AoE x-Chapters, 4x.26, MOSFET current source, nodal analysis

On Wednesday, 14 August 2019 13:00:54 UTC+1, Chris Jones  wrote:

> I would say that that a wire on a schematic is not a valid 
> representation of a transmission line, and if necessary I would 
> approximate a transmission line as a ladder of (ideally infinitely) many 
> series inductors and shunt capacitors. Of course very many components 
> are required for this to be reasonably accurate.
> 
> At frequencies where the number of required components is excessive, I 
> would then say that a schematic is not a good way to describe the 
> physical system.

draw the schematic more realistically, with the line as a long inductor with C all along it


> I guess I might have a rather unusual idea of what a schematic is, and 
> this might be what causes me to take issue with what you said. To me, a 
> schematic ought to be something that, when simulated (by some ideal 
> simulator!), applying Kirchoff's laws, Ohm's law, i=C.dv/dt and so on, 
> would sufficiently accurately predict the behavoiur of the real system.
> 
> To me, if the predictions are wrong, then I blame the schematic as being 
> an inaccurate representation of the system, rather than blaming the 
> equations used to simulate the behaviour of the schematic. Perhaps my 
> philosophy on this topic comes from having had the job of making a 
> schematic (sometimes pulling in netlists from field solvers) in order to 
> simulate my design as implemented in a physical product. There was an 
> expectation that I would use a circuit simulator provided to me, that 
> did try to apply Kirchoff's laws (though not perfectly in the case of 
> KCL). I did at least have the luxury that the physical dimensions of the 
> system were a tiny fraction of a wavelength.

Really it's the sim that's wrong, but you can tackle its shortcomings by adding in parts to the sim's input so it sims more feaures of the real circuit.


NT

On Wed, 14 Aug 2019 22:00:44 +1000, Chris Jones
<lugnut808@spam.yahoo.com> wrote:

>On 13/08/2019 00:02, Phil Hobbs wrote:
>> On 8/12/19 9:11 AM, Chris Jones wrote:
>>> On 10/08/2019 17:05, Phil Hobbs wrote:
>>>> On 8/9/19 4:50 PM, Winfield Hill wrote:
>>>>> Here's a new section I'm hoping to complete, so it can be added to
>>>>> the x-Chapter book before it goes to the printer in a few weeks.
>>>>> Please look it over, but don't be too harsh, about its lack of
>>>>> mathematical vigor.&#4294967295; It's closer to our usual back-of-the envelope
>>>>> approach to calculations. Fixes for errors, suggestions for
>>>>> clarification, improved accuracy, and comments welcome.
>>>>>
>>>>> https://www.dropbox.com/s/7zl3yi789idg3s8/4x.26_Loop%20%26%20Nodal%20Analysis.pdf?dl=1
>>>>>
>>>>>
>>>>
>>>> Nice.&#4294967295; I like your making a virtue out of a necessity (hand-drawn
>>>> figures). ;)
>>>>
>>>> One point that might be worth a footnote is that Kirchhoff's laws are a
>>>> low-frequency approximation, applicable only when radiation and
>>>> self-capacitance are negligible.
>>>
>>> If your schematic is really complete, then I think that the laws apply
>>> usefully, at least until the point where radiation is efficient. I am
>>> assuming here that current through parasitic capacitances is counted
>>> just as much as if it were a current flowing through a terminal of an
>>> intentional capacitor. If, in your schematic and arithmetic, you leave
>>> out things like the inductance and self-capacitance of wires, (and in
>>> difficult cases, even the distributed capacitance at different points
>>> along the inductance of wires), then of course the result of applying
>>> Kirchoff's laws to the (incomplete) schematic won't predict the
>>> behaviour of the actual construction. I suspect that radiation could
>>> also be modelled in a way that allows Kirchoff's laws to be applied but
>>> that the resulting schematic would be too complicated.
>> 
>> Nope.  Transmission lines at the schematic level are non-local, i.e. you
>> can't write a system of ODEs to describe a circuit with transmission
>> lines or significant radiation.  Kirchhoff's laws are derived from
>> Maxwell's equations in the limit of low frequency (or alternatively, of
>> small size for a fixed frequency).
>I would say that that a wire on a schematic is not a valid 
>representation of a transmission line, and if necessary I would 
>approximate a transmission line as a ladder of (ideally infinitely) many 
>series inductors and shunt capacitors. Of course very many components 
>are required for this to be reasonably accurate.

The number of LCs goes as the square of Td/Tr. Gets ugly quick. And
the step response rings.

