Output section impedance questions

[silverfox]

Something I don't understand and now have to since I'm kludging together an output section from parts on the shelf: How changing the output tap or speaker impedance changes the primary load on the output tube. I've seen suggestions, when you don't have a particular output transformer that matches the tube and voltage, the output tap or speaker load can be changed and that works to match the impedance on the primary side load.

Q1: How does that work? Would changing the output impedance on a 5K primary OT result in the tube seeing a load of say, 6K if done right?

Q2: When matching an impedance load to the output tube the solution is primarily about keeping the dissipated watts in the tube within the data-sheet guide lines, and the plate voltage from exceeding the max allowable voltage. Is this an over generalization?

I would think changing the output tap and speaker load to cause a mismatch would also change the sonics of the amp..

Regards,

silverfox.

[HotBluePlates]

... How changing the output tap or speaker impedance changes the primary load on the output tube. ...

Q1: How does that work? Would changing the output impedance on a 5K primary OT result in the tube seeing a load of say, 6K if done right? ...

Theoretically, yes; in practice, not often.

Start by understanding the basics of an ideal transformer.  Bottom-line for an ideal transformer is Power In = Power Out.  There are primary turns and secondary turns; if the number of turns for each is the same, the transformer's turns ratio ("K" in the link) is 1:1.

A 1:1 transformer is fine for electrical isolation of two circuits, but often we want a different voltage on one winding.  Since the volts/turn are the same on each winding, voltage transformation requires a different number of turns on each winding.  If you watch the subscripts closely in the link, voltage and current change in opposite directions: if voltage is stepped up from primary to secondary, current is stepped down.  This conforms to the earlier statement that Power In = Power Out.

Imagine we have a transformer that steps voltage down from primary to secondary; say the turns ratio is 25:1.  250vac on the primary of this transformer yields 10vac on the secondary.  If 25w is being applied to the primary, this implies the primary current is 25w/250vac = 100mA.  Since there is 25w transferred to the secondary, the secondary current is 25w/10vac = 2.5A.

If we apply Ohm's Law intuitively, 250v/0.1A = 2500Ω on the primary, while 10v/2.5A = 4Ω on the secondary.  So we see that the apparent impedance for a step-down transformer is lower on the secondary than on the primary.  The ratio of the impedances is 2500Ω:4Ω, or 625:1.  We could derive the relationship between turns ratio and impedance ratio using Ohm's Law and abstract variables, or notice that √625 = 25, and that the impedance ratio is the square of the turns ratio.

Notice the 2500Ω:4Ω transformer is the same as a 5000Ω:8Ω transformer.  The impedance ratio of 625:1 is true for both.

The transformer doesn't have an "impedance of its own" (which matters beyond understanding low frequency response), but only takes whatever external impedance is attached to the secondary and "levers it up" by the impedance ratio to reflect an impedance on the primary.  So our transformer looks like a 2.5kΩ primary if 4Ω is attached to the secondary (4Ω * 625 = 2.5kΩ).  Or it looks like 5kΩ is 8Ω is attached to the secondary (8Ω * 625 = 5kΩ).

You asked whether this transformer could be made to look like a 6kΩ primary.  Yes, if you attach a 6kΩ/625 = 9.6Ω load to the secondary.  It's do-able, but you won't find "9.6Ω nominal" speakers.  An odd series-parallel arrangement could probably get there, as could adding a series resistor (which would waste some output power as heat).

[shooter]

 
Thank you, I was just gonna go surfing in the weeds for just that info that I forgot 40yrs ago!

[HotBluePlates]

... Q2: When matching an impedance load to the output tube the solution is primarily about keeping the dissipated watts in the tube within the data-sheet guide lines, and the plate voltage from exceeding the max allowable voltage. Is this an over generalization? ...

Yes, over-generalization.

The OT primary impedance is not "matched to the tube" (although folks who don't understand how simple the output stage really is often say this; I mistakenly thought the same thing for more than a decade before I really grasped how the output stage works).

 - When designing an output stage, the designer simply chooses an amount of output power as a target.
 - Choices are then made about power supply voltage, perhaps based on typical tube limitations or the availability of power transformers or other parts.
 - The chosen supply voltage implies a boundary on the a.c. voltage swing component of the output power.
 - Ohm's Law is used to find the needed a.c. current swing component of output power.
 - Ohm's Law also uses the voltage & current found previously to define the impedance needed between the tube plate & power supply the allow the power output to happen.
 - The impedance found may be equal to, 1/2 of, or 1/4 of the total primary impedance, depending on whether the design is single-ended or push-pull (and the class of operation if the latter).

