Tuesday, 24 September 2013

Passive Analog High and Low Pass Filters

To better understand the way in which guitar wiring works, it is necessary to be able to recognise two fundamental electrical circuits. These are the passive analog high-pass and low-pass RC (resistor/capacitor) filters. Low-pass RC filters are used on nearly every guitar available in the form of "tone circuits". Not as common, but just as useful, high-pass RC filters can be found in wiring mods such as the popular 'Treble Bleed' mod (more on that in a future post). Here's a rundown of each type of filter circuit.

The Passive Analog Low-Pass Filter

The passive analog low-pass RC filter is shown below. In this circuit, the capacitor sits across the output (in parallel) and the resistor is inline (series).


Such a circuit only allows sufficiently low frequency components of the input waveform to appear across the output. The theory of RC (Resistor/Capacitor) filters tells us that passive analog low-pass filters like the one shown here have a cut-off frequency in Hz equal to: 

 fcut-off = 1/(2πRC)
 
An ideal low-pass filter would allow any frequency below this cut off to pass unattenuated while eliminating signal frequencies above this cut off. In the real word the cut off frequency is not a sudden all-or-nothing threshold but the middle of a gradual sloping transition from frequencies that are completely attenuated to frequencies that are completely transmitted.


The Passive Analog High-Pass Filter

The passive analog high-pass RC filter is shown below. In this circuit, the capacitor sits in series with the signal input whilst the resistance sits in parallel with the output.

 

Such a circuit only allows sufficiently high frequency components of the input waveform to appear across the output. Interestingly, the function defining the cut-off frequency for the high-pass filter is exactly the same as that for the low-pass filter:
 fcut-off = 1/(2πRC)

As with the low-pass filter, an ideal high-pass filter would allow any frequency above this cut off to pass unattenuated while eliminating signal frequencies below this cut off. 

So there you have it. Simple circuits with relatively simple functions describing their operation. As guitar enthusiasts and builders, it is not important for us to understand the physics that underlies these filter circuits. We can accept that they function as specified. But, it is useful for us to be able to recognise these circuits when they crop up in guitar wiring diagrams. The more you learn to recognise them, them more you see them everywhere!