I'll keep the math to a bare minimum, but you can't describe impedance without a little math. When I was in college, the professor in an introductory course on circuit theory shared this anecdote: "As part of their oral exam, PhD electrical engineering students were asked to define the term 'impedance'. The review board was dismayed to find that many of them were unable to provide an adequate answer." He went on to explain that impedance is a very simple concept. By definition, impedance is the slope of the V-I (voltage/current) curve. Now that you know that, you're smarter than some PhD students.
For the purposes of pedal building, what is impedance and why do we care about it?
Impedance is the AC equivalent of resistance. It governs how electrical energy, in the case of effects pedals the guitar signal and DC power, move thru the circuit. Every electrical component, including wire, has impedance. The input impedance of the first pedal in the chain can influence the tone because if the impedance is low, it will load the pickups. Pedals like the Tube Screamer have a high input impedance and allow all of the signal to get from the pickup to the pedal's input circuit. The classic Fuzz Face, on the other hand, has a relatively low input impedance that loads the pickups, absorbs energy and dampens the pickup's resonant peak. For the first pedal in the chain, input impedance strongly influences a pedal's response to the guitar's Volume & Tone controls because the pedal loads those things too. Lower impedance pedals are generally more responsive to guitar control settings. The output impedance of a pedal influences how the guitar signal passes to the next pedal in the chain or the amp. Lower output impedance pedals can drive long cables without losing brightness. They can also drive the shit outta the next pedal in the chain. The reason some pedals don't get along is mostly about input and output impedance.
Impedance is expressed in Ohms and is given the symbol Z. Impedance showed up late and was last in line. By the time it got its symbol assigned all of the other letters had been taken.
Resistors
Resistors have an impedance equal to their resistance. Zr = R. Simple enough.
Reactive Components
Capacitors and inductors are called reactive because they store energy and their impedance is dependent on frequency. Their impedance equations presented below are slightly simplified, but are adequate for this discussion.
Inductors
Inductor impedance: ZL = 2 x π x f x L
where Z is in Ohms, f is in Hz and L is in Henries. The 500mH choke we use in wah-wahs and Conqueror pedals has an impedance of 691 Ohms at 220Hz, the frequency of the A string at the 12th fret. For inductors, impedance goes up as frequency goes up.
Capacitors
Capacitor impedance: Zc = 1 / (2 x π x f x C)
where Z is in Ohms, f is in Hz and C is in Farads. A 47nF capacitor has an impedance of 41K at 82.4Hz, the frequency of the open bottom E string. With capacitors, impedance goes down as frequency goes up.
Semiconductors
Semiconductors (diodes & transistors) are non-linear. Their impedance varies with current (or voltage). If we plot voltage vs. current, at any point on the curve, the impedance is the slope of the curve. The convention is to plot current on the vertical axis and voltage on the horizontal axis. In that case, the slope of the curve is the admittance, which is the inverse of impedance. Take a look at the v-i curve for a silicon rectifier diode.
Below 0.56V the curve is essentially flat, which means that the impedance is very high, could be megohms. At 0.82V, the slope is about 10mA per 200mV. 200mV / 10mA = 20 Ohms. At 0.9V, the slope is around 60mA per 100mV. 100mV / 60mA = 1.67 Ohms. People like to simplify diodes and think of them as either OFF or ON. But there is a smooth transition from OFF (high impedance) to ON (low impedance) and that transition is what gives diode clippers their signature sound.
Filters
Getting back to inductors and capacitors, it is their impedance, and how it varies with frequency, that makes it possible to build electronic filters. The calculations used to design and analyze filters take into account the impedance of the capacitor (or inductor) and how it interacts with the other parts (resistors, diodes, transistors) to determine the frequency response.
Example: A simple low-pass filter can be realized with a resistor and a capacitor. We see that all the time in pedal circuits. The corner frequency is given by:
Fc = 1 / (2 x π x R x C)
At that frequency, the impedances of the resistor and capacitor are equal. Half of the signal power is lost in the resistor. Below Fc, very little signal is lost and the frequency response is flat. Above Fc, more and more signal is lost as frequency goes up. For every doubling of frequency, the voltage is cut in half.
