Question in RDH4

[Steve Conner]

Yeah, magnetics calculations used some crazy units in the old days. "Lines per square inch" and so on. We learnt everything in SI units: teslas, webers, amps per meter and so on.

In Tesla's lab notes, he writes capacitances in "centimeters". He used the old CGS system where the permittivity of free space was 1.

[Alan0354]

I have question in p212 of RDH4.





But I use the real transformer equivalent circuit to derive the upper and lower frequency limit and it is different, totally different!!!



The top is the equivalent circuit of the real transformer.
(1) is the equivalent circuit refer to the primary.
(2) is the low frequency equivalent.
(3) is the equation of RA using my equivalent circuit which is different from the book in the first image.
(4) is the high frequency equivalent.

As you can see, the way I draw the equivalent circuit is different from the book, I don't think I can agree with the derivation of the book, I don't think you can lump the referred secondary winding resistance to the primary side and lump with the primary winding resistance to form RW. They are on the opposite side of L0. Even the equivalent circuit in Handbook of Transformer Design and Application by Flanagan and Wikipedia agree with me as drawn in (1) of my drawing:

http://en.wikipedia.org/wiki/Transformer

The high frequency calculation in the book is really off. It left out the primary and secondary interwinding capacitance that is even being written as the gating factor in rolling off at the high frequency. This just cannot be correct as it only describe the roll off by LS!!! AND if you look at (4) in my drawing, I don't even see why rp is in the picture regarding to high frequency roll off because it is in parallel with the rest of the circuit.

I did not even draw in the C21....the miller cap as this even more complicates the situation and being a step down transformer, the miller cap is small anyway.

[Alan0354]

Now, this is getting frustrating, Just too many things questionable and not well explained by the RDH4 in this cpt 13. Page 214:



It said R is in series with the primary, BUT:



How can R be in series with the primary? You can see in the equivalent circuit in the former post that there is no way R can be put in series. This is so common in BJT circuit with a high impedance transconductance current source driving a load. The output impedance of the current source ( which is rp in this case) is in parallel with the load!!! The current drives the parallel combination of rp and the referred load resistance at the primary side. It is just that simple.!!! This is really getting old and thin. These are important things!!!

I can be totally missing it, but this is thin!!!

[jazbo8]

I sense your frustration arise from not having the actual theory in place or worse the given formulas or derivation are somehow "wrong" in your estimation. Anyway, I refer you to www.next-tube.com/articles/Veen/VeenEN.pdf it gets a bit more theoretical, but even Veen used some simplifications and approximations, and claimed the results matched well with reality (90% is good enough for most I think). I think it also addresses your question on the equivalent circuits re voltage vs current source, i.e., if you use the voltage source model for the output tube, then Rp is in series with the Zpri.

Jaz

[Alan0354]

Thanks for the reply, I'll read into this when I find time today, my grandson is coming over today and stay over!!! So today is more like playing cards and game!!!

Yes, nothing is more frustrating to try to study and then found it doesn't make sense AND cannot find other ways to double verify it. I just feel I got stuck.

What do you mean by voltage model? Can you explain this, I have been looking at this as current source literally as it is a current source. You mean you literally use Norton theorem?

Thanks

Alan

[jazbo8]

Thanks for the reply, I'll read into this when I find time today, my grandson is coming over today and stay over!!! So today is more like playing cards and game!!!

Yes, nothing is more frustrating to try to study and then found it doesn't make sense AND cannot find other ways to double verify it. I just feel I got stuck.

What do you mean by voltage model? Can you explain this, I have been looking at this as current source literally as it is a current source. You mean you literally use Norton theorem?

Thanks

Alan

From wikipedia:

"Current and voltage source comparison

Most sources of electrical energy (mains electricity, a battery, ...) are best modeled as voltage sources. Such sources provide constant voltage, which means that as long as the amount of current drawn from the source is within the source's capabilities, its output voltage stays constant. An ideal voltage source provides no energy when it is loaded by an open circuit (i.e. an infinite impedance), but approaches infinite power and current when the load resistance approaches zero (a short circuit). Such a theoretical device would have a zero ohm output impedance in series with the source. A real-world voltage source has a very low, but non-zero output impedance: often much less than 1 ohm.
Conversely, a current source provides a constant current, as long as the load connected to the source terminals has sufficiently low impedance. An ideal current source would provide no energy to a short circuit and approach infinite energy and voltage as the load resistance approaches infinity (an open circuit). An ideal current source has an infinite output impedance in parallel with the source. A real-world current source has a very high, but finite output impedance. In the case of transistor current sources, impedances of a few megohms (at DC) are typical.
An ideal current source cannot be connected to an ideal open circuit because this would create the paradox of running a constant, non-zero current (from the current source) through an element with a defined zero current (the open circuit). Also, a current source should not be connected to another current source if their currents differ but this arrangement is frequently used (e.g., in amplifying stages with dynamic load, CMOS circuits, etc.)
Similarly, an ideal voltage source cannot be connected to an ideal short circuit (R=0), since this would result a similar paradox of finite nonzero voltage across an element with defined zero voltage (the short circuit). Also, a voltage source should not be connected to another voltage source if their voltages differ but again this arrangement is frequently used (e.g., in common base and differential amplifying stages).
Contrary, current and voltage sources can be connected to each other without any problems, and this technique is widely used in circuitry (e.g., in cascode circuits, differential amplifier stages with common emitter current source, etc.)
Because no ideal sources of either variety exist (all real-world examples have finite and non-zero source impedance), any current source can be considered as a voltage source with the same source impedance and vice versa. These concepts are dealt with by Norton's and Thévenin's theorems."



