## Simplified Bass and Treble Control

Comment:

This feedback loop assumes that if the amplification factor before positive feedback is even slightly less than (1.0), the resulting infinite series will converge, on some finite amplification factor. However, as the reader can see, ‘VR1′ and ‘VR2′ can be turned all the way to the right, thus connecting the feedback summations directly to the Source of the two MOSFETs.

I am assuming that the gain there is slightly less than unity, as following from changes in Gate voltage. However, because there are tolerances in all the resistors, the feedback gain may reach unity in theory. (:1)  If this should happen, the user of the appliance should have a tremendous experience and learn not to do that again.

Explanation:

The resistor-capacitor combinations of (R11,C4) and (R12,C5) produce a rudimentary first-order, low pass and high pass filter each. The MOSFETs achieve that their Source voltages will follow their Gate voltages simply, while small changes to their Drain voltage should be the inverse of those to Source voltage, times (9), as long as the current flowing through ‘R2′ and ‘R3′ can be neglected.

Two resistors were removed from an earlier version of this circuit, that were meant as an enhancement, but that would have prevented the circuit from working.

The way the inverse-logarithmic-taper Variable Resistors (=Potentiometers) work is, that with their wiper at centre-position, its resistance to the right electrode should be 10kΩ, while its resistance to the left electrode should be 90kΩ. This leads to a design barrier because the resistances of ‘R8′ and ‘R10′ automatically need to be 9x ‘R7′ and ‘R9′, so that the inverted signals cancel out on the wipers.

An added complication to this arrangement is that, due to the phase-shifts of the first-order filters, (α) is some multiple of a complex number, that multiple being determined by the setting of the Bass and Treble controls, the complex number determined by the frequency, which will appear normally in the denominator, and thus result in an attenuation, which my notes above are only a gross simplification of. However, well below and above their corner-frequencies, the low-pass and high-pass filters will exhibit little phase-shifting, so that the final result below is still correct:

This also achieves that the maximum attenuation can become:

1 / (( (200kΩ / 220kΩ) * (90kΩ | 220kΩ) / 10kΩ) + 1)

In other words, with the wiper of each potentiometer turned all the way to the left, ‘R2′ and ‘R3′ will act as though in parallel with ‘R8′ and ‘R10′, thus diminishing the achievable inverted gain somewhat.

‘R1′ … ‘R6′, together with the operational amplifier, form a summation circuit, with the input to this circuit as one of its inputs.

(Updated 10/21/2019, 19h35 … )