Warning!!! MEGA Techno-Nerd stuff to follow!!!
You've been warned, turn back now!!!!
I got interested in just what the frequency response looked like for the 4002 circuit and just what difference having 10M resistors or 300k resistors would make. So, I did what all Techno-Nerd Engineers do, decided to
simulate it!
First off, I have made reasonably detailed measurements of a HB-1 pickup and got the following:
Freq Ls Rs Cp
100 7.45 14.59k 31.7n
120 7.45 14.63k 30.4n
1k 7.24 20.51k 2.9n
10k 3.43 50.18k 70.1p
The formatting is messed up, but the 2nd column is the series inductance in Henries, the 3rd is series resistance in Ohms, and the 4th is parallel capacitance in Farads. Notice that the resistance changes with frequency, this along with the other parameters is why just taking a reading with an ohm meter doesn't really tell you a whole lot.
Now, modelling a pickup is kind of difficult, but it's basically a big inductor (the coil) in series with a resistor (the resistance of the wire) with a capacitor across it (the capacitance from winding to winding). There's also a voltage source, which is the action of the strings moving in the magnetic field created by the magnet, this is also in series with the resistor and inductor.
Now, the simulator I used doesn't really do pots, so I used a pair of resistors to simulate a 500k pot. In the following circuit, there are 3 copies, one with the "pot" fully "down" so low resistance to the cap, one mid way, equal resistance on each side, and one fully "up" with largest resistance to the cap. The top 3 are with the 10M resistor, the bottom 3 are the same as the top 3, but with a 300k resistor. The 500k resistor at the end represents a 500k volume pot turned up full.
Edit: Ignore the following, I messed up the circuit!
See the next post for the right results.
End Edit...
So, here's what we get:
Cool, huh? So, what does all of this mean? Well, vout1 (lt blue), vout2 (red), and vout3 (dk blue) are the 10M circuits, "pot" down, mid, and up respectively, vout4 (green), vout5 (magenta), and vout6 (gray) are the 300k circuits. As the "pot" is turned "up" we can see that the response curves move up, showing that more bass is allowed through, at the half way point (equal resistance on each side) the curve stays fairly flat out to about 300Hz, instead of rolling off from the start. All of them have a big roll-off at about 5.8kHz, then come back up above that. BUT, the model doesn't take into account that the inductance really starts to drop off above 1kHz, down to half it's value at 10kHz, so this isn't terribly valid up in these "high" frequencies.
The big difference that 300k vs. 10M makes is that there is a bit flatter response down in the 20-40kHz range. The 10M tends to roll off these low frequencies, especially below 30Hz. So, the 300k resistor will give a bit better deep bass response - at least with a HB-1 pickup. I'd LOVE to get a 4002 pickup to measure!
So, there you have it, this is what the 4002 circuit frequency response looks like with a HB-1 pickup.
Techno-Nerd stuff is done, you can wake up now!