Once done with the above, the designer has to check if the answers found make sense with the desired output tube(s).  We'll stick with our 25w example from earlier.  If the supply voltage was decided to be 150v (which might only allow a 120v peak swing), the current required would be 50w Peak/120v Peak = ~417mA Peak.  Do we have any tubes which can support 400mA+ with only 30v on the plate (we'd investigate screen voltage and plate current for beam power tubes or pentodes)?

If we did have a tube which could managed such large peak currents at low voltage, the implied OT primary impedance would be 120v Peak/417mA Peak = ~288Ω for a single-ended stage (or maybe 576Ω plate-to-plate for a class A push-pull stage, or 1152Ω plate-to-plate for a class AB push-pull stage).

In this view, you're looking to match tubes up to the current demands imposed by a power output goal, with the given load, at the given supply voltage.  You're not looking to "match the OT to the tube".

That said, natural matches do crop up.  Most designers didn't strive to leave a lot of tube capability "on the table" as in using push-pull KT88's to deliver 8w RMS clean output.  Convenience and/or convention resulted in "typical answers" to the design problem, where different tube types were used to develop different classes of output power (i.e., the 4w SE 6V6/EL84, the 12-15w push-pull 6V6/EL84, the 30-50w push-pull 6L6/EL34, etc).

Rather than design from scratch, most would copy typical known-good-plans, using same tubes, at similar supply voltages, in the same configuration and class of operation, for same/similar output power.  As a result, the different amps land on same/similar OT primary impedances, but only because everything else is so similar.

But it doesn't necessarily have to be that way.

[HotBluePlates]

You could notice that if we increased the impedance of the output section, things might be easier.  Higher OT impedance means we could use higher supply voltage but also lower peak plate currents to arrive at the same power output.  Our common tubes can handle higher voltage and less current pretty easily.

Let's imagine we'll use a 5kΩ plate-to-plate OT in class A.  Each side of the output stage will see 2.5kΩ as the load to its plate, and √(25w*2.5kΩ) = 250v RMS.  Peak voltage swing would need to be 250v * 1.414 = ~354v, so a supply voltage of 400-425vdc ought to leave a enough excess plate-to-cathode voltage to enable good peak current.  50w Peak/354v Peak = 141mA peak.  We'd need a tube and a screen voltage which allows 141mA peak plate current as the control grid approaches 0v.

If we peep a data sheet, the 6V6 might just barely manage 141mA peak at likely screen voltage.  In fact, we're not far off from what a 60's Deluxe does.  But when we check another stipulation for class A (the tube current never shuts off), we find we'll not get there with a 6V6 (14w/425v = 33mA, much less than half the peak current).  However, a 6L6GC would have no trouble getting at least very close (30w/425v = ~71mA).

Someone might steal from our design, noting "5kΩ matches a 6L6GC running Class A at 425v."  They might even notice the same output tube and same supply running in Class AB (bigger peak currents, but shut off longer, for more power output) "wants a lower OT impedance."

But you'll see from above that's not how we got there.  And it would be better to say for the Class AB situation that a lower OT impedance was selected to result in bigger peak currents and more power output at the same supply voltage.

[shooter]

Yes, over-generalization

can I generalize that on the primary side of the OT I want the largest Voltage swing possible (within norms) which results in the most power,(stepped up current), possible at the speaker?

[silverfox]

shooter: can I generalize that on the primary side of the OT I want the largest Voltage swing possible (within norms) which results in the most power,(stepped up current), possible at the speaker?

We seem to be hacking through different parts of the same weed patch, (power amp design). I'm going to guess an analogy something like: You can order the biggest motor available for the truck but do you need all that horsepower? is forthcoming. Seems to me the voltage level is going to determine how much headroom you have to swing the output signal within. It also would be a cost vs. marketing decision and we know what that would lead to.

Thanks for the detailed explanation HBP. I'm off to determine the impedance ratio of an OT I'd like to use. I've also bulldozed through the determination process by spending the past several hours looking at power amp schematics but now have more of an understanding of the circuit operation.

Regards,

silverfox.

[PRR]

> You can order the biggest motor available for the truck

Transformer is more like gears. The same gears can be 8000RPM to 8RPM or 4000RPM to 4RPM.

