To convert our theoretical knowledge into a practical strategy we translate the equations that determine frequency response based on parts values into equations that determine parts values based on the desired frequency response. I'll demonstrate this using a concrete example: giving the CP103 a more Bassman-like midrange scoop. Here is the simulated response of the Fender Bassman 5F6-A tone stack with its bass control at maximum, its midrange control at minimum, and its treble control at maximum:
It has a bass transition frequency of 142Hz and a treble transition frequency of 2.5kHz. Let's modify the CP103 tone stack to use these transition frequencies. A rough approximation of the expected response (with bass and treble controls at maximum) can be seen by drawing two lines. The blue line below shows a modified CP103 bass response that starts at 142Hz, 0dB, and ends one decade higher (1.42kHz) at -20dB. This represents 20dB-per-decade attenuation that begins at 142Hz.
Likewise the red line shows a treble-to-midrange attenuation of 20dB per decade that begins at 2.5kHz and ends at 250Hz. (Nothing really "ends" there - it's just a convenient reference point to give the line the correct slope.) From the intersection of the blue and red lines we observe midrange scoop centered around 600Hz. Let's determine the CP103 component values needed to produce this result.
From our analysis of the CP103 tone stack the bass transition frequency is
and the treble transition frequency is
These two equations represent two constraints, and since there are many more parts values than constraints it appears we have a lot of freedom of choice. There are other factors to consider, however. The overall circuit impedance needs to be high enough not to bog down the driving circuit and low enough not to be bogged down by the stage it drives. We'll therefore keep the CP103's R1 value at 100k. Out of convenience, we'll also retain the CP103 tone control values of RB = 1M and RT = 250k.
Another consideration is the midrange-treble transition frequency:
For effective tone control performance this need to be below the midrange scoop frequency. The CP103 uses a midrange-treble transition of 254Hz for a scoop frequency of 316Hz and a treble transition frequency of 2.8kHz. From the equations above this means the ratio
is equal to fMT/ftreble, where fMT is the midrange-treble transition frequency and ftreble is the treble-transition frequency. We can turn this concept into a design formula with just a little algebra:
For our design, let's set fMT = 400Hz for a scoop frequency of 600Hz and set ftreble = 2.5kHz. From the formula R2 is 19k. (We'll use the more common value of 20k.)
Everything is now known except for the capacitor values, which we can determine by turning around the formulas for the bass and treble transition frequencies:
For our desired transitions at 142Hz and 2.5kHz we get C1 = 0.012uF and C2 = 240pF. Here are the final results:
Here is the response using Electronics Workbench Multisim®. This plot assumes ideal conditions: zero source impedance and an infinite-impedance driven stage. These were the conditions we used to determine the parts values.
(The horizontal axis is a log scale of frequency from 10Hz to 10kHz and the vertical scale is from -35dB to 0dB.) Here is the same plot using CP103 operating conditions: a driving circuit output impedance of 49k and a driven circuit consisting of a 250k volume control.
For the same conditions, here is the response with the bass control at maximum and the treble control at minimum:
Bass control at minimum and treble control at maximum:
Both controls at minimum:
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