Pickup Operation

How electromagnetic pickups transduce string vibration into electric voltage

Watch how the output voltage (colored) is the derivative of string position (gray). Higher frequency = faster motion = stronger signal.

The Setup

There are three components to consider in order to understand how a guitar pickup works:

Permanent Magnets

Usually one per string, each creating a static magnetic field in the region of space near the string

Guitar String

Made of magnetically permeable material (e.g., steel, nickel) that interacts with the magnetic field and alters it when it vibrates

Wire Coil

Thousands of turns of thin copper wire wrapped around the magnets, forming an inductor that picks up changes in magnetic flux

Why metal strings? Nylon strings don't work with magnetic pickups because they're not magnetically permeable. The string must be able to interact with the magnetic field, which is why electric guitars use steel or nickel-wound strings.

Faraday's Law of Induction

A pickup works because of one of the most important laws in electromagnetism: Faraday's Law. In this context, it states that a changing magnetic field through a coil induces a voltage:

V = -N · dΦ/dt
  • VThe induced voltage (EMF) across the coil.
  • NNumber of turns in the coil (typically 5,000-10,000 for guitar pickups)
  • dΦ/dtRate of change of magnetic flux through the coil

As a magnetically permeable guitar string vibrates, it changes the magnetic field through the coil at the same frequencies as it is vibrating at. According to Faraday's law, this changing flux induces a voltage in the coil that mirrors the string's motion. By this mechanism, mechanical vibrations aretransduced into an electrical signal!

The Pickup Outputs Velocity, Not Position

When the string vibrates, it perturbs the magnetic field passing through the coil. Since the amount of flux through the coil is determined by the position of the string, the rate of change of the string's position is what actually induces the voltage. In other words:

Vout ∝ dΦ/dt ∝ dy/dt = velocity

And so, the output voltage of the pickup is related to the derivative of the string position. In the simulation above, notice how:

  • When the string is the limits of its motion (top or bottom), the voltage is zero because the string has momentarily stopped
  • When the string crosses through the center, the voltage is at maximum because the string is moving fastest
  • The voltage waveform is out of phase with the position waveform by 90° (quarter cycle)

Frequency Response and Treble Boost

For a string vibrating sinusoidally at frequency f with amplitude A:

Position: y(t) = A · sin(2πft)
Velocity: dy/dt = A · 2πf · cos(2πft)

We can see that the peak velocity is proportional to both amplitude AND frequency:

Vpeak ∝ A · f

So, even if two frequencies have the same displacement amplitude (i.e., two normal modes of the string have the same amplitude), the higher frequency will produce a stronger signal because the string moves faster. In the absence of any other effects, this gives pickups a natural treble boost. As we'll see later, the coil's inductance and parasitic capacitance actually modify this response quite a bit.

Try it: In the simulation, increase the frequency while keeping amplitude constant. Watch the output voltage waveform grow larger even though the string displacement stays the same.

The Role of Coil Turns & The LC CircuitAdvanced

Recall from Faraday's law above that voltage scales linearly with the number of turns N. In order to produce a strong enough signal for downstream preamplifiers, guitar pickups typically have thousands of turns of wire. But there is another consequence to incrasing the number of turns: more inductance and capacitance, which together fundamentally shape the pickup's frequency response.

More Turns = Higher Output

A pickup with 8,000 turns produces roughly twice the voltage of one with 4,000 turns (all else being equal).

But Also More L (inductance) and C (capacitance)

The presence of inductance and capacitance creates a resonant peak in the frequency response, which shifts lower with more turns, resulting in a darker tone.

The Equivalent Circuit

Also including hte DC resistance of the coil, a pickup can be modeled as an RLC circuit.

  • Vemf: The induced voltage from string motion (proportional to frequency)
  • R: DC resistance of the coil (typically 5-15 kΩ)
  • L: Inductance of the coil (typically 2-8 H)
  • C: Parasitic capacitance between windings (typically 100-200 pF)

Try increasing L or C to see the resonant peak shift lower (darker tone). Higher R reduces the peak height (lower Q).

Impedance and Resonance

The impedance of the coil varies with frequency. For a series RLC circuit:

Z = √(R² + (XL - XC)²)
where XL = 2πfL (inductive reactance) and XC = 1/(2πfC) (capacitive reactance)

To find the output voltage, we use the voltage divider. The EMF source Vemf is in series with L and R, while C appears in parallel across the output terminals:

Vout = Vemf · ZC / (ZLR + ZC)
where ZLR = R + jωL and ZC = 1/(jωC)
Substituting and simplifying:
Vout = Vemf · 1 / (1 − ω²LC + jωRC)

The transfer function H(jω) = Vout/Vemf has magnitude:

|H(jω)| = 1 / √((1 − ω²LC)² + (ωRC)²)

At the resonant frequency, the term (1 − ω²LC) becomes zero, which occurs when:

f₀ = 1 / (2π√LC)

Remember that Vemf itself is proportional to frequency (from Faraday's law). We see the complete frequency-dependent output of the pickup by combining the frequency dependence of both the input EMF and the transfer function:

|Vout| ∝ ω / √((1 − ω²LC)² + (ωRC)²)

This creates a resonant peak in the frequency response. The output rises with frequency (Faraday's law), peaks at f₀, then rolls off as the capacitive reactance dominates.

Try it: In the circuit simulator above, increase the inductance L or capacitance C and watch the resonant peak shift to lower frequencies. This is why "hot" pickups with more windings sound darker because more inductance lowers f₀.

Summary: The Signal Chain

  1. The permanent magnet creates a static magnetic field extending toward the string
  2. The steel string, being magnetically permeable, concentrates the field lines near itself
  3. When the string vibrates, it moves these concentrated field lines, changing the flux through the coil
  4. By Faraday's law, this changing flux induces a voltage proportional to the string's velocity
  5. Higher frequencies produce larger voltages for the same amplitude, a natural treble boost
  6. More coil turns increase output but also increase capacitance (darker tone)