PG2DTA: Determining the operating point and cathode bias resistor

In an earlier post I discussed how to choose a tube and an appropriate output transformer. The primary value of the transformer is known as the load and is often referred to as RL. The load can be drawn as a straight line on the grid curve graph and is called the loadline. The slope of the loadline can be determined using Ohm's Law again:

I = V / R

Using 5K ohms, the RL we determined for the 6V6 tube, and 100 volts an arbitrary value for V that makes the math easy, I can be calculated with the following equations:

I = 100 / 5000
I = 0.02
I = 20mA

Which means that the slope of the line rises 20mA every 100 volts. Each of the lines on the following graph has a slope of 5K.


The loadline is useful for determining a number of things when designing an amplifier. So, how do you know where to draw the load line? There are many approaches, but the following seems to work. Start by plotting the maximum plate dissipation on the grid curves as was done in my earlier post, Choosing a Power Tube and Transformer. Then draw a loadline that is tangent to the maximum plate dissipation curve. Why tangent? Well, if you go over the maximum plate dissipation curve, then you risk damage to the tube, premature failure or at least distortion. If you go under the curve, then you are wasting power.


If you look closely, you will see that the point at which the loadline is tangent to the curve is around 250V and 48mA. Of course, the easier way to get these values would be to look at the tube data sheet. According to the 6V6 datas heet, the Plate Voltage and Plate Current should be 250V and 49.5 mA - very close to what we came up with above.

These values are known as the quiescence or operating point, sometimes referred to as Iq and Vq. Once you know your operating point, you can calculate the cathode resistor. This is done by looking at the operating point and determining the grid voltage. The operating point does not intersect one of the grid lines already on the graph so you have to guess. In this case the point falls in the center of the -10V and -15V grid lines so -12.5V is a reasonable value.

Once you have the grid voltage, you determine the cathode resistor value using Ohm's law again:

R = V / I
R = 12.5 / 49.5
R = 252.525... Ohms

Once you have calculated the value, then look for a standard resistor value that is close to the calculated value. In this case, 255 Ohms.

The next question is what power rating should the resistor have. This is determined by calculating the power dissipated by the resistor and then doubling the value (at least) for safety. The power dissipation can be calculated using several different but related formulas:

P = I * I * R
P = .0495 * .0495 * 255
P = 0.625 watts

or

P = I * V
P = .0495 * 12.5
P = 0.619 watts

The values are different because the first formula uses the standard resistor value instead of the value originally calculated. Regardless, the values are close enough so that if you double the results you will end up with around 1.2 watts. There aren't a lot of 1.2 watt resistors out there, so round up to the next highest rating - 2 watts should be fine while 3 watts will be extra reliable.

PG2DTA: Choosing a Transformer for the 300B

In my last post of the Practical Guide to Designing Tube Amplifiers I described how to choose an output transformer for a triode-connected 6V6. If you recall, a reasonable load for a triode is twice the Plate Resistance:

RL = 2 * ra

In summary, you calculate ra using the following steps:

• Locate the tube data sheet
• Determine the maximum plate dissipation (Pa-max)
  
• Determine the maximum plate voltage (Va-max)
• Plot Pa-max and Va-max on the Average Plate Characteristics graph
• Draw a line tangent to the grid curve closest to where Pa-max and Va-max intersect
  
• The slope of the tangent is equal to ra

This time I will go over the steps again for a 300B, but with a little less detail.

I located a copy of the 300B data sheet (135K PDF) at the Western Electric website. I figure they are probably a pretty reliable source. The Pa-max and Va-max are reported in the Maximum Ratings section.

The following is the grid curves graph with the Pa-max, Va-max and ra lines plotted.

Examining the tangent line you can see that it rises around 180mA over 125V. We determine the plate resistance using the following formula:

ra = V / mA
ra = 125 / 0.180
ra = 694.444

By doubling the value of ra we have determined that a transformer with a primary of around 1400 Ohms would be appropriate. Suggested values I have seen range from 1250 to 5000 Ohms so again I think the calculations are correct.

PG2DTA: Choosing a Power Tube and Transformer

In my first post of the Practical Guide to Designing Tube Amplifiers (PG2DTA) I defined 10 steps for designing an amplifier. This post will go over Steps 1 and 2:

1. Choose a power tube
   
2. Determine the output transformer to use
   

While I'm sure there are a number of technical reasons that determine why an output tube is suitable for a particular application, I'm not going to attempt to describe them. These days, people aren't building tube amplifiers for technical reasons, they are building them because they like tube amplifiers. The tubes that are suitable for audio output are pretty well known so I'm not going to deviate from the list (tube depot, boi audio works, the tube store).

