Plate resistors on preamps

[hasserl]

I worried my reply might annoy people because the question had been approximately answered in the first reply by jrfrond, sorry about that. Unfortunately some of the explanations were inaccurate and both of the quotes you selected there are good examples like: "The tube amplifies current, not voltage". A tube has an extremely high input impedance so you're not putting a current into it for amplification like a BJT. Only the voltage on the control grid matters, but this doesn't control another voltage it controls a current. I thought maybe this point was being overlooked, a relationship where a voltage controls a separate current is called transconductance and this is all a tube does. It doesn't amplify a current or a voltage. It can be used as part of a circuit to do those things, but that's determined by the circuit not the tube.

And the second quote about no gain without a plate load, well I've been through that argument here years ago and don't want to start it again. People who work mostly with these high input impedance devices in voltage amplification circuits tend to think the word "gain" can only mean voltage gain. I'm nobody to tell you it aint so, build in peace.

This is just discussion where we all hopefully learn a little. You aren't insulting anyone. It would be hypocritical of me to get annoyed at someone correcting my being inaccurate when that is what I was attempting to do with my posts. So, please, post away.

I suppose my sentence about the tube amplifying current was inaccurate. It does read as if you insert a smaller current in and get an increased current out. That is not what I meant, but poor writing skills and fast posting, (it is a message board after all. I usually stop by for small breaks from the tedium of work; get in and out quickly) don't always make for well constructed posts.

But your second example does bother me, if you're going to criticize it, criticize it. But to point it out as being inaccurate, then drop it without explaining, that is a bit annoying.

Whatever, like you said, build in peace.

[carlg]

But your second example does bother me, if you're going to criticize it, criticize it. But to point it out as being inaccurate, then drop it without explaining, that is a bit annoying.

Sorry, it's just that "gain" by itself is a wide open term. It could mean voltage, current, or power gain. Saying a cathode follower doesn't have gain would be untrue because it can take a weak signal and produce a more powerful version of it. It doesn't have voltage gain, that's true, but it has gain. It's just a stupid nit pick, I don't expect everyone to start typing "voltage gain' everywhere when that's almost always what they mean anyhow.

I was never very good at posting things here without annoying people, I don't know why. I haven't come around regularly in years but I still pop in and scan the front page every now and then when I'm bored.

[kg]

Well, triode tubes aren't quite transconductance devices, either. The electric field of the plate causes a kind of negative feedback: the plate voltage affects the space charge the same way that the control grid voltage does.

i have to step in here and point out that a triode absolutely IS a transconductance device. no ifs ands or buts about it! a V controls an I. the reduction in effective gain and rp that occurs in a triode IS a form of NFB (for a detailed analysis see here) but that does not change the Vin = Iout fundamental relationship: the electric field "seen" at the cathode (specifically the space charge around the cathode) determines the magnitude of the electron flow from it.

So a triode looks like a current source (the transconductance part) shunted by an internal resistance which we call the plate resistance, rp. For gain calculations, you have to consider rp as being in parallel with whatever plate load resistor you use. This puts a fundamental limit on the gain of a triode, no matter how large a plate load resistor you use. This is why mu is a popular figure of merit for triodes: it's gm * rp.

did you mean to type gm steve? mu makes a lousy figure of merit! who thinks that the 12ax7 is a meritorious tube? not me! it has miserably high rp. high rp "buys" you nothing.

the classic figure of merit is gm... transconductance, baby. why? because high mu and low rp are ALWAYS good things. having either of them will "buy" you something.

http://www.guitarstudio.tv/Splawn/ex..._must_read.htm

^^ i think looking carefully at that page you'll see that having a high gm is the gold standard for how "useful" a tube can be in various circuits. he doesn't state it directly but it's between the lines.

With pentodes, the plate is isolated from the control grid by the screen grid. So rp is almost infinite, hence pentodes have higher gain.

true. you'll rarely see a quoted mug1 for a multigrid tube for that reason.

still, the multigrid tube with higher gm is generally speaking a "better" tube... it will have a lower rp that will improve frequency response into the load and/or it will have a higher voltage gain that can be used in an NFB loop with similar effect.

[Steve Conner]

No, I meant what I said Mu is what determines the maximum voltage gain you can get from an amplifying circuit based on the tube.

If it has a high gm, but a low rp, the rp will eat the current and the gain will be low.

If it has a low gm and a high rp, the gain will be low just because gm was low.

