The fourth stage is a voltage amplifier DC coupled to a cathode follower. It is driven by a 220k grid stopper at the output of the previous stage. This serves the same purpose as the 470k resistor at the input to the second stage - it minimizes bias excursion to reduce the chance of blocking distortion. The smaller resistor value and higher voltage gain create 3.6dB attenuation at 4 kHz, so treble attenuation is a bit less than at the input to the second stage.

The voltage amplifier has the same configuration as Soldano's first stage. Small signal voltage gain increases from 51 at 82Hz to about 74 at 400Hz due to the relatively small, 1uF cathode bypass capacitor. The cathode follower has a gain of almost unity. Its output passes through a voltage divider with a "gain" 2.2k / (100k + 2.2k) = 0.02, representing 34dB of attenuation. There is hardly any loss at any audio frequency across the voltage divider formed by the 1uF capacitor and 1M grid resistor for the next stage. Net gain for both triodes is thus (51)(0.02) = 1 at 82Hz and (74)(0.02) = 1.5 at 400Hz.

The DC load line for the cathode follower is marked by one end at the DC plate supply voltage of 380 volts and the other end at a plate current of (380) / (100k + 2.2k) = 3.7mA.

The grid voltage relative to ground is equal to 380 volts minus the voltage drop across the 220k plate resistor. From our analysis of the first stage the DC plate current is 0.83mA, so the voltage drop is

(220k)(0.83mA) = 183 volts

The grid-to-ground voltage is thus 380 - 183 = 197 volts. If the grid-to-cathode voltage is zero, then the current through the 100k + 2.2k tail resistance is 197 / 102k = 1.93mA. If, on the other hand, the grid voltage is minus 2 volts, then the current is 199 / 102k = 1.95mA. The DC operating point is at the intersection of a line representing these conditions (in green) and the DC load line.

The voltage amplifier is directly coupled to a cathode follower with a very high input impedance and its 1.8k cathode resistor is fairly small, so the AC load line is nearly the same as the DC load line. Using the DC load line and DC operating point for the first stage we get a maximum plate voltage swing from 55 volts to 297 volts.

Large signal gain for the driving triode is (297 - 55) / 3 = 81.

According to the cathode follower load line, a positive input signal swing that brings the grid voltage to zero creates a plate current of 2.6mA. This puts the cathode at (2.6mA)(102.2k) = 266 volts. So the grid-to-ground voltage is 266 volts and the plate current through the driving triode's 220k plate load resistor is (380-266) / 220k=0.5mA. The driving triode is thus well above cutoff. The cathode follower reaches its limit of swing before the driving triode.

In the opposite direction, when the driving triode's grid swings positive to zero volts, its plate current swings to 1.4mA. There is (1.4mA)(220k) = 308 volts across the plate load resistor, so the cathode follower's grid-to-ground voltage is 380 - 308 = 72 volts. For the cathode follower to be in cutoff its grid-to-cathode voltage needs to be approximately minus 5 volts and the cathode-to-ground voltage must be zero, because no plate current flows. This theoretically makes the driving triode's plate voltage minus 5 volts, which is an impossibility. So in this direction of swing the driving triode reaches its limit first.

Without the cathode follower there is severe clipping as the driving triode's grid voltage approaches zero and more gradual clipping as the triode transitions into cutoff. The directly coupled cathode follower evens out the score. Soldano's fourth stage thus produces a more symmetrical output waveform. Second-order harmonics are reduced. Third-order harmonics are enhanced.

Using 34 for the gain of the first stage, 60 for the gain of the second stage, 0.68 for the gain of the second stage output circuit, and 1.8 for the gain of the third stage, the signal amplitude at the amplifier input jack required to drive the fourth stage into overdrive (volume control set to maximum) is less than

1.5 / 34 / 60 / 0.68 / 1.8 = 600 microvolts

This is much lower than in traditional guitar amp designs, so it takes very little input signal to force this stage into overdrive.

## Distortion

One of the most important aspects of an amp designed to overdrive a directly coupled cathode follower is the effect on clipping of the output waveform. Overdriving the cathode follower in the positive direction causes a drop in the plate-to-cathode voltage, making electrons more attractive to the grid. The resulting increase in grid current causes more current to flow through the driving triode's plate load resistor, thus limiting the decreasing voltage across it. The effective gain of the driving stage is reduced and positive peaks in the cathode follower's output signal are flattened.

As the driving triode approaches cutoff the cathode follower's input impedance drops from an extremely high value, representing a very light load, to a very low value that bogs down the driving circuit. This sharpens the clipping of the signal and makes it a more symmetrical match to clipping in the opposite direction. As Rutt observes, there is no equivalent to this phenomenon in transistor circuits.4

Let's take a look at the final stage of Soldano's overdrive channel.

## References

1Richard Kuehnel, Circuit Analysis of a Legendary Tube Amplifier: The Fender Bassman 5F6-A, 3rd Ed., (Seattle: Pentode Press, 2009).

2Richard Kuehnel, Vacuum-Tube Circuit Design: Guitar Amplifier Preamps, 2nd Ed., (Seattle: Pentode Press, 2009).

4T.E. Rutt, "Vacuum Tube Triode Nonlinearity as Part of The Electric Guitar Sound," 76th Convention of the Audio Engineering Society, New York, 1984.