Relationship between Q factor and the coupling factor of two wireless coils

CataM · Mar 12, 2017

bhl3302 said:
(2) regarding the equivalent capacitance of the Rx side, there is another DC block cap connected to the output of the receiver, and then feed as the input of a logic inverter. This is the picture that showed in an earlier post in this treadView attachment 136867. I am using this inverter (https://www.ti.com/lit/ds/symlink/sn74lvc1g97.pdf).
My guess is, if we assume the Cgs of the input MOSFET of the inverter is still in pF level, Cgs will connect in series with this 10nF DC blocking cap, then stay in parallel with that 10nF cap C_SEC. So the overall load of the secondary data coil is still several pF level, like what you have pointed out, around 130pF. Is this analysis correct?

1)Which circuit have you used to make the bode plot from post #12. I have assumed the circuit used is the one in post #6, in which the red dashed line at the right means open circuit. Am I right ?

2)I will take the bold text in the above quote as a typo and think you wanted to say 10 pF.

3) You have to see the equivalent circuit of what you have after the "DC block capacitor" because I guess it does not end there. If you take the simple internal circuit of a CMOS inverter (one P channel and one N channel) and nothing else connected to its output i.e. with the drain of the CMOS inverter's ouput open, then the capacitance seen by the "DC block capacitor is" :
(Cgs1+Cgs2)//(Series of Cgd1+Cgd2 and Cds1+Cds2)

bhl777 · Mar 13, 2017

CataM said:
1)Which circuit have you used to make the bode plot from post #12. I have assumed the circuit used is the one in post #6, in which the red dashed line at the right means open circuit. Am I right ?

2)I will take the bold text in the above quote as a typo and think you wanted to say 10 pF.

3) You have to see the equivalent circuit of what you have after the "DC block capacitor" because I guess it does not end there. If you take the simple internal circuit of a CMOS inverter (one P channel and one N channel) and nothing else connected to its output i.e. with the drain of the CMOS inverter's ouput open, then the capacitance seen by the "DC block capacitor is" :
(Cgs1+Cgs2)//(Series of Cgd1+Cgd2 and Cds1+Cds2)

Hi CataM, thank you for your help!
(1) For all the circuits I did the Bode test, I used the one connected to the input of the inverter. There is an additional 100k resistor in parallel with the inverter, to bias the inverter at its linear mode.
So the post #6 is not accurate, I am sorry for the confusion.

(2) you are right, that is my typo.
(3) Thank you for advising the calclation of the Cin of the inverter.

Right now my question has changed a little bit, is it any easy way (changing R, C or adding some blocks) to get a >0dB gain over the target 1MHz to 5MHz case? For example, I am replacing C_PRI and C_SEC with two caps 390pF, and it resonants at around 3MHz. But using this structure it cannot provide a >0dB gain between 1MHz to 5MHz.

Ideally I want to achieve the frequency response like a bandpass filter, that it can have a flat band with ~0dB gain (or positive gain), am not sure if it is easy to achieve. If not, can I at least get a >0dB gain in the entire 1MHz to 5MHz frequency range?

FvM · Mar 13, 2017

You are calculating a "gain" of the resonant circuit as below.

(1) I model the parasitic resistance (DCR and trace impedance of the pcb) to be in series with the L, and calculate the peaking.

View attachment 136866

But the circuit is driven by a voltage source, thus the resonance only shows as a reduced input current, but the coil voltage is kept constant.

As previously asked, what's the source impedance in your real circuit?

would you provide some reference (the name of the paper/textbook) that I can use to know more about this phenomenon? Thank you!

Any basic literature about magnetic circuits. Consider that a ferromagnetic core increases the inductance of an air coil. The coil is embedded by a ferrite core on one side, the open side forms a large air gap. Bringing a second coil with ferrite core next to it reduces the effective air gap.

As an experiment, place both coils with zero distance and measure inductance.

