Pickup Integrator

Charles Eric LaForest, PhD., 2026

When exciting a guitar pickup with an external magnetic field to measure its frequency response, you have to account for the fact that the amplitude of a magnetically induced signal is proportional to its derivative, and so to the frequency of the exciting signal. Thus, for a constant amplitude exciting signal, the output amplitude increases by 6 dB per octave, which makes any variation in frequency response hard to see. We can undo this slope by using an integrator, whose output falls by 6 dB per octave.

The Wikipedia Op amp integrator page contains all the necessary theory in a really accessible way, and the CircuitJS1 simulator file is here.

Circuit Description

From left-to-right, input-to-output, the total circuit goes as follows:

• A Bias Voltage (V_bias) generator so we can operate on a single supply. The op-amp buffering is necessary to provide a stable ground reference to the input and output gain stage feedback networks. You can increase the supply voltage to give you more headroom to amplify weak signals.
• An input stage with a maximum gain of 10 (+20 dB), a 1K input protection resistor, a 72.3 Hz input filter and DC blocker, and a feedback network whose gain reduces towards unity at 79.5 Hz and 15.9 KHz (at max gain). The input impedance is 1M, which prevents loading the pickup too much and thus altering its frequency response.

  Adjust the input gain to provide the highest possible signal amplitude into the integrator without clipping, which would corrupt the results. Set the input gain on the highest test frequency you plan to use, which will have the highest output amplitude from the guitar pickup. Note that the pickup resonnant freqency can have a peak of +12 dB easily. You will have to do a couple passes to adjust the gain. A test point allows an AC-coupled scope probe to monitor this.

• An integrator, begining with a DC blocker and 79.5 Hz input filter which is necessary to prevent any output offset voltage from the input stage from eventually saturating the integrator. The integrator is configured to have a unity gain at 106 Hz, and so a -3 dB point at 1/10th that frequency to minimize error.
• An output stage, identical to the input stage. The output gain is adjusted to provide the highest possible output signal without clipping, which is necessary since at the highest test frequencies, not including the +6 dB/oct of the exciting signal, the integrator output is reduced by -30 to -36 dB (200 Hz to 10 KHz is a range of between 5 and 6 octaves!).

  Set the output gain on the lowest test frequency you plan to use, which will have the highest output amplitude from the integrator. A test point allows an AC-coupled scope probe to monitor this.

• An output network with a 1K protection resistor and a 15.9 Hz DC blocker and output filter. This is only meant to drive a 1M scope probe or similar.

Design Notes

Since this integrator is solely meant for pickup measurements, we don't really need a precise response below about 200 Hz, where a pickup's response is always flat, or above about 10 KHz, where no pickup should have its resonance peak. So the integrator's unity gain point is set to 106 Hz, and every opportunity is taken to filter or refuse to amplify signals below that point, which both helps reduce ambient 60 Hz interference (which a pickup is great at receiving), and works against the greater-than-unity gain of the integrator below 106 Hz, which isn't useful.

Chaining a number of first-order filters as shown is simple, but imprecise. The Q factor become quite low, and the resulting -3 dB point ends up at about 200 Hz. However, in this case, it happens to work well enough: the effective integrator gain remains constant below the unity gain point, and a 60 Hz input ends up attenuated by -20 dB at the output relative to a 1 KHz input of the same amplitude.