# Narrow bandpass filter using maximally flat LPF prototype design

I'm doing a project involving wireless power transfer, where an LED will be turned on via 2 induction coils (tx and rx). The interfacing power circuitry for this has already been figured out (an arduino, transistor, caps, and resistors). What I want to do is transmit the wireless power at a specific frequency though (13.56kHz), so I'm trying to design a narrow band-pass filter that will allow for transmitting at this frequency. My understanding is that the transmitting coil already transmits at it's own frequency, dependent on the capacitors, and its own inductance value, but I'd like to 'fine tune' this to only transmit at 13.56kHz. This is where I think I'd need a bandpass filter, right before the transmitter coil, right?

The problem I'm having involves the filter design itself:

I'm doing my design by calculating component values for a 3rd order filter, using the "maximally flat LPF prototype design" method, then using impedance and frequency scaling to transform to a BPF. My bandwidth is 5%, so 678Hz. The element values I'm using are for "maximally flat time delay LPF prototypes"; so for N = 3, I obtain g1= 1.2550 g2 = 0.5528 g3 = 0.1922 g4 = 1. I'm simulating all this in LT Spice.

My dilemma is that I'm not getting as narrow a pass-band as what I think I need? It seems to be centered around 13.56kHz, but with a wide pass-band. What else can I do to make the bandwidth narrow? Secondly, is this the right method to use in order to have a filter that will allow for a specific transmission frequency?

Lastly, is it better to go for an active filter design method, where you use op-amps in the filter circuit? Or is this mostly for audio applications?

Below is my circuit in LT Spice, and the frequency response.

I also tried the g1 to g4 element values from "maximally flat LPF prototypes", where g1 = 1, g2 = 2, g3 = 1, g4 = 1 and get the following response:

The element values I'm talking about (g1 to g4) are taken from my lecture notes, which I assume are a standard in theoretical filter design.

• Pointless given that the coil and resonating capacitor in the final stage will be resonant to achieve best power transfer. – Andy aka May 8 '16 at 10:28
• It would be better if you told us the details of your application and let us help you with how to make it happen instead of assuming that solving a particular problem - which you think is the cause of your grief, but aren't sure - will fix everything. – EM Fields May 8 '16 at 17:10
• I've edited the first paragraph where I've included more information on what I'm trying to do. Is that okay? – deki May 9 '16 at 4:04
• By the way, you are aware that the standard is 13.56 MHz not kHz. – Andy aka May 9 '16 at 13:16
• I didn't know that. I thought kHz was okay for my application of turning on an LED via induction? – deki May 10 '16 at 1:48

'Andy aka' has stated the best answer. Adding any kind of filter to the final driver stage will be pointless, as the coil and cap values are chosen to be resonant at 13.56kHz. If these L and C values are resonant at 13.56kHz, then they will oscillate at exactly 13.56kHz (ignoring parasitics) and thus, give you the most optimal power transfer.

The Q, quality factor, is a measure of the “goodness” or quality of a resonant circuit. A higher value for this figure of merit corresponds to a more narrow bandwith, which is desirable in many applications. More formally, Q is the ratio of power stored to power dissipated in the circuit reactance and resistance.

So in other words, if you want a high Q for the transmitter, use:

• High-voltage, low-ESR (and low inductance), quality capacitors (NP0, X7R, etc.)
• Low-resistance, low-capacitance wire in the coil (Litz wire?)
• Good PCB layout design (low parasitic effects.)

You may find that driving the output stage via a squarewave at 13.56kHz will yield more output power, as doing so creates faster transients (imparts more harmonics) into the coupled magnetic field. But it does so at a higher input power, so thus is not most optimal both in terms of power usage and signal purity. The whole point of parallel resonance is, that as little energy as possible is added to the system to keep it oscillating.

I think we are scratching our head at why you want very pure-frequency transmit energy. If you want the receiver to be very selective and only allow this particular transmit frequency, use the 13.56kHz bandpass filter on the receiver end. Note that -3dB is half the power, -6dB is a quarter, etc. How little power does the receiver need to function? That will allow you to estimate a frequency response:

• The coil distance (in air?)
• The magnetic coupling efficiency (a core material other than air?)
• "Q" or steepness of the transmitter
• "Q" (order) of the receiver and filter network
• The minimum required receiver power to function

This all said, I'd consider a frequency higher than 13kHz. That is within the range of human hearing, and microscopic movement of the components (the opposite of microphonics) is likely, leading to us physically hear the high-pitched 13.56kHz tone. (Human hearing has a sensitivity of 20 micropascals!) 25kHz would be better for most of the population.

• Thanks for the response rdtsc. It makes sense to me now that the coil and cap values will be resonant at a specific frequency corresponding with their component values. As for why I'm after a specific transmission frequency: it's the main criteria of the project, that the transmitting coil transmit at a specific frequency (now it will be MHz) So basically I have two options (?): 1. Reconfigure the transmit coil and capacitors so that they are resonant at my desired frequency. 2. Place the bandpass filter on the receiver end. I think I might try out both and see which one is better. – deki May 10 '16 at 1:52
• If you are going to rectify the received signal into DC, the choice of diodes (and designed impedance) will matter. Schottky are fast, have a lower forward voltage drop, but have more reverse leakage. Silicon will be unusable in the MHz range. Higher frequency = more demanding of design. Also consider the reverse voltages expected - if very high, it might rule out many high-efficiency Schottky types and make more sense to use a HF transformer for impedance matching (and peak voltage reduction) prior to rectification. Sounds like a fun project! :) – rdtsc May 10 '16 at 12:07