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LNF in gain stage or CF?

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I'll use an analogy: lens making.

Now probably not very many people here are 'up' on this specialized field, but it has a lot of design criteria that taken general also have applicability in making multistage amplifiers.

It has been found that if economics is not much of a consideration, and also if brightest light transmission is not an absolute ideal, then the highest resolution that one can achieve with a given compound lens design basically maximizes when the number of individual lenses and lens-groups is also maximized. When each lens/group bends light the smallest, then the impact of its various aberrations is also minimized. And thus minimized, easiest to correct down wind.

However, like as with amplifiers real lenses are not 'free'. Neither are their curves: the deeper a curve, the more expensive. The more exotic the glass type (to counteract aberrations, say, the more expensive and rare. The more individual elements, the more expensive … and multiply so due to the whole contraption becoming heavier and heavier, requiring a more robust containment shell.

TAKING THE ANALOGY forward …

The 'best' performing amplifiers (with one very crucial exception) would use close to the most stages each amplifying the least … in order to move the signal from LINE levels (± 2 to 4 volts) to DRIVE levels (± 20 to 70 volts). In so doing, one could optimize each stage to local degenerative feedback (or even enhance it through coupling), so that it is as linear and “non-coloring” as possible. Maybe that gain of 30 to 50 decibels (using 20 log VO / VI as the decibel calculator) could be done in 3 dB steps!

Thing is, that again analogous to the build-a-fine-lens case, stages aren't free. At least in the tube world they're definitely not. So, we try to eek out a bit more gain from them than the optimum minimum. Economy. Convention. Prudence. Best Practices. Supporting math. All that.

The one exception from this idea is that unlike lenses (sort of), amplification stages each add a bit of uncorrectable noise to the signal stream. Yet, if you do the math, you find that the most important stage for squashing noise is the first stage. With reasonable stage-to-stage gain after the first stage, their TOTAL contribution is typically less than 10% of the total overall noise figure. So … designers have gotten accustomed to the idea of giving "stage 1" a bunch of gain.

Hence, why bypassed cathode resistors are much/commonly specified. To give more gain to the first stage, which in a way minimizes the subsequent stage(s) noise contributions. UNFORTUNATELY, this is also (in the lens example) like using substantially nonlinear, high refraction glass … which introduces the maximum single-stage asymmetries to the signal. We lovingly (cheekily?) call these second order distortion, and upsell it as being pleasant on the ear. Musical. Opens the sound stage. Insert weasel-words here.

But the truth is somewhat different: if - as you surmise - the first stage is not just intentionally hobbled thru NOT bypassing its cathode resistor, and it is further hobbled in gain at the expense of adding greater linearity thru local negative feedback, the impact on overall signal linearity is substantial. Yes, the subsequent gain stages have to be either(or both) more numerous, higher gain, more carefully designed for low-noise impact. But so what?

Once - about 20 years and 3 house-moves ago - I decided to cobble together an amplifier that had just this design criteria. It had over 8 gain stages, each having only the smallest gain hops. +3 dB to +6 dB was the criterion. It was also a polarity-symmetric amplifier, having the same devices amplifying both the normal and inverted signal, to induce complete distortion symmetry on the signal. No attempt was made to conserve power (so that input triodes and pentodes operated at high currents.), and little attempt was made to save money. (Well… not so: my revered uncle had saved over 2,500 tubes in various giant boxes, culled from hundreds of yard sales and going-out-of-business TV repair sales. So the tubes were free. It is a pity they disappeared during one of the three house moves.)

The result? Actually remarkable: huge dynamic range, linear, musical.

But it was just an experiment. Only 1 channel was ever built, and I never found the time to work out a different, alternative, and perhaps better other channel.

POINT IS? That from that multi-element lens-building optics example, comes an analogy that may be remarkably applicable to conventional multi-stage amplifier design.

GoatGuy
 
GoatGuy, As an amateur telescope builder, I really appreciate this analogy. Thanks! --Jeff

You're welcome. My 6" turned out as oblate as an egg (but I was 11, what was I to expect?), my 8" was great but the heavy paper tube self-destructed due to the leak in the barn, and my 10" never got past the “decorative planter pad glued to its grinding post” stage for the wife. No longer do I look forward to weekends spent fishing 40, 60, 100 and 150 grit carbide out of my fingernails. However, in one of my "if born again bucket list" wishes, it would be to go all Dobsonian, and make a tightly coupled pair of 18" Dobs, with off-axis collimation correction, to power a nice pair of Plössl ultra-wide eyeball friendly "stereo" objectives.

I got to peer at K. Baldwin's dual 16 one fine Palomar evening in the 1980s, and it was … an eye-opener. I think he was running f/4.5 or something ridiculously wide-field. Crazy-bright. Nebulæ and everthing. Not quite “astrophotography level” with many-minute photon integration, but still … delicious. And kind of satisfying to watch Earth's rotation moving the interesting stuff across the field ever so slowly.