High gm and high rp is good because it allows you to achieve more gain in a single stage.

I guess what you're saying is that voltage gain isn't actually a figure of merit?

[kg]

No, I meant what I said Mu is what determines the maximum voltage gain you can get from an amplifying circuit based on the tube.

sure!

If it has a high gm, but a low rp, the rp will eat the current and the gain will be low.

first we have to define a context. since you were talking about the deleterious effects of the relatively low plate impedance found in triodes, i'll restrict my focus to those.

what effect does "low gain" have? i don't know about your amps but in mine i am constantly throwing away signal with voltage dividers. there's an abundance of gain.

the thing is, this low rp tube can come in very handy. maybe i use it to drive an effects loop directly, without using a cathode follower as a low z buffer. or maybe i use it to drive a tone stack. that frees up a previously used gain stage that i can cascade to MORE than make up for the lower mu.

maybe i use it to drive a transformer. the lower rp allows me to use a lower turns ratio which means i lose less signal amplitude as it passes through the tranny. if i design the tranny to net the same Vout, i haven't given up any "gain" but my tranny design has less deleterious characteristics like DCR and stray capacitance.

having a low z circuit path has a lot of advantages, the two biggest being frequency response and noise immunity.

plus, if you really wanted to, you could take your high gm/low rp/low mu tube and (carefully) wrap positive feedback around it, essentially emulating a pentode stage with a triode stage. you'd effectively get a rise in rp and a corresponding rise in mu (obviously the physical tube characteristics themselves can't change, but the way that it behaves due to the PFB circuit will change the way it reacts to signals). if you do this with a tube with low rp you have a lot more latitude to increase it before it becomes ridiculous.

If it has a low gm and a high rp, the gain will be low just because gm was low.

well, this is basically what i define as a useless triode, because it does nothing well.

High gm and high rp is good because it allows you to achieve more gain in a single stage.

your op amp rudiments are coming through again steve! like i said above, "more gain in a single stage" is rarely a big issue or deal breaker for me. unlike a SS design that loops feedback all over the place, what does a surplus of gain get you in a (mostly if not completely) open loop guitar amp? we end up throwing MOST of it away, purposely!

I guess what you're saying is that voltage gain isn't actually a figure of merit?

i don't think it is. certainly not nearly the way it has been defined as with op amps. i can honestly say that i have never and probably will never choose a particular tube over another because it has a higher mu.

every once in a while i might swap in a 12AT or even an AU into an amp designed for AXs to tame it down a bit, but that's only because it's easier than opening up the amp to change a bunch of components around just to dump off surplus gain.

ken

[BackwardsBoB]

Confused yet?

Bluefoxicy - There's nothing really factually misleading about any of the answers you've received. What you're reading isn't really semantics. They are attempts at a more pointed understanding of what's going on that will serve you well moving forward.

For a given set of grid bias voltage and plate voltage, a change in grid bias will result in a change in the negative current flow of electrons from the cathode to the plate, which looks like positive current flow into the plate. That is, a voltage change on the grid causes a current change at the plate, even and especially if the plate voltage is held constant. This voltage in vs. current out model makes a tube a transconductance device. V=IR, so I=V/R, and 1/R is the transconductance, measured in 1/Ohms, called mhos or Siemens. The usual name is gm, where m is a subscript. A 12AX7 datasheet will give a value for a specific set of operating conditions of gm = 1600 umhos.

Now when we add an anode (plate) resistor, and we really should, which we can think of as a load for the current, we find that the voltage at the anode now varies with the grid voltage. Suddenly, for very small voltage changes at the grid, the tube looks like a voltage device, and the anode voltage varies proportionately. For a specific set of operating conditions, which includes a very high value anode resistor tied to a ridiculously high anode voltage, we can define a voltage amplification factor, mu, such that the change in anode voltage equals mu times the change in grid voltage. Mu is frequently represented by the Greek letter Mu, which looks kind of like a lower-case cursive U with a long tail in front.

If fact, the grid is controlling a current, so transconductance is closer to reality. Also, in fact, in a preamp, anode voltage will change with grid voltage, and the anode resistor won't be extremely high value. Without these limitations, we can't really model the tube as an ideal current or voltage source, even for small signals.

