Crystal Earplugs and Piezo Elements

For use with a Crystal RadioDavid Wagner 2007/11/02 00:11

Modern ceramic piezoelectric earphones seem to have the following characteristics1).

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Piezo Driver Test Circuit

20 MΩDC Impedance
15000 pFCapacitance
57 dB@1000HzSensitivity
200-8000 HzFrequency Response

In addition, the following need verification.

500-50 ΩImpedance from 500-10,000 Hz 2)

The blue (Kyocera KBT-44SB-1A) piezo measures 68700 pF capacitance.

The crystal radio driving circuit to try has these controls.

  • Low-frequency Detector Bias
  • Radio-frequency Detector Bias
  • Volume
  • Treble

Crystal Earplug Circuit

Some initial experimentation has led me to consider seriously complicating the use of a crystal earplug with a crystal radio set. I think most of this information will also apply to using piezoelectric elements, as well.

I noticed a few things concerning the basic crystal earplug when playing with my first crystal radio set. First I found it helps a great deal to wire two piezo earplugs in series and use one in each ear.

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A series capacitor and a resistor protect the earplug from DC.


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Two potentiometers are needed to adjust the speaker bias independently.

Then I solved a problem. An earplug might work for a few seconds, then stop until I reversed the leads. Then it would work again for a few seconds, then stop again. Luckily I purchased more than one (volume discounts and spares for when I break them), and not all of them did this. At first I thought I had broken one, but when a second did the same, I got to thinking. It turns out ceramic earphones really do not like, and can even be damaged by DC current. A decoupling capacitor in series with the earplug solves the problem, as shown at right. Since this capacitor is part of a high-pass filter, it should have a value high enough to avoid losing too much low frequency content, but because of its very high impedance, only 33pF is necessary. A 0.22 µF series capacitor should be large enough to avoid significant audio signal loss, and 0.1 µF is the conventional value. A large resistor (1 megohm is fine) is also needed to prevent a slow buildup of voltage through component leakage.

Then I thought about how crystal radios and piezo elements work, and realized the potentiometer was adjusting the bias on the diode and the piezo element simultaneously, and it seemed unlikely both would be optimally biased at the same setting. So I did a little experiment and found I could greatly increase the sound quality and radio performance by using separate adjustments. Precise adjustment of the speaker bias is necessary to maintain good sound quality. The correct resistance seems to depend mostly on the detector and piezo series capacitor in use.

Next I found that even greater series capacitance values (up to perhaps 4.7 µF) seems to improve lower-frequency response since the inductor and this capacitor form a bandpass filter. 3) However, it becomes more difficult to find the sweet spot in piezo bypass resistance since the response to each adjustment is delayed more while the larger capacitor charge equalizes. The capacitor polarity is marked on the schematic since it may be more convenient to use a high-quality tantalum or electrolytic capacitor, but sound quality is much improved by using only film capacitors. FIXME This paragraph isn't right here.

Tantalum caps are fine, and you may be able to get away with using some polarized components when receiving local stations with at least 10% film capacitance in parallel, though doing so makes it critical to adjust the bias pot properly. I haven't tested regular (aluminum) electrolytic capacitors yet, but those rated for low-voltage use should be fine in parallel with some film caps.

A reasonable compromise is to use a smaller (0.1 µF) mylar capacitor in parallel with a larger (2.2 µF) tantalum capacitor, or better, a 1 µF tantalum in parallel with a 0.47 µF film capacitor. In series with a 27 mH choke, these form a bandpass filter with a center frequency of 800 Hz. 4)

At these very low power levels, the nonlinear characteristics of the capacitors are quite noticeable. I'm not kidding; the audiophiles are right on this. A combination of nonpolar tantalum5), mylar film, and ceramic capacitors yields good results. High-quality audio capacitors would likely be best, but can get very expensive.

Further experimentation indicates the best performance when the resonant frequency of the electrical circuit matches a resonant frequency of the mechanical system.

The 33 pF bypass cap in the horn-loaded circuit below may be useful at times, but removing it improved the sound quality immediately, even when the potentiometer was adjusted to 1M. Further experimentation seems to indicate five things.

