What is Impedance?
You can see a term "Impedance" on the spec of an amp, speaker, or effector. Normally values like 4 Ω, 8 Ω, and 16 Ω are on the speaker and Input Impedance : 1M (Mega Ω) / Output Impedance : 10K (Kilo Ω) on Moollon effectors.
Also it is well known that "impedance matching" is very important when connecting two instruments.
Now we will talk about basic concept of impedance for practical use in guitar playing.
By definition, impedance(abbreviated "Z") is the ratio of voltage to current. We call this concept resistance(R) in DC(Direct Current), and impedance(Z) in AC(Alternating Current). Both resistance and impedance use the same standard unit "ohm(Ω)", and have exactly the same behavior in that they interfere with the current flow.
Nevertheless, the fact that impedance is a phenomenon in AC circuit makes the intuitive understanding of impedance a bit more difficult than of resistance.


ω = 2πƒ, ƒ : frequency
The transformed equation above with frequency looks a little more complicated, but we can understand it as simple as we need to.
  • R (Resistance) : Constant value regardless of frequency. Embodied by resistors.
  • L (Inductance) : Interferes with the flow of the higher frequency signals. Embodied by coils.
  • C (Capacitance) : Interferes with the flow of the lower frequency signals. Embodied by capacitors.
As you can see on the equation above, impedance varies with frequency. For datums, we use the impedance value at 1kHz(1000 vibrations per 1 second) frequency.

This is the very basic concept of impedance. If you don't want to care about it, just remember the facts below :
  • Impedance is a factor that interferes with a current flow. As an impedance gets higher, the harder a signal to break through a path.
  • A signal with high Z(impedance) like in an electric guitar is susceptible to the ground noise and a loss of treble/punch by the cable length.
Impedance of an electric guitar
Impedance of an electric guitar can be calculated by the above equation.
As a magnetic pickup is made of a very long coil wound aroung magnets, we can measure inductance(L, standard unit is Henry : H) and resistance(R, standard unit is Ohm : Ω) from this coil. Capacitance by a coil is ignorable.
1) Single coil pickup
In general, a traditional single coil has resistance R = 5.8 KΩ = 5800 Ω and inductance L = 2.3 H, approximately. As mentioned above, ƒ = 1000 Hz because impedance is measured at this frequency.

Z = R + 2πƒL = 5800Ω + 2π x 1000Hz x 2.3H = 20251Ω = 20.251KΩ

With higher output single coil pickups, values of R and L will increase and impedance gets higher accordingly.
2) Humbucker pickup
A traditional humbucker pickup has resistance R = 8.5 KΩ = 8500 Ω and inductance L = 4.6 H, approximately. With the same reason as in a single coil pickup, ƒ = 1000 Hz.

Z = R + 2πƒL = 8500Ω + 2π x 1000Hz x 4.6H = 37403Ω = 37.403KΩ

With higher output humbucker pickups, values of R and L will increase and impedance gets higher accordingly.

So we can say the range of electric guitar impedance is around 20 ~ 40 KΩ.
Note that this is just for a passive pickup without an onboard preamp circuit. In active pickups, impedance is as low as 10 KΩ or less due to the amplification by the active circuit.
Input Impedance and Output Impedance
All the instruments connected to/for electric guitars have input and output impedance except for pickup and speaker.
A pickup has only an output impedance because it is a kind of signal generator without an input connection, and a speaker has only an input impedance because it is the end of a signal path without an output connection.
All the other instruments like effectors, pre-amps, and power amps have both input and output impedances.

