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Understanding Beta

beta24

Understanding Beta

Postby BesPav » January 6th, 2017, 11:59 pm

Hi, Ti!
Hi, all!

Please let me briefly introduce to this story.
First of all - sorry for my ugly English. It's non-native to me, but i will try to use correct verb time forms and do not pull down the indefinite articles.
Second - i want the reading to be interesting, so the whole story will not be showed fully at one time and it will be fulfilled with many short episodes woven together around Beta.
Third - i will try the story not to be boring, so excuse me to a bit of humor. Because i doesn't want to show the [del]boobs[/del] build and leave, the story will be written straight under your eyes and the overall path must be passed.

Prologue.
Being an active participant of many audio-gear forums i am continuosly interested in corner ideas and conceptions.
This is just hobby and amusement in the background of real life, of my family - wife and two little doughters, of my work - radioastronomy, of other interests and my friends.

Let the story begin.

Amplifier.
Just realizes simple mathematical function of multiplying to a constant? Wire with gain?
:)

There are two basic conceptions: non-feedback and feedback.
Around second there are three corner ideas: low-feedback without compensation, medium-feedback with more or less complicated compensation and deep-feedback with carefully tuned comprehensive correction.
There are a huge amount of mathematics written about in the articles and monographyes by:
Harry Niquist
Image
Hendrik Wade Bode
Image
John Milton Miller:
Image
Boris Lurie
Image

I have learned most of this being student and i must say that academical representation of material are really boring.
Just one episode:
"From written formula we can see..."
Usually we can see nothing.
:)

Please let me recommend this more understandable book:
Image
Cover image show a result of improperly designed control system, that's irony by author.
https://www.amazon.com/Modern-Control-S ... 0136024580
Or
http://sv.20file.org/up1/951_0.pdf

Now Pros and Cons.

Non-feedback:
+ simple
+ stable
- distortionable (often carefully tuned for good sounding distortion)
- can be really complicated

Low-feedback ~20 dB
+ simple
+ easy to design
- distortionable (as measured, but this can have no common with distorted sounding)

Medium-feedback ~40-60 dB
+ still simple
+ still easy to design
+ already hard to measure
- feedbacky sound reproduction (as criticists say)

Deep-feedback ~80-100 and more dB
+ unable to measure
- hard to design


Where are Beta?
In this classification it is medium-feedback amplifier.


Next.
[del]To be, or not to be?[/del]
Inverting or noninverting.

Beta24 is a fully-differential amplifier, so it can be easily to understand as two inverting amps coupled together.
Image
Image

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Re: Understanding Beta

Postby BesPav » January 7th, 2017, 10:16 pm

Let's go deeper inside Beta.

Being more or less classical amplifier Beta can be redrawn at this manner:
Image

I will take some images from the other authors, but this is everyday laziness, not stealing. For this image i must say thanks to Bruno Putzeys, hypex.nl and diyclassd.com.

So there are input stage (IPS), voltage amplification stage (VAS) and output stage (OPS).

Input signal are get to the input stage. Let's take our eyes here.

I will try not to show most sensitive points, but Ti, please, take care to check further images.

Beta's input stage must be named as dynamically cascoded complementary self-biased four-quadrant differential stage with medium degeneration.
Image

I can draw idle and signal currents, voltages and so on, but this mostly was be done and showed by Pavel Macura here:
http://pmacura.cz/diyaudio/jfetdist.htm

I have uploaded this page as pdf here:
https://www.dropbox.com/s/hezymo6n2j6ho ... s.pdf?dl=0

Ti, please, can you edit my post and attach this file from your datastore?

This stage have one pair of inputs and two pair of outputs.
Beta22 and Beta24 uses this input stage mostly equally, but this is only at first sight.

Are there some difference?
Image

Yes, Beta22 is a non-inverting amp and connected as left image, Beta24 is inverting amp and connected as right image. Being more clearly - Beta22 is a classical non-inverting ground-referred amplifier, while Beta24 is a fully-differential difference amplifier. This is mean that Beta24 are internally referenced by itself.

