Sparked by the recent discussions of how the TS Tone Control REALLY works, and all the simplified explanations of it, I decided to model the circuit in 5Spice to try to shed some light on the function of specific components, specifically the RC filters throughout the circuit.
Here's the basic TS circuit, minus input buffers, with a few adjustments to the input output bias resisters so as not to add unwanted filtering. I used an LT1498 Model because I didn't have a 4558, and for this study we weren't focusing on that.PART I - Gain Response
First off, you can see 3 test points:
TPv1 - (RED) - Output of Clipping Amp
TPv2 - (GREEN) - Circuit Output (Volume Pot is always at Full)
TPv3 - (BLUE) - Signal after R6/C5 Low-Pass but Before Tone Control Amp.
Lets look at all three Points for Various Gain Settings, using a LINEAR Pot. Tone Pot is set at Noon, remember this is without Output Attenuation.
First, Minimum Gain. Full Treble content coming from the Clipping Amp. Nice Mid-Hump Post R6/C5. No Effect from Tone Circuit.
I think its most apparent here that the C4/R5 Frequency Cut-Off (720Hz) limits the gain to frequency OVER 720 in the clipping amp.
50% Gain. Less High Frequency Response from the Clipping Amp. 20dB Louder than Minimum Gain. Same Mid-Hump Post R6/C5. No Effect from Tone Circuit
Maximum Gain. Even Less High Frequency Response from the Clipping Amp. Additional 5dB louder than 50% Gain. Same Mid-Hump Post R6/C5. No Effect from Tone Circuit. So it looks as if we are seeing the effect of the 51pF Cap across the Gain Control of the Clipping Amp. I'm not going to make an attempt to explain it entirely, but I believe it is common knowledge that increasing that value of cap to 100pF or 220pF will roll-off even more highs and "soften" the distortion, but the effect is seen most at high gain settings. Again, I have not gone into details regarding the specific RC Filter/Feedback loop response.PART II - Tone Control
Next I will fix the Gain setting at 50%, and adjust the Tone Control Pot. The 4 curves are evenly space settings on the Tone Control Pot, 0, 1/3rd, 2/3rds and Full. As ycan see the sweep of the Pot does not have a steady affect on the frequency response. I believe this is why people have used the radical S or W taper Pots as mods instead of Linear Pots. The effect of the tone control is bunched up at the extremes on a Linear pot, whereas a W Taper allows a more rapid change of resistance near the center, and so the effect seems to have a smoother sweep. Just a theory, I don't know exactly what the W or S Taper actually does, but I have one in my TS and it works much better! Its also evident here that the Tone Control shifts the mid hump higher in its upper settings.PART III - Changing Values in the Tone Section
The Dubious 220 ohm resistor (R9). In some earlier simulations I did, we discovered that a resister in this configuration (Low Pass Filter) creates a High Shelf in the frequency response. This shelf levels off the 6dB/Octave created by the original R/C network, at a frequency that appears to be given by 1/(R9*C). Anyway, in this configuration its a bit more complicated, and I'm not prepared to explain it in words at the moment. BUT, I simulated the effect of shorting R9 and how it effect the Frequency Response.
First off, Tone set to 50%. R9 Does NOTHING! I believe this is because the Tone control actually has no effect at all in this setting. If we refer back to PART I, we'll see that there were no significant differences between the signal before and after the Tone Control Amp. Thus, I did not create a graph for this. What I did do is simulate the effect of shorting R9 at Minimum and Maximum Tone Settings.
1. Minimum Tone Setting (Darker Tone from TS, same as lowest curve from PART II)
Here we are seeing a slight DECREASE in Treble Content when R9 is shorted.
B. Maximum Tone Setting (Brighter, Highest cuver from PART II).
Here the effect is most prominent. With R9 shorted, we lose a lot of upper harmonic content out of the TS Tone Control. This is the setting where the RC Filter is applied to the feedback of the Op Amp. Filtering the feedback would increase the amount of treble content in the output. Thus, a treble shelf in the feedback filtering would limit the highest treble increase, controlling the highest harmonics (usually considered harsh). Also notice that the frequency response begins to deviate significantly around 3kHz or so (3.2kHz being the 1/RC value of R9 and C6).CONCLUSIONS
Its been said that to make a good distortion box, you need to control the EQ/Harmonics between and after gain stages. Here's a good example of what that means in a classic box. Personally I had no idea the Mid Hump was so apparent, but remember, these simulations are done with a flat frequency source, whereas an actually guitar has a lot more amplitude in the mids and lows.
From this data I believe we can conclude that the Mid Hump is induced as a combination of the C4/R5 (720Hz) cut-off in the Clipping Amp Gain, and the R6/C5 Low Pass Filter immediately following the clipping stage (cut-off also ~720Hz).
Honestly, this was just me looking for an excuse to try out a new tool. I hope you find this info useful as I did.