Hi Steve,

Steve Evans said:

There\s obviously something still amiss with my understanding, then. I

have a friend whos a radio ham and he says that to eliminate

capacitive reactance, you "add a bit of inductance until it's

cancelled out." Is this the same as cancelling out the phase-shift?

Yes, that's what he's saying.

Here's a little bit of 'Phasors 101' without any proof whatsoever (you'll

find it in any circuits text):

-- The impedance (Z) of a resistor is R

-- The impedance (Z) of an inductor is j*2*pi*F*L, where j is sqrt(-1), F is

the frequency you're worrying about, and L is the inductance.

-- The impedance of a capacitor (Z) is -j/(2*pi*F*C), same symbols as

before.

-- Ohms law is now V=I*Z, and all of V, I, and Z are typically complex.

-- Complex numbers are often expressed as a magnitude and phase. E.g.,

1.414+j1.414 is the same as '2 angle 45 degrees'

Now, notice that for an inductor or capacitor, V/I is some purely imaginary

number, that is, something with an angle of +/-90 degrees. This confirms

what you know that the voltage and current in a capacitor or inductor leads

or lags either other by 90 degrees.

If I do something like put a resistor and capacitor in series and power it

up from a 1V source, the current through _both_ will be

I=V/Z=1/(R-j/(2*pi*F*C)) -- notice that it'll now be some arbitrary complex

value. But the voltage across the resistor is just V=I*Z=I*R, so it'll just

be that same complex value multiplied by a scalar, implying that voltage and

current are still in phase. For the capacitor, V=I*Z=I*-j/(2*pi*F*C). Now,

whenever you multiple a complex number by +/-j[something], the result is a

complex number with a magnitude [something]*[magnitude of what your started

with] and angle [+/-90 degrees]+[angle of what you started with]. I.e.,

current and voltage across the inductor are still 90 degrees out of phase.

If

so, it suggests it is possible to have varying degrees of shift due to

varying degrees of inductance. If that weren't the case, you could

simply use *any* coil; its value wouldn't matter because whatever it

was, it would only change the phase by 90'.

What you're missing here is that while the phase across the an inductor and

capacitor is always +/- 90 degrees, you can only 'null out' the two when the

MAGNITUDE of the signal across them is equal as well. That is, if we're

dealing with voltage, (5 angle +90) + (5 angle -90) is, indeed, zero, but (3

angle +90) + (5 angle -90) is (2 angle -90), i.e., you still have something

that looks like a capacitor or inductor. (This means that if you start

with, say, a capacitor -- Z=-j*something Ohms -- and add an inductor --

Z=j*something_else Ohms -- as the inductor gets bigger and bigger, you'll

reach a point where the two are a short circuit. This is resonance. If you

keep adding inductance, the network then starts looking inductive.)

You can _not_ just 'add phases' across a bunch of components in series and

get the overall phase change through the network. You can (and _must_) add

_impedances_ .

So are you saying if I have 3 caps and 3 coils in series the overall

phase shift will be zero because they all cancel eachother out?

If the _impedance_ of all the caps and coils in series adds to zero, yes,

they will all cancel each other out. This will only happen when the sum of

the voltage magnitudes across the capacitors is equal to the sum of the

voltage magnitudes across the inductors.

What

if they're all different values?

Then the voltage magnitudes across the inductors won't sum to the same thing

as that across the capacitors, and you'll end up with something like that

likes a single inductor or capacitor (at one frequency).

From what you say if you get 90

degrees of shift (fixed) per element, that must be true, regardless of

the different values of those elements:

Again, only if you arrange things such that the magnitudes of the voltage

across each one is the same as well.

ac

source------0.1nF------1uH------22nF------4uH-------33pF-------180nH---->

In your network here, let's assume the frequency is 1/6.28 to keep things

simple. Hence, Z(res)=R, Z(ind)=j*L, and Z(cap)=-j/C. So, in your network,

the series impedance is -j/0.1e-9 + j*1e-6 -j/22e-9 + j*4e-6 - j/33e-12 +

j*180e-9 -- Obviously this won't sum to zero! If you pick the right

frequency, though, it will. (Bonus question: What is this frequency?)

Regardless of the frequency of the source and the values of these

components, the overall phase shift is zero. Is that what you're

saying?

At a certain frequency the phase shift is zero. Otherwise, no.

You know, if you really want to get into this, just sign up for your local

college's first engineering first 'circuits' (or 'networks') class. I took

mine the summer of 1995, and it was really a blast.

---Joel