Thus, the amount of noise that the cathode follower input sees must be amplified by the inverse of the resulting decrease in the bottom triode's transconductance (X). Wrapping all of these considerations into one formula:
   Ratio = [R_k(mu +1) + r_p] / [R_k(mu +1) + 2r_p]   
where R_k equals both the intermediate and the second stage's bottom triode's cathode resistor. Once we know this ratio, we must realize it with a capacitive voltage divider. First we specify a value for C1 and then we apply the following formula:
   C2 = C1 / Ratio - C1
In the example given here, the ratio roughly equals 5/6. This means that 83% of the power supply noise should make it to the bottom triode's grid to cancel the noise present at the cathode follower's grid. (Of course, 0.83 is close to 1; thus many would simply omit capacitor C2 and boldly cover up their unwillingness to do some math with a proclamation that they have "Ultra-Pathed" the circuit; soon afterwards, I will receive emails asking to explain the brilliant Smith's Ultra-Pathed line-stage amplifier.)
     So is there anymore blood to be wrung from this circuit? Well, since we have added two extra triodes, the number of possible variations on this theme is probably ten times larger than it was with only two triodes.

     The resulting current draw would equal about 100-mA through the load and the 5.1k resistor. On the other hand, if the top three tubes were removed and the bottom triode sees a 2-volt pulse at its grid and the resulting downward current draw would equal about 50-mA. Still the parts count is low and the output impedance is fairly low. Improving this amplifier requires adding a feedback loop across the amplifier or using more and/or higher current triodes. To substantially improve the performance of this amplifier, however, will take us into the realm of the push-pull view of the SRPP.

SRPP headphone amplifier
     The circuit to the right illustrates how four triodes (two envelopes) can be used to make a headphone amplifier powerful enough to drive 32-ohm headphones. This amplifier is a blend of single-ended and push-pull operation, as the three top triodes work into an active load (the bottom triode) and the 5.1k resistor. The result is that the amplifier can swing more voltage positively than it can swing negatively. Imagine the sole bottom triode plucked from the circuit while it was in use. The top three triodes would effectively see a +2-volt pulse on their grids.

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