[shooter]

Transformer is more like gears.

I like it!, when I blew up the 1st dif on my jeep I switched everything from 4:10 to 4:58, she would only do 50mph, but over anything!

Silver fox: I believe we are, I've got 18 proto-types from cut n paste, some keepers, but I would like to know the deeper aspects of how you kill a tube
I hope to take the wisdom and plug into a spreadsheet so I can "predict" outcomes, before I solder!  I do like my ghetto bread-board, it scares the hell outta everyone

[HotBluePlates]

can I generalize that on the primary side of the OT I want the largest Voltage swing possible (within norms) which results in the most power ...

Everything depends on everything else.

If you only had a 100vdc supply and wanted 25w of output, 25v RMS and 1A RMS might get you there (very low impedance at the plate), but there few tubes which will manage it.

You might work with 1kV RMS plate swing and only need 25mA RMS plate current swing (quite high impedance at the plate), but wiring & socket insulation (and tube maximum ratings) are now a problem.

If you're looking at a set of curves from a data sheet, you can plot a loadline of the load impedance.  You'll draw vertical lines at idle and peak plate voltage ("peak" being the lowest voltage the tube swings toward), and horizontal lines at peak plate current and idle current (or at zero-current if this is a Class AB stage).

This rectangle is your peak power output; half of it is your RMS power output.  RMS output is also the area below the loadline within this rectangle.

You can have a tall, skinny rectangle (low load impedance, little variation along the X-axis of voltage, huge variation along the Y-axis of current), or you can have a short, wide rectangle (high load impedance, wide variation along the X-axis of plate voltage, little variation along the Y-axis of plate current).  You can come up with many rectangles which have differing dimensions for the side but the same area.  Likewise, there can be many loads which enable a given amount of power output.

The devil is in the details:
  - On your way to your desired power output target, you might run into some limit of the tube (maximum voltage, maximum peak plate current, exceed plate dissipation in the chosen class of operation).
  - You might find that everything is working for the tube, but the loadline strays into an area which results in distortion (so less clean output power than you'd figured).
  - Or you have the perfect design that calls for power supply or output transformer components that simply aren't available.

Design comes down to either copying a known-good plan (often a good idea), or running through many iterations on the way to a happy final result.  That is, running through the design process until you run into some obstacle, then going back a few steps and changing aspects of the design, then rinse & repeat.  Many times...  Until you've either side-stepped all the obstacles or changed your expectations/goals for the project.

[jjasilli]

The OT primary impedance is not "matched to the tube" (although folks who don't understand how simple the output stage really is often say this; I mistakenly thought the same thing for more than a decade before I really grasped how the output stage works).

This discussion is very informative.  However I think it applies primarily to power & gain, along with headroom & overdrive issues, considered in isolation.  I.e., it does not address THD, or signal "linearity" (in the sense that the output signal waveform conforms to the input signal, even for clean guitar amp tone).  Roughly analogous to optics:  magnification vs. resolution.  Granted this may be considered a "feature" for guitar amps, though a "bug" for hi-fi or PA amps.  If signal linearity or certain frequency response is desired, then I think impedance matching of plate(s) to OT primary is necessary. 

[shooter]

If signal linearity or certain frequency response is desired, then I think impedance matching of plate(s) to OT primary is necessary. 

That is important for my app, I want the signal at the speaker to "mirror" the input, no bends or kinks or happy guitar shapes.  Amplitude, now I want the best bang for my buck.

[PRR]

> If signal linearity or certain frequency response is desired, then I think impedance matching of plate(s) to OT primary is necessary.

Pentode has two impedances. Above the knee maybe 10K, the number on the sheet. Below the knee, more like a few hundred Ohms, the steep rise from zero to many dozen volts.

The maximum Power point almost always touches near the knee.We need that data, not the single number Rp.

The maximum Linearity is almost always for "zero signal current swing", infinite load, no output power.

Compromise must be made.

As this is a POWER stage, power is the first concern. Linearity is tough and best attacked other ways.

For the usual audio power pentodes("tetrodes"), the exact loading is not a function of Rp, but rather of the V and I you choose to run the tube at.

Vg2 matters also. For supply designer convenience, most audio power pentodes are scaled so Vg2 can be 75%-100% of Vp.

