The third stage has a 12AX7 triode sharing the same plate supply as the second stage.

The AC load consists of a 2.2M resistor in parallel with a 330k resistor and the output impedance Zo of the normal channel's second stage. Here is what that stage looks like:

For audio frequencies its output impedance is 74k plus the impedance of 120pF in parallel with 2.2M. If we ignore the small capacitor, then the overdrive channel's load for midrange signals is equal to

2.2M || 330k || (2.2M + 74k) = 255k

This is the value we will use as the effective output load when we plot the AC load line.

The DC load line has one end at the DC plate supply voltage of 350 volts and the other end at a plate current of (350) / (100k + 39k) = 2.5mA.

As the grid voltage varies from minus 3.5 to minus 4.5 volts the current passing through the 38k cathode resistor rises from 0.09mA to 1.1mA, as shown by the green grid line shown below.

The triode is thus biased very close to cutoff at a grid voltage of about minus 4 volts. Such a situation may seem a bit perilous, but having a whopping 39k at the cathode creates substantial negative feedback to counteract changes in grid voltage due to the input signal. We'll take a look at why this stage is not as close to cutoff as it appears and then examine the distortion effects of operating in this region of the curves.

This stage has a 0.001uF plate bypass capacitor to prevent high-frequency parasitic oscillation. It serves the same purpose, for example, as the 47pF capacitor between the plates of the Fender Bassman's long tailed pair. In this case, however, the value is much higher, creating significant treble attenuation.

At high treble frequencies the 0.001uF plate bypass capacitor acts as a short circuit and gain is zero. At bass frequencies the capacitor is open and there is an effective gain of about 1.8 (5dB), providing significant bass boost but not a lot of voltage gain compared to upstream stages. For audio signals the capacitor is in parallel with an output impedance of 98k and an effective load of 255k (as described earlier). This creates a -3dB treble cutoff frequency of 2.2kHz.

Potential gain is dramatically reduced by the large, unbypassed cathode resistor which creates substantial negative feedback. This makes the cathode "follow" the grid. (This is not a cathode follower, however, because the output is taken from the plate, not the cathode.) Thus the grid-to-cathode voltage, which is the value shown in the characteristic curves below, is much less than the grid-to-ground voltage, which represents the input signal.

For bass and midrange frequencies the plate circuit resistance is

39k + 100k||255k = 111k

This means that a drop in plate voltage from 335 volts (the DC value) to zero volts creates an increase in current of 335 / 111k = 3mA. The current thus rises from 0.1mA (the DC value) to 3.1mA, which forms the upper left end of the blue AC load line show here.

A grid voltage swing of about plus or minus 0.3 volts relative to the DC operating point of minus 4 volts is all that can be achieved without the tube going into cutoff. The corresponding plate current swing is plus or minus 0.1mA, which creates a voltage swing across the cathode resistor of plus or minus (0.1mA)(39k) = 3.9 volts. Thus the signal needed at the input is plus or minus 3.9 + 0.3 = 4.2 volts. There is thus more headroom in this stage than in previous stages, despite a DC operating point barely above cutoff.

Using 34 for the gain of the first stage, 60 for the gain of the second stage, and 0.68 for the gain of the second stage output circuit, the signal at the input jack required to overdrive the third stage is

4.2 / 34 / 60 / 0.68 = 3 millivolts

This is very easily achieved. Even with low-gain pickups, when the volume controls are at maximum it takes very little pick pressure to force the third stage well into overdrive. Under typical volume control settings this stage transitions into overdrive long before the previous stages.

## Distortion and Overdrive

Operating this stage close to cutoff and far from saturation affects harmonic distortion and the dynamics of how rapidly the circuit transitions into overdrive. Because negative signal swings are flattened long before positive swings, the output signal shape is unsymmetrical, creating primarily second harmonic distortion. Placing the DC operating point closer to the center of the load line would cause both positive and negative swings to be flattened, creating mostly third harmonic distortion.

A DC operating point close to saturation also would create second harmonic distortion. The dynamics, however, would be quite different. Because of the driving circuit's high output impedance (made even higher by the 470k grid stopper) the flattening on positive signal swings is relatively sharp and well defined. The grid swings to zero volts in its most linear range and then immediately stops, refusing to go positive by any appreciably amount. At cutoff, on the other hand, the tube is operating in its least linear range. Parts of the tube go into cutoff before others, creating compression that reduces gain gradually until ultimately the plate current reaches zero. Soldano's third stage thus has a softer transition into overdrive.

We conclude that as the signal level increases, second harmonic distortion gradually increases, becoming more severe as the stage is overdriven. Input sensitivity is quite low compared to traditional designs, so overdrive is easily achieved. The Soldano SLO, however, doesn't end voltage boost here - there's more gain and overdrive to come, as we will see when we examine the fourth stage.

## 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).

3Technical Correspondence with Paul Reed, Rutgers University.