I went to www.DuncanAmps.com and downloaded a GL211 model so I could play with the inductive load line. Mikey wanted to see what what the load line did with a 16 K impedance with 27 H and 127 H of primary inductance.

This is the model I drew up to make these plots:

L1 is the primary inductance of the output transformer.
R1 is the reflected speaker load resistance (AKA: reflected primary impedance or plate load impedance). 
R2 is a grid stop resistor.
R3 is my guess for the DCR of the primary of the transformer.
C1 is my guess for the capacitance of the primary of the transformer.

I won't be varying R3 and C1 in the plots below as I vary both the primary inductance and the reflected load impedance. If we wanted to, we could design a transformer that makes R3 whatever value we want.

Keep in mind that C1 does not affect the phase shift at low frequencies. C1 is just there to remind us that we need to keep an eye on the high frequencies too while we are adjusting the low frequency performance.

Keep in mind that this is just the small signal (low power) frequency response. It will not tell us how the amp performs with a full power signal input. At the end of this web page, I have an overview of the differences between large and small signal circuit analysis.

Notice that the gain and phase response is changing at 30 Hz more with a 27 H primary inductance than with 127 H.. The change in performance with a 27 H primary inductance does not look that drastic. With 27 H of primary inductance, the low frequency response is 3 dB down at 20 Hz. This normally would not be considered to be "bad."

We are now starting to look at the large signal analysis. This is where the non linearity of the tube and the limitations of the bias point starts to come into play. The load line shows some of the practical/ "real world" issues in the design..

For a reference, I set the primary inductance to 100 k H so we can see the resistive load line. I can do this trick because the circuit model will let us use unreal values (this is both a good and bad feature.)

Now we'll look at the full output power load line with a 127 H primary inductance.
This is full power because with any more grid drive voltage into the GL211, we will be driving the grid positive. This is not too bad of a load line.

Note: When I am saying -50 V grid bias with +/ - 50 V drive, the grid is going from 0V down to -100V, or -50V with +/ - 50V excursions around the -50V bias point.

Next we'll change the primary inductance to be 27 H. The grid drive voltage is staying the same. This load line does not look too good. It spends a lot of time down near zero plate current. Remember when we don't have any plate current, we can't control the output, we can't drive the speaker and we get distortion. This is because the tube is spending all it's hard earned bias current to drive the primary inductance instead of the primary load impedance (the speaker.)

Notice that the 127 H primary inductance with "full input power" to the grid generates lower and fewer harmonics from the tube than with the 27 H.  This is because the magnetization current of the 27 H is driving the tube into cutoff (current clipping.)

Because the 27 H primary inductance tilts the load line into an larger ellipse, the 27 H primary inductance causes the amplifier to go into cut off (run out of drive current/ or "current clip") sooner. Since the amplifier is going into cut off, it will have more nasty harmonics than one not going into cut off.

I did run a sweep with a 100 k H primary inductance. The distortion products were only 3 to 4 dB lower than with the 127 H primary inductance. I did not include the plot because it was too difficult to read..

I'm using a 31.25 Hz sine wave for the test because:

1. It has a period of 32 milliseconds which is a nice number to use in the model.
2. It is near the lowest normal musical frequencies.
3. I did not want to hear complaints about 20 Hz isn't a realistic frequency if I used 20 Hz.

To prevent the 27 H from causing distortion, let's just roll the output tube's grid drive off at low frequencies. I went to the model and made the drive +/ - 25 V instead of +/ - 50V peak. This is what should happen to the distortion if we half the 31.25 Hz drive (output reduced by 6 dB):

Yes the distortion goes down with less output. But the 127 H primary impedance still has less distortion than the 27 H.

GL211 PSPICE Distortion Calculations (Table Format)

As the load line varies, the tube characteristics (gain) will vary. This variation causes intermodulation distortion (IMD). To keep this example reasonable, the grid drive was set to be +/ - 25V at 31.25 Hz and +/ - 25 V at 3125 Hz. This results in a +/ - 50 V waveform at the grid of the 2A3 which is the same as what we had at just 31.25 Hz.