As a raw-rock guess, find a spec-point that works the tube fairly hard. Figure it as a Triode. Find Gm and Mu(g2). Mu(g2)/Gm is the approximate plate resistance as a triode, and a guide to the tube's ability to handle current and voltage. A happy triode load would be twice Rp. Try that as a pentode load.

To really optimize pentode linearity you must define the several signal levels you care about (small, large, and clipped) and plot them on the curves. No single number can approximate the bends and weaves and scrunch of pentode curves.

[HotBluePlates]

The OT primary impedance is not "matched to the tube" (although folks who don't understand how simple the output stage really is often say this; I mistakenly thought the same thing for more than a decade before I really grasped how the output stage works).

This discussion is very informative.  However I think it applies primarily to power & gain, along with headroom & overdrive issues, considered in isolation.  I.e., it does not address THD, or signal "linearity" ... 

You gotta crawl before you walk, before you run.  If someone understands the difference between peak & RMS values (of voltage, current and power for a sine wave), and can use Ohm's Law to calculate current through a resistance given an applied voltage, then they can design an output section to at least a first-approximation.

This stuff shouldn't be shrouded in Guru-smoke...

If we lurch into all those "complicating factors" mentioned before sorting out that ultimately OT impedance is all about Ohm's Law, it's like explaining Calculus to someone who can't add/subtract/multiply/divide.  Some broad concepts can be grasped without math fundamentals ("Acceleration is the derivative of velocity/speed; a derivative is how fast something is changing"), but pretty soon their intuitive grasp will run into roadblocks.

What I've outlined so far mostly applies to designing for an "ideal tube" (perfect linearity, zero distortion).  The only aspect of the end-result that substantially differs from thinking in terms of an ideal tube is that you'll get less clean output power than the ideal version predicts.

[HotBluePlates]

... impedance matching of plate(s) to OT primary is necessary. 

... The maximum Power point almost always touches near the knee. ...

I described a rectangle in my earlier post.  The upper left corner of that rectangle is usually at/near the knee PRR mentions for a max power output condition.

RCA's tube manuals describe 2 design procedures for an output stage: one for pentodes/beam tubes and one for triodes.  The triode method is essentially as PRR described (2*Rp).

For pentodes, RCA tells the reader to "draw arbitrary loadlines from the knee extending downward."  Then you are to evaluate the output power and linearity of the various loads represented by the lines, because one of them will have the most output power and least distortion for whatever condition you will use.  The downside is you need curves for the specific screen voltage you will be using (and you can't fake it with estimating just the 0v gridline, you need all the gridlines to understand where they scrunch up and distort).

[jjasilli]

"If someone understands the difference between peak & RMS values (of voltage, current and power for a sine wave), and can use Ohm's Law to calculate current through a resistance given an applied voltage, then they can design an output section to at least a first-approximation.This stuff shouldn't be shrouded in Guru-smoke...If we lurch into all those "complicating factors" mentioned before sorting out that ultimately OT impedance is all about Ohm's Law, it's like explaining Calculus"


Agreed.  I only meant to round-out that aspect of the topic.  Moreover, the heavy design lifting has presumably been done by the tube manufacturer, as set forth in the tube chart.  Presumably, the chart examples of "Typical  Operation" show good power design choices with signal linearity in mind -- with distortion percentages stated -- for various Watts out.

[silverfox]

  PRR:
Transformer is more like gears. The same gears can be 8000RPM to 8RPM or 4000RPM to 4RPM. 

Don't know if I can get anyone else interested in this particular analogy but: The esoteric nature of electronic principles requires, for me at least, a period of reflux in contemplation. However, if the output transformer relationship were describe as an analog to a three speed bicycle, and the power source as the rider. For example: The operator inputs power to the drive train. this power ultimately appears as "torque", transmitted to the output section which has three ratios. The same power is matched or mismatched depending upon the terrain. The operator will, in a sort of sense, blow up if the demands placed on them are mismatched at the other side of the output section; Distortion? Either in the form of: Need to Hercules the pedals or pedaling like crazy and very unstable in the process.

Overloads can easily damage system components while an under loading will cause the system to race, burn up. Caveat- Component failure under heavy loads can cause severe damage to the power source... or drive components.

I'm trying to correlate all of these analogies, if they are correct, to the topic in question. Momentum is current, potential energy is magnetic field, voltage is torque, gear ratio is turns windings, a happy system is cruising speed,, cruising speed is volume,  distortion is mismatch, Terrain is the reflected load. The frequency is input at the operator's discretion to attain a particular cruising speed. If the terrain changes, so does reflected load and while the power supplied may be sufficient to continue operation, an output component may fail trying to operate.