There is another layer of complexity that I completely glossed over, but that's the quick tour. Any questions?
For the purposes of pedal building, what is impedance and why do we care about it?
Impedance is the AC equivalent of resistance. It governs how electrical energy, in the case of effects pedals the guitar signal and DC power, move thru the circuit. Every electrical component, including wire, has impedance. The input impedance of the first pedal in the chain can influence the tone because if the impedance is low, it will load the pickups. Pedals like the Tube Screamer have a high input impedance and allow all of the signal to get from the pickup to the pedal's input circuit. The classic Fuzz Face, on the other hand, has a relatively low input impedance that loads the pickups, absorbs energy and dampens the pickup's resonant peak. For the first pedal in the chain, input impedance strongly influences a pedal's response to the guitar's Volume & Tone controls because the pedal loads those things too. Lower impedance pedals are generally more responsive to guitar control settings. The output impedance of a pedal influences how the guitar signal passes to the next pedal in the chain or the amp. Lower output impedance pedals can drive long cables without losing brightness. They can also drive the shit outta the next pedal in the chain. The reason some pedals don't get along is mostly about input and output impedance.
Impedance is expressed in Ohms and is given the symbol Z. Impedance showed up late and was last in line. By the time it got its symbol assigned all of the other letters had been taken.
Resistors
Resistors have an impedance equal to their resistance. Zr = R. Simple enough.
Reactive Components
Capacitors and inductors are called reactive because they store energy and their impedance is dependent on frequency. Their impedance equations presented below are slightly simplified, but are adequate for this discussion.
Inductors
Inductor impedance: ZL = 2 x π x f x L
where Z is in Ohms, f is in Hz and L is in Henries. The 500mH choke we use in wah-wahs and Conqueror pedals has an impedance of 691 Ohms at 220Hz, the frequency of the A string at the 12th fret. For inductors, impedance goes up as frequency goes up.
Capacitors
Capacitor impedance: Zc = 1 / (2 x π x f x C)
where Z is in Ohms, f is in Hz and C is in Farads. A 47nF capacitor has an impedance of 41K at 82.4Hz, the frequency of the open bottom E string. With capacitors, impedance goes down as frequency goes up.
Semiconductors
Semiconductors (diodes & transistors) are non-linear. Their impedance varies with current (or voltage). If we plot voltage vs. current, at any point on the curve, the impedance is the slope of the curve. The convention is to plot current on the vertical axis and voltage on the horizontal axis. In that case, the slope of the curve is the admittance, which is the inverse of impedance. Take a look at the v-i curve for a silicon rectifier diode.
Below 0.56V the curve is essentially flat, which means that the impedance is very high, could be megohms. At 0.82V, the slope is about 10mA per 200mV. 200mV / 10mA = 20 Ohms. At 0.9V, the slope is around 60mA per 100mV. 100mV / 60mA = 1.67 Ohms. People like to simplify diodes and think of them as either OFF or ON. But there is a smooth transition from OFF (high impedance) to ON (low impedance) and that transition is what gives diode clippers their signature sound.
Filters
Getting back to inductors and capacitors, it is their impedance, and how it varies with frequency, that makes it possible to build electronic filters. The calculations used to design and analyze filters take into account the impedance of the capacitor (or inductor) and how it interacts with the other parts (resistors, diodes, transistors) to determine the frequency response.
Example: A simple low-pass filter can be realized with a resistor and a capacitor. We see that all the time in pedal circuits. The corner frequency is given by:
Fc = 1 / (2 x π x R x C)
At that frequency, the impedances of the resistor and capacitor are equal. Half of the signal power is lost in the resistor. Below Fc, very little signal is lost and the frequency response is flat. Above Fc, more and more signal is lost as frequency goes up. For every doubling of frequency, the voltage is cut in half.
There is another layer of complexity that I completely glossed over, but that's the quick tour. Any questions?