  1. The parasitic capacitance of regular potentiometers seems to be a problem here.
  2. This bypass capacitor is useful when you want to load the tank more than what you get with the total loading potentiometer set to zero.
  3. This bypass capacitor seems to be particularly helpful when the inductors are acting capacitively.
  4. Sometimes the best capacitor value to use varies with frequency, so though a 33 pF capacitor works well below 1200 kHz, a 2.2 pF seems to worksbetter at higher frequencies. However this may be because using this capacitor seems to dramatically effect the tank tuning, or because there happens to be less excess RF on this set when tuned to these stations.

Although I'm still working on nailing this down, it seems that when the self-resonant frequency of the inductor is less than the tuned frequency, (and perhaps also when it is less than the harmonics produced by detection), RF power backs up behind it and starts flowing all over. For example, using the bypass capacitor nearly eliminates hand-capacitance effects, both on the tuner knob and on the inductor.

The solution seems to be to use a series of low-DC-resistance chokes starting and ending with low inductance values so the high-value inductor is in the middle. If the need for this RF bypass cap can be eliminated, it may still be useful to have a variable capacitor (perhaps 0-100 pF) here to allow heavy tank loading. No, this would add another variable resonance. Better may be to use smaller inductors and larger capacitors so the bandwidth extends into RF. FIXME Look into bias tee designs.

However, there will always be some RF present since diode back-leakage the detector's non-linear response will always leave some unmodulated RF which cannot be filtered to DC or audio frequencies. a passive LCR circuit will always leaves some RF.

Twenty turns on an FT37-436) should serve to reject RF so it doesn't pass into the larger audio inductor. A very small capacitor (2.2 pF) or a larger capacitor in series with a resistor (FIXME 56 pF & 100 kΩ?) should suffice.

Horn-loaded Piezoelectric Driver

“There have been some studies that indicate loud speakers set apart from the listener at some feet AND within a small soundproof room do better than headphones in a soundproof environment. Also, little horns on piston transducers do better than standard headphone shapes; the piston does a better job of matching to the air.” –W0XI on Rap 'n Tap

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A 28” air horn bell with a 1” throat and a 7” mouth resonates at a fundamental frequency of 150 Hz.7) This frequency is lower than the 300 Hz necessary for speech intelligibility, but sounds great with music. However, closed pipes resonate at odd harmonics and the next resonant frequency is a bit high.

The 0.1 µF capacitor is used to adjust the audio loading and can range from less than 100pF to 1µF or higher, and can even be bypassed entirely for maximum loading.

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Powerful 28” Horn Driver!


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Alternative for careful use of polarized capacitors.

FIXME

FrequencyInductanceCapacitance
Harmonic (Hz) (mH) (µF)
1st 140 13.45 96.09
Music 140 19.4 66.62
140 27 47.87
140 32.85 39.34
140 54 23.93
3rd 420 13.45 10.68
Speech 420 19.4 7.40
420 27 5.32
420 32.85 4.37
420 54 2.66

A side effect of tuning the electronics to the horn's resonant frequency is the occasional honking of the horn, similar to the sound made by blowing over a bottle, when this frequency or an overtone is present.

The 7” mouth of this horn should cut off the frequency response below 500 Hz.8) Tuning the LC filter to this frequency literally rings the bell when reproducing this frequency, its overtones, or impact sounds, a very annoying distortion.

The idea is to match the impedance of the circuit to the horn's impedance over the AM broadcast audio frequency spectrum. Since the horn is a resonator, an LC resonator matching both the center frequency and the bandwidth of the horn would be ideal.

Original Idea

FIXMEWhere does this go?

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Nominal Layout

Some more thought about how best to tap as little energy as necessary led me to think of this mess. The idea is to control how the energy in each frequency range is used. The top section controls the total midrange audio frequency load and how much of it is used to bias the speaker. The second section controls how much low frequency and DC is used to bias the diode. The bottom section controls how much upper audio and RF is allowed to bias the diode. The three frequency range controls on the left will be pots with maximum values of 1-10 MΩ, and a 100-250 kΩ pot should be sufficient to adjust the speaker bias. Audio (log) taper pots should be easier to control, and all pots should adjust down to near zero resistance.

