# The phase-shift problem revisited...

Discussion in 'Electronic Basics' started by Steve Evans, Nov 18, 2004.

1. ### Steve EvansGuest

Hi there,

Tak a look at this series circuit if you will.
Theres an ac voltage source at the left hand end, which feeds a signal
into a capacitor, an inductor and a resistor in sequence before being
ruturned to ground.
Now, have i got this right: the AC source feed is in-phase before it
hits the capacitor. The cap causes a phase-shift that leaves the
voltage lagging the current by 90'. The signal then arrives at the
coil, where its reactive properties reverse the previous phase-shift
by 90' and the signal is back in phase again. It passes through the
resistor still in phase and is returned to ground. Is that right?
Thnx, Steve.

AC~------------>-------------CAP------------------------COIL--------------,

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RES

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GND

2. ### Robert MonsenGuest

How much math do you know? Do you feel comfortable with complex numbers?
That's the easiest way to analyze the waveforms.

The phase of the current through the string is equal to the voltage
divided by the impedance of the string. The impedance will have a 0 'j'
value if the reactance of the capacitor equals the reactance of the
inductor. This happens when

2*pi*f = 1/sqrt(LC)

This is the resonant frequency of the inductor capacitor pair. At this
frequency, there is no affect on the current at all by the
inductor+capacitor pair. It's like the two were not there.

When the frequency is lower than this, the capacitor wins (its inductive
reactance is bigger), and the phase of the circuit acts more like there
is only a capacitor. Thus, the phase of the current leads the phase of
the voltage. If the frequency is higher than this, the reactance of the
inductor is bigger, so the phase of the current lags the phase of the
voltage.

--
Regards,
Robert Monsen

"Your Highness, I have no need of this hypothesis."
- Pierre Laplace (1749-1827), to Napoleon,
on why his works on celestial mechanics make no mention of God.

3. ### John LarkinGuest

Only in the special case that the capacitive reactance is equal to the
inductive reactance, in which case the L and C are series resonant and
the pair acts like a short circuit, so the full supply voltage appears
across the resistor with no phase shift. That only happens at one
frequency...

Xl = 2 * pi * f * L = Xc = 1 / (2 * pi * f * C)

which happens at frequency f = 1 / ( 2 * pi * sqrt(L * C) )

At any other frequency, there will be some net phase shift of the
voltage across the resistor relative to the source. Vectors and stuff.

John

4. ### Anthony FremontGuest

<snip ascii-art>

It's like Robert said Steve, your statement is correct when the AC
signal matches the (series) resonant frequency of your circuit. Outside
of that there is an overall inductive or capacitive reactance that
results in things not coming back into phase perfectly. That's my
understanding of it anyway, I could be wrong.

5. ### Steve EvansGuest

Thanks all. So you're saying that apart from the special case when the
pair are in resonance together, there will be some residual phase-
shift left which will appear across the end resistor?
I mean, although pure resisotrs dont introdcue any phase shift by
themselves, they will retain phase shift if it arose further back up
the line?

6. ### Anthony FremontGuest

In an ideal world this would be true, however the reality of the
situation is that all components have "some amount" of inductance and
capacitance. The effect may be negligible at low frequencies, but
becomes significant as the frequency rises.

Look at this for a decent one-page description of impedance, resistance
and reactance:
http://whatis.techtarget.com/definition/0,,sid9_gci212333,00.html

7. ### CBarn24050Guest

Subject: Re: The phase-shift problem revisited...
For a series circuit it's best to use the current as the reference as the
current is the same throughout the cicuit. The voltage accros the resistor will
allways be in phase with the current, the volage accros the capacitor will lag
by 90deg for any non electrolitic cap and accross the inductor it will allways
lead but not quite by 90 since practical inductors have a series resistance.

8. ### Bob MyersGuest

Well, yes, but you're probably not doing yourself any
favors by thinking of it in that matter. Rather than
saying "retains the phase shift," it may be better just
to note that the relationship between the voltage
across any two points, and the current through them,
is related by the equation V=IZ, where ALL of these
are "complex" quantities - meaning that they have both a
"real" and "imaginary" component, or better, both a
magnitude and a phase. Exactly what the phase relationship
between I and V will be depends on how much of the Z
(impedance) is pure resistance, and how much is reactance
(i.e., the impedance present by a capacitance or an
inductance). To get a better "feel" for how this works, just
keep in mind that only the resistances are actually
dissipating any energy - reactances (the capacitances and
inductances) merely store energy during part of the
cycle, and return it to the circuit at another part of the
cycle.