We must introduce a third tube characteristic, the plate resistance, Rp (properly written as a small r with a p subscript). This isn't the result of some high resistance connection from the tube pin to the plate. It's a bit more nebulous than that. What it lets us do is make a small-signal AC model of the tube as either an ideal current source with output gm x Gs (Gs is the AC grid signal voltage sitting on top of the grid bias voltage) in parallel with the plate resistance (Rp), or an ideal voltage source with gain equal to mu x Gs in series with the plate resistance. For a given set of operating conditions, for a small change in grid voltage, mu equals gm times Rp, and mu is widely touted in specs as being 100 for a 12ax7 under certain conditions.

Only it isn't even that easy, because, like transconductance (gm) and voltage amplification factor (mu), Rp varies with operating conditions. Check out the extremely interesting last page of the 1955 Sylvania 12AX7 datasheet, which shows the variance of gm, mu, and Rp with grid voltage for various plate voltages:

http://www.drtube.com/datasheets/12ax7-sylvania1955.pdf

Our analysis is only accurate as long as the input signal is disappearingly small, so that gm, mu, cathode voltage and Rp are fairly constant. This seems like a curse, and if you are trying to figure out the actual large-signal gain of a circuit without measuring it, or provide low-distortion amplification, it is. We're trying to make an amp that sounds good, and the resulting non-linearities can generate mucho second harmonic distortion. One thing to note from Sylvania's worm invasion is that gm goes up dramatically as Rp goes down dramatically, but mu, which equals gm x Rp, doesn't vary much. Once we get an equation for a circuit, it's the "gm"s and "Rp"s that aren't in Gm x Rp terms that get you non-linearity, and this can frequently be maximised or minimized by varying Ranode, Rcathode Ibias and the supply voltage.

For example, for a triode with a well-bypassed cathode driving a very high impedance,

vp= (gm x Rp x Gs x Ranode)/(Rp + Ranode)

where Ranode is the "load" resistor from the plate to the supply, and vp is the output voltage at the plate. The numerator has Gs, gm x Rp, and Ranode, which are at least fairly constant. The denominator has a lone Rp term which will vary dramatically, and non-linearity can be maximized if we maximize its contribution by minimizing Ranode. A low-gain stage can be more non-linear than a high gain stage, as long as you avoid saturation and cutoff in the high-gain stage! Of course, for a large value of Ranode, there is still the change in gm x Rp which is graphed as the change in mu. But Rp falls as mu rises, so non-linearity (change in gain as DC grid voltage changes) is increased by decreasing Ranode.

Back to plate resistance (Rp). If plate resistance were zero, and remembering that the small-signal voltage change at the grid is Gs, the voltage change across the anode resistor would be Gs x gm x Ranode. Want more gain? just increase Ranode (and the supply voltage, so that the anode voltage stays the same). With Rp present, using the current source model, which has Rp in parallel with the current source, the current Gs x gm drives Ranode and Rp in parallel (this is an AC model). We can see that as Ranode gets as large or larger than Rp, most of the current flows through Rp, not Ranode, reducing gain. Now a 12X7 has a plate resistance in the ballpark of 65K, and anode resistors in preamps are usually larger, by maybe a factor of 3. That's why you don't get a voltage gain of 100 out of your pre-amp, even with cathode bypassing. Instead, you're down in the 30s. decreasing Ranode to reduce this effect reduces gain in itself, so you can't really get to a voltage gain of mu.

Once you grok this, you need to learn to draw DC and AC load lines on characteristic curves (the other figure in the Sylvania data sheet, which will also aid your understanding), understand triodes without bypassed cathode resistors, and learn to graph the impedance of simple RC circuits. Richard Kuehnel's "Guitar Amplifier Preamps" book does a great job, but it helps if you are already a bit of a nerd. It will take you all the way through the preamp and tone stack, and his Bassman book will help you to understand at least one tube amp power supply and class AB output stage with a Schmidt phase inverter in way too much detail. Kevin O'Connor's TUT series is weak on this type of analysis (he argues that if you start with an existing circuit, you don't really need to do it much, and he's pretty much right, though he definitely knows how to do it), but O'Connor will expose you to a wealth of options, and you'll want to take a knife and soldering iron to just about everything.

[kg]

nice post, bob!

don't worry, bluefox... with time things will become clearer.

-ken

[Steve Conner]

Of course, if all this theory is too much for you, you could always just copy the application circuits straight out of the tube maker's manual, like Leo Fender did. Or just copy a Fender design like Jim Marshall did.

I agree with everything BackwardsBob said, except in the second last paragraph, surely you meant to say "If plate resistance were infinite..." rather than zero. Assuming you were talking about the Norton model at that point, I guess.