LT Spice has two transmission line models that seem to work well. I
use them all the time.

"Phil Hobbs"  wrote in message 
news:eae0dac9-c6fe-5300-719c-63f69bfc347f@electrooptical.net...


> Hmm Phil, to put this in my own words... and please correct me if I'm 
> wrong..
> or I'm only part right.  I think a limitation of K's laws is that they
> treat V and I as instantaneously the same everywhere.
>
> George H.
> (every theory is an approximation at some level)

>Everywhere on a given circuit node or loop, right.  Anything with
>transmission-line behaviour can't be modelled as an ODE--the fields

Not really.... An ODE (Ordinary Differential Equation) is pretty much any 
differential equation of one variable, in contrast to a Partial Differential 
Equation. Once the length of a line is fixed its usual partial differential 
equations become ODE.

What you probably mean is that an ideal transmission line is a pure delay. 
This means an exp(-tau.S) transfer function, which is not a rational 
function of S.

Spice has to do extra stuff, as in convolution, to handle TLines. It slows 
it down a tad...


>inside the T-line can be modelled with PDEs (Maxwell), but circuits are
>all ODEs.  The T-line has invisible internal state, so its circuit
>behaviour is nonlocal.

Not really....

"Non local" pretty much universally means FTL (faster than the speed of 
light). A transmission line is most certainly local.

What you probably mean is that a transmission line requires spice to do some 
special stuff, as above.

-- Kevin Aylward
http://www.anasoft.co.uk - SuperSpice
http://www.kevinaylward.co.uk/ee/index.html

On Monday, August 12, 2019 at 12:25:12 PM UTC-7, Phil Hobbs wrote:

> transmission-line behaviour can't be modelled as an ODE--the fields
> inside the T-line can be modelled with PDEs (Maxwell), but circuits are
> all ODEs.  The T-line has invisible internal state, so its circuit
> behaviour is nonlocal.

If Spice converged much faster, the transmission line could be a few
hundred series inductors and a few hundred parallel capacitors...
the practical hardware  (a spool of good coax cable) is just 'way cheaper
to operate than an accurate model is.

On 8/14/19 4:42 PM, Kevin Aylward wrote:
> "Phil Hobbs"  wrote in message 
> news:eae0dac9-c6fe-5300-719c-63f69bfc347f@electrooptical.net...
> 
> 
>> Hmm Phil, to put this in my own words... and please correct me if I'm 
>> wrong..
>> or I'm only part right.  I think a limitation of K's laws is that they
>> treat V and I as instantaneously the same everywhere.
>>
>> George H.
>> (every theory is an approximation at some level)
> 
>> Everywhere on a given circuit node or loop, right.  Anything with
>> transmission-line behaviour can't be modelled as an ODE--the fields
> 
> Not really.... An ODE (Ordinary Differential Equation) is pretty much 
> any differential equation of one variable, in contrast to a Partial 
> Differential Equation. Once the length of a line is fixed its usual 
> partial differential equations become ODE.

Nope. ODEs don't have memory, T-lines do.  (At least from a circuits POV.)

> 
> What you probably mean is that an ideal transmission line is a pure 
> delay. This means an exp(-tau.S) transfer function, which is not a 
> rational function of S.

Kirchoff's laws do not apply to transmission lines.  Current disappears 
into one end and emerges from the other end sometime later.  The 
currents into the circuit nodes don't sum to zero, and neither do the 
voltages around loops.

> Spice has to do extra stuff, as in convolution, to handle TLines. It 
> slows it down a tad...

As I said, the approximation can often be patched up by hand like that.
> 
> 
>> inside the T-line can be modelled with PDEs (Maxwell), but circuits are
>> all ODEs.  The T-line has invisible internal state, so its circuit
>> behaviour is nonlocal.
> 
> Not really....
> 
> "Non local" pretty much universally means FTL (faster than the speed of 
> light).

Nope.  It means that the governing equations require information from 
more than one space-time point.  All differential equations are local. 
Nonlocal systems need integral equations.

  A transmission line is most certainly local.

Nope, not from a circuits point of view.  To find out what's going to 
come out at time t, you have to know the what went in at time t-tau.

> What you probably mean is that a transmission line requires spice to do 
> some special stuff, as above.

Nope.  I wasn't talking about SPICE at all.

