonance circuit so that you can transfer more power without loss. You are looking into ways to have the Tx circuit sense the resonant frequency of the Rx coil and tune itself to stay matched. You are also looking into ways to increase the distance between the Tx and Rx coils.

#### decaf14

TL;DR Summary
I would like to increase the frequency range for which the impedance of my system is 50 ohms in order to reduce power losses due to impedance mismatch.
Hello,

Some trouble came up today with designing a 50 ohm system for a wireless powering project. I'd like to increase the frequency range for which my system impedance is 50 ohms in order to reduce power losses due to mismatch. I've simulated two RLC circuits in OrCAD SPICE to demonstrate my issue.

In one circuit, I simply simulated the RLC circuit by itself and measured the impedance. I did so by applying a 1A constant current and measuring the voltage. We know that Z=V/I, so the voltage I measure is proportional to impedance. In this circuit, I see what I expect to see: a constant real component of resistance (green) and a reactance (red) that crosses zero at the resonant frequency.

In the second circuit, I used an L network to match the impedance at resonance to 50 ohms.

The issue here is that my system impedance is only 50 ohms at the very peak. A very small mismatch in frequency can cause a very large mismatch in system impedance which can result in very large power losses.

I tried googling some terms to see if a topology exists to remedy such a problem, but I didn't find one. I'm basically looking for a "bandpass" transfer function where I have a 50 ohm pass band. I'm not looking to be spoon-fed the answer if a common one exists, but rather, I need some advice on where to start. Any references (textbooks, papers, articles, etc...) would be greatly appreciated. If not, your practical experience would be greatly beneficial. Do most RF engineers pick an exact system frequency and just stick to that?

Typical way for to increase bandwidth of 50 Ohm parallel resonance circuit is to have impedance at resonance at about 100 Ohm.

You should search for “broadband impedance match.” You are basically looking for a complex network of Ls, Cs and, if you are at high frequency, transmission line segments, that wrap the impedance around and around 50 ohms on the Smith chart. It’s not easy.

Here is a summary list of approaches that will give you an entry into the literature.

decaf14 said:
Summary: I would like to increase the frequency range for which the impedance of my system is 50 ohms in order to reduce power losses due to impedance mismatch.

Some trouble came up today with designing a 50 ohm system for a wireless powering project.
So you are transferring power wirelessly between two tuned coils? And you are worried that a small mismatch in resonant frequencies between the Tx coil and the Rx coil will result in less power transferred, correct?

In that case, I would recommend that you look into ways that you can have your Tx circuit sense the resonant frequency of the Rx coil, and tune itself continuously to stay matched. You can do this several ways in a closed-loop fashion, and that will also account for drift over temperature and over time.

Can you think of a couple ways that this could be done?

BTW, how far are the two coils separated in this project? How much power are you wanting to transfer?

sophiecentaur, decaf14 and marcusl
Good point, berkeman, I should have read the post more carefully. A narrow bandwidth is fine in this case so long as you are tuned to it.

decaf14 and berkeman
berkeman said:
So you are transferring power wirelessly between two tuned coils? And you are worried that a small mismatch in resonant frequencies between the Tx coil and the Rx coil will result in less power transferred, correct?

In that case, I would recommend that you look into ways that you can have your Tx circuit sense the resonant frequency of the Rx coil, and tune itself continuously to stay matched. You can do this several ways in a closed-loop fashion, and that will also account for drift over temperature and over time.

Can you think of a couple ways that this could be done?

BTW, how far are the two coils separated in this project? How much power are you wanting to transfer?
Thank you guys for all the responses.

This is a great idea. I can't think of an analog way to do so, but digitally, I could place a small current sense resistor and use a microcontroller to continuously adjust the frequency until the current is highest. I think this is ringing a bell from a paper I read a while ago on WPT, actually.

My issue more lies in the actual Tx circuit for now, or at least I think it does. The trouble is that my impedance matching network cannot get s11 suficiently low. I'm inputting 20 ohms into an impedance matching calculator (the reactance should cancel at the resonant frequency), but I'm not getting a perfect impedance match because of a slight mismatch of component values that's impossible to get 100% accurate in practice. the issue is that even a small component mismatch will cause the reactance to skyrocket (relative to the resistance) away from 20 ohms, causing a large mismatch.

I've simulated this circuit because It's easier to demonstrate to people on forums, but I'm actually constructing it in real life and measuring it on a VNA. I've wrapped a 25 turn 25mm ID 30 AWG copper magnet wire inductor that measures 25 uH. I've placed it in series with ~40 pF of capacitance. The resistance due to wire losses is ~20 ohms. I was able to perfectly match previous circuits with smaller inductors (1 uH), but for some reason this circuit with a larger inductor is not matching well. I'm theorizing that the large inductor will work better for WPT purposes because it will create a larger magnetic field.

