How would you describe plate impedance?

[Ptron]

I've always had a nebulus mental picture of what plate impedance is. It's fairly easy to picture it when a tube is in a queiscent state: The resistance of current flow presented by the bias on the gate + whatever resistance electrons encounter getting off the cathode through the vacuum and on to the plate. (Or is that even right?) For one thing I get confused by the instantaneous impedance of a tube in actual operation, which is when plate impedance really matters. I see it pointed out that plate impedance is a dynamic impedance (I've been reading this http://www.freewebs.com/valvewizard1...Gain_Stage.pdf page 22) which confuses me more because it makes think of reactance. Although it's stated that plate impedance is an AC impedance, it's there even in quiescent conditions, is it not? I'd really like to get a grip on what plate impedance is. Anyone got a way of explaining it that might clear things up? What does plate impedance mean to you?

[Old Tele man]

...well, dynamic plate resistance (rp) is change in plate voltage (delta-Ep) over change in plate current (delta-Ip) on the tube's EbIb curve...starting and ending at the same points on the EbIb curve, with tetrodes & pentodes it's always measured "past" (to the right) of the "knee."

...remember, with pp & OT's there are actually two loads:

A) the DC-load line that's almost vertical (very low R of OT-primary) which affects the 'idle' (DC) condition.

B) the AC-load line that's about 30-45-degrees upward and "reflected" across the OT from the load, which affects signal (AC) conditions (in parallel with the DC load).

...with preamp tubes (and no OT), the DC-load doesn't exist (AC-coupling through capacitors), so only the AC-loads are paralleled.

[mooreamps]

In my mind, this can be a very simple concept to understand. The question one must ask is, what really is a vacuum tube in the first place ? One answer is ; it functions as a "variable resistor". If such a part could exist ; one could replace a vacuum tube, with this really large "variable resistor" ; and it could function just the same as the tube. It's static resistance would be the same value as the tubes plate resistance. Then, if one could vary the resistor ; at the audio rate ; it's varying resistance then would memic the tubes ac transconductance.

Now I know all of this may seem a bit over simplified, but actually it's just about that easy.





-g

[Ptron]

...well, dynamic plate resistance (rp) is change in plate voltage (delta-Ep) over change in plate current (delta-Ip) on the tube's EbIb curve...starting and ending at the same points on the EbIb curve, with tetrodes & pentodes it's always measured "past" (to the right) of the "knee."

Thanks OTM,

I get the mathmatical definition of (if you want to call it that) of plate impedance as delta-Ep/delta-Ip but it doesn't mean that much to me (sort of like it's one thing to see some force-distance fulcrum formulas and another to be able to visualize a lever in action). I guess I'm trying to get a grasp of what the physical "cause" of plate impedance is. Maybe it doesn't make sense to try to think about it that way. I was mostly trying to think about preamp tubes for now for simplicity's sake.

Perhaps a related question is why there is no equivalent thing with transistors or fets, or at least you never hear about it. I understand that transistors are higher current/lower impedance devices but it seems like there should still be an equvalent thing, just to a smaller degree.

...with preamp tubes (and no OT), the DC-load doesn't exist (AC-coupling through capacitors), so only the AC-loads are paralleled.

I don't quite get this. Ignoring the following stage or capacitive coupling, the preamp stage will amplify down to DC, so what's the difference between an AC and DC load?

[Ptron]

In my mind, this can be a very simple concept to understand. The question one must ask is, what really is a vacuum tube in the first place ? One answer is ; it functions as a "variable resistor". If such a part could exist ; one could replace a vacuum tube, with this really large "variable resistor" ; and it could function just the same as the tube. It's static resistance would be the same value as the tubes plate resistance. Then, if one could vary the resistor ; at the audio rate ; it's varying resistance then would memic the tubes ac transconductance.

Now I know all of this may seem a bit over simplified, but actually it's just about that easy.





