PSPICE Modeling of Guitar Circuits with Effects of the Instrument Cable

I have used one of the world's most prevalent circuit analysis tools (PSPICE) to explore the effects of guitar electronic parts on tone. This includes:

• Pickup inductance
• Volume potentiometer resistance
• Tone potentiometer resistance
• Tone capacitor
• Treble bypass capacitor
• Instrument coax cable

I've spent most of my life in the electronics industry and understand what these parts do, but I received a greater understanding of the interdependencies of the parts after doing this analysis. We spend lots of money on pickups and we change pots and caps frequently. One of the big effects on the sound is the instrument cable, depending on the other parts used.

Something wonderful happens with a pickup inductance L (especially single coil), volume pot resistance R, and cable/amp capacitance C, especially in the Fender Telecaster. The resonance of that RLC circuit is in the critical audio range, generally from 1kHz to 4kHz. Unleashing that resonance with high resistance volume controls (like 1 megohm) makes the change in sound more affected by the instrument cable. Damping the circuit with a 250K volume pot reduces that treble resonance and makes the change in tone from the cable length less observable.

Most of the beginning of this is very technical, but after going through the simulations results, you will see the various effects of the parts. I'll also show simulations where a high inductance humbucker is not affected so much by cable capacitance and length.

Simulations

Here is the baseline modeling schematic:

The pickup above is modeled after a typical Telecaster bridge pickup. It has about 2.9 henrys of inductance. The inter-winding capacitance and wire resistance has little effect. That whopping 2.9 henrys of inductance dominates what it does to the circuit. The most important parameter of the pickup is the inductance. In the famous words of pickup manufacturing giant Bill Lawrence:

"The DC resistance of a pickup tells you as much about a pickup's tone and output as the shoe size tells you about a person's intelligence!"

I surmise that the reason the DC resistance has become a popular parameter used in pickups is that almost anyone can read it with an ohmmeter. If the pickup structure and wire diameter are the same, a larger resistance will be indicative of more windings, meaning more inductance. Otherwise, all bets are off.

The tone network above is modeled as a fixed value. It is shown as a 250K resistor and a 0.05µF capacitor, which is like a tone control on the max clockwise (CW) position. I will vary the resistance to simulate various settings to simulate more counter-clockwise positions.

The volume control is modeled as a simple voltage divider. I will vary the values of R4 and R6 for different volume control settings, but keep the total resistance equal to the potentiometer's nominal value.

The cable (T1) is modeled with a standard PSPICE transmission line. I'm assuming a standard dielectric constant that yields a group delay of about 1.45 nanoseconds (ns) per foot. So the 30ns delay is about a 20-foot cable to start with. It will vary in the examples below. Most examples are with a characteristic impedance of 50 ohms, and some with 75 ohms. It is important to state that the only thing that matters about the cable at audio frequencies is the capacitance. The longer the cable, the more capacitance; the higher the characteristic impedance, the lower the capacitance. Low capacitance cables are great, but it still has capacitance.

The amplifier input is modeled as a 1 Megohm resistor and a 100 picofarad (pF) capacitor. This is typical of most amplifiers.

The voltage generated by the pickup in the simulation is 2mV, but it could be most anything for a passive circuit analysis.

My baseline response plot conditions are:

• 250K volume pot max CW
• 250K tone pot max CW
• 20ft cable (50-ohm characteristic impedance)
• Tele Bridge pickup

Notice the resonance peak at 3kHz. The peak is a little greater than 3mV relative to the 2mV bass region.

Let's first show the effects of the cable. Here are the same parts except the cable is now 6 feet long.

Observe how the shorter cable "tunes" the resonant peak up to 4kHz. Bear in mind that any changes in resonance between 1-5kHz are very sensitive to the ear.

Here is the simulation with a 3" cable, consistent with maybe a wireless transmitter. The resonance is now bigger and up to 5.2kHz.

Now let's change the volume and tone pots to 500K with a 20 ft cable.

The peak is still at 3kHz, like the other 20ft cable plot with the 250K pot, but now the peak is higher at 4.75mV

Here are 500K pots and a 6ft cable:

The peak moves to 4kHz, the same resonant frequency as with the 250K pots and a 6ft cable.

Now let's go to 1 Meg pots and a 20-foot cable:

The resonant frequency is the same as any example of a 20 foot cable at 3kHz. The amplitude is now a whopping 6.5mV !!!!

Here is the 6ft cable with 1 Meg pots:

The peak is 4.3kHz at 6mV.

For grins, let's see what happens with 75 ohm cable. This is 75-ohm, 20-foot cable with 1 Meg volume pot.:

The resonance is pushed out to a higher frequency than the 50 ohm equivalent, simply because the net capacitance is less. Notice that this resonance is closer to a 50-ohm, 6-foot cable.

So the previous examples show the following:

1. The volume pot load varies the amplitude of the resonance, but does not move it in frequency.
2. The cable and amplifier capacitances move the frequency of the resonant peak.
3. In the case of the 1 Meg pot, changing the cable length is kinda like moving a wah-wah pedal's position.

Let's look at a humbucking pickup (L1 changed to 10 henrys inductance), 250K pots, and a 20-ft cable:

The peak barely exists. This means that reasonable cable length variations will have little effect on the response.

Volume Control Adjustment

It is common knowledge that turning the volume control down results is high-frequency loss, unless a treble bypass capacitor is used. Here is the response with R6 as 100K and R4 at 150K (volume turned down some):

• 250K tone pot max CW
• 20ft cable (50-ohm characteristic impedance)
• Tele Bridge pickup

Notice the resonant peak is gone, and the rolloff begins at 2kHz. The bass signal is down to just a little over 1mV.

Now let's add a 0.001µF treble bypass capacitor:

The resonant peak is restored, and the bass spectrum is attenuated down to almost 1mV.

So, the series resistance in the circuit with the volume turned down reduces the interaction of the LC resonance.

Tone Control

Finally, here is the tone control turned down to a total resistance of 100K:

• 250K Volume pot max CW
• 20ft cable (50-ohm characteristic impedance)
• Tele Bridge pickup

The resonance treble peak is flattened, and the roll-off occurs at 3KHz.

Here is the response with the tone control all the way down (max CCW) with the 0.05µF capacitor:

The roll-off occurs at 400Hz, and you have thrown a blanket over your guitar.

Conclusions

• All electronic parts of the guitar and guitar cable affect the tone
• The cable capacitance (i.e. capacitance increases with length) and the tone control tune the resonant frequency.
• The resistance of the volume pot does not effect the resonant frequency, but does affect the amplitude of the resonance.
• Guitars that have higher resistance pots (like 1M or volume pot bypassed with a switch) will see that the cable type and length will change the sound more.
• Guitars that have lower resistance pots (like 250K) will see that the cable type and length with change the sound less, but the overall treble will be reduced.

There is no such thing as a "better" cable. You can buy a low-capacitance cable to help keep the resonant frequency as high as possible IF that is what you are looking for.

Bottom line is that:

• High resistance volume pots create more treble, but allow various cables to cause a more drastic change in tone.
• Lower resistance pots results in less overall tone change with cable variation, but result in less treble overall.
• The volume control pot is like a damping resistor to the resonant circuit. Lower values reduce the peak amplitude.

Examples of Cable Capacitance

Here are some cables I had laying around to test just for reference. I'm not advocating any one cable above another.

©2005 Terry Downs Music™