For the purposes of the guide I am going to use a triode-connected 6V6. Why? Because I like 6V6 tubes in guitar amps and the 6V6 is reasonable inexpensive. In addition, there is a local amplifier competition that I am entering so this is a good exercise.

The simplest way of determining which transformer to use is to look up what other people are using (Hammond, VT4C). However, you will notice that there is not a single value to use for a particular tube. Recommended values for the 6V6 range from 3,500 Ohms to 8,000 Ohms. This value is known as the load and will be used to draw the loadline in step 3 of the PG2DTA. For now, let's try to figure out where these numbers came from.

Generally speaking, a reasonable load for a triode is twice the Anode Resistance or Plate Resistance:

RL = 2 * ra

So, all we need to do is look up the Plate Resistance for the tube and we are done, right? Wrong! Unfortunately the Plate Resistance value changes depending upon the operating point of the tube. This is where things start to get more technical in the books and I get lost, but its really quite simple.

First thing to do is find the data sheet for the tube you want to use. A great source for finding tube data sheets is Duncan Amp's Tube Data Sheet Locator.

Find the maximum plate voltage (Va-max) and the maximum plate dissipation (Pa-max) on the tube datasheet. Unfortunately, there doesn't seem to be a consistent naming convention for these values. Some use the term Anode, some use Plate so you will have to become familiar with all of the terms. I am using General Electric's 6V6 data sheet for this example.

Find the graph that plots the plate current against the plate voltage labeled average plate characteristics. For the 6V6 tube, find those that are for triode connection. Draw a vertical line representing the maximum plate voltage (Va-max). For the 6V6 this will be 315 Volts.

Determine points on the graph representing the maximum plate dissipation (Pa-max). This requires some math, but its simple math. Using Ohm's law P = I * V we can calculate the current required for 9 watts at a number of different voltages with a quick rewrite of the formula. In other words, I = P / V where P = 9 and V = voltages we choose. For example:

9 / 60 = 0.150 or 150mA
9 / 100 = 0.090 or 90mA
9 / 120 = 0.075 or 75mA
9 / 200 = 0.045 or 45mA
9 / 250 = 0.036 or 36mA
9 / 300 = 0.030 or 30mA
9 / 320 = 0.028 or 28mA
9 / 340 = 0.026 or 26mA

You will end up with a graph that looks something like this:


To determine the Plate Resistance, find a grid curve that is closest to the intersection of Va-max and Pa-max and draw a line tangent to the curve. A tangent is the straight line that just touches a curve at a specific point on the curve. Without having the formula that determines the curve, I think the only way to determine the tangent is to do your best drawing it. Here is what I came up with:

Now that we have the Plate Resistance line plotted, calculate the slope of this line by using another of Ohm's laws V = I * R. Because the graphs are not exactly high-resolution, the easiest thing to do is look where the line intersects the grid. In this case, I=0, V=240 and I = 30 and V = 320. Thefore:

I = 30 (30 = 30 - 0)
V = 80 (320 - 240)
R = V / I
R = 80 / 0.030
R = 2,666

As I said above, optimal load for a triode is twice the Plate Resistance:

RL = 2 * ra
5,332 = 2 * 2,666

So, a tranformer with a primary of around 5K is appropriate for a triode-connected 6V6. This is consistent with many designs so I think that we calculated the plate resistance correctly.

A Practical Guide to Designing Tube Amplifiers (PG2DTA)

I've been reading the Radiotron Designers Handbook Version 4 (25MB PDF), the Morgan Jones Valve Amplifiers book, Steve Bench's web pages, and a number of other old books, but there is one thing I cannot seem to find described well - the single-ended amplifier. Maybe its just so simple that nobody goes over it in detail. Maybe its because the authors wanted more power so they focused on pentodes, push pull amps and feedback. Maybe I just missed the forest through the trees because I don't understand all the math and terminology. Whatever the reason, those books don't work for me. While the Boozhound Laboratories site is a great starting point, there are a number of places where I want to know the general idea of why a value was chosen so that I can design my own amplifier.