CataM · Mar 13, 2017

bhl3302 said:
For example, I am replacing C_PRI and C_SEC with two caps 390pF, and it resonants at around 3MHz. But using this structure it cannot provide a >0dB gain between 1MHz to 5MHz.
View attachment 136877

The Bode plot in that picture shows 13 dB gain at ~3 MHz. That is what happens when you tune a circuit to 1 frequency, that it boosts only 1 frequency.

bhl3302 said:
Ideally I want to achieve the frequency response like a bandpass filter, that it can have a flat band with ~0dB gain (or positive gain), am not sure if it is easy to achieve. If not, can I at least get a >0dB gain in the entire 1MHz to 5MHz frequency range?

>0 dB can be achieved at only 1 frequency and its surroundings (very small bandwidth).
If you want at that large bandwidth to have similar voltage on the secondary, use the first circuit showed in this thread with -4dB and then use an amplifier...

bhl777 · Mar 13, 2017

FvM said:
You are calculating a "gain" of the resonant circuit as below.

But the circuit is driven by a voltage source, thus the resonance only shows as a reduced input current, but the coil voltage is kept constant.

As previously asked, what's the source impedance in your real circuit?

Any basic literature about magnetic circuits. Consider that a ferromagnetic core increases the inductance of an air coil. The coil is embedded by a ferrite core on one side, the open side forms a large air gap. Bringing a second coil with ferrite core next to it reduces the effective air gap.

As an experiment, place both coils with zero distance and measure inductance.

Thank you FvM. I will look for the references by myself.
I am using a function generator with 50 Ohm terminator at the BNC cable. So I think the source impedance is 50 Ohm.
Would you tell me (1) what is wrong in my model or the calculation of the gain? How can I use the combination of V/I source to represent the "coil voltage is kept constant"?
(2) do you think I still need the primary side capacitor C_PRI? It seems like if I use function generator, it is not useful.

CataM · Mar 13, 2017

Easy peasy said:
The Q of the coils and any components connected to them, is to a very large degree independent of the coupling between coils, when an adjacent coil pulls power out of a driven coil - it may look like the Q is reducing - indeed the Q of the overall system is - as you are introducing a load or losses - but the Q of the individual coils is independent of coupling.

I just want to make this clear because seems like Easy peasy's post is contradictory to my post #2.

Easy peasy is correct and I agree and his post complements my post #2. I have said that "k" is related to Q of coil (ωL/ESR) but did not let clear that is just that way and not the other way around.
"k" is related to the Q of coil i.e. k=f(Q, distance between coils) but the Q of coil IS NOT a function of the coupling in air core inductors.

bhl777 · Mar 14, 2017

CataM said:
I just want to make this clear because seems like Easy peasy's post is contradictory to my post #2.

Easy peasy is correct and I agree and his post complements my post #2. I have said that "k" is related to Q of coil (ωL/ESR) but did not let clear that is just that way and not the other way around.
"k" is related to the Q of coil i.e. k=f(Q, distance between coils) but the Q of coil IS NOT a function of the coupling in air core inductors.

Hi CataM, I am a little bit confused. Are you talking about "for the coils, the ratio of the Vpp at Tx and Rx is a function of Q (ωL/ESR) and distance between coils"? And "for air cored coupled inductor (or transformer), the ratio of the Vpp at Tx and Rx has nothing to do with Q, because the inductance of the primary side and secondary side will determine it"?

CataM · Mar 14, 2017

No. I am talking about the coefficient of coupling (magnetic coupling) which relates the flux linkage between the coils to the total flux produced and which is usually denoted by "k".

The ratio between voltage at Rx and Tx is just that.. a simple voltage ratio.

bhl777 · Mar 14, 2017

CataM said:
No. I am talking about the coefficient of coupling (magnetic coupling) which relates the flux linkage between the coils to the total flux produced and which is usually denoted by "k".

The ratio between voltage at Rx and Tx is just that.. a simple voltage ratio.

Hi CataM, thank you for the clearification. I think I have asked similar questions before, this simple voltage ratio (VRX/VTX) seems to be a complication function of the L, Q, "k", and the distance. Is this correct? Are you aware of any textbook/paper that discusses the investigation that how can we relate this simple voltage ratio to the individual parameters? For example, can I get any equations to describe VRX when VTX is fixed?

