Calculating total impedence....

[Jim Thompson]

I read in sci.electronics.design that Fred Bloggs <[email protected]>


It's how I do it in practice. YMMV.

Same here. No j•omega until the end... much easier to be error-free.

...Jim Thompson

 

[Jim Thompson]

There was a really neat monograph in, I believe, Electro Technology (long
since out of publication) circa 1963 about performing impedance calculations
graphically using a straight edge, compass and protractor. It was brown and
brittle the last time I saw it and I can't seem to find it now (so what's
new) but one could solve reasonably complex problems rather simply and
without advanced math. Solutions even approached slide rule (what the hell
is that?) accuracy.

Actually I believe it was Heaviside who came up with the notational
trickiness using "S".

...Jim Thompson

 

[Paul Burridge]

The impedance of the 25pF capacitor at 10MHz is 636 ohms (times -i).
This means that the parallel resistance of 50K is almost negligible.

The impedance of the 10 uH inductor at 10 MHz is 628 ohms (times i).

You are very near resonance at 10 MHz... as a result the combination of
the L and the C gives a near-zero impedance. The 33 ohm resistor then
dominates. So effectively at resonance (which is I assume why you're
asking about 10MHz) the stuff to the right of "A" is almost exactly like
a 33 ohm resistor to ground.

Does this help any?

Yes it does, Tim, thanks. It's yet another way of looking at the
problem and I find it's invaluable to have as many different
perspectives as possible when trying to get to grips with something
like this. Some explanations on this thread have been rather
impenatrable, I'm afraid, but yours is not one of them! Thanks again.

 

[Paul Burridge]

Because the j way is messy on paper. Work out all the stuff with sL,
1/sc and R, then plug in the s=jw at the end.

Well I've had a peek at your link and one of my reference books and it
appears this Laplace stuff involves calculus. Algebra's one thing, but
I never got around to studying Leibnitz's little contribution to
science and don't plan to start now. So I guess I'm stuck with the
messy way!

 

[Paul Burridge]

Your circuit includes a capacitor and an inductor. To calculate the
impedance oof the whole circuit you have to recognise the fact that
the impedance of a circuit including reactive elements has to be
represented by a complex number

a+ib

where "i" is the square root of minus one.

The impedance of a capacitor at a particular frequency f Z(c)= -i/wC

where w is the frequency in radians per second, which is two pi times
the frequency in Hz, and c is the capacitance in farads.

The impedance of an inductor is similarly Z(L)= iwL

Complex impedances, so defined, can be added in series and in
parallel, just like simple real resistances.

"s" is just electrical engineers shorthand for iw or 2.i.pi.f.

Hope this helps. But I guess that what you really needed was a good
night's sleep.

Indeed, Bill and looking at some of today's follow-ups I'm beginning
to regret waking up this morning. :-/
I'd like to thank everyone for their contributions, nevertheless.
They'll all be scrutinised and I'm optimistic I'll be able to gleen
all the info I need from them in due course....

 

[Jim Thompson]

Well I've had a peek at your link and one of my reference books and it
appears this Laplace stuff involves calculus. Algebra's one thing, but
I never got around to studying Leibnitz's little contribution to
science and don't plan to start now. So I guess I'm stuck with the
messy way!

The Heaviside (S) approach never gets "heavier" (pun intended than
factoring Algebra.

Of course I've only been using it for 44 years ;-)

...Jim Thompson

 

[Baphomet]

"S" is the circuit expresd via Laplace transforms.

http://www.anasoft.co.uk/EE/laplace/laplace.html

There was a really neat monograph in, I believe, Electro Technology (long
since out of publication) circa 1963 about performing impedance calculations
graphically using a straight edge, compass and protractor. It was brown and
brittle the last time I saw it and I can't seem to find it now (so what's
new) but one could solve reasonably complex problems rather simply and
without advanced math. Solutions even approached slide rule (what the hell
is that?) accuracy.