I think in Veen's AES' paper that I linked to on the other thread, he mentioned it was easier to use the voltage model and the same was used in the RDH as well. You could use the current model if you feel more comfortable with it, either model should reach the same conclusion - they are equivalent after all.

Jaz

[Alan0354]

I worked through using Thevenin theorem to transform the current source to voltage source. Still part don't make sense.



If you read the first part that using the rp alone as the thevenin resistor and calculate the voltage source, it can make sense. But the book go on and talk about if the secondary is loaded with R2 and the R is parallel combination of rp with R2(N1/N2)^2. Then the book talk about R is in series with the primary!!!! That's just WRONG.

When you use R, that is the TOTAL circuits, there is no more primary to talk about any more. The R already includes the RL referred back to the primary already. This is really weak.

My statements hold whether you use Norton or Thevenin conversion. The book is blind shooting!!!

[Alan0354]

I have question in p212 of RDH4.

[ATTACH=CONFIG]20148[/ATTACH]

[ATTACH=CONFIG]20149[/ATTACH]

But I use the real transformer equivalent circuit to derive the upper and lower frequency limit and it is different, totally different!!!

[ATTACH=CONFIG]20150[/ATTACH]

The top is the equivalent circuit of the real transformer.
(1) is the equivalent circuit refer to the primary.
(2) is the low frequency equivalent.
(3) is the equation of RA using my equivalent circuit which is different from the book in the first image.
(4) is the high frequency equivalent.

As you can see, the way I draw the equivalent circuit is different from the book, I don't think I can agree with the derivation of the book, I don't think you can lump the referred secondary winding resistance to the primary side and lump with the primary winding resistance to form RW. They are on the opposite side of L0. Even the equivalent circuit in Handbook of Transformer Design and Application by Flanagan and Wikipedia agree with me as drawn in (1) of my drawing:

Transformer - Wikipedia, the free encyclopedia

The high frequency calculation in the book is really off. It left out the primary and secondary interwinding capacitance that is even being written as the gating factor in rolling off at the high frequency. This just cannot be correct as it only describe the roll off by LS!!! AND if you look at (4) in my drawing, I don't even see why rp is in the picture regarding to high frequency roll off because it is in parallel with the rest of the circuit.

I did not even draw in the C21....the miller cap as this even more complicates the situation and being a step down transformer, the miller cap is small anyway.

I really looked into this also. My assertion also backed up by "Handbook of Transformer Design & Application" by Flanagan. It even explained why the secondary winding resistance HAS to be on the other side of Lo, not on the same side as the primary winding resistance. The only way the RDH4 work is like their example where they just assume Rw=0 and then it doesn't matter anymore. But then, they should have never pull the Rw out to confuse people.

[jazbo8]

I worked through using Thevenin theorem to transform the current source to voltage source. Still part don't make sense.

[ATTACH=CONFIG]20152[/ATTACH]

If you read the first part that using the rp alone as the thevenin resistor and calculate the voltage source, it can make sense. But the book go on and talk about if the secondary is loaded with R2 and the R is parallel combination of rp with R2(N1/N2)^2. Then the book talk about R is in series with the primary!!!! That's just WRONG.

When you use R, that is the TOTAL circuits, there is no more primary to talk about any more. The R already includes the RL referred back to the primary already. This is really weak.

My statements hold whether you use Norton or Thevenin conversion. The book is blind shooting!!!

Hey, it is just an old handbook... Please take a look at the following equivalent circuit (also from Veen's article that I posted on the transformer thread), I think this shows what RDH4 was trying to convey, un-successfully in this case. The takeaway for me, is that the plate resistance (push-pull is used in the example below) + winding losses (omitted in the example below) are in series with the voltage source and Zpri, which has two components - Raa and Lp. This is where most people would stop, but since you are delving into the inner working of the transformer, you do need to go down to the material level, where more fun awaits...



Jaz

[Steve Conner]

I agree with the points raised, I think the whole line of argument in that section of RDH4 is technically wrong.

Even driven from a zero-impedance source, the transformer can still generate distortion: the magnetising current causes an IR drop across the primary resistance.

The IR drop across the secondary resistance doesn't contribute to distortion because only the load current flows in it, not the magnetising current.

The only possibility I can see to save the argument is the voltage divider action of the winding and load resistances. In this sense, the secondary resistance does contribute to distortion, because it forces a higher voltage across L0 for a given output voltage, than if the transformer had no secondary resistance.

Also to be fair, in all practical cases, rp of the valve would dominate and you would get the right answer whichever formula you used.

[Alan0354]

I am not trying to continue criticizing RDH4, I just want to have a closure to the two questions I raised. I kind of half way give up this OT stuff already as it is pointed out by you and other that there are just too many variables. I am planning to spend a few days on the Handbook by Flanagan and move on. I already caught a big mistake in the book already, it is so obvious that I don't need to post it here.

What's the matter with the materials on Transformers?!!! I've never seen any text books with so many mistakes like in this subject.

[Alan0354]

Hey, it is just an old handbook... Please take a look at the following equivalent circuit (also from Veen's article that I posted on the transformer thread), I think this shows what RDH4 was trying to convey, un-successfully in this case. The takeaway for me, is that the plate resistance (push-pull is used in the example below) + winding losses (omitted in the example below) are in series with the voltage source and Zpri, which has two components - Raa and Lp. This is where most people would stop, but since you are delving into the inner working of the transformer, you do need to go down to the material level, where more fun awaits...

[ATTACH=CONFIG]20185[/ATTACH]



Jaz

Yes, this make sense, you have 2rp( push pull) in series with the Lp parallel with the referred resistance from the secondary raa. The voltage source and the 2rp on the left side is the Thevenin of the current source in parallel with the plate resistance in the original circuit.