To jump to a conclusion, an effector with stable performance has a high input impedance and a low output impedance.
"An effector with stable performance" means it can deliver a guitar signal to an amp minimizing the loss by cable capacitance.
Ratio of signal transmission by impedance
Z1in : Input Impedance of FX1
Z1out : Output Impedance of FX1
Z2in : Input Impedance of FX2
Z2out : Output Impedance of FX2
V0 : Total Voltage on Z1out and Z2in
V1 : Voltage on Z1out
V2 : Voltage on Z2in
This is a situation when two effectors are connected. We can apply the same situation not only to effectors, but to a direct connection from a guitar to an amp.
The signal transmission ratio is closely related with the ratio of input impedance to output impedance. More precisely, it is the ratio of the input impedance of FX2 (= Z2in) to the output impedance of FX1 (= Z1out).
Let the voltage of the original signal be V0, the voltage loss by output impedance of FX1 be V1, and the voltage on the input of FX2 be V2. Then the following equations are completed.
Example 1) When connecting a guitar to a tube amp directly :
Lets say the voltage of the guitar signal V0 = 100 and ignore the signal loss by a cable.
The output impedance of a passive electric guitar is around 20 ~ 40 KΩ and the input impedance of a tube amp is 1MΩ.
Assuming the output impedance of a guitar is 30KΩ, Z1out = 30000Ω and Z2in = 1000000Ω, and then V1 = 2.91 and V2 = 97.09.
This result means that only 97.09% of guitar signal is transmitted to amp and the rest 2.91% is lost by the output impedance of a guitar.
Numerically, you can say 97.09% is almost all of the signal, but the real problem of 20 ~ 40 KΩ impedance signal is that it is very susceptible to the capacitance by cable length. If you want to use pedal(s) between a guitar and a amp or use a cable longer than about 18 ft (5.5 m), you have to lower the impedance of signal using a buffer so it can break through the cable capacitance.
We will talk about this more in detail on Cable Talk and Buffer (Line Driver).

 Example 2) When connecting an effector with output impedance 10 KΩ to a tube amp :
Similarly with Example 1, lets say the voltage of the guitar signal V0 = 100 and ignore the signal loss by a cable.
Then V1 = 0.99 and V2 = 99.01, which means 99.01% of signal is transmitted to an amp.
Not a big deal compared with 97.09% of Example 1? Yes, it is a big deal!
A signal with 10 KΩ impedance can break through over 100 ft (30 m) of cable length without losing treble and punch. As stated in Guitar Electronics, capacitance of a cable lets high requency range leak to the ground resulting in a serious loss of treble and punch of a high impedance signal.
Here are direct examples :
  • Compare the same cables with different lengths in 12 ft (3.5 m), 18 ft (5.5 m), and 23 ft (7 m) or longer, then you can notice a significant treble loss in longer cables.
  • Or when you put a true bypass effector between a guitar and an amp, similar treble loss occurs compared to when you connect a guitar to an amp directly.
These problems can be easily settled by lowering impedance with a buffer between a guitar and an amp. We will talk about this more in detail on Cable Talk and Buffer (Line Driver).

 Example 3) When connecting a guitar to a Fuzz vs. When connecting a buffer bypass effector to a Fuzz :
Fuzz has a very low input impedance. This means it takes much smaller part of signal for processing than an amp does.
A Fuzz has an input impedance of 65 KΩ, approximately. This is very low compared to 1 MΩ of tube amps or most drive pedals.
Assuming the output impedance of a guitar 30 KΩ, you can see only 68.4% of signal is transmitted to a Fuzz.
The attractive and somewhat weird sound of the vintage Fuzz is caused by this structural defect(?). Vintage pedals from 60's like Fuzz, Octavia, and Germanium Treble Booster have similar low input impedances. For these pedals, true bypass was a must as a serious degradation of tone may occur if over 30% of signal would be lost when bypassed.

If a pedal with low output impedance around 10 KΩ was placed before a Fuzz, about 86.7% of signal would be transmitted to the Fuzz. Then Fuzz will sound very strange as it is receiving excessive amount of signal than it is supposed to. So just a guitar, Octavia, or Wah can be placed before a Fuzz. Even in this case, Wah has a very narrow or almost no sweep because of the low input impedance of a Fuzz.

Conclusion
Here we looked over some simple calculations and examples to understand concept of impedance. It is OK even if you do not fully understand the contents, but you need to know the impedances of your instruments and how to connect them in order to take full advantage of the instruments.
Impedance abbreviated as Z, keep in mind the facts below :
  • High Z signal : A signal with impedance of 20 ~ 40 KΩ. A signal from normal passive pickups. The maximum allowable cable length is about 18 ft (5.5 m), or loss of treble and noise problem occur.
  • Low Z signal : A signal with impedance of 10 KΩ or below. A signal from active pickups or FET/IC effect circuits. Almost no loss of treble/punch by cable capacitance and insusceptible to ground noise.
For a solution of problems in high impedance signal, refer to sections Cable Talk and Buffer (Line Driver).