Making good measuremnets with imperfect driver coils

[Mike Sulzer]

In this previous discussion (Syscomp Scope and application) the properties of the driver coil were considered. The coil discussed there was resistive at the lower frequencies and inductive at the higher frequencies. When driven with a voltage, this means that the current through the coil is a complicated function of frequency, and so is the magnetic field it produces. This discussion shows a way around this; that is, a way to use such a coil and still get a good measurement of the frequency response. The technique consists of two steps:
1. Measure the current through the coil as a function of frequency as well as the pickup output.
2. Use both measurements together to find the corrected output voltage of the pickup, effectively dividing through by the measured current.

I use Electroacoustics toolbox (dual fft analyzer) on my mac to make this measurement. I do not think that the software that comes with the Syscomp scope can do this, but there I think that there is no reason why it could not be modified to do so.

The first attachment shows the results of applying this technique without a necessary additional correction that makes it easy to see the pickup response. (The second shows a better result, but let's examine the first.) The driver coil is a small one like the ones I use for six coil pickups with about 275 ohms of resistance. The coil is resistive below about 450 Hz, and inductive above. A 47 ohm resistor is used in series with the ground lead to sense the current. The junction of the coil and resistor feeds one of the inputs while the pickup feeds the other.

Random noise is connected to the driver coil, and cross spectral analysis is used to analyze the response. The result is a spectrum that increases at 20 db per decade over several decades. The pickup resonance is seen at the top at the high frequencies. The increasing ramp response is due to the law of induction; all magnetic pickups do this. However, the wide dynamic range that must be displayed hides the specific response of this pickup.

The solution is to divide the magnitude of the response by the frequency before plotting. This takes out the increasing ramp and allows the details to appear. Now one can see (in the second attachment) the dip in the middle that is typical of steel cores. (This is a humbucker.) The response at the lowest frequencies is in error; the electronics is not good down to 10 Hz.

[mickmutante]

Thanks Mike for the info.
Does the Electroacoustics toolbox works with the Syscomp Scope? Or does it need special hardware?

[Mike Sulzer]

Thanks Mike for the info.
Does the Electroacoustics toolbox works with the Syscomp Scope? Or does it need special hardware?

Electroacoustics toolbox is intended to work with whatever sampling hardware you have on your Mac. I use it with the built in sound circuitry. I suspect that it would be possible to design hardware that it would not work with, hardware that it could not properly identify or access. But I know very little about this, and cannot answer your question about whether it would work with the Syscomp scope.

[Mike Sulzer]

By the way, the Syscomp scope samples at 20 Msamples/second, much faster than you need for audio, but it has only eight bits per sample. This is enough for some types of waveforms, but it is not adequate for all audio waveforms that you might want to use.

[fieldwrangler]

Now one can see (in the second attachment) the dip in the middle that is typical of steel cores.

Mike -

Could you remind me why this effect exists?

Bob Palmieri

[salvarsan]

By the way, the Syscomp scope samples at 20 Msamples/second, much faster than you need for audio, but it has only eight bits per sample. This is enough for some types of waveforms, but it is not adequate for all audio waveforms that you might want to use.

For comparison, 8-bit amplitude = 48 dB dynamic range, 10-bits = 60 dB, 12-bits = 72 dB.

Most analog recording media can provide 50-60 dB range while the human ear can sometimes discriminate another 10 dB into the noise floor.

The takeaway is that 8-bit resolution is good enough for bulk amplitude-frequency tests,
but more resolution is needed for dynamic range tests.

[Mike Sulzer]

Mike -

Could you remind me why this effect exists?

Bob Palmieri

The short answer is "loading down the output of the coil". For example, the cable capacitance does this. At very high frequencies, the impedance of the cable capacitance is very small, while the impedance of the inductance is very large, and as a result the output is very small because the capacitance tends to short it out. (But at some intermediate frequency range, the inductance and capacitance act together to produce a resonance to boost the output.)

When ac current flows in the coil, significant voltages are induced around closed paths with the correct geometry. If such a path contains a conductor (such as a steel core), then current flows. Energy is lost in the conductor due to its resistivity. However, it is not that simple. There is also an inductance associated with coupling current into the conductor. In general the loading effect of a conducting path can be modeled as an inductor in series with a resistor across the pickup coil. Since there are many possible paths, the result could be complicated, but, for example, in the case of steel cores, a series inductor and resistor is a good model.

So we have a series R and L loading down the pickup coil, which is a resistor in series with an inductor. At low frequencies, both inductors have low impedance, but the resistance across the coil has a has a fairly large value, that is, compared to the pickup coil series resistance. So there is little loading effect. At higher frequencies, the impedance of the coil becomes important, and the resistor has a loading effect. However, the inductance in series with the resistor can also matter, and so the effect is not so simple. Also the resistor has a value that increases slowly with frequency due to the skin effect. And as the frequency increases, the pickup coil inductance and its capacitance (combined with the cable capacitance, if there is one) make the resonance that causes the output to rise, overcoming the small dip from the loading.

So it is really pretty complicated.

[fieldwrangler]

Mike -

Thanks for the comprehensive response. Many of these elements have been apparent to me for awhile, but this particular integrated summary is very useful!

Bob Palmieri

[PeterDH]

By the way, the Syscomp scope samples at 20 Msamples/second, much faster than you need for audio, but it has only eight bits per sample. This is enough for some types of waveforms, but it is not adequate for all audio waveforms that you might want to use.

Just to clarify, the Syscomp CGR-101 A/D is a 10 bit unit, so as pointed out elsewhere the dynamic range is about 60db, assuming the signal fills the entire 10 bits.

But the dynamic range of the VNA (vector network analyser) is much larger, because it uses correlation and an averaging process. This extends the dynamic range significantly. So: real time audio digitization depends on the number of bits in the converter, but other types of analysis such as spectrum analysis or amplitude-phase measurements can have a much larger dynamic range.

[Mike Sulzer]

Just to clarify, the Syscomp CGR-101 A/D is a 10 bit unit, so as pointed out elsewhere the dynamic range is about 60db, assuming the signal fills the entire 10 bits.

But the dynamic range of the VNA (vector network analyser) is much larger, because it uses correlation and an averaging process. This extends the dynamic range significantly. So: real time audio digitization depends on the number of bits in the converter, but other types of analysis such as spectrum analysis or amplitude-phase measurements can have a much larger dynamic range.

I am sorry; I thought I saw eight.

The dynamic range of the instrument is indeed a function of the processing and the type of signal. (Some of you might remember one bit correlators, which can give perfectly good spectra of noise-like radio astronomy signals, although the total power must be kept track of separately. A more recent potential use of this historical technique is described here: One-bit correlator concept for high-resolution speckle imaging: a computer simul) But bits do matter for one shot analysis of high dynamic range audio signals.