Bob M.

9. ### Steve EvansGuest

This is at odds to what I believe others here are saying. Perhpas I
havent explained it clearly what I'm getting at. I'll restate the
question:
Say an AC signal leaves a reactive chain of components with a phase
difference between its voltage and its current. The signal is fed over
an arbitrary length of PCB tracking, then through a (non-inductive)
carbon resistor and down to ground.
Now, there is clearly a phase difference across the last reactive
component in the chain. What I need to know - is this phase difference
*still* present:

a) along the PCB track?
b) across the end resistor?

(ignoring paracitic effects and treating all parts as 'ideal')
What\s the difference with an electrolytic?? I've never heard of this
before.

10. ### Robert MonsenGuest

a) ignoring parasitic effects, no.
b) ignoring parasitic effects, no.

You are confusing the idea of phase shift across a component with phase
shift across the series string. The phase shift depends on which
component you measure voltage across.

There is NO phase shift 'across' a resistor, if by that you mean

1) Measure the voltage by putting a probe on either side of a resistor.
2) Measure the current going into the resistor somehow.
3) Compare the resulting waveforms.

If, however, you mean

1) Measure the voltage across the entire string of reactive components
2) Measure the current going into the resistor.
3) Compare the waveforms.

then there will be a phase shift. However, it's hardly fair to say that
the phase shift occurs "across the resistor" in this case. It occurs
across the entire string of components.
--
Regards,
Robert Monsen

"Your Highness, I have no need of this hypothesis."
- Pierre Laplace (1749-1827), to Napoleon,
on why his works on celestial mechanics make no mention of God.

11. ### john jardineGuest

Steve. Your queries are perfectly logical. I know cos I've been down the
same path and never got a straightforward answer.
Problem is that VI phasing is a circuit aspect that's quite awkward to
mentally grasp or visually model what's going on in the first place, even
less to describe it in words.

The resistor doesn't care about any phase difference that exists elsewhere.
The resistor will develop a voltage across itself in sympathy with the
current through it. I.e Its volts and amps are in phase, measured -at- the
resistor.
But ... to complicate things, adding that resistor changes all the other VI
phasing angles throughout the whole of the rest of the network

Electrolytics are not perfect and electrically look like a cap and (small)
resistor in series. Here though, it just confuses the issue.

Getting ones head round the VI phase displacements in even a very simple
reactive network is nigh on impossible. -Everything- depends on everything
else in the circuit. Mentally you have forget Ohms law and try to step
rotate your imagery, through parts of a circle as each component is looked
at in turn. Sinewaves are an appalling shape to mentally deal with.
With massive effort it is sometimes possible to get a grip.
Most humans drop out at this point and either give up the electronics
subject completely, start to draw phasor diagrams or turn to the maths such
as J notation, Laplace etc. Which although giving little understanding does
Add just a couple more reactive components and even the most hair shirted
mathematicians start to run for their Spice programmes.

regards
john

12. ### Steve EvansGuest

Thnx, John. An answer I can understand perrfectly for a change!
That was going to be my next question, actually. Ive found that if I
simulate the problem in Sp;ice, then I get varying degrees of phase
shift depending on the value of the load resistor! This apperas
contrary to al the text books which simply state you get a 90 degree
shift one way or the other depending on whether ist a coil or a cap
youre' studying. I"ve found that i get between 90 and 180' of shift
across a cap by varying the load resistance by between 5 ohms and 5k
so there's obviously somethig else very significant going on here that
the books have missed out on! Can anyone explain?
tnx, John. it's nice to know I"m not alone, anyway. I had decided if I
coudn't get my head around something as fundamental as phase shift and
reactance, i might as well call it a day because you *must* be
familiar with this stuff or esle forget the whole thing. But
"fundamental" and "simple" are not the same thing. This is a
fundamental problem, but not a simple one, obviously! :-(

13. ### Steve EvansGuest

Tnx, Robert. One queston that springs to mind from the above:
Let's say I have this series arrangement:

AC source-----------cap---------- coil---------res-----------GND

At the cap, there will be a phase shift where the current will lead
the voltage, right?
At the coil, there *would* normally occur a phase shift were the
travelled through the cap which has put the current ahead of the
volts, its phase-shift will only be brought back to zero again in the
coil, right?
(assuming appropriate component values and ignoring paracitcs, of
course)

14. ### John LarkinGuest

No, it's really not bad, but you do have to accept vectors as a way to
describe both the amplitude and the phase angle of a sine wave.
Vectors aren't bad to visualize with a little practice, just think in
terms of "how far" and "which direction"; any time you deal with
locations on a 2-d surface, vectors become pretty obvious.