CataM · Mar 14, 2017

Yes. "Optimal design of ICPT System Applied to Electric Vehicle Battery Charge" from IEEE discusses all 4 types of resonant topologies and gives expressions for the voltages and currents in an elegant form, but without including the source impedance/resistance unfortunately.

For this circuit

You have:
v1/V1 =

Code:

+ ( K1 RL ) s
------------------------------------------------------------------------------
+ (  R2 RL + R2 R3 + R1 RL + R1 R3 )+ (  C1 R1 R2 RL + C1 R1 R2 R3 + C2 R2 R3 RL + C2 R1 R3 RL + Ls_K1 R2 + Ls_K1 R1 + Lp_K1 RL + Lp_K1 R3 ) s
+ (  C2 C1 R1 R2 R3 RL + C1 Ls_K1 R1 R2 + C1 Lp_K1 R1 RL + C1 Lp_K1 R1 R3 + C2 Ls_K1 R2 RL + C2 Ls_K1 R1 RL + C2 Lp_K1 R3 RL + Lp_K1 Ls_K1 - K1 K1 ) s^2
+ (  C2 C1 Ls_K1 R1 R2 RL + C2 C1 Lp_K1 R1 R3 RL + C1 Lp_K1 Ls_K1 R1 - C1 K1 K1 R1 + C2 Lp_K1 Ls_K1 RL - C2 K1 K1 RL ) s^3+ (  C2 C1 Lp_K1 Ls_K1 R1 RL - C2 C1 K1 K1 R1 RL ) s^4

bhl777 · Mar 14, 2017

CataM said:
Yes. "Optimal design of ICPT System Applied to Electric Vehicle Battery Charge" from IEEE discusses all 4 types of resonant topologies and gives expressions for the voltages and currents in an elegant form, but without including the source impedance/resistance unfortunately.

For this circuit

You have:
v1/V1 =

Code:

+ ( K1 RL ) s ------------------------------------------------------------------------------ + ( R2 RL + R2 R3 + R1 RL + R1 R3 )+ ( C1 R1 R2 RL + C1 R1 R2 R3 + C2 R2 R3 RL + C2 R1 R3 RL + Ls_K1 R2 + Ls_K1 R1 + Lp_K1 RL + Lp_K1 R3 ) s + ( C2 C1 R1 R2 R3 RL + C1 Ls_K1 R1 R2 + C1 Lp_K1 R1 RL + C1 Lp_K1 R1 R3 + C2 Ls_K1 R2 RL + C2 Ls_K1 R1 RL + C2 Lp_K1 R3 RL + Lp_K1 Ls_K1 - K1 K1 ) s^2 + ( C2 C1 Ls_K1 R1 R2 RL + C2 C1 Lp_K1 R1 R3 RL + C1 Lp_K1 Ls_K1 R1 - C1 K1 K1 R1 + C2 Lp_K1 Ls_K1 RL - C2 K1 K1 RL ) s^3+ ( C2 C1 Lp_K1 Ls_K1 R1 RL - C2 C1 K1 K1 R1 RL ) s^4

Thank you CataM. That helps greatly! It seems like this paper is mainly related to the high power EV applications. (1) Is the theory also applied to low power biomedical implant applications?

I also have a question regarding the effect of C1 in your schematic. I am using a function generator (which can be modeled as V1 and R1 in your schematic, while R1=50 Ohm). If we assume R2 is the parasitic resistance of the Tx coil. (2) Is C1 used for resonant with the Tx coil? Or its perpuse is to create a complex impedance with the Tx coil to make sure the Vpp amplitude obtained in Tx coil is almost identical to what Vpp set at the function generator?

The last question is regarding your answer in poster #24. Is it possible to damp the Q by adding the external comoponents to make the bode plot covers a wider range? In another word, if the black one is the bode results I have showed, it is possible to damp the Q and convert the bode plot to the red curve?

Thank you!

CataM · Mar 15, 2017

bhl3302 said:
(1) Is the theory also applied to low power biomedical implant applications?

Of course.

(2) Is C1 used for resonant with the Tx coil? Or its perpuse is to create a complex impedance with the Tx coil to make sure the Vpp amplitude obtained in Tx coil is almost identical to what Vpp set at the function generator?