So here is my Practical Guide to Designing Tube Amplifiers (PG2DTA). I'm going to start with the following circuit - which is about a simple as you can get. There are two stages; a driver stage and a power stage. Personally, I like to refer to the power stage as the output stage, but for the purposes of this guide I will call it the power stage because many of the texts refer to power amplifiers and most websites refer to power tubes.


As you can see, the circuit does not include the values for the different tubes, resistors, capacitors, and voltages. In addition, the power supply is not represented in the diagram except for the magic B+ symbol. I call it magic because it seems to me that B+ is frequently referenced without any details of how to get it.

I have broken down the approach to determine which values to use into the following 10 steps:

1. Choose a power tube
   
2. Determine the output transformer to use
   
3. Determine the operating point
   
4. Calculate the cathode resistor, grid resistor, etc.
   
5. Choose an appropriate driver tube
   
6. Determine the load
7. Determine the operating point
8. Calculate the cathode resistor, grid resistor, coupling capacitor, etc.
9. Choosing a power transformer
10. Modeling your power supply with PSUD

Later I will expand the guide into different areas. For example, going from a single-ended output stage to parallel output tubes or different drivers stages (mu follower, srpp, etc).

Bottlenecks 6V6 Amp

At the last Bottleneck meeting (Mid-Atlantic, Md, Va, DC Bottlehead enthusiasts) we started discussing having everyone build an amp based on the same tube on a limited budget. I commented that I like 6V6 tubes for guitar amps but don't see many audio amps using them. With that, everyone agreed that we should use the 6V6 tube. Then we decided the budget should be $150. The complete rules can be found at RayP's 829B Amplfier site.

So begins my journey of learning how to build an amp from scratch. So far, I have only built kits where someone has provided the components and step-by-step instructions. Now, I want to build an amp of my own design. I've been reading a number of sites including Boozhound Labratories and DIY Paradise. The great thing about these sites is that they present the information in a very simple manner. I have tried reading the Morgan Jones book, and have read the grounded cathode amplifier article on the Tube Cad website, but I was never able to understand what to do. I still don't really, but I feel like I'm a little closer after reading these sites repeatedly.

Jordan JX92S Aurum Cantus G2si Part 2

I put the mini-monitors together and I must say they sound great. I brought them to a local audio meet and everybody had very nice things to say about them. Their only downside is they are not very efficient. They sounded pretty bad on a triode-strapped single ended KT88. Just not enough power for them. Once they were hooked up to a KT88 running ultra-linear, they sounded much better. I look forward to hearing them with my DIYTUBE ST35 EV once its complete.

Now for a confession... I find it hard to pass up a good deal. I came across the group buy for Jordans on the diyAudio forum and Parts Express had the G2si tweeters on sale again, so I just had to buy them.

This time around, I want to build the transmission line version of Jim Griffin's design and upgrade the crossover components. The components are the same for the mini-monitors and the tl's so it will be interesting to compare how the crossover components effect the sound compared to the enclosure.

I bought the upgraded parts from SonicCraft. Here's the BOM - they are an upgrade but not an extreme upgrade. I really wish I could afford Mundorf Silver in Oil caps, but they are just too much right now.

• 2 - AlphaCore 1.5mH 12awg ($100.16)
• 2 - AlphaCore 0.3mH 16awg ($24.38)
• 2 - Sonicap 6.8uF 200VDC ($28.40)
• 2 - Sonicap 5.1uF 200VDC ($23.20)
• 2 - Sonicap 15uF 200VDC ($44.60)
• 2 - Mills 8R 12W ($7.00)
• 2 - Mills 3R 12W ($7.00)
• 4 - Mills 2.5R 5W ($8.60)
• 4 - Dayton BPA-38SN HD Binding Post Pair Satin Nickel ($23.60)
• 2 - Aurum Cantus G2si Tweeters ($138.66)
• 2 - Jordan JX92S Group Buy ($253.00)
  

So the total excluding shipping and stuffing is $788.60. That comes in less than my original mini-monitors. That is why I cannot resists a good deal.

I don't really need the larger gauge inductor for L2, but the cost of buying a 20awg inductor from another source made the price the same. Because the 16awg inductor has lower DCR (0.129) compared to the specified 20awg (0.36), I had to change the value of R3 in the crossover.