I'm trying to transmit 5 W of power and receive 750 mW of power for ~15% efficiency. This is from 1cm away. I've already done a demo where I light and LED from 1cm away with 1W of input power, but this circuit was only 8% efficient so I'm trying to play around with inductor designs to improve it. The trouble is, I'm transmitting to quite a small inductor. It's a ~30 turn 30 AWG 2mm diameter cylindrical air core inductor.

decaf14 said:
My issue more lies in the actual Tx circuit for now, or at least I think it does. The trouble is that my impedance matching network cannot get s11 suficiently low. I'm inputting 20 ohms into an impedance matching calculator (the reactance should cancel at the resonant frequency), but I'm not getting a perfect impedance match because of a slight mismatch of component values that's impossible to get 100% accurate in practice. the issue is that even a small component mismatch will cause the reactance to skyrocket (relative to the resistance) away from 20 ohms, causing a large mismatch.
Have you done much reading about how to optimize the wireless transmission of energy? You probably have, but it seems like you would want to minimize the resistive loss in both the Tx and Rx coils and circuits, to try to increase the efficiency. So 20 Ohms of parasitic resistance from such fine wire seems high to me.

I did a Google search on Optimizing Wireless Energy Transmission, and got lots of hits:

I only briefly skimmed a few of the hits (and many of them are for unusual configurations, like multiple Tx sources or multiple Rx sinks), but it seems like there must be some information in there that could help you with your optimization work.

What information have you been using so far to try to optimize the transfer of the energy across your gap?

Added to berkeman's post, I'd say your description is very confusing. You want to match to 50 ohms but then its 20 ohms instead, and the coil is 25 mm in diameter except when it's 2 mm? You're all over the place.

You are trying to operate at too high a frequency for a 25 uH coil, so the inter-turn parasitic capacitance and stray capacitance in the leads is throwing you off. Increasing C to maybe 1 nF or more will help. As far as geometry is concerned, a solenoid loses compared to a flat pancake coil. (Can you see why?) I second the advice to do some research (and some EM analysis!).

marcusl said:
Added to berkeman's post, I'd say your description is very confusing. You want to match to 50 ohms but then its 20 ohms instead, and the coil is 25 mm in diameter except when it's 2 mm? You're all over the place.

You are trying to operate at too high a frequency for a 25 uH coil, so the inter-turn parasitic capacitance and stray capacitance in the leads is throwing you off. Increasing C to maybe 1 nF or more will help. As far as geometry is concerned, a solenoid loses compared to a flat pancake coil. (Can you see why?) I second the advice to do some research (and some EM analysis!).
Hi Marcus,

The Rx coil is 2mm inner diameter. The transmitter is 25mm diameter. The load is 20 ohms. The characteristic impedance (system impedance to which I should match to) is 50 ohms. You can visualize the load in the circuit schematic (it's 40 pF in series with 25 uH and 20 ohms).

To be honest, I've been having a tough time researching this topic. I prefer textbooks to papers because the papers are often too cutting edge for the simple implementation that I'm looking for. In most papers I read (notably, a 2008 paper from MIT in which they near perfectly match their analytical to their experimental), they optimize using analytical equations and k coupling factors. I'm not sure how to measure the coupling factor with a VNA so I've been optimizing using s21 from a VNA instead, which has also been reported in literature.

I will do some research tonight to see if I can get a better process for design optimization. I'm still just trying to figure out this issue with s11 and impedance matching for the moment, though. I have measured that my impedance-matched WPT system works better than the non impedance matched system, but I see in the literature that they leave some systems totally unmatched.

From what I understand, the magnetic field strength of a solenoid is larger in the center, but a pancake coil mantains it's magnetic field for greater distances so I've chosen a pancake coil. It's also partially inspired by the pancake transmission coils we see in Qi wireless charging systems.

decaf14 said:
To be honest, I've been having a tough time researching this topic. I prefer textbooks to papers because the papers are often too cutting edge for the simple implementation that I'm looking for.
Have a look at this paper, which is one of the first on the Google hit list that I linked to:

https://aip.scitation.org/doi/full/10.1063/1.5007276

The math is pretty accessible, and there is pretty good information in it for geometries similar to what you are implementing. It looks like they are assuming a 50 Ohm source impedance Rs for the power source, but they are minimizing other resistances (like wire resistance). They explore optimizing the power transfer based on resonant frequencies, coil separation distance and load resistance, for example.

You might also try altering the source impedance Rs of the input power source in their equations, to see if it should be something different because of the loosely-coupled Tx and Rx coils.

