Calculating gain, I don't get it, and I MUST be missing something simple...

[jakejoseph]

I built an amp - one of many. It works fine, but I want to tame the gain of the first stage a bit. So I start to compare designs that I have around the house and I compare it with a Ampeg Gemini I with 12ax7's and 7591's

My calculations and circuits are here

http://picasaweb.google.com/jakejose...54045809591730

I am just looking at the 1st Tube in the amp, the one that the guitar is connected to.

The first figure in the Ampeg is a 12AX7A. It has a mu of 100. It uses a plate resistor of 270k ohms, a cathode resistor of 4k7 ohms and is unbypassed. The spec for r sub p is 62500 ohms. There is a 5.6M resistor to ground and a 100k grid stopper. It feeds a 1M pot.


My design (as much as it can be called mine, it rips off from everyone), figure 2,uses a 5691 . It has a mu of 70. It uses a plate resistor of 120k ohms, a cathode resistor of 1k5 ohms and has a 25 microfarad cathode bypass cap. There is a 1M resistor to ground and a 68k grid stopper (not in the same order as the Ampeg). It feeds a 1M pot.

My calculated gain for the ampeg stage is 81. The actual gain as measured feeding a 500 Hz signal at 1 volt through the tube is 25. I disconnected subsequent loading of the tube, and the value went up, but only to 30.

My calculated gain for my stage is 51. The actual gain as measured by feeding a 500Hz signal at 1V through the tube is 38 - close enough to take into account subsequent loading of the tube.

What gives? I switched the JJ 12ax7a in there with a westinghouse 12Ax7a and the gain changed from 25 to around 26 (By the way, the gain was EXACTLY 25.000 when I calculated it for the first tube... really weird). I then swapped in a 12AU7 and the gain dropped to 10 - as is expected.

I MUST be missing something - can someone help me out as to what that something is? I want to reduce the gain in that 5691 stage to around 25 as well, that works out perfect for feeding the James eq stage I have after it. What ampeg mojo am I missing?

The ampeg schematic can be found here (more or less, on mine, the 12AX7 connections appear to be switched between tube halves.)

http://members.aol.com/portaflex/schems/g12.gif

Thanks,

Jake

[chipaudette]

For your 12AX7 configuration (your top figure), your equation for calculating the gain is not correct for your particular circuit. Your circuit has no cathode bypass capacitor, so its gain will be reduced. The correct equation for this configuration is

A = mu * RL / (rp + RL + Rk * (mu + 1))

Where Rk is the cathode resistor.

Also, the value you used for the "RL" in your equation is not correct -- it should be the value of the plate load resistor (270K) in parallel with the value of the resistor-to-ground that follows (1M). Your total "RL", therefore, is 1/(1/270K+1/1000K)=213K.

Finally, the tube parameter values that you get out of a tube manual (mu and rp) are often not correct for modern-built tubes. For example, I hear that it's tough these days to actually get a 12AX7 with a mu of 100. I gather that they often fall far short (I've never checked). Additionally, I *think* that the plate resistance (rp) varies based on the actual operating point of the tube...so your 62.5k value might not be right even if the tube were built perfectly. But, for now, let's assume what you did...mu = 100 and rp = 62.5K. Rk is the cathode resistor...4.7K in your diagram.

A = 100 * (213000) / (62500 + 213000 + 4700*(100+1))
A = 28.4

This is pretty close to your measured value of 25. Allow for some real-world variation in mu and rp and you're on the money.

Chip

[Wakculloch]

There is no mojo. There is an unbypassed cathode resistor.

[jakejoseph]

Crud

You guys are great - thanks. I had the radiotron manual out all morning - I missed that equation. I will have to look to find where it appears.

Now I know how to reduce the gain on that first stage to where I want it.

J

[Bruce / Mission Amps]

There is no mojo. There is an unbypassed cathode resistor.

Seems like I remember reading that "mu" is figured out with the cathode at ground, no biasing resistor.... a "mu amp".
Is that right?

[CitizenCain]

Great information along with all the math you can shake a stick at, at Randall Aiken's site in his Tech pages, http://www.aikenamps.com/CommonCathode.htm