Memories.
And wishes for my "reincarnated bucket list"

GoatGuy
 
It's a lot easier to get linear gain when the signal is still small and the load can be high Z (CCS). That will save you trouble in the later stage(s) where gain is distorting and loads are low Z. If you don't want noise in the 1st stage, use something like a 12GN7, instead of a wimpy 12AX7. The 12GN7 could give you a highly linear 50X gain in triode mode when CCS loaded, and could drive a lot of output stages directly.
 
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OP didn't say “cathode follower stage.
Said “first stage”, which conventionally implies “nominally highest voltage gain stage”.

Wherein, if instead of using a “fixed bias” (either a true fixed negative bias off a negative bias supply, or a pseudo-fixed bias by creating a small 'positive power supply' to lift the cathode using a resistor and capacitor … or even using a string of diodes or a suitably chosen LED as a near-fixed cathode-lifting bias), which maximizes the voltage swing that the grid-to-cathode field sees, thus maximizing the tube's amplification, if instead one takes 'just the resistor without the bypass capacitor' approach, the "lifting" of the cathode is not fixed, but tracks with the same sign as the input signal.

The net effect is that there is a much smaller grid-to-cathode relative voltage difference than the bypassed resistor or fixed-bias by LED/neg supply methods. This in turn drops gain considerably. Lower gain confines the stage transfer function to a narrower band … which by how tubes work then is also closer to straight-line linear. In combination with the anti-phase (and amplified) signal impressed on the anode due to the current-to-voltage converting anode load impedance (which is another source of negative feedback), the net result is significantly improved linearity.

smoking-amp notes that if one loads the stage with a suitable constant current source (which is not really 'constant' current, but does pretty closely approximate it), then the tube's (or stage's) transfer function further degenerates to an almost linear relationship to MU, the gain characteristic of the tube. This does not diminish gain, but just tightly couples it to μ instead of gM and the complex load imposed by both an anode resistance and the following (driven) stage's impedance.

DO NOTE … (especially smoking-amp) that the real impedance of the next, driven stage imposes a substantial load on the otherwise near-perfect CCS characteristic. This load can be made trivial with selection of high enough grid-to-ground hold-down resistors, but of course with the downside of increasing noise. Its all such a grand tradeoff, isn't it?

GoatGuy
 
Is there any benefit to NOT bypassing the cathode to use local negative feedback in the first gain stage (preamp triode/12AX7) over the negative feedback in a cathode follower when one is used as the last output stage?

If you want higher output resistance, so yes, unbypassed resistor is better. And vice verse. It is feedback by CURRENT.
 

dgta

Member
2011-05-30 8:08 pm

Yes, a cathode follower has 100% NFB. What I don't understand is what you are asking. Your thread title is "LNF in gain stage or CF?", implying you want to make a choice between the 2.

That's like asking "I'm buying a new car. Is there any benefit to getting a sunroof instead of traction control?"

The answer is that they are not mutually exclusive, nor do they accomplish the same results, so depending on your design goals you can use one or the other or both or neither. What is it you're trying to accomplish?
 
Is there any benefit to NOT bypassing the cathode to use local negative feedback in the first gain stage (preamp triode/12AX7) over the negative feedback in a cathode follower when one is used as the last output stage?

No, it's not a good idea. especially with a 12AX7. Triodes aren't like transistors, and any resistance in the cathode adds to the plate resistance accordingly: You also don't have that nonlinear re that needs swamping out by means of an unbypassed emitter resistor. The only reason not to bypass the cathode resistor of a small signal triode is if you're using the cathode as an NFB summing node. If you don't want to use a bypass capacitor, consider LED bias as an alternative.

r`p= rp + Rk(1 + u)

Considering the nominal rp= 80K, you don't want to drive it up. Triodes like the lightest plate loading you can manage for good linearity. All the complaints regarding disappointing sonic performance from 12AX7s goes back to the use of plate load resistors that're too small. If you don't have the DC rail voltage, then go with active plate loading.

This is also why 6SL7s are widely praised as being superior to the 'AX7s: lower u-factor and an rp= 44K -- almost half, and thus much easier to provide with light plate loads.
 
Wherein, if instead of using a “fixed bias” (either a true fixed negative bias off a negative bias supply, or a pseudo-fixed bias by creating a small 'positive power supply' to lift the cathode using a resistor and capacitor … or even using a string of diodes or a suitably chosen LED as a near-fixed cathode-lifting bias), which maximizes the voltage swing that the grid-to-cathode field sees, thus maximizing the tube's amplification, if instead one takes 'just the resistor without the bypass capacitor' approach, the "lifting" of the cathode is not fixed, but tracks with the same sign as the input signal.

The net effect is that there is a much smaller grid-to-cathode relative voltage difference than the bypassed resistor or fixed-bias by LED/neg supply methods. This in turn drops gain considerably. Lower gain confines the stage transfer function to a narrower band … which by how tubes work then is also closer to straight-line linear. In combination with the anti-phase (and amplified) signal impressed on the anode due to the current-to-voltage converting anode load impedance (which is another source of negative feedback), the net result is significantly improved linearity.

