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'Frizzles dumb question #1'
Author:Andrew Guy (guest: search)
Date: Mon, Mar 10th, 2008 @ 19:59 ( . )

Alright. Working from a design perspective, what you would start with is a tube datasheet with characteristic curves. What you're looking for is a I(anode)-V(anode) graph, with various lines drawn representing different grid voltages. What this graph tells us is the current through the anode (or anode resistor) when the anode is at a specific voltage, and the grid is at a specific voltage (or vice-versa). For example (if you pull up a datasheet), lets assume that the grid is 1.5V below the cathode (a fairly standard, middle of the range value). If the voltage at the anode was 200V, then we would calculate that there was a current of 1.2mA through the anode. (find the 1.5V curve, and see where it intersects with the 200V value) Note that these values might vary slightly in real life, but it's good enough for now.

Now if you were designing a gain stage, you would first decide what grid voltage (with respect to the cathode) you want with no signal going into the stage. This determines i) how much headroom a stage will have, and ii) how a stage will clip (ie which side of the waveform clips first). As I hinted at before, -1.5V ensures that both sides of the waveform will clip at roughly the same time, and will ensure maximum headroom. So now we're using the -1.5V curve in our designing.

At this point it's a good idea to print out a copy of the datasheet, so you can draw on it. We're going to be drawing what's called a loadline - often confusing, but actually really simple for a single stage with nothing fancy about it. We have three points of interest. i) The intersection with the x-axis (voltage). ii) The intersection with the y-axis (current). iii) The intersection with the -1.5V curve.

At this point, lets assume we have a B+ of 300V.

To find i), the anode voltage with no anode current, we simply use the B+. Note that with no current through the anode resistor, there is no voltage drop across it. So the anode is sitting at B+. That would be 300V.

To find ii), we have to know the value of the anode resistor. This is chosen depending on what you want from the stage. 100k is standard for a 12AX7, but higher values (like 220k) can be used to produce more gain. Lets use 100k. Remember, we're looking for the y-intercept, or the point at which anode current is a maximum, and anode voltage is zero. Using ohms law (V=IR), we want to drop 300V across the anode resistor. This will give us maximum current. 300=I*100,000 --> I=3mA. This is our second point for our 'load-line'.

At stage, we can draw a straight line joining points i) and ii). It should be sloping downwards, and go from 3mA on the y-axis, to 300V on the x-axis.

Now we look for the most important point, point iii), the intersection with the -1.5V curve. Right now it should be jumping out at you, if you've drawn your load line correctly. Draw a cross at this point, and trace down to find the anode voltage at this point, and across to find the anode current at this point. From a rough glance, it looks like the anode will be at 195V, with a current of 1.1mA. That's good so far, but it hasn't actually helped us yet - we still have to figure out the value of the cathode resistor, which is why we did this exercise in the first place. Here's how to go about it.

Because the grid draws very little current biased at -1.5V, we can say that the current through the cathode is the same as the current through the anode. Remembering that we chose a bias point of -1.5V, and knowing that we have a current of 1.1mA through the cathode resistor, we can now calculate the value of the cathode resistor. Remember that V=IR. We get 1.5=0.001*R ----> R=1500 or 1.5K. We know our cathode resistor!

Now, there are several ways we can vary this. If you want to raise or lower the B+, but maintain the same operating point, use a load line to calculate the new value for your cathode resistor. If you want to change the way a stage clips, choose a new bias voltage, and plot your load-line around that. Moving towards 0V will move the stage closer to saturation (warm bias), moving it the other way will move the stage closer towards cutoff (cold bias). If you want to use a different value anode resistor, again, draw a load line to make sure you retain the 'correct' operating point.

That might sound a little complicated, but work your way through it slowly. There's also a good explanation of load line in the P1 documentation. Randall Aiken also has some good stuff.

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Replies:
--* Frizzles dumb question #1
3/11/2008 @ 03:35--michaeleinem
3/11/2008 @ 09:56--JoshFrizzle
3/11/2008 @ 18:16----Andrew G
3/19/2008 @ 10:38------JoshFrizzle

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