 

[Paul Burridge]

I think Newton made a "minor" contribution also ;-)

Yes. *Minor* being the operative word. In between odd bouts of
character assassination, plagarism and vote-rigging with the RS., to
mention some of his better qualities. Let's not waste valuable
bandwidth discussing that over-rated PoS, please!

 

[Baphomet]

The impedance of the 25pF capacitor at 10MHz is 636 ohms (times -i).
This means that the parallel resistance of 50K is almost negligible.

The impedance of the 10 uH inductor at 10 MHz is 628 ohms (times i).

You are very near resonance at 10 MHz... as a result the combination of
the L and the C gives a near-zero impedance. The 33 ohm resistor then
dominates. So effectively at resonance (which is I assume why you're
asking about 10MHz) the stuff to the right of "A" is almost exactly like
a 33 ohm resistor to ground.

Does this help any?

Tim.

We just can't have that Tim...it's too simple:

(from page 50 - TI Programmable 58/59 Electrical Engineering module)

Rs = Resistance series
Rp = Resistance parallel
Xs = Reactance series
Xp = Reactance parallel

Rs = ((( 1 / Rp ) + ( Rp / ( Xp ) ^ 2 )) ^ -1 )

Xs = (( Rs * Rp ) / Xp )

Add up the R's

Subtract the X's

Add the R and the X and voila!

Now isn't that better? :-(

 

[Baphomet]

Actually I believe it was Heaviside who came up with the notational
trickiness using "S".

He was quite an operator ;-)

 

[Michael]

Hi,

It's midnight here and I'm suffering from brain failure.
Can anyone come to my rescue and show me how to work out the impudence
of this circuit fragment? (I know, but everyone's brain's entitled to
not function once in a while and I'm getting my -js and +js all mixed
up). :-(

Sine wave input to left of 50R resistor (representing Rgen) at
frequency of 10Mhz.
Need to know total impedence from point A through to ground. Thanks.

<knackered>



50R 33R 10uH
___ A ___ ___
Sig ---------|___|---------|___|----------UUU--+
input |
|
|
|
+---+-----+
| |
| .-.
--- | |
--- | |
25p | 50k'-'
| |
| |
| |
+----+----+
=+=
GND

created by Andy´s ASCII-Circuit v1.24.140803 Beta www.tech-chat.de

If you do a lot of calculating, you might want to consider buying a
calculator that handles complex numbers. I have a HP48G, I have
buttons programmed for XL, XC and parallel with a single button press.
It makes the imedance of a bunch of caps+inductors no more difficult
to calculate than a bunch of resistors.

 

[Baphomet]

Well I've had a peek at your link and one of my reference books and it
appears this Laplace stuff involves calculus. Algebra's one thing, but
I never got around to studying Leibnitz's little contribution to
science and don't plan to start now. So I guess I'm stuck with the
messy way!
--

From the "How quickly they forget" Department.............

I think Newton made a "minor" contribution also ;-)

"Windows [n.], A thirty-two bit extension and GUI shell to a sixteen bit patch
to an eight bit operating system originally coded for a four bit
microprocessor and produced by a two bit company."

 

[Paul Burridge]

If you do a lot of calculating, you might want to consider buying a
calculator that handles complex numbers. I have a HP48G, I have
buttons programmed for XL, XC and parallel with a single button press.
It makes the imedance of a bunch of caps+inductors no more difficult
to calculate than a bunch of resistors.

Great stuff! So the impedance of the network above at 10Mhz is.....?
(shouldn't take you more than 2 minutes, I would imagine.)

 

[Bill Sloman]

From the "How quickly they forget" Department.............

I think Newton made a "minor" contribution also ;-)

Newton invented it first, but Leibnitz published first, which is why
we use the notation invented by Leibnitz.