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Re: Understanding Beta

Postby BesPav » January 8th, 2017, 9:27 pm

What is reference? Why IPS so matter?

Let's see what it do, and how it do this.

For your understanding i have painted idle and signal currents on this image:
Image

Idle are in yellow and magenta.
Signal are in red and blue.
You can imagine them all as some kind of X-over. This is not exactly as it works, but very easy to understand.

Now, what is matter, the reference.
IPS are needed to move (realign, reroute, rebind, relink) signal from one reference to another, let's see:
Image

Input are in green colour.
Output are in red colour (only upper shown).

One can say, that the output signal are taken from different points, like this:
Image

But this is no matter.
At the input one of the points is the INPUT reference.
At the OUTPUT the reference are supply rails, or other point.
This is exactly why good low-noisy low-impedance supply rails are must need to the amplifier with this topology.

IPS have second, no less important, function - rescale input signal to the best sensitivity range of the next stage.

The third task of the IPS - is to be as immune as possible to:
1. Overloading.
2. Common mode noise/error.

First achieved by JFETs source resistances, as shown at the picture in red circles:
Image

Second achieved by untouching IPS centerpoint from ground. You can imagine this stage as shown:
Image
If we replace VR1 by two resistors (each with half of actual VR1) than on first sight we can tie centerpoint to ground. But doing this we will throw away simplicity of adjusting idle current and some of the common mode immunity.


So, choosed IPS are best to fully-differential amps. Hard-to-find JFETs are now sourced from Micross/Linear, the story to be continued.

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Re: Understanding Beta

Postby cobretti » January 10th, 2017, 1:42 pm

Interesting reading. I want to ask, how is the output stage damping factor calculated. And where did this number 0.0035Ω @1KHz (copied from website) come from. IRFP140N transistors have RDSon 52mOhm (I know it is for Id=16A) plus there are R45,R46,R47,R48 resistors in the path. Amplifier output impedance should be greater than that.?
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Re: Understanding Beta

Postby amb » January 10th, 2017, 4:59 pm

cobretti wrote:Interesting reading. I want to ask, how is the output stage damping factor calculated. And where did this number 0.0035Ω @1KHz (copied from website) come from. IRFP140N transistors have RDSon 52mOhm (I know it is for Id=16A) plus there are R45,R46,R47,R48 resistors in the path. Amplifier output impedance should be greater than that.?

No. The MOSFETs' internal on resistance isn't necessarily the output impedance. With overall negative feedback, the output Z can be (much) lower than that.
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Re: Understanding Beta

Postby BesPav » January 10th, 2017, 10:06 pm

What's further?

IPS have rebinded our sugnal, we are taking it to the next stage - VAS.
On the next image the inputs are topmarked by red circles, real outputs are marked with red circles.
Image

What is marked with blue circles and where is the reference?

Let's begin from the latter - reference, this is simpler.
Just see the image:
Image
VAS reference are marked by yellow circles.

Who, how and for what have rebinded our signal again?

Left part of the symmetrical VAS, all inside orange circle:
Image

You can see, resistor loads (marked by magenta colour) in left and right halfs are different.
The left half works as helper for right part by decoupling it from supply rails. Having idle and signal current it can create Vdropout on the R14 and R15.
It virtually "knows" input signal and "knows" ground potential in the resistor network, as marked by magenta colour.
So it helps rebind our signal again.

Both halves do the more sophisticated thing - VAS output signal are rebinded again!

Where now, one can ask???

Here:
Image

Input signal are now referenced to the amplifier ground!

Beta22, being a non-inverting amplifier, are very immune to the common mode noise.