Calculations

[FIXME Explain where 150 kΩ or R1=15 kΩ, and R2=33 kΩ comes from: R=1/{{1/150000}+{1/150000}+{1/150000}}=50 kΩ.]

Opinions vary, but take 300-5000 Hz as the frequency range most important for intelligible speech. First, the capacitor in series with the piezo element forms a high-pass filter, f=300 Hz. Ignoring the large internal resistance9), the high-pass cutoff frequency of just the piezo element is,

omega = 2 pi f = 1/{(R_1 + R_2) C} right f=1/{2*pi*15000*15000*10^{-12}}=707 Hz, and

f=1/{2*pi*15000*50000*10^{-12}}=212 Hz.

The piezo capacitance is limiting, so series capacitor should be a high enough value to make little difference. For example,

C = 1/{{1/0.015}+{1/0.15}}=0.014 µF or even 1/{{1/0.015}+{1/0.1}}=0.013 µF.

However, too large and the capacitor may take too much time to charge, especially when the reseistance are set high.

A low-pass inductor filter for 5000 Hz is impractical, requiring many henries of inductance, but at least the RF can be blocked while bypassing lower frequencies.

omega = 2 pi f = {R_1 + R_2}/L right L = {R_1 + R_2}/{2 pi f} = 150000/{2 pi 500000} = 47.7x10^{-3} approx47 mH.

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Another Test circuit.


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     VVV---------+---||---+
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This configuration looks less useful.

It would be nice to block annoying whiny noise above 5000 Hz so it doesn't get to the speaker, but that would be impractical, requiring a very large 1.5 or 10 H inductor. Instead, frequencies above 5000 Hz can be bypassed using a second capacitor across the speaker.

C = 1/{2 pi f (R_1 + R_2)} = 1/{2*pi*5000*150000} = 212.2x10^{-12} approx220 pF.

Radio frequencies can be used to bias the detector.

C = 1/{2 pi f (R_1 + R_2)} = 1/{2*pi*500000*50000} = 6.37x10^{-12} approx10 pF.

A pot in series with this (or a larger value) capacitor makes this a treble control, but it may be better to bypass only higher audio frequencies (over 10 kHz) with a smaller (100 pF) capacitor, Also, it wouldn't be a bad idea to prevent RF from passing with the higher audio frequencies.

L = {R_1 + R_2}/{2 pi f} = 48000/{2 pi 500000} = 15.3x10^{-3} approx15 mH.

This makes the other inductor redundant.

1) Info from a datasheet from mouser
3) f=1/{2 pi sqrt{LC}} right C=1/{4 pi^2 f^2 L} = 1/{4*pi^2*1000^2*0.027} approx 1µF.
4) f=1/{2 pi sqrt{LC}} = 1/{2*pi*sqrt{0.027*0.00000147}}=800 Hz.
5) Make nonpolar tantalum caps by soldering the negative terminals of two like capacitors together. The pair has half the capacitance of the originals, so you need four times as many components.
7) See Design of a Front Loaded Exponential Horn
  • L_{horn}=28in = 0.712 in = 0.712 m
  • S_{mouth}={pi/4}*7^2 =38.48 in² = 0.02483 m²
  • S_{throat}0.7854 in² = 0.0005067 m²
  • m=ln(S_{mouth}/S_{throat})/L_{horn} = ln({0.02483/0.0005067})/0.7112 = 3.892/0.7112 =5.473 1/m
  • f_c = {mc}/{4 pi} = {5.473*342}/{4 pi}=148.9 Hz
8) 7 = {1/4}lambda right lambda =28 in; f = c/lambda = 14000/28 =500 Hz.
9) f_{serial} = 1/{2 pi R_{internal} C_{internal}} right f = 1/{2*pi*20*10^6*57000*10^{-12}}=7.16 Hz f_{parallel} = {R_1 + R_2}/{2 pi R_1 R_2} C_{internal} right f = 100/{2*pi*100*57000*10^{-12}}=2.8 MHz

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