Here we will examine the treble effects of Marshall's modification to the value of C1, raising it from 250pF to 500pF. Intuitively we anticipate increased treble boost. This is indeed the result, but not in the way we might expect.
Like we did with bass and midrange, we will determine the key gain and transition frequencies through the use of a Bode magnitude plot. Once these are known, the effects of Marhall's C1 modification will be clearly evident. Finally, we describe the overall conclusions that can be drawn.
At high frequencies the large capacitors C2 and C3 act as short circuits, shorting out the bass control.
With the middle-range control at minimum, it is also shorted out.
Under these conditions the frequency response is
where t varies between zero (treble control at minimum) to 1 (treble set to maximum). With some algebra we put this into a form suitable for a Bode plot:
There is a zero at s = 0 and a pole at s = -a. Notice that the control setting t has no influence on the zero or the pole and comes into play only in the overall gain constant K. The treble control setting therefore has no influence on which frequencies are included in the treble range, only their overall volume level.
Let's take a look at the extremes of frequency. At DC, where s = 0, we note that H(s) = 0 and there is zero output. At extremely high frequencies, where s approaches infinity, its magnitude becomes much larger than the other variables and the response approaches
Both of these conditions make sense, because at DC the capacitor is an open circuit and the output becomes connected to ground through the treble control. At extremely high frequencies the capacitor is a short circuit, so the gain is a constant equal to 1 with the treble control at maximum and zero with the control set to minimum. With the midrange control at minimum, we obtain a high-pass filter that passes all that we consider to be treble and attenuates middle-range and below.
For the Bassman the break frequency is
The Marshall design cuts this in half to 1.25kHz by doubling the value of C1. Here is the Bode magnitude plot for Fender's 5F6-A with the treble control set to maximum and the midrange control at minimum.
Here's how we constructed this plot. For the term
we plot a line rising at a slope of 20dB per decade passing through the 0dB line at a frequency of
The break frequency of the term
Similar to what we saw for bass frequencies, the crossing frequency for the zero is identical to the break frequency for the pole, regardless of the resistor and capacitor values. From the Bode magnitude plot we see that this means that the response is -3dB at the crossing frequency and then nearly 0dB for all frequencies higher than this. Since middle-range frequencies are attenuated by at least 10dB in the case of Fender, or 7dB for Marshall, setting the treble control to maximum effectively causes 10dB (or 7dB) of treble boost.
For the pole we begin by plotting a horizontal line at 0dB. At 2.5kHz we extend a line that decreases at a rate of 20dB per decade.
The approximate gain is the sum of the two components that we have just plotted and the actual gain is 3dB lower at the break point, as shown in the figure. For the Marshall design the plot is identical, except it is shifted left by 1.25kHz.
By reducing the lower cutoff frequency, the Marshall JMP50 Model 1987 shifts more guitar frequencies into the range of the treble control. At high treble control settings these frequencies are boosted along with the rest of the treble range. This is very similar to what we saw at low frequencies, where the upper cutoff for the bass passband was shifted higher by 54 percent. When observed in this context, we conclude that Marshall modifications effectively narrow the range of frequencies defined to be middle-range, shifting the upper and lower extremes of 5F6-A midrange to Marshall's bass and treble controls.
Both the 5F6-A and the JMP50 have 0dB gain at treble frequencies. Increasing the size of C1 thus provides no additional treble boost for high-frequency harmonics that are well into the treble passband. Instead, increasing this value allows lower frequencies to share in the overall boost.
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