Cheers

Phil Hobbs

-- 
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC / Hobbs ElectroOptics
Optics, Electro-optics, Photonics, Analog Electronics
Briarcliff Manor NY 10510

http://electrooptical.net
http://hobbs-eo.com

On Thu, 15 Aug 2019 11:17:35 -0400, Phil Hobbs
<pcdhSpamMeSenseless@electrooptical.net> wrote:

>On 8/14/19 4:42 PM, Kevin Aylward wrote:
>> "Phil Hobbs"&#4294967295; wrote in message 
>> news:eae0dac9-c6fe-5300-719c-63f69bfc347f@electrooptical.net...
>> 
>> 
>>> Hmm Phil, to put this in my own words... and please correct me if I'm 
>>> wrong..
>>> or I'm only part right.&#4294967295; I think a limitation of K's laws is that they
>>> treat V and I as instantaneously the same everywhere.
>>>
>>> George H.
>>> (every theory is an approximation at some level)
>> 
>>> Everywhere on a given circuit node or loop, right.&#4294967295; Anything with
>>> transmission-line behaviour can't be modelled as an ODE--the fields
>> 
>> Not really.... An ODE (Ordinary Differential Equation) is pretty much 
>> any differential equation of one variable, in contrast to a Partial 
>> Differential Equation. Once the length of a line is fixed its usual 
>> partial differential equations become ODE.
>
>Nope. ODEs don't have memory, T-lines do.  (At least from a circuits POV.)
>
>> 
>> What you probably mean is that an ideal transmission line is a pure 
>> delay. This means an exp(-tau.S) transfer function, which is not a 
>> rational function of S.
>
>Kirchoff's laws do not apply to transmission lines.  Current disappears 
>into one end and emerges from the other end sometime later.  The 
>currents into the circuit nodes don't sum to zero, and neither do the 
>voltages around loops.

The LT Spice tline part acts as if it has an ideal DC-true 1:1
transformer inside. The ends can be at radically different common-mode
voltages and it works fine.

That avoids dealing with the em effects of the "shield". Modeling a
twisted pair takes three tlines.

>
>> Spice has to do extra stuff, as in convolution, to handle TLines. It 
>> slows it down a tad...

I've wondered how the tline is implemented inside, and how it relates
to the current time step size.

On 8/14/19 8:00 AM, Chris Jones wrote:
> On 13/08/2019 00:02, Phil Hobbs wrote:
>> On 8/12/19 9:11 AM, Chris Jones wrote:
>>> On 10/08/2019 17:05, Phil Hobbs wrote:
>>>> On 8/9/19 4:50 PM, Winfield Hill wrote:
>>>>> Here's a new section I'm hoping to complete, so it can be
>>>>> added to the x-Chapter book before it goes to the printer in
>>>>> a few weeks. Please look it over, but don't be too harsh,
>>>>> about its lack of mathematical vigor.  It's closer to our
>>>>> usual back-of-the envelope approach to calculations. Fixes
>>>>> for errors, suggestions for clarification, improved accuracy,
>>>>> and comments welcome.
>>>>> 
>>>>> https://www.dropbox.com/s/7zl3yi789idg3s8/4x.26_Loop%20%26%20Nodal%20Analysis.pdf?dl=1
>>>>> 
>>>>> 
>>>>> 
>>>>> 
>>>> 
>>>> Nice.  I like your making a virtue out of a necessity
>>>> (hand-drawn figures). ;)
>>>> 
>>>> One point that might be worth a footnote is that Kirchhoff's
>>>> laws are a low-frequency approximation, applicable only when
>>>> radiation and self-capacitance are negligible.
>>> 
>>> If your schematic is really complete, then I think that the laws
>>> apply usefully, at least until the point where radiation is
>>> efficient. I am assuming here that current through parasitic
>>> capacitances is counted just as much as if it were a current
>>> flowing through a terminal of an intentional capacitor. If, in
>>> your schematic and arithmetic, you leave out things like the
>>> inductance and self-capacitance of wires, (and in difficult
>>> cases, even the distributed capacitance at different points along
>>> the inductance of wires), then of course the result of applying 
>>> Kirchoff's laws to the (incomplete) schematic won't predict the 
>>> behaviour of the actual construction. I suspect that radiation
>>> could also be modelled in a way that allows Kirchoff's laws to be
>>> applied but that the resulting schematic would be too
>>> complicated.
>> 
>> Nope.  Transmission lines at the schematic level are non-local,
>> i.e. you can't write a system of ODEs to describe a circuit with
>> transmission lines or significant radiation.  Kirchhoff's laws are
>> derived from Maxwell's equations in the limit of low frequency (or
>> alternatively, of small size for a fixed frequency).
> I would say that that a wire on a schematic is not a valid 
> representation of a transmission line, and if necessary I would 
> approximate a transmission line as a ladder of (ideally infinitely)
> many series inductors and shunt capacitors. Of course very many
> components are required for this to be reasonably accurate.
> 
> At frequencies where the number of required components is excessive,
> I would then say that a schematic is not a good way to describe the 
> physical system.
>> And if you have to model the circuit "in a way that allows
>> Kirchhoff's laws to be applied", you've implicitly admitted that
>> they don't apply to the actual circuit.
> If by actual circuit we mean the physical object, then really I only
>  expect Maxwell's equations to describe it, and I'm not very good at
>  solving those. In a completely general sense I'm not even sure how
> one would try to apply Kirchoff's laws to an arbitrary three
> dimensional piece of electronics.


