[A2029]

Hi all,
I've created this thread to discuss tube bias when using constant current sink (CCS) cathode coupled OTL amps.

Here is the basic diagram for a CCS OTL:

Note that in the CCS OTL design there are no cathode resistors to set cathode bias. Instead, a specific current is chosen for the CCS, and the CCS itself lets the cathode voltage rise until the tube current (at rest - without music playing) is equal to the chosen CCS current (Iccs).

What happens to the cathode bias at different B+ voltages, but at fixed CCS current?
Let's take the example of a 6AS7 tube at rest with a CCS current of 50 milliamp:
At 140V B+, cathode voltage stabilizes around 40V
At 170V B+, cathode voltage stabilizes around 50V
At 195V B+, cathode voltage stabilizes around 60V
At 225V B+, cathode voltage stabilizes around 70V

How do we know where the cathode bias voltage will stabilize?
This can be found either by running simulations of the circuit in software such as LTspice, or roughly by looking at the tube curves. Here is an example of how to find the cathode bias voltage for a CCS current of 50ma and a B+ of 140V. Note that the plate voltage on the X-axis is actually read as the plate-to-cathode voltage (I.e. 100V on this graph, with a cathode bias of 40V, is 140V B+ and 100V plate-to-cathode voltage).

A well designed constant current sink in this application will provide a massive AC impedance (on the order of 0.5-2 million ohms) while having very low DC impedance. Similar to a constant current source, the constant current sink results in a completely flat loadline no matter where the bias point stabilizes:

When there is a music signal on the grid, the cathode voltage swings in lock step. The B+ does not swing in voltage, but instead in current - this is changes in current flowing through the tube due to the grid signal. The amount of current swing depends on the headphone load coupled to the cathode via the cathode output capacitor:

The swing in tube current does not come from the constant current sink (as remember, the current through the CCS stays constant), but is instead sourced from the output capacitor/headphone load. Lower impedance headphone loads will require more current for the same voltage swing (as can be calculated from Ohm's law - V=IR). Note that for very high impedance loads, max power output is related to maximum swing in the cathode voltage, as long as Iccs provides sufficient current (bounded by V=IR).

 

[A2029]

Bit more reading on constant current sinks: http://valvewizard.co.uk/ccs.html

 

[Xcalibur255]

So if I understand correctly, the bias current is a fixed value and the CCS keeps the tube on the load line so distortion stays low as the voltage is raised or lowered? That almost makes the plate current value seem arbitrary in this case. Chosen primarily for a desired output power level and dissipation and not for the intention of maximizing sound quality.

Or am I completely off track? The biggest problem I've had with learning about tube circuit design is that there are oversimplified "for beginner" explanations and then there are detailed and technical ones that really only a builder would understand...... and nothing in between. So a person trying to learn about this stuff wanting to make that leap from one to the other has to leap very very far because there is no middle ground learning area to land on in the mean time.

I appreciate your taking the time to write this though, it's a good read even if I'm struggling to understand it all.

 

[A2029]

You are correct, the bias current is fixed by the CCS so the load line is always a horizontal line no mater what voltage is applied to the tube anode. As the linearity of the tube is always maximized at all voltages, the sound quality and distortion should not change much, if at all, based on chosen anode voltage.

The primary factor involved in choosing the current setting for the CCS and the plate voltage at the anode is the headphone impedance. High impedance loads (e.g 200-1000 ohms) are typically known as "voltage hungry" as they require larger voltage swings for high power than low impedance loads (e.g 2-100 ohms). Low impedance loads are more "current hungry" as indicated by V=IR, where for a set voltage, I increases as R decreases.

CCS current setting is best illustrated with some examples. Let's first take the example of a pair of headphones with a high 600ohm impedance. To maximize output power, we'd want to have a large potential cathode swing. If we choose to bias the cathode at 50V, that means that maximum capacitor coupled voltage swing would be approx 46V positive & negative (92V peak-to-peak) (Note: can't reach the full 50V pos/neg as the CCS itself needs some minimum voltage across it to function). Using V=IR, we can see that 46V = I x 600ohm. I = 0.077amps. To have a 50V bias at 77ma, the tube curves suggest a needed plate-to-cathode voltage of 130V, and therefore a plate voltage of approx 180V. Dissipation would be 130V x 77ma = 10.01w, which is 77% of the max dissipation of 13W. This gives an RMS power output of ~1.76 watts into 600 ohms. But what if we connected a 300ohm headphone load instead of the 600ohm and kept the same bias point? If the CCS is still set at 0.077amps, then the max voltage swing will be V = 0.077amp x 300ohm = 23.1V. This gives 0.89 watts into 300ohms. These are also poor settings for lower impedance loads, as this gives only 0.47W into 160ohm, 0.123W into 50ohm.

Now let's say we wanted to optimize power output for low impedance loads. We would want to maximize current in this case. The max current per section for a 6AS7 is 125ma, so let's use this value. Let's also use a nice and toasty 90% dissipation on the plate, or 11.7W dissipation. For a 11.7W dissipation at 125ma, we get V = 11.7W/125ma = 93.6V plate-to-cathode. Looking at the tube curves, we find that a bias voltage of ~24V at 93.6V plate-to-cathode would mean that anode voltage would need to be set to around 118V (94V + 24V). Using 20V pos/neg swing of the cathode voltage, we can find using V = IR that maximum power for this plate voltage and CCS settings would occur with a headphone load of R = 20V/125ma = 160ohm. Power into 160 ohm would be ~1.25W. Power into 50ohm is 0.391W. Power into 300 ohm is 0.66W. Power into 600ohm is 0.48W.

So where is the ideal CCS bias point? As 6AS7 OTL amps have very high output impedance (in the range of 80-100+ ohms if using only 1 section of the 6AS7 per headphone channel), they should really only be used with headphones of 200ohms impedance or above. Common pairing headphones are the Sennheiser HD600/HD650/HD800 that have an impedance of 300ohms. So if we wanted to maximize output power for these Sennheiser headphones, and maintain a tube dissipation of say 80% (10.4 watts), then we find that a bias of 100ma and 104V plate-to-cathode would result in a cathode bias voltage of approximately 34V, and give ~1.5W output power.

 

[Xcalibur255]

This is super interesting and I really appreciate you taking the time to write these up. I always assumed for an OTL design that it would natural to improve the low impedance performance as much as possible because good high impedance performance would just be a given, but it's probably entirely possible to design an OTL amp that struggles to drive a 600 ohm headphone isn't it?

 

[A2029]

Happy to share my knowledge

It is possible to design an OTL amp that would struggle to drive really inefficient 600 ohm loads. If the amp was designed to provide maximum current to low impedance loads, the low cathode bias voltage of that amp would mean less voltage swing for high impedance loads. For high impedance loads, less voltage swing most often means less power/drive.

 

[rosgr63]

Very interesting design, thanks for sharing.

Next would the implementation which hopefully will be soon.

 

[jmpsmash]

Thanks for sharing. How does one calculate the output impedance in this case? I assume the formula of 1/transconductance don't apply anymore?

 

[A2029]

Thanks for sharing. How does one calculate the output impedance in this case? I assume the formula of 1/transconductance don't apply anymore?

Output impedance can still be approximated as 1/transconductance. Output impedance is still high for CCS OTL amps just like cathode coupled OTL amps. Both should only really be used with high impedance headphones (unless enough tubes are paralleled to bring down output impedance - e.g. the Atmasphere M-60 which uses 8 6AS7 per channel for speakers).