Yes if designed so. ESR of coil (~2 Ohms @3 MHz) will influence the voltage across the coil.

The last question is regarding your answer in poster #24. Is it possible to damp the Q by adding the external comoponents to make the bode plot covers a wider range? In another word, if the black one is the bode results I have showed, it is possible to damp the Q and convert the bode plot to the red curve?

Of course. As already said, if you use the 1st circuit shown in this thread with 10 pF capacitor, you will have a flat band from 1 MHz to 5 MHz. But then.. that would not be efficient WPT. In my view, WPT's purpose is to transmit energy as efficiently as possible, but here, you want to damp your circuit on purpose. Maybe you want to transmit only data in which other techniques more suitable for that purpose should be used.

bhl777 · Mar 15, 2017

CataM said:
Of course.

Yes if designed so. ESR of coil (~2 Ohms @3 MHz) will influence the voltage across the coil.

Of course. As already said, if you use the 1st circuit shown in this thread with 10 pF capacitor, you will have a flat band from 1 MHz to 5 MHz. But then.. that would not be efficient WPT. In my view, WPT's purpose is to transmit energy as efficiently as possible, but here, you want to damp your circuit on purpose. Maybe you want to transmit only data in which other techniques more suitable for that purpose should be used.

Thank you CataM. You helped me so much and taught me the theory in details.
Regarding your view that "WPT's purpose is to transmit energy as efficiently as possible", is this statement also true for the data transfer? If I have a specific power coil for the WPT, and the coils I mentioned in this thread are used for the forward data transfer only (which means I only want to generate a sine signal with acceptable Vpp at the Rx coil, when there is a function generator to send a fixed Vpp at Tx coil), does the losses in the data coil also contribute a lot to the entire system (for example, my WPT consume more than 100mW, but the data at Rx coil is used for the input only)?

D.A.(Tony)Stewart · Mar 15, 2017

try a series resonance input and buffer with a DC biased emitter follower if necessary.

https://www.falstad.com/afilter/circuitjs.html?cct=$+1+0.000005+5+50+5+50%0A%25+0+970162751.8766195%0Ac+80+128+144+128+0+3.3e-8+0%0Ar+384+128+384+192+0+50%0AO+384+128+496+128+0%0Ag+208+192+208+224+0%0A170+48+128+16+128+3+20+1000+5+0.1%0Ar+48+128+80+128+0+5%0Al+208+128+208+192+0+0.000009999999999999999+0%0Aw+144+128+208+128+0%0Aw+272+192+336+192+0%0Aw+272+128+336+128+0%0Al+272+128+272+192+0+0.000009999999999999999+0%0Ag+336+192+336+224+0%0Ac+336+128+336+192+0+5e-9+0%0Aw+272+112+272+128+0%0Aw+208+128+208+112+0%0Al+272+128+208+128+0+0.0000010000000000000002+0%0Aw+336+192+384+192+0%0Aw+384+128+336+128+0%0Ao+4+16+0+34+5+0.00009765625+0+-1+in%0Ao+2+16+0+34+2.5+0.00009765625+1+-1+out%0A

bhl777 · Mar 15, 2017

SunnySkyguy said:
try a series resonance input and buffer with a DC biased emitter follower if necessary.

https://www.falstad.com/afilter/circuitjs.html?cct=$+1+0.000005+5+50+5+50%0A%25+0+970162751.8766195%0Ac+80+128+144+128+0+3.3e-8+0%0Ar+384+128+384+192+0+50%0AO+384+128+496+128+0%0Ag+208+192+208+224+0%0A170+48+128+16+128+3+20+1000+5+0.1%0Ar+48+128+80+128+0+5%0Al+208+128+208+192+0+0.000009999999999999999+0%0Aw+144+128+208+128+0%0Aw+272+192+336+192+0%0Aw+272+128+336+128+0%0Al+272+128+272+192+0+0.000009999999999999999+0%0Ag+336+192+336+224+0%0Ac+336+128+336+192+0+5e-9+0%0Aw+272+112+272+128+0%0Aw+208+128+208+112+0%0Al+272+128+208+128+0+0.0000010000000000000002+0%0Aw+336+192+384+192+0%0Aw+384+128+336+128+0%0Ao+4+16+0+34+5+0.00009765625+0+-1+in%0Ao+2+16+0+34+2.5+0.00009765625+1+-1+out%0A

Hi SunnySkyguy, this is a very elegant solution to get a flat response above zero. However, since I have Tx coil and Rx coil, it seems this circuit cannot be directly used in either side. Ideally, is it possible to to achive this kind of response between Rx to Tx, by placing most components in the Tx side and avoid placing bulky inductors in the Rx side? Thank you!