The three impedances add up: Resistance, capacitance, inductance are
in series. The resistance vector is R long and, at zero degrees,
points due east. The inductor is Xl long (Xl=2*pi*f*L) and points 90
degrees, north. The cap is Xc long and points -90, south. Draw the
vectors end-to-end on a map and you get the total impedance, Z

The current is Vsource/Z, just another vector. Dump that current into
the resistor and you have the voltage across the resistor, as a vector
(voltage and angle.)

This is fairly instinctive. And then if you express the vectors as x-y
coordinates (rectangular notation, instead of polar) the math is a
little easier. The real axis is just east-west, and the imaginary, j,
axis is just north-south. It's just like pacing off distances with a
compass.

John

15. ### john jardineGuest

Never say die!.
Half the battle in electronics seems having the nous to know which are the
Bit of a wide ranging statement but generally phasing is only of direct
relevance in maybe 20% of analogue design work.(90% if filters are
involved). Maybe concentrate on the bulk of the subject and allow the
phasing aspects just to creep up on you.

Btw. One thing I noticed going back through a few posts is that your Spice
doesn't appear to be cleanly showing the direct, absolute, perfect, 90deg,
1/4 cycle, VI phase shift that occurs across all reactive components.
(Disregarding the relative phase shifts compared to the signal source).
You may be doing this correctly already (so ignore following) but for
'floating' components the 90deg shifts can -only- be seen and measured
across the component itself and not wrt the Spice ground point. I.e a
capacitor voltage graph should be plotted as the -difference- between the
voltages at either side of the cap (eg plot vc1-vc2), only then compare that
'differential' waveform to the current running through the component.
regards
john

16. ### CBarn24050Guest

Subject: Re: The phase-shift problem revisited...
You are measuring the voltage to ground and not the voltage accros the
capacitor thats where the error is. The text books are correct as is the spice
program.

No it doesn't, the overall effect does but that applies to everything in life.

17. ### Robert MonsenGuest

No. It depends on the values of the capacitor and the coil. It will be
brought back to zero *only* if the frequency of the AC signal is equal to

f = 1/(2 * PI * sqrt(L*C))

Otherwise, the phase shift across the LC combination will be something
different.

--
Regards,
Robert Monsen

"Your Highness, I have no need of this hypothesis."
- Pierre Laplace (1749-1827), to Napoleon,
on why his works on celestial mechanics make no mention of God.

18. ### john jardineGuest

Yes, components each act individually but I think I'd defy anyone to figure
out what point X in (say) this simple two capacitor circuit is liable to do
when the input is swept, just from a mental inspection of the individual
parts. Unless one has a Stephen Hawking mindset, then it's out with a pencil
and paper. (or the Spice!)
Although you will have come across this type of arrangement before and also
the Wein bridges, Twin Ts, lattices etc, many newcomers haven't and can
waste much energy trying to get to grips with it from a mental model POV.
1u
||
.--||-----------.
| || |
| |
| || ___ |
o--o--||-o-|___|---o
AC || | 100k |
IN 1u | .-.
o o | |100k
| Point X | |
| o '-'
| | |
=== === ===
GND GND GND

regards
john

19. ### Robert MonsenGuest

It's like the old puzzle: you plant a flag, walk a mile south, a mile
east, and a mile north, and find you are standing next to your flag,
when suddenly you are attacked by a bear!. What color is the bear?

Actually, I was in a used book store the other day, and happened to find
a 1973 AARL "The Radio Amateur's Handbook" for \$5. It was completely
unused, since it had the original purchase receipt in it from 1973. It
has a great descripton of all of this stuff, and nice charts, rules of
thumb, descriptions of low pass and high pass filters, etc. Maybe Mr.
Evans should pick up a copy at a swapmeet...

--
Regards,
Robert Monsen

"Your Highness, I have no need of this hypothesis."
- Pierre Laplace (1749-1827), to Napoleon,
on why his works on celestial mechanics make no mention of God.

White.

John