-g

...And thanks Gary. Your reply came after I started mine. That's the sort of visualiztion I'm grasping for. For a long time I actually thought of plate resistance pretty much the way you describe it. But then I got confused by statements that plate resistance is the dynamic or ac resistance of the tube. I'm still confused actually

[tubeswell]

well to my oversimplified reptilian brain, resistance = voltage divided by current. So the dynamic plate resistance is the result of any particular voltage and the concurrent current (no pun intended), assuming that the plate resistance is constant. I.e.; as the current changes with the voltage, the only thing that's not changing is the plate resistance - ipso facto that is the resistance of the plate no matter what voltage/current you have on the plate. (Not sure if my understanding is right tho' as I'm just a humble hobbyist and I've been bitten before)

Edit - or to put it another way, it is the inherent resistance of the plate that you work out from calculating the current that is present with any given voltage (since the inherent resistance of the plate is assumed to be fixed - and that things like heat etc don't change it much). Now as I said before - I could be wayyyy wrong here

[tbryanh]

The formal term used in data sheets and textbooks is plate "resistance" not "reactance."

Reactance can include resistance, inductive reactance, and capacitive reactance, so if only resistance is being referred to, it is more precise to use the term resistance instead of the term reactance.

Static, dynamic, and instantaneous resistances of the plate are not inductive or capacitive reactances.

If the triode were linear, the static, dynamic, and instantaneous resistances would be equal, so it appears the resistances are used to help describe the non-linearity of the triode.

The resistances can be found using a simple circuit, a circuit that provides no useful purpose other than revealing the triode’s characteristics. Just ground the cathode and apply a fixed voltage to the grid.

Now, apply a fixed voltage to the plate to find a static resistance of the plate, and apply a varying voltage to the plate to find a dynamic resistance of the plate. Instantaneous resistances of the plate are any of the static resistances that exist within the dynamic resistances.

[Steve Conner]

The reason why plate resistance exists is that the plate of a triode is just another control grid.

In other words, if you push the control grid more positive in order to fire more electrons at the plate, the plate current will increase. This will cause the plate voltage to fall because of the plate load resistor, and this lowered plate voltage will make the plate less attractive to electrons than it was. So the plate current won't increase quite as much as you thought, which amounts to the same thing as making the control grid slightly less positive than you actually did.

If you analyze this "grid-like" action of the plate mathematically, it appears as a resistor in parallel with an ideal current source (of value gm*Vg1) and the value of the resistor is what we call the plate resistance.

In pentodes and beam tetrodes, the screen grid shields the control grid from the electric field of the plate. So the plate resistance of these tubes is practically infinite: they can be considered as current sources.

BJTs, MOSFETs and JFETs are similar to pentode tubes in this respect, their "plate" resistance is very high (a few megohms typically for a 2N3904 or the like) I don't know why this is, I always reasoned that they should behave like triodes since they have no screen grids.

As for plate impedance: The above argument relates to a resistance. But the plate impedance can have reactive parts because of transit time and Miller effect. Heck, sometimes it can have negative parts. The famous example being if you put an inductance in the cathode, it gets transformed to negative resistance in the grid circuit, which is one cause of parasitic oscillations. This happens with MOSFETs and the like, too, and is the reason why grid and gate stopper resistors are used: ordinary resistance to cancel out the negative stuff.

[Ptron]

Yay! We're back in business.

And yay for that explaination Steve. That was excellent. Current source models are harder for me to think about so I haven't %100 wrapped my head around it but I'll get there.

[tbryanh]

The formal term used in data sheets and textbooks is plate "resistance" not "reactance.

Reactance can include"

Correction:

The formal term used in data sheets and textbooks is plate "resistance" not "impedance."

Impedance can include . . .

[Steve Conner]

Yeah, current sources are one of these EE things.

Voltage sources we all know, since you can buy them in your local store, 1.5V, 9V and so on. A voltage source is basically a mathematical idealization of a battery: the voltage stays at 9V (or whatever) no matter what current you draw from it.

Of course a real battery's voltage will sag somewhat, it might be 9.2V sitting on the shelf, and 9.0 when running a stomp box. We would model that as a voltage source with a small resistor in series to provide the sag.

Current sources are also mathematical idealizations, but harder to understand, because you can't go to the store and buy a 30 milliamp battery. They are the duals of voltage sources: they deliver the same current no matter what you connect to them.

This means that an ideal current source will produce infinite voltage sitting on the shelf, so it's just as well they are mathematical fictions and don't exist in real life. Real current sources always have a "sag resistor" like the one I mentioned above for the voltage source, but this time it's in parallel with the source. (A resistor in series with an ideal current source would have no effect on the current, because it's always the same.)

