Finding a Pickup's Resonant Peak with a USB Oscilliscope
Oct 16, 2016 1:59:53 GMT -5
pablogilberto likes this
Post by antigua on Oct 16, 2016 1:59:53 GMT -5
This is an addendum to Measuring the Electrical Properties of Guitar Pickups.
The purpose of this thread is to show how to easily get the resonant peak of a pickup with nothing more than a USB Oscilliscope and a 1 meg resistor. The relative simplicity of this method might hold appeal to anyone who is short on time, or has no interest in anything but the resonant peak of the pickup.
This method is also described here, by the people behind the CGR-101. The basic idea is that you use a USB Oscilliscope that is equipped with an internal function generator and bode plotter to plot the frequency dependent voltage difference across a 1 meg resistor. The voltage will be at it's highest at the resonant peak, which will (usually) be clearly visible in the bode plot.
The downside of this method is that it will not expose damping losses, at least nowhere near as accurately as the "driver coil" method will. The reason for this is because a real guitar string presents a changing magnetic field externally to the pickup, and many of the eddy current induced damping only occurs when this magnetic fielt-to-guitar pickup geometry is respected. We're also jacking up the effective resistance for the sake of voltage dividing.
What you need...
- A USB oscilliscope with built in fucntion generator and bode plotter. I recommend the Velleman PCSGU250
- An extra BNC probe, as you need two and the Velleman only comes with one
- A 1 meg resistor. It doesn't have to be exact, it can be a 820k, or 1.2 megs, it's not critical. The value will effect the Q factor, but we're not trying to measure for that here, so it doesn't matter. I recommend getting an assortment.
- optional, but recommended; a 470pF capacitor with a tolerance of 5% or better.
The setup:
Here is a picture of the whole set up.
Note that there is a lead from the function generator ouptut (far right of the Velleman), and a "Channel 1" a "Channel 2" with 10x probes connected.
Here's a close up of the connections.
All three probes and leads connected to the Velleman have a black ground (far left), they should all be connected together, along with one lead of the pickup.
In the center, you have the 1 meg resistor.
- To one side of the resistor (depicted left), you have the the probe tip from "Channel 2", and the hot side (red clip) of the function generator's leads.
- On the other side of the resistor (depicted right), you have the probe tip from "Channel 1" and the other lead from the guitar pickup all together. I'm using the little hook on the end of the probe tip to also secure the white lead wire from the pickup to the resistor.
So, there's that.
The Software:
In the software provided by Vellemen, or the the oscilloscope / function generator you have on hand, the output voltage will have to be set rather high since there is a 1 meg resistor in series with the pickup. I had it cranked up to 7 Vpp.
In the bode plotting function of the software provided, you only have to make sure that the measure plot scales correctly. The configured values for the software provided for the Vellement PSCGU250 can be seen in the screen shot below:
You can also see from the screen shot that the peak resonance is 7.46kHz . That's what we went through this trouble to find, and there it is.
A technical note; this peak resonance is derived with the added capacitance of the "Channel 2" probe, which is likely some value between 10 and 20pF, so in reality the resonance peak is a little higher. There is a way to calculate that true peak if you figure out the inductance, and then solve for capacitance, then subtract the probe capacitance, and then solve for the true peak resonance from that inductance and revised capacitance, but I don't think it's worth the trouble, for the reasons I'll explain....
Wait, don't leave yet!
I also strongly suggest also measuring the resonant peak with a 470pF capacitor across, or "loading" the pickup. That will give you a lower resonant peak, something in the area of 4kHz, but it's a resonant peak that to be expected when the pickup is in series with a typical guitar cable. The 470pF value is standard to testers on this forum, the Helmuth Lemme. The resonant peak with an additional 470pF capacitance is a valuable data point that should be recorded if you've gone through this much trouble already.
Truth be told, the unloaded resonant peak of the pickup (what we measured here) is not especially useful, because we don't know exactly how much capacitance the pickup contains. It might have 80pF, it might have 200pF. That difference alone will cause the resonant peak to vary dramatically. When you add that 470pF capacitance, it effectively mutes the smaller capacitance of the pickup by heaping on a lot more capacitance.