Had Newton published before Leibnitz, one might be able to talk about
his contribution (and it wouldn't have been minor), but as it was
Newton sat on the technique. Had he published it earlier, Hooke or
Wren (or perhaps both together - they were good friends and close
colleagues) would perhaps have been able to do do the maths required
to take the inverse square law (which they seem to have come up with
before Newton) and use it to explain Kepler's Laws of planetary motion
(derived from Tycho Brahe's observations). Had they done so, Newton
would now be much less famous.

Newton wasn't a Linux kind of person ...

 

[Tim Shoppa]

Yes it does, Tim, thanks. It's yet another way of looking at the
problem and I find it's invaluable to have as many different
perspectives as possible when trying to get to grips with something
like this. Some explanations on this thread have been rather
impenatrable, I'm afraid, but yours is not one of them! Thanks again.

I made a number of approximations and at least one big assumption (that you
didn't want to know the precise value of impedance at 10MHz, instead you
really wanted to know it at resonance, which 10 MHz is nearly at).

Others with different experience than mine will tell me it's a mistake
to assume that you meant "at resonance" when you clearly asked about 10MHz.
But *all the other numbers you gave us were only given to 2 significant
digits*...

Being able to plug numbers into the calculator and get a number out to
8 decimal places does have some value... but in my experience, getting
some understanding out (instead of 8 decimal places) has vastly more
value. Even though my answer probably wasn't even good to two decimal
places

Tim.

 

[John Woodgate]

I read in sci.electronics.design that Bill Sloman <[email protected]>

Newton wasn't a Linux kind of person ...

Well, it's lucky that he wasn't a Windows kind of person, otherwise
gravity would keep crashing. (;-)

 

[John Woodgate]

I read in sci.electronics.design that Tim Shoppa <shoppa@trailing-

Even though my answer probably wasn't even good to two decimal
places

Well, no. I was surprised that the 50 kohm reflects as 8 ohms in series.

 

[Baphomet]

Yes. *Minor* being the operative word. In between odd bouts of
character assassination, plagarism and vote-rigging with the RS., to
mention some of his better qualities. Let's not waste valuable
bandwidth discussing that over-rated PoS, please!

My my...how bitter we have become.

"Windows [n.], A thirty-two bit extension and GUI shell to a sixteen bit patch
to an eight bit operating system originally coded for a four bit
microprocessor and produced by a two bit company."

 

[Baphomet]

Newton invented it first, but Leibnitz published first, which is why
we use the notation invented by Leibnitz.

Had Newton published before Leibnitz, one might be able to talk about
his contribution (and it wouldn't have been minor), but as it was
Newton sat on the technique. Had he published it earlier, Hooke or
Wren (or perhaps both together - they were good friends and close
colleagues) would perhaps have been able to do do the maths required
to take the inverse square law (which they seem to have come up with
before Newton) and use it to explain Kepler's Laws of planetary motion
(derived from Tycho Brahe's observations). Had they done so, Newton
would now be much less famous.

Thanks for a more comprehensive explanation.

 

[Paul Hovnanian P.E.]

Your circuit includes a capacitor and an inductor. To calculate the
impedance oof the whole circuit you have to recognise the fact that
the impedance of a circuit including reactive elements has to be
represented by a complex number

a+ib

where "i" is the square root of minus one.

As does "j", if you don't want to confuse a bunch of electrical
enginers. ;-)

The impedance of a capacitor at a particular frequency f Z(c)= -i/wC

where w is the frequency in radians per second, which is two pi times
the frequency in Hz, and c is the capacitance in farads.

The impedance of an inductor is similarly Z(L)= iwL

Complex impedances, so defined, can be added in series and in
parallel, just like simple real resistances.

"s" is just electrical engineers shorthand for iw or 2.i.pi.f.

s = a + jw = a + 2*PI*j*f

This is particularly important if you are trying to solve for a
transient response rather than a steady state solution. If not, the jw
approach results in simpler algebra which may be important in the wee
hours of the morning.