GoatGuy

No, it's not a good idea. especially with a 12AX7. Triodes aren't like transistors, and any resistance in the cathode adds to the plate resistance accordingly: You also don't have that nonlinear re that needs swamping out by means of an unbypassed emitter resistor. The only reason not to bypass the cathode resistor of a small signal triode is if you're using the cathode as an NFB summing node. If you don't want to use a bypass capacitor, consider LED bias as an alternative.

r`p= rp + Rk(1 + u)

Considering the nominal rp= 80K, you don't want to drive it up. Triodes like the lightest plate loading you can manage for good linearity. All the complaints regarding disappointing sonic performance from 12AX7s goes back to the use of plate load resistors that're too small. If you don't have the DC rail voltage, then go with active plate loading.

These posts seem contradictory. Which is right?

For the record the plate resistor is 220k, 227VDC regulated B+, and cathode resistor 3.3K unbypassed. I only have two gain stages and then the cathode follower output. Right now both gain stages are un-bypassed.

My question was really:
1) If you don't need maxumum gain (which I don't, at least not from the first stage), is it better to use LNF at each stage, just the first stage, last stage, etc?
2)Since I have a cathode follower as the last stage (buffered output), and it introduces feedback, would it provide as much/less/more benefit (as far as removing unwanted signal artifacts like noise/hum etc.) as the only source of feedback.

What are other benefits, besides noise reduction, to using LNF?

For the most part I think these questions have been addressed.
 
winegamd… I agree, the pair of posts are pretty contradictory. However, we're looking at the bottles (tubes) from different design criteria. Miles likes to use fixed bias (don't jump on me yet Miles), either of the now-popular LED bias, or string of rectifiers, or 'real' negative bias supply, or a capacitor-bypassed cathode resistor; these are all (pseudo-)fixed bias solutions. ONLY the cap-bypassed-cathode-resistor version is automatically adaptive to tube ageing, tube variation, manufacturer variation. The others ("hard fixed value") are not.

Miles jumps in with the idea that “tubes are not transistors” (we know that Miles!), but somewhat more concretely, with the idea that R'a = Ra + Rk(1 + μ), where big μ values in 'AX7 type valves goes to multiply a seemingly small cathode resistor (as in 1.5 kΩ) by the tubes nominal μ, which for an AX7 is what … 70 to 100? So, 1.5 × (70 to 100) = 100 to 150 kΩ effective R'a.

THIS IS TRUE… just as advertised. Yet when designing, it is not harmful. Instead (yes) you have a stage that offers substantially more linear amplification at the expense of increasing output impedance, and reducing gain overall. Which … if you read my other paragraphs, is exactly what I both expect, and am offering as a solution worthy to embrace. And yes Miles … one needs to account for the higher output impedance by making the subsequent stages “lighter in the load department”.

In fact, to mitigate this effect, I usually don't specify the AX series at all, but more medium μ devices such as the AT series, or even the AU series. Even the decidedly more square-law AY series can be nice if you want to 'warm up' the signature of an amp.

GoatGuy
 

dgta

Member
2011-05-30 8:08 pm
2)Since I have a cathode follower as the last stage (buffered output), and it introduces feedback, would it provide as much/less/more benefit (as far as removing unwanted signal artifacts like noise/hum etc.) as the only source of feedback.

The part you are missing is this:
Global feedback attempts to correct distortion generated in ANY of the stages inside the feedback loop. Local feedback applied to an individual stage only affects the distortion of THAT ONE stage. It may affect the preceding and following stages indirectly because of changes in its Zin and Zout, but that is a separate story.

So if, where and how you apply LFB depends on your specific design and goals. If you have too much distortion in the 1st stage, adding a CF 3d stage will not change that.
 
The part you are missing is this:
Global feedback attempts to correct distortion generated in ANY of the stages inside the feedback loop. Local feedback applied to an individual stage only affects the distortion of THAT ONE stage. It may affect the preceding and following stages indirectly because of changes in its Zin and Zout, but that is a separate story.

Ok, that answers that question. I was thinking that since any output from a stage is the input signal+stage signal (noise, hum, etc.) and is fed back into the input with a phase shift, that this would take care of anything in the original signal. What you are saying is this is incorrect, and LNF only takes care of the noise induced by that stage and the original input signal remains unaffected.
 

dgta

Member
2011-05-30 8:08 pm
Correct. The input noise TO a stage cannot be corrected IN that stage because the stage doesn't know what is a "valid" input and what is unwanted noise, distortion, etc.

This is why I wanted to clarify the OP question. Often a question is asked and answered where the players all have different assumptions as to what is being asked and what level of expertise the OP has. It's best to state the question with clarity and any assumptions. Particularly important in a forum like this, where the expertise level varies from none to PhD.
 
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