In fact, this Tele neck pickup that we're testing has over 200pF capacitance, quite a lot. When you see that value of 7.46kHz, you might even think this a rather dark single coil when you see Strat pickups that are regularly 10kHz and beyond, but the truth is that this Tele neck pickup actually has a lower inductance than most Strat pickups, and it just that high capacitance that would fool you into thinking it's a dark pickup. Once you plug these pickups into a guitar, and the high capacitance of the guitar cable takes over, and thanks to the underlying low inductance, this Tele neck pickup might actually be brighter than those Strat pickups that had unloaded resonant peaks of 10kHz. It turns out that the Tele neck pickup being tested has a loaded peak resonance of 4.41kHz, which is bright compared to a typical loaded Strat pickup.
Since 470pF is a reasonable amount of capacitance for a good quality guitar cable, the frequency given will also more closely match what you will hear when the pickup is in your guitar, and plugged into a guitar amp.
Bonus: determining a pickup's inductance
Since you now know the resonant peak of the pickup, you can also determine the inductance if you have a capacitor on hand that is of a much higher value than that of the pickup (pickups contain roughly 100pF capacitance on average). The inductance is also arguably the most valuable metric to have for a pickup. More useful than the resonant peak, and certainly more useful than the DC resistance.
A variety of capacitor values can be used in theory. The trick is to choose a value that will combine with the pickup in parallel which will result in a low resonant peak, and one that is easy to identify. I'd recommend using a capacitor that results in a resonant peak near 1kHz, and a 10 nanofarad capacitor should accomplish that, though I would keep slightly lower and higher value capacitors on hand, just in case.
When you're ready to test, you put the 10 nanofarad capacitor in parallel with the pickup, and you measure the resonant peak, using the USB oscilloscope as described above. Let's suppose you find that the resonant peak is only 1kHz, and that's a very low resonant peak for a pickup, but the 10nF of capacitance drives the frequency down that far.
Now you take your values, 10nF capacitance and 1kHz resonant peak, and you plug them into a calculator that solves for inductance, such as this one: www.sengpielaudio.com/calculator-XLC.htm You enter the capacitance in terms of "microfarads", so 10nF becomes "0.01uF", and you enter the frequency in terms of hertz, so 1kHz becomes "1000Hz". You enter those values into the calculator, and you press "calculate", and you get a calculated inductance of 2533.03 millihenries, or 2.533 henries. Due to the lack of precision involved with this method, it is probably best to round off to the first decimal place, and call it 2.5 henries, or 2.5H. Be sure to make it known that you have determined a "calculated inductance".
Ken Willmott told me about this method, though his method included a few extra steps for added accuracy. I just call it "capacitance swamping", as I don't know the more technical term, if there is one.
The purpose of this thread is to show how to easily get the resonant peak of a pickup with nothing more than a USB Oscilliscope and a 1 meg resistor. The relative simplicity of this method might hold appeal to anyone who is short on time, or has no interest in anything but the resonant peak of the pickup.
This method is also described here, by the people behind the CGR-101. The basic idea is that you use a USB Oscilliscope that is equipped with an internal function generator and bode plotter to plot the frequency dependent voltage difference across a 1 meg resistor. The voltage will be at it's highest at the resonant peak, which will (usually) be clearly visible in the bode plot.
The downside of this method is that it will not expose damping losses, at least nowhere near as accurately as the "driver coil" method will. The reason for this is because a real guitar string presents a changing magnetic field externally to the pickup, and many of the eddy current induced damping only occurs when this magnetic fielt-to-guitar pickup geometry is respected. We're also jacking up the effective resistance for the sake of voltage dividing.
What you need...
- A USB oscilliscope with built in fucntion generator and bode plotter. I recommend the Velleman PCSGU250
- An extra BNC probe, as you need two and the Velleman only comes with one
- A 1 meg resistor. It doesn't have to be exact, it can be a 820k, or 1.2 megs, it's not critical. The value will effect the Q factor, but we're not trying to measure for that here, so it doesn't matter. I recommend getting an assortment.
- optional, but recommended; a 470pF capacitor with a tolerance of 5% or better.
The setup:
Here is a picture of the whole set up.
Note that there is a lead from the function generator ouptut (far right of the Velleman), and a "Channel 1" a "Channel 2" with 10x probes connected.
Here's a close up of the connections.
All three probes and leads connected to the Velleman have a black ground (far left), they should all be connected together, along with one lead of the pickup.
In the center, you have the 1 meg resistor.
- To one side of the resistor (depicted left), you have the the probe tip from "Channel 2", and the hot side (red clip) of the function generator's leads.
- On the other side of the resistor (depicted right), you have the probe tip from "Channel 1" and the other lead from the guitar pickup all together. I'm using the little hook on the end of the probe tip to also secure the white lead wire from the pickup to the resistor.
