All,

I'm an Advanced studying for my Extra, and so far I am getting 66% on
the practice exams without even studying after about 3 years of
homebrewing. I need a few extra points to make it over the top, and
since I am a builder (of sorts) I would like to do it using the
electrical principles part of the exam.

However, the questions pool provides the answers but not how to get
them. I'd rather be able to understand how to arrive at it without a
calculator.

Problem class 1: impedance and phase angle of RLC parallel circuit
where component values and frequency are known.

Problem class 2: impedance and phase angle of RLC series circuit where

component values and frequency are known.

Could I calculate these graphically using tip-to-tail summation of
impedance vectors?

From what I understand, |Z| = 2 pi F L, |Z| = 2 pi / (F C), |Z| = R
But how can I get the phase angle or the conjugate pair so that I can
do the vector addition?

Thanks in advance,

The Eternal Squire

wrote:

All,

I'm an Advanced studying for my Extra, and so far I am getting 66% on
the practice exams without even studying after about 3 years of
homebrewing. I need a few extra points to make it over the top, and
since I am a builder (of sorts) I would like to do it using the
electrical principles part of the exam.

However, the questions pool provides the answers but not how to get
them. I'd rather be able to understand how to arrive at it without a
calculator.

Problem class 1: impedance and phase angle of RLC parallel circuit
where component values and frequency are known.

Problem class 2: impedance and phase angle of RLC series circuit where

component values and frequency are known.

Could I calculate these graphically using tip-to-tail summation of
impedance vectors?

From what I understand, |Z| = 2 pi F L, |Z| = 2 pi / (F C), |Z| = R
But how can I get the phase angle or the conjugate pair so that I can
do the vector addition?

Thanks in advance,

The Eternal Squire

I was going to ask what study materials you're using -- but you're not,
are you?

IIRC this is discussed in the ARRL handbook, which you should have if
you're homebrewing.

You calculate the series circuit impedance by adding the impedances of
the parts, which you can do graphically, or by adding all of the real
parts and all of the imaginary parts. You must calculate the parallel
circuit impedance as 1/(the circuit admittance), the latter being the
sum of the admittances of all the parts.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

wrote:
All,

I'm an Advanced studying for my Extra, and so far I am getting 66% on
the practice exams without even studying after about 3 years of
homebrewing. I need a few extra points to make it over the top, and
since I am a builder (of sorts) I would like to do it using the
electrical principles part of the exam.

However, the questions pool provides the answers but not how to get
them. I'd rather be able to understand how to arrive at it without a
calculator.

Problem class 1: impedance and phase angle of RLC parallel circuit
where component values and frequency are known.

Set up axes with R being the horizontal axis and X the vertical axis. To
enter a value of R of, say, three ohms, begin at the origin and draw a
vector that points to the right, 3 units long. To add a reactance to
that, draw a vector from the tip of the R vector, but going up or down
-- inductive reactance goes up, capacitive reactance down, with length
equal to the amount of reactance. [XL = 2 * pi * f * L, XC = 1/(2 * pi *
f * C)] You can add any number of Rs and Xs this way. When you're done,
draw a vector from the origin to the tip of the last vector. Its length
is the magnitude of the total impedance and the angle it makes with the
real (R) axis is the phase angle. In terms of R and X, the horizontal
distance from the origin to the tip of the last vector is the resistance
of the total impedance, and the vertical distance is the X.

What you've been doing is adding impedances in series, so that's
appropriate for figuring the total impedance of a series RLC circuit. To
work with parallel circuits, do the same thing but with conductance and
susceptance rather than resistance and reactance. The horizontal axis is
conductance (1/R) and the vertical axis is susceptance (1/X). Vectors
representing conductance point to the right; inductive susceptance
points down and capacitive susceptance points up. When you get finished,
the distance from the origin to the tip of the last vector is the
magnitude of the admittance (1/|Z|) and the angle from the real axis is
the angle of the admittance. This is the negative of the angle of the
impedance.

This is hard to explain without diagrams, but I'm sure there are lots of
good graphical explanations available in handbooks and on the web.

Roy Lewallen, W7EL


Problem class 2: impedance and phase angle of RLC series circuit where

component values and frequency are known.

Could I calculate these graphically using tip-to-tail summation of
impedance vectors?

From what I understand, |Z| = 2 pi F L, |Z| = 2 pi / (F C), |Z| = R
But how can I get the phase angle or the conjugate pair so that I can
do the vector addition?

Thanks in advance,

The Eternal Squire

From: on Aug 30, 3:38 pm

All,

I'm an Advanced studying for my Extra, and so far I am getting 66% on
the practice exams without even studying after about 3 years of
homebrewing. I need a few extra points to make it over the top, and
since I am a builder (of sorts) I would like to do it using the
electrical principles part of the exam.

However, the questions pool provides the answers but not how to get
them. I'd rather be able to understand how to arrive at it without a
calculator.

You need some DEFINITIONS made clear first. See following...

Problem class 1: impedance and phase angle of RLC parallel circuit
where component values and frequency are known.

Problem class 2: impedance and phase angle of RLC series circuit where
component values and frequency are known.

Could I calculate these graphically using tip-to-tail summation of
impedance vectors?

...if you have some polar-coordinate graph paper, yes.

From what I understand, |Z| = 2 pi F L, |Z| = 2 pi / (F C), |Z| = R

WRONG. Impedance Z = Resistance R + j Reactance X for a series-
resonant circuit. Further, X_L = 2 pi F L and X_C = -1 / (2pi F C).

"|Z|" is MAGNITUDE of impedance; you can't do "phase calculations"
using just magnitudes of either Z or Y.

Note: Admittance Y is composed of conductance G = 1 / R (real
part) and susceptances B_L = -1 / (2 pi F L) and B_C = 2 pi F C
(imaginary part).


But how can I get the phase angle or the conjugate pair so that I can
do the vector addition?

A "conjugate match" (or "pair") results when the magnitude of
inductive reactance is exactly equal to the magnitude of capacitive
reactance. Their relative phase angles are 180 degrees and
opposed; they "cancel" each other. In a series-resonant circuit
that leaves you with ONLY the RESISTIVE part of the complex
number expression for impedance.

|Z| = SQRT ( R^2 + X^2 ), Impedance phase PHA = Tan (X / R)

You must assