# Introduction

Recently I was asked about whether I could write on my blog about how to design a filament bias stage. My immediate answer was:

1. I don’t have much time these days am afraid to write extensive articles (and sometimes to even write-up at all)
2. Thomas Mayer has written about it (see here). Of course, I completely forgot that Thomas never completed his intended series of posts around filament bias, so I decided to attempt explaining the practical aspects of its design in this blog.

Before you continue reading this post, I suggest you read first Thomas’ article above and get yourself acquainted with DHTs and triode amplification. I’m not going to cover any of that theory which I will give it for granted that the reader is experienced with valve circuits and in particular with the hybrid mu-follower amplification stage with gyrator load.

## 3A5 DHT example

Long time ago I played around with the 3A5 DHT. This lovely sounding valve has a high μ for a DHT and also its filaments aren’t current demanding so it’s a nice candidate for filament bias.

When I tested this valve I found that it performed really well at low level signals and with both triodes connected in parallel. At Ia=10mA / Vak=100V distortion was minimised and sounded really nice. We will start with that point as our target operating point for this example.

This valve has a highish anode resistance around 8.3KΩ and 1.8mA/V transconductance with a gain (μ) of 15 when you look at the specifications. When I traced it, my sample had a lower μ around 12.4-13. When triodes are in parallel the transconductance will double, voltage gain is maintained so anode resistance also is halved. My DUT with both sections in parallel delivered about less than 5KΩ of anode resistance and 2.5mA/V of transconductance at the selected operating point. μ was about 12.45. With a gyrator load, this triode is a nice candidate for a preamp stage given the x12 – x15 (or 22-23.5dB) gain that can be achieved as well as decent anode current which will avoid any slew rate issues when driving the next stage (the main amplifier for example). The μ output of gyrator will deliver low impedance which is great.

When we look at the triode curves of both sections in parallel, we can see that the grid to cathode voltage (Vgk) required for the Ia=10mA at a anode to cathode voltage (VaK) of 100V is somewhere around -2 and -3V curves. In fact the point is -2.3V:

The actual load of the triode with the gyrator is the output load in parallel with the bootstrapped μ resistor from the gyrator which presents a very high impedance. Therefore, the actual reflected load is simply the 100K input impedance of next stage in this example.

In filament bias, we want to elevate the cathode DC level to the bias point we want. For that we have to take into account the following points:

1. Filament current (IF)
2. Cathode current (IK)
3. Target voltage (VGK)

The filament resistor needed (RFIL) is:

$R_{FIL}=\frac{V_{GK}}{I_{F}+I_{K}}$

This is due to the fact that the anode current which is also the cathode current in a triode, adds to the voltage drop across the resistor. In practice, the valve parameters vary greatly (+20%) so we don’t need to be very accurate here. In fact, if we use a gyrator load, the anode voltage and anode current can be adjusted by the gyrator CCS reference voltage.

So in our example we can derive the filament resistor by using the formula above:

$R_{FIL}=\frac{V_{GK}}{I_{F}+I_{K}}$

$R_{FIL}=\frac{2.3V}{(200mA+10mA)}=10.95\Omega$

You can be precise and look for a 11Ω resistor by combining 10Ω and 1Ω ones. I will stick to 10Ω simply because we can use one resistor and the variance will be minimal. One point to consider is the power dissipated in the RFIL. This is the killer in the filament bias circuits. In this case, thanks to the low power filaments and currents in place, the dissipated power (Pd ) is

$P_{d}= (I_{F}+I_{K})^2\cdot R_{FIL}$

We want at least x2 Pd capability on the resistor. I have a 5W wire wound at hand, so will use that one.

Sometimes you will find that there can be an offset voltage in your calculations/simulations due to the way the triode curves have been plotted. The ones from the data sheet are typically for AC heater or DC heaters with cathode referenced to mid-point via a pot. I generally trace my curves with the negative filament to ground. So the difference you may experience in anode voltage may be due to the way the elements are connected and how the original curves were derived:

So If we set the gyrator voltage to about 105V like above, the actual Vgk will be 103V if we subtract the bias voltage which is the reference for the triode.

The above circuit performs really well with a very low distortion for low-level signal (THD<0.1% @1Vrms). I measured less than 0.3% @10vrms, so we should expect really low distortion. The current drive is excellent at 10mA so it can take some heavy loads. The frequency response is excellent and flat above 1Mhz so we should expect some oscillation potentially if we don’t add the proper stopper resistors and or ferrite beads.

Just bear in mind that if you build yourself the 01A Preamp Gen2, you can adapt it very easily to fit the 3A5 with minimum modifications.

Hope you found this example clear enough for your to embark in designing the filament bias yourself. A simple and delightful experience in my view!