> 
>> Don't get me wrong--K's equations are useful and all, but they
>> have limits.  Being a physicist, I fully recognize the usefulness
>> of sleazy approximations, but you have to remember that that's what
>> they are, or you'll get snookered.
> Agreed.
> 
> I guess I might have a rather unusual idea of what a schematic is,
> and this might be what causes me to take issue with what you said. To
> me, a schematic ought to be something that, when simulated (by some
> ideal simulator!), applying Kirchoff's laws, Ohm's law, i=C.dv/dt and
> so on, would sufficiently accurately predict the behavoiur of the
> real system.
> 
> To me, if the predictions are wrong, then I blame the schematic as
> being an inaccurate representation of the system, rather than blaming
> the equations used to simulate the behaviour of the schematic.
> Perhaps my philosophy on this topic comes from having had the job of
> making a schematic (sometimes pulling in netlists from field solvers)
> in order to simulate my design as implemented in a physical product.
> There was an expectation that I would use a circuit simulator
> provided to me, that did try to apply Kirchoff's laws (though not
> perfectly in the case of KCL). I did at least have the luxury that
> the physical dimensions of the system were a tiny fraction of a
> wavelength.

Well, you're kind of using a private language there, as you say.


Cheers

Phil Hobbs


-- 
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC / Hobbs ElectroOptics
Optics, Electro-optics, Photonics, Analog Electronics
Briarcliff Manor NY 10510

http://electrooptical.net
http://hobbs-eo.com

tabbypurr@gmail.com wrote...
>
> Really it's the sim that's wrong, but you can tackle
> its shortcomings by adding in parts to the sim's input
> so it sims more features of the real circuit.

 LTSpice lets you add parasitic aspects to basic parts,
 like resistors, but these are hidden on the schematic,
 so you have no idea whether the modeller made additions,
 or whether he made the right ones.  I prefer seeing a
 SPICE schematic, with the parasitic parts explicitly
 showing, so you know what was taken care of, and how.
 To my mind, these aspects are up to the engineering
 doing the SPICE schematic drafting, and not up to the
 SPICE program.  The LTSpice approach is bad, not good.
 So I disagree, it's not the sim that's wrong.


-- 
 Thanks,
    - Win

Winfield Hill <winfieldhill@yahoo.com> wrote:

> tabbypurr@gmail.com wrote...

>> Really it's the sim that's wrong, but you can tackle
>> its shortcomings by adding in parts to the sim's input so it sims more
>> features of the real circuit. 
 
>  LTSpice lets you add parasitic aspects to basic parts,
>  like resistors, but these are hidden on the schematic,
>  so you have no idea whether the modeller made additions,
>  or whether he made the right ones.  I prefer seeing a
>  SPICE schematic, with the parasitic parts explicitly
>  showing, so you know what was taken care of, and how.
>  To my mind, these aspects are up to the engineering
>  doing the SPICE schematic drafting, and not up to the
>  SPICE program.  The LTSpice approach is bad, not good.
>  So I disagree, it's not the sim that's wrong.
 
Where it is important, I add the parasitics externally.
 

"Phil Hobbs" <pcdhSpamMeSenseless@electrooptical.net> wrote in message 
news:qj3t2i$941$1@dont-email.me...
>
> Nope. ODEs don't have memory, T-lines do.  (At least from a circuits POV.)
>

Great.  Now I have to go buy 20GB of SRAM!


> Kirchoff's laws do not apply to transmission lines.  Current disappears 
> into one end and emerges from the other end sometime later.  The currents 
> into the circuit nodes don't sum to zero, and neither do the voltages 
> around loops.

So ports.....don't exist?

Tim

-- 
Seven Transistor Labs, LLC
Electrical Engineering Consultation and Design
Website: https://www.seventransistorlabs.com/