CataM · Mar 15, 2017

bhl3302 said:
If I have a specific power coil for the WPT, and the coils I mentioned in this thread are used for the forward data transfer only (which means I only want to generate a sine signal with acceptable Vpp at the Rx coil, when there is a function generator to send a fixed Vpp at Tx coil), does the losses in the data coil also contribute a lot to the entire system (for example, my WPT consume more than 100mW, but the data at Rx coil is used for the input only)?

To see if "a lot" or not, you have to do some measurements. In PP resonant topology, current from the source generator is much less than series resonant.

it seems this circuit cannot be directly used in either side

I believe Sunny suggested series resonant input like this. This is the circuit shown by Sunny:

And its Bode plot:

bhl777 · Mar 15, 2017

CataM said:
To see if "a lot" or not, you have to do some measurements. In PP resonant topology, current from the source generator is much less than series resonant.

I believe Sunny suggested series resonant input like this. This is the circuit shown by Sunny:

And its Bode plot:

Thank you CataM, I am going to test on board for this configuration and let you know how it works.

- - - Updated - - -

CataM said:
To see if "a lot" or not, you have to do some measurements. In PP resonant topology, current from the source generator is much less than series resonant.

I believe Sunny suggested series resonant input like this. This is the circuit shown by Sunny:

And its Bode plot:

Hi CataM, is the principle of this "flat band response" based on the resonance of the two seperate loop in Tx side and Rx side, along with the mutual inductance between Tx and Rx coils? How can I theoratically explain this circuit?

I also did a simulation before doing the experiments on the bench. And the bode plot is depends on the coupling coefficient between Tx and Rx. If we assume the distance between the coils can cause the variation of the coupling coefficient, can I say "the mutual inductance is changed by the coupling coefficient and thus vary the resonance of the Rx side loop"? Thank you!

CataM · Mar 15, 2017

How can I theoratically explain this circuit?

This circuit is exactly Sunny's circuit shown in post #34. You can analyze it however you want to.

bhl3302 said:
can I say "the mutual inductance is changed by the coupling coefficient and thus vary the resonance of the Rx side loop"?

Yes. That is exactly how it works.

bhl777 · Mar 16, 2017

CataM said:
This circuit is exactly Sunny's circuit shown in post #34. You can analyze it however you want to.

Yes. That is exactly how it works.

Hi CataM and SunnySkyguy, I have tried this circuit and tuned it to meet my needs (1MHZ to 5MHZ flat band). I have made some progress but have not succeeded yet.
This is my current problems on bench:
I am using this setup to test the bode plot, and the parameters of the components are tuned to achieve the target frequency response.

You can see my tuned parameters are very different from your simulation. And especially for C2, even if I place nothing there, the parasitic capacitance from the inveter can make the bode plot like this

No matter how I tuned C2 and R2, I am not able to extend the bandwidth to 5MHz (Now it is a little bit less than 4MHz).
(1) Is there anything wrong with this circuit? How can I extend the bandwidth further?
(2) I am testing the transient waveform in using this circuit, it is now look like this

However, when I send 1MHz, 1.5MHz and 2MHz sine signal from the function generator, the probed waveform at the secondary coil showed distortion. Especially the 1MHz signal is completely wrong.

Do you have an idea why the frequency performance is so different from the transient waveform? How can I fix this?
Thank you!

CataM · Mar 16, 2017

Measure the coupling at the distance you want to operate the coils to know where we are.
You will have to get rid of those parasitics because you do not know their values. Place output and input buffer (to reduce those 50 ohms from the source).

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Relationship between Q factor and the coupling factor of two wireless coils

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