Original resistance of shunt on tweeter: 0.36DCR + 1R = 1.36R
Upgraded resistance of shunt on tweeter: 0.129DCR + 1.25R = 1.379

In addition to the parts I ordered, it was recommended to me that I bypass C2 and C3 with a Sonicap Platinum 0.1uF capacitor. These guys are $29 each totaling $116. I decided to pass on these for now and use the Russian Telflon caps that Grainger Morrison (there is only one) gave me.

Finally, I'm considering making the enclosures using a very different construction technique this time. I want to make them using layers of Baltic Birch Plywood so that the front, top and rear would be striped and the sides would be the birch veneer. I could make the enclosures from 2 sheets of 5x5 BB so the cost really isn't that much more than if I used traditional construction techniques.

More on this later.

Jordan JX92S/Aurum Cantus G2si Mini-monitors

I'm still working on the diytube st35 but am waiting for a custom top-plate from Front Panel Express. Once I get all the parts I will post more details about the build.

In the mean time, I have finally assembled all the parts to build Jim Griffin's Jordan JX92S/Aurum Cantus G2si mini monitors. In short, Jim's design won the 2001 Atlanta DIY competition using only the Jordan driver. In 2004, Jim won again! This time, he augmented his design with the Aurum Cantus ribbon tweeter.

While the design pak for this speaker includes the dimensions required for building the speaker cabinet, I discovered that the Parts Express .25 ft³ cabinets were roughly the same dimensions. Most importantly, the front baffle is exactly the same size as specified in the design.

Almost all the parts to build these monitors are available from a single source - Parts Express. However, if you are in the USA you must buy the Jordan drivers from Mark Audio.

• 1 - Dayton TW-0.25CH .25 ft³ 2-Way Cabinet Pair ($111.88)
• 2 - Dayton BPA-38G HD Binding Post Pair Gold ($13.82)
  
• 2 - Jantzen 1.5mH 15 AWG Air Core Inductor ($35.04)
• 2 - Jantzen 0.30mH 20 AWG Air Core Inductor ($6.48)
• 2 - Solen 6.8uF 400V Polypropylene Capacitor ($8.74)
• 2 - Solen 5.1uF 400V Polypropylene Capacitor ($7.62)
• 2 - Solen 15uF 400V Polypropylene Capacitor ($15.02)
• 2 - Dayton DNR-8.0 8 Ohm 10W Non-Inductive Resistor ($2.50)
• 2 - Dayton DNR-1.0 1 Ohm 10W Non-Inductive Resistor ($2.50)
• 2 - Dayton DNR-3.0 3 Ohm 10W Non-Inductive Resistor ($2.50)
• 2 - Aurum Cantus G2Si Ribbon Tweeter ($184.90)
• 1 - Pair Jordan JX92S Drivers ($400 shipped to the USA)
  

So, for a total of $791.00 (+$21 shipping) you can build a pair of these monitors too. I did not include stuffing or materials for assembling the crossover so count on a little bit extra cost. Also, I went with Solen capacitors. Using higher quality exotic capacitors will increase the cost (significantly depending upon what you choose). However, I have not been able to find exotic capcitors in the values specified above.

Power Supply Transformer

The power supply I have for the ST-35 project was custom made by Electra-print. According to Jack, "This will power a tokomak."

Here are the specs that came with it:

• Secondary is 310-0-310VAC at 200 ma DC
• 6.3V at 3.0 amp windings for filaments
• Primary is 120VAC 50/60 Hz.
• Measures 5 5/8 inches high X 3 3/4 inches wide by 4 1/8 inches deep over end bells.
  
• Mounting hole bolt pattern us 2 15/16 inches by 3 5/8 inches
• 9 lbs

This thing is a monster!!! Now I need to figure out what to do with it.

DIYTube ST-35

Its been a while since I've posted. I'm about to start building a DIYTube ST-35 amplifier. At least, that is what I started out to build. When I first started investigating this project I wanted to use Magnequest's version of the Z-565 output transformers. Unfortunately, Mike quit making them when I contacted him. Fortunately, I came across a listing on Audiogon for a set of MQ transformers with M3 laminations and brass bells, as well as an Electra-print power transformer custom designed to support a tube rectifier.

After a few exchanges with the seller, I discovered Vaughn Audio and its associated forum. While I have only started one thread, the folks there appear to be very knowlegable and eager to share the novice.

I've decided to learn a little more than how to solder and follow directions this time around. I'm going to start off with the power supply. We'll see how things go.