Hmm... Tear it down and scatter the pieces if you want, it will help me understand this better, or perhaps I'm crazy like a "...Fish needs a bicycle".

silverfox.

[drgonzonm]

calculus,  once exposed, can be easier than algebra and quicker, or a deal breaker.  (But laplace tranformations have made our lives a lot easier especially when dealing with Ohms Law in AC circuits).   

I like the comment about designing using Ohm's Law,  It reduces the stochastic nature of amp operation to  a more non-random evaluation. plus it works. 
stochastic variables (call them, complicating factors) 
nominal impedance of speaker, commonly stated at the 400 Hz value.  fortunately, the speakers impedance at 1kHz is usually close to the impedance at 400 Hz.  Many O/T's use the 1kHz as a reference frequency, what happening in the amp is different at 40 Hz or 4000 Hz. 
Tube Data,  published data is bogey data, from a statistical standpoint, the tubes you have will not meet bogey data,  The stochastic nature of other variables allows this simplification).  We assume that those new tube characteristics actually follow the data sheet info from 50-60 years ago.   
The signals were are feeding the O/T's are not sine waves, but harmonics, occasional clipped waves, but designing and testing with sine waves makes it a lot easier.   
Operating amps in Class A or Class AB operation. 
and don't forget those design differences between SE and PP amps.   

[HotBluePlates]

... I'm trying to correlate all of these analogies ...

I got lost.  Ohm's Law and the Equation for Power seem much easier to work with.

And tubes don't blow up when they're "overloaded" (which wasn't really defined).  The Unified Theory of Analogies starts to break down (for my brain anyway...).

If the tube sees an infinite load impedance, current swing is zero, so Power = Any Volts * Zero Current = Zero Power.
If the tube sees zero load impedance, voltage swing is zero, so Power = Zero Volts * Any Current = Zero Power.

You might say the zero-load case is equal to a short-circuit, but the tube is unharmed while the power supply blows a fuse.  The infinite-load case could create voltage spikes which will kill transformer inter-winding insulation, but again the tube is unharmed.

Between those cases, tube-unique behaviors happen.
Plate voltage swing in the negative direction (towards 0v on the plate) can't go less-than-0 because a tube can't conduct in that direction.  And before the plate gets to 0vdc, either plate current will collapse (plate not positive-enough to support plate current), or will be limited by grid-conduction as G1 (control grid) is driven positive and attempts to draw current from the previous stage which then causes that previous stage's output voltage to collapse.

At some low plate voltage, all grid curves converge into roughly a single curve below the knee... This represents severe distortion on this half of the signal swing, and can be seen as a related impact along with reduced power output.

The above effects tend to limit viable options when you raise the output tubes' plate load impedance.  Whether or not they are a problem might depend on how much output power you're seeking.
On the other side of things, there are some limits when you run an ever-lower plate load.  When plate current falls from idle and the plate voltage is swinging above the idle value, the grid curves crowd together at low plate currents.  This is a source of distortion especially for single-ended amps (because there's not an opposing tube to conduct more and offset the first tube's falling conduction).

But you might imagine a tube with a much-lower-than-optimum plate load might be able to conduct way-too-much plate current.  However, the 0v grid curve imposes an upper limit of plate current.  So unless the amp was specially-constructed to be able to drive the grid positive, the tube reaches its upper limit, the driving grid voltage collapses due to grid current conduction, and the tube isn't damaged.

An exception to the above is a way-too-low load combined with too hot an idle bias, and the tube overheats due to too much average power input.  But really this is a fault of the idle bias rather than the loading:  the transformer primary is just a coil of wire and its resistance to direct current is very much less than its impedance to alternating current (for a useful transformer design).
The above cases also help explain why "mismatching" a load tends to reduce output power and/or increase distortion.

There is always some optimum loading, bias, etc for a given set of tubes running at a given supply voltage which will deliver maximum clean power output.  But the more I look around, the more I see hobbyist guitar players for whom 30-50w is too much to be useful (sometimes even 4w is too much), and "non-optimum design" which doesn't yield all the possible clean power output may in fact be an ideal design for these players.

It seems like a good idea to highlight designing towards a power target, especially if these are the kinds of amps more folks will start building for their use at home.