To see the effects of the variation in tube gain I put a buffered filter on the load to strip out the 31.25 Hz.

With 27 H, the 3125 Hz waveform is modulated by the 31.25 Hz signal. The 3125 Hz signal varies from 246.6 V peak to 225.9 V peak or 20.7 V peak to peak modulation.

Even with 127 H primary inductance we can see some distortion. The amplitude varies from 243.1 V peak to 234.9 V peak for 8.15 V peak to peak variation (a 2.54:1 improvement.)

With the 100,000 H plate choke, the amplitude varied from 242.5 V peak to 235.5 V peak for a 7.0 V peak to peak variation. I'm not showing the plot for 100,000 H because it basically looks the same as the 127 H plot.

So far, we have been just talking about the low frequency performance of the tube and transformer with a resistive load. The phase angle of the speaker impedance actually does change at low frequencies. Doesn't this change affect the load line and cause distortion?

To answer this question, lets throw out any problems from a poorly designed crossover networks and consider what happens if we drive just a single driver. This is the impedance plot an 8 ohm wide range driver:

Notice that the impedance never drops below about 110% of the voice coil resistance. Even at DC, the speaker will have at least the voice coil resistance as a limit of how low the impedance will go.

When a speaker does go into low frequency resonance, the impedance goes up towards a lighter load as the phase is shifting from the resonance!

The phase angle of the load from the speaker is changing, but it is changing at a point where the total impedance is higher than normal. Because the impedance is high at the speaker resonance, the phase shift does not mess up the load line. This is because the speaker is not drawing enough out of phase current to drive the tube closer to cut off (current clipping.)

So far, the phase shift of the transformer primary inductance seems to be the sole problem. What if we just change the primary load impedance and keep the primary inductance the same?

Here is the load line with a 27 H primary and a 32 k reflected impedance and a 8 k reflected impedance:

Notice that the tube is still going into cut off (running out of drive current) with different reflected primary impedances (plate load impedances). The 27 H plate inductance is still drawing too much current. When the tube goes into cut-off, (0mA in anode), it can't do anything. It cant make more low frequency energy and it cant' make more high frequency energy either.

At 10 times greater than 31 Hz, the load line will be more resistive just like adding more inductance. However, at high frequencies (20kHz) the load line can again become elliptical because of capacitive loading.

Lets look at the small signal analysis with a 32K plate load and 27 H primary inductance. It still does not look that bad. The voltage gain from the input of the tube to the plate load dropped with an 8 k load. This drop in voltage gain with an 8 k load is expected. Just as the slight increase in voltage gain with a 32 k load is expected.

The low frequency- 3 dB point did not change much with a 27 H primary inductance as the load impedance changes. This is because the small signal -3 dB point is dominated by the plate resistance of the tube.

Well, we varied the load impedance with a 27 H primary. Now lets see what happens to the load lines with a 127 H primary:

With the 127 H primary inductance, both the 8K and 32K load have current to spare before the tube goes into cut off.  With the 27 H primary inductance, the 27 H is sucking up all our bias current with 8 k, 16 k and 32 k primary loads.

With 27 H, the load line is nasty. With a 27 H primary if there is any low frequencies making it from the preamp to the output transformer, I would expect the sound to be a bit nasty too. These low frequencies can be wanted (drum/ organ/ piano etc.) or unwanted (record warp.)

Appendix A:

Keep in mind that we are looking at both large signal and small signal models for the tube amplifier model above.

The small signal model does not know about:

1. Distortion. The small signal model is distortion free.

2. The circuit model does not know about practical aspects of the design.

3. The small signal model is good for dealing with frequency response analysis.

4. The large signal model is good for modeling the real time circuit with all the distortions your model accounts for.

With 27H and 16K reflected load, there is some fattening of the load line even at 440 Hz.

At 1/2 input drive to grid, the load line is still significantly tilted with 27H of primary inductance.