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Re: Understanding Beta

Postby cobretti » January 11th, 2017, 6:33 pm

amb wrote:
cobretti wrote:Interesting reading. I want to ask, how is the output stage damping factor calculated. And where did this number 0.0035Ω @1KHz (copied from website) come from. IRFP140N transistors have RDSon 52mOhm (I know it is for Id=16A) plus there are R45,R46,R47,R48 resistors in the path. Amplifier output impedance should be greater than that.?

No. The MOSFETs' internal on resistance isn't necessarily the output impedance. With overall negative feedback, the output Z can be (much) lower than that.

OK. Thank you. So, is it the number I mentioned above 0.0035Ohm just simulation figure? Or a real measurement number?
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Re: Understanding Beta

Postby amb » January 11th, 2017, 7:13 pm

It's simulation figure, but verified with the resistor load method. Keep in mind that's super low impedance, less than most wires...
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Re: Understanding Beta

Postby BesPav » January 12th, 2017, 12:36 am

cobretti wrote:So, is it the number I mentioned above 0.0035Ohm just simulation figure? Or a real measurement number?


This order of output impedance says only that effective output impedance of the amp calculated/measured at the speaker terminals (or speaker moving coil connectors) would be mostly determined by connecting wires.
:)

Further lowering needs another approach, that is called "wire resistance compensation". This allows to create a schematic with even negative output resistance, or tune output resistace by the one's choice.
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Re: Understanding Beta

Postby BesPav » January 12th, 2017, 4:10 am

Backing to understanding.

At last step we get our signal effectively referenced to the ground.
Now we just need to bufferize it.

What bufferize is?

This is only providing all needed current to the load with keeping output voltage as close to the input.

First approach to the very effective buffering was offered by the Bart Locanti in the last 1960's. Here are the original article:
http://leachlegacy.ece.gatech.edu/papers/tcir/tcir.pdf
Or some words about here:
http://leachlegacy.ece.gatech.edu/lowtim/output.html
Also very good related reading can be founded here:
http://hifisonix.com/ovation-e-amp/

Modern transistors have the very higher hFE (beta) than in 1970's, so effective current gain can be like 10.000.000 (multiply beta's of BC550*2SC4793*2SC5200)

The more current gain have the OPS - the lower loading of the VAS - the lower distortion.

There are unspoken rule - all gain stages must work at stable current or stable voltage.

So there are some OPS design goals:
1. Relatively high input resistance
2. Relatively low input capacitance
3. Relatively high current gain
4. Relatively easy achieved thermocompensation
5. Relatively high corner frequency (widebandness)
6. As high as possible Safe operating area (SOA)

Now we have great idea of cascode, some words from Papa Pass here:
https://passlabs.com/press/cascode-amp-design

Let's return to the Beta24's OPS.
It's very sophisticated.
It is not statically cascoded, but dynamically and capable of near rail-to-rail OPS supply output.
Image

Widebandness are achieved by effective neutralising of input capacitance. Yes, IRFP140 have huge ~2000 pF, but upper and lower transistors provide stable voltage to the centered ones. So, there are no voltage change - no capacitor charging/discharging - virtually no capacitance. In terms of hightening of widebandness we are limited mostly by Zeners dissipation and parasitic inductance of the gate traces.

Ultrasonic pole frequency can be easily tuned by gate resistances as gate-stoppers.

Current gain are very high (not to say infinite) and limited mostly by wire resistances and SOA of the rugged MOSFETs.

Thermocompensation was discussed here:
simulating-beta24-t3213-10.html#p32670
Having ~10-15 mV/degree sensitivity and 15-20 A/V transconductance with idle current ~200 mA or 1,4 A the Beta24's OPS are thermally stable.

Bias circuitry are loaded on relatively high 1 uF capacitor, have a corner frequency at about of ones of Hertz and can't oscillate in any conditions.

SOA are very good based on series connection of the transistors and dividing actual OPS supply rails voltage between them. Even with realistic 45-50-55 degree of current phase lag this OPS can dissipate large amount of heat and provide amperes and tens of load current in short bursts.

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