Keep in mind that a piezo transducer IS a capacitor, but it actually has quite small capacitance itself. Any piezo element which is suitable over the full audio range as an instrument pickup will intrinsically have low enough picofarads to keep from rolling off the highest audio frequencies to ground at the source. That is the first high-pass filter problem; if the cable from the piezo to the preamp is too lenghty there is then enough additional picofarads of cable capacitance (in parallel with the internal piezo picofarads) to where it adds up enough to roll off audible highs and then you get a dull sound.
Now to consider impedance, the problem here can be simplified without having to know everything there is about impedance itself. In this case the piezo simply puts out such a small millivolt-range signal with so little milliamperage oomph behind it, that unless you have at least 5 to 10 megohms of input impedance at your preamp input, like for instance only 1megohm commonly seen on regular guitar amps, a good portion of the signal will be lost straight to ground through that 1meg resistor since it it too low an impedance load for this source, even though its plenty for a magnetic pickup. So to begin with the volume is too low. A mere 1meg *loads down* a small piezo source like it does not do to a magnetic pickup's output. When you drive a 10meg load from a decent piezo, the output signal is not that much lower in amplitude than when you drive a 1meg load from a nominal magnetic PU, so you may not actually need a dedicated piezo preamp for its extra gain as much as for its impedance matching and buffer ability to allow a longer cable to be used between the preamp and the main guitar amp. A 5meg load is not too bad either, a naked ceramic piezo (Yamaha) in a flat-top acoustic without an internal preamp can be excellent straight into my Ampeg V-3 without any preamp at all. You don't have to set the volume very much higher than a regular electric guitar. But you do need to use a short guitar cable or lose high end. Old Ampegs maintained the 4.7M input impedance for many years since they were orignally primarily for amplifying the early piezos of the '50's when they were installed in upright string basses, before the appearance of the solid-body bass guitar. The *amplified peg*.
At the same time the other high-pass filter that David was mentioning begins to take effect. This is kind of like the way you have to make sure that the coupling cap from a plate of a 12AX7 to the grid of the next tube is not too few uF compared to the megohm or fractional megohm of its grid load resistor which goes to ground. (or you will have less bass frequencies appear at that grid) That cap plus the grid load are in series to ground and they themselves combine to form a *high-pass* filter where a full-range signal comes from the 12AX7 plate, but it only allow frequencies above a certain Hz to fully pass through the cap, depending to a definite extent on the ohm value of the grid load. So its a high pass filter but the intention here is for it to let ALL the desirable audio frequencies pass on to the input of the next gain stage, and only filter out the subsonics that are too low to hear and unwanted.
So the analogy here would be the piezo preamp takes the place of the second tube stage in the above example, and the piezo element itself represents the coupling cap where the incoming signal will be coming to the preamp from. However, the piezo is a physical capacitor where you can not select a different capacitance without changing to a piezo with different properties (or putting additional sensors in parallel), so once you have the sensor(s) selected the capacitance is fixed. Therefore you must vary the ohms of preamp input impedance if you want to adjust this high-pass filter so it does not keep too many audible bass frequencies from appearing at the preamp input. In practice once you get it up into the 5 to 10meg range is usually where it starts to sound good. When you get up to 22meg or above it can have too much noise. Even though your choices are limited, you can still get excellent tone when things are fairly optimized.
When you put more sensors in parallel (or maybe use a physically larger enough piece of the same sensor material), it can lower the impedance requirement of the preamp to where a 1meg input impedance is as adequate as a 5meg or 10meg for a single sensor. As long as the piezo material is truly suitable for audio (and you don't introduce too much cable capacitance when wiring them in parallel), you will be adding more signal-producing capability faster than you add physical capacitance, but you will be adding physical capacitance nonetheless. Therefore the absolute increase in picofarads within the combined sensors then allows them to drive a lower-impedance preamp (or regular guitar amp) input like 1meg without being badly loaded down or losing audible bass frequencies. At least for acoustic guitars.
I guess maybe with solid-body bass guitars there may not be enough acoustic energy for the piezo to make much output to begin with, then the requirement for lower octave(s) to pass through the series high-pass may combine to give you frustratingly diminishing returns when you experiment with multiple sensors.
Plus it seems like it would be kind of a black art not unlike paralleling speakers of differing ohms and db efficiency, so its probably easiest to work with multiple identical sensors rather than trying to parallel widely varying sizes or types in positions with dissimilar levels of acoustic vibration as well.
Now maybe that coaxial oil-well-logging piezo wire could really blow someone's mind. I expect the oilfield service companies discard thousands of feet of this stuff per year. The physical capacitor here is not a crystallized ceramic (acting as dielectric) having opposite sides metallized to form capacitor plates (at the same time being the + & - signal sources). Instead with coaxial the inner conductor acts as one plate of the capacitor, then the shield acts as the opposing plate (just like noisy guitar cord). The dielectric coaxial insulation is a special plastic having piezoelectric properties so the unterminated wire itself produces signal depending on acoustic impact. Hopefully a lot more than just noisy guitar cord.
Maybe you could just carefully clip the open end of the coaxial making sure there was no shorting between the shield and the inner conductor, then glue or otherwise attach enough length of the piezo coaxial underneath the top of the acoustic guitar to where it puts out enough signal to do the job into the selected outboard preamp, when the other end of the coaxial is stripped and soldered to the phone jack just like regular coaxial. When somebody looked inside the guitar, on careful inspection they could see no battery, pickup, or preamp, just the place where it looks there should be a preamp, pickup, or obvious signal source but the wire has been cut clean off

Music comes out anyway. It could happen.
That would be a head-scratcher
Anyway, with something like the coaxial or PVDF film piezos, it would seem like you would not need to put more sensors in parallel (for increased output into lower impedances for example) unless you wanted to amplify specific discrete locations upon the guitar body. Using a single piece of bulk sensor material having additional length instead actually does act like having additional sensors in parallel, even though it seems like having longer coaxial cable would be series rather than parallel.
But something tells me we may not yet have advanced enough materials for the output increase to exceed the capacitance increase as you increase sensor length, except for lengths of sensor placed directly under the saddles where the acoustic impact is greatest.
It would be interesting to see signal data comparing a ceramic piezo under-saddle sensor's output to that of the stripped & silvered coaxial (assumed to be highest output without a shock-absorbing outer layer or two which could serve as an acoustic damper) as well as the PVDF film when all other things such as the guitar, saddle, string gage & tension were identical. Carefully measured raw sensor output amplitude using a very high impedance low-noise ocilloscope, as well as additional readings when loaded as a test rig with various metal-film resistor values such as 500K, 1meg, 2meg, 5meg, 10meg & 20meg should allow the differences in acoustic suitability and impedance drive capability to be quantified with some degree of accuracy.
Mike
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