Possibly the closest real-life analog of a current source is those funky series connected streetlights that American towns used to use. The bulbs were all in series, and the whole lot was driven by a big pole-mounted regulating transformer that supplied a constant current of 1 amp, or whatever it was. Each bulb only had 110V across it, because they were 110V, 1 amp bulbs, but if you tried to unscrew one from its socket, you'd get zapped with the full string voltage of 4,400V. And in engineering, forty times what it should be is close enough to infinite.

[Old Tele man]

...well, to get really technical and nit-pickly, impedance (Z) is a vector-summation of DC-resistance (R) and AC-reactances (XL and XC):

Z = SQRT[ R^2 + (XL-XC)^2 ]

...and:

Phase Angle = ARCTAN[ (XL-XC)/R ]

...the EbIb curves show the tubes' DC-characteristics, but tubes ALSO have AC-characteristics (check the inter-element capacitances), such that, depending upon the frequency of any applied AC-signals, the tubes' TOTAL opposition (ie: impedance!) becomes a complex combination of input/tube/output loadings, some of which could be (but seldom are) purely DC-resistances, but most are combinations of capacitive-reactances (tube, wiring, small part of OT) and inductive-reactances (mainly OT).

...things get "really" interesting when you start calculating the input-to-output frequency response and bandwidth of an amplifier, especially one with negative-feedback...phases angles become VERY important to whether things "work" as designed or "howl" due to unwanted 'feedback' at certain frequencies.

[mooreamps]

...And thanks Gary. Your reply came after I started mine. That's the sort of visualization I'm grasping for. For a long time I actually thought of plate resistance pretty much the way you describe it. But then I got confused by statements that plate resistance is the dynamic or ac resistance of the tube. I'm still confused actually

That's because one way to measure, and/or calculate the plate impedance of a vacuum tube is how it performs dynamically with an ac signal applied. These are required since the plate impedance can vary as a function of frequency. Frequency meaning IF and RF radio frequencies, not just the audio frequencies that we use here. In my mind, I treat the audio frequencies [like in guitar amplifiers] like DC, and then just go from there. I do consider the stage gains at radio frequencies, but only to ensure those frequencies are attenuated, not amplified.


-g

[Ptron]

The reason why plate resistance exists is that the plate of a triode is just another control grid.

In other words, if you push the control grid more positive in order to fire more electrons at the plate, the plate current will increase. This will cause the plate voltage to fall because of the plate load resistor, and this lowered plate voltage will make the plate less attractive to electrons than it was. So the plate current won't increase quite as much as you thought, which amounts to the same thing as making the control grid slightly less positive than you actually did.

If you analyze this "grid-like" action of the plate mathematically, it appears as a resistor in parallel with an ideal current source (of value gm*Vg1) and the value of the resistor is what we call the plate resistance.

In pentodes and beam tetrodes, the screen grid shields the control grid from the electric field of the plate. So the plate resistance of these tubes is practically infinite: they can be considered as current sources.

So how does all this work with say, a cathode follower, with no plate resitor and the voltage on the plate is fairly constant? I would guess that means plate resistance will be very low.

Same with diode/rectifier...very little plate impedance.

[Steve Conner]

The plate resistance of a cathode follower is like the sound of a tree falling in the forest when nobody's around to hear it.

The output impedance of a cathode follower is not the plate resistance, but 1/gm. For a triode, mu, gm and rp are related: if you know any two you can calculate the third, so the impedance at the cathode is related to the plate impedance. (For all you math geeks: mu=gm*Rp. Thus high-mu tubes must have either higher gm, or higher Rp, than low-mu ones: compare the datasheets for a 12AX7 and a 12AU7.)

I suppose a rectifier does have plate resistance, but the tube designer tries to keep it as low as he possibly can because it causes sag and wastes power. It's typically a few hundred ohms, and the plate resistances of large power triodes like the 6C33 or 6080 are designed as low as that, too, so they can pass high currents efficiently with low voltage drop. If you examine one of these triodes, you'll see they have an internal structure not unlike a 5U4 or the like, with a control grid stuffed in there.

The unavoidable side-effect is that these big triodes have very low mu and so need massive grid drive to do anything much. Pentodes and beam tetrodes were great because they broke out of this compromise.