So, there's that.
The Software:
In the software provided by Vellemen, or the the oscilloscope / function generator you have on hand, the output voltage will have to be set rather high since there is a 1 meg resistor in series with the pickup. I had it cranked up to 7 Vpp.
In the bode plotting function of the software provided, you only have to make sure that the measure plot scales correctly. The configured values for the software provided for the Vellement PSCGU250 can be seen in the screen shot below:
You can also see from the screen shot that the peak resonance is 7.46kHz . That's what we went through this trouble to find, and there it is.
A technical note; this peak resonance is derived with the added capacitance of the "Channel 2" probe, which is likely some value between 10 and 20pF, so in reality the resonance peak is a little higher. There is a way to calculate that true peak if you figure out the inductance, and then solve for capacitance, then subtract the probe capacitance, and then solve for the true peak resonance from that inductance and revised capacitance, but I don't think it's worth the trouble, for the reasons I'll explain....
Wait, don't leave yet!
I also strongly suggest also measuring the resonant peak with a 470pF capacitor across, or "loading" the pickup. That will give you a lower resonant peak, something in the area of 4kHz, but it's a resonant peak that to be expected when the pickup is in series with a typical guitar cable. The 470pF value is standard to testers on this forum, the Helmuth Lemme. The resonant peak with an additional 470pF capacitance is a valuable data point that should be recorded if you've gone through this much trouble already.
Truth be told, the unloaded resonant peak of the pickup (what we measured here) is not especially useful, because we don't know exactly how much capacitance the pickup contains. It might have 80pF, it might have 200pF. That difference alone will cause the resonant peak to vary dramatically. When you add that 470pF capacitance, it effectively mutes the smaller capacitance of the pickup by heaping on a lot more capacitance.
In fact, this Tele neck pickup that we're testing has over 200pF capacitance, quite a lot. When you see that value of 7.46kHz, you might even think this a rather dark single coil when you see Strat pickups that are regularly 10kHz and beyond, but the truth is that this Tele neck pickup actually has a lower inductance than most Strat pickups, and it just that high capacitance that would fool you into thinking it's a dark pickup. Once you plug these pickups into a guitar, and the high capacitance of the guitar cable takes over, and thanks to the underlying low inductance, this Tele neck pickup might actually be brighter than those Strat pickups that had unloaded resonant peaks of 10kHz. It turns out that the Tele neck pickup being tested has a loaded peak resonance of 4.41kHz, which is bright compared to a typical loaded Strat pickup.
Since 470pF is a reasonable amount of capacitance for a good quality guitar cable, the frequency given will also more closely match what you will hear when the pickup is in your guitar, and plugged into a guitar amp.
Bonus: determining a pickup's inductance
Since you now know the resonant peak of the pickup, you can also determine the inductance if you have a capacitor on hand that is of a much higher value than that of the pickup (pickups contain roughly 100pF capacitance on average). The inductance is also arguably the most valuable metric to have for a pickup. More useful than the resonant peak, and certainly more useful than the DC resistance.
A variety of capacitor values can be used in theory. The trick is to choose a value that will combine with the pickup in parallel which will result in a low resonant peak, and one that is easy to identify. I'd recommend using a capacitor that results in a resonant peak near 1kHz, and a 10 nanofarad capacitor should accomplish that, though I would keep slightly lower and higher value capacitors on hand, just in case.
When you're ready to test, you put the 10 nanofarad capacitor in parallel with the pickup, and you measure the resonant peak, using the USB oscilloscope as described above. Let's suppose you find that the resonant peak is only 1kHz, and that's a very low resonant peak for a pickup, but the 10nF of capacitance drives the frequency down that far.
Now you take your values, 10nF capacitance and 1kHz resonant peak, and you plug them into a calculator that solves for inductance, such as this one: www.sengpielaudio.com/calculator-XLC.htm You enter the capacitance in terms of "microfarads", so 10nF becomes "0.01uF", and you enter the frequency in terms of hertz, so 1kHz becomes "1000Hz". You enter those values into the calculator, and you press "calculate", and you get a calculated inductance of 2533.03 millihenries, or 2.533 henries. Due to the lack of precision involved with this method, it is probably best to round off to the first decimal place, and call it 2.5 henries, or 2.5H. Be sure to make it known that you have determined a "calculated inductance".
Ken Willmott told me about this method, though his method included a few extra steps for added accuracy. I just call it "capacitance swamping", as I don't know the more technical term, if there is one.