What is your load circuit going to look like eventually? Will it look purely resistive (like an incandescent light bulb)? Or will it have a low power factor like a full-wave rectifying bridge into a storage capacitor? If you really want to optimize the power transfer, you should probably look into using a power factor corrected AC to DC converter circuit after your Rx coil...

Last edited:
decaf14
Thanks.

I'm not quite sure what the load circuit will look like. I have a design consideration to make for it. It's going to be a heating element, so right now I'm thinking that I can keep the ~MHz signal as is and gain additional heating via skin effect. It may have some slight inductance because it will likely be wrapped wire. Since it's a high frequency signal, the inductance may impede the current so I may have to use a rectifier anyways.

A resistive heating element would make a perfect load (power factor PF = 1.0). Don't use a rectifier unless you need it for some reason, and avoid the inductance of a coiled load resistance if you can.

Fun project!

decaf14
decaf14 said:
Since it's a high frequency signal, the inductance may impede the current so I may have to use a rectifier anyways.
To avoid the inductance, try the approach used to make non-inductive wirewound resistors. Fold the wire in half, like a hairpin, then coil it as needed. You end up with a bifilar winding where you have the same number of turns but they are wound in opposite directions, cancelling each others magnetic field.

Of course this only works if the heating coil is separate from the pick-up coil.

Cheers,
Tom

Tom.G said:
bifilar
Thanks Tom, you expanded my vocabulary.

berkeman said:
Have a look at this paper, which is one of the first on the Google hit list that I linked to:

https://aip.scitation.org/doi/full/10.1063/1.5007276
View attachment 250195

The math is pretty accessible, and there is pretty good information in it for geometries similar to what you are implementing. It looks like they are assuming a 50 Ohm source impedance Rs for the power source, but they are minimizing other resistances (like wire resistance). They explore optimizing the power transfer based on resonant frequencies, coil separation distance and load resistance, for example.

You might also try altering the source impedance Rs of the input power source in their equations, to see if it should be something different because of the loosely-coupled Tx and Rx coils.

What is your load circuit going to look like eventually? Will it look purely resistive (like an incandescent light bulb)? Or will it have a low power factor like a full-wave rectifying bridge into a storage capacitor? If you really want to optimize the power transfer, you should probably look into using a power factor corrected AC to DC converter circuit after your Rx coil...

Thanks for this berkeman. Also thanks Tom for the input on making a bifilar coil to create a purely resistive load.

I've run some simulations using the model they provided and my target frequency should be much, much, higher based on the dimensions of my Rx coil. The small inner diameter lends itself to better reception at higher frequencies, which makes sense. For a 25 turn 25mm ID Tx and a 2mm ID 30 turn Rx coil that are 1 cm away, maximum power transfer (not efficiency) occurs at 1.9 GHz. I may consider changing the dimensions of my Rx coil but it's hard because I'm size constrained.

I would also like to test this model against a physical model. It's something the authors didn't do but probably should have.

That frequency is a non-starter because your coil circumference equals the wavelength so it cannot be described by lumped element models (you can no longer talk about a coil or an inductance value, e.g.). Spice fails utterly in this regime. Suggest you stay in the HF regime.

berkeman
marcusl said:
...your coil circumference equals the wavelength...
Did I miss something?

<speed of light> / <freq> = wavelength
(3x108) / (1.9x109) = 0.158 meters = 158mm wavelength (≈6.2inches)

Diameter of receive coil = 2mm. Circumference = 6.28mm (≈0.25inches)

Broadcast-band radios use loop antennas smaller than a wavelength.

decaf14 said:
my target frequency should be much, much, higher based on the dimensions of my Rx coil.
Please keep in mind that you need to be careful about launching moderate power EM in the MHz and GHz bands. You have to have a license to transmit in much of the EM spectrum above a certain threshold of power (which varies by band), or you will be in violation of FCC rules (or whichever government agency regulates the EM spectrum usage in the different countries).

Wireless transmission of energy has to obey those rules just like radio operators do. If you do closely-coupled Tx/Rx systems and keep your coils well away from "antenna resonance", then you should probably be okay. But if you get close to using a resonant antenna type structure and start pushing several watts of energy into the setup in the MHz or GHz bands, expect a knock at your door fairly soon after you turn on the power.

https://www.extremetech.com/extreme/146585-a-closer-look-at-the-wireless-spectrum-crunch

dlgoff, marcusl, decaf14 and 1 other person
Tom.G, I was referring to the 25mm transmit coil. I did make a mistake—the circumference is close to half (not one) wavelength—but it doesn’t alter the conclusions. (Note to self: don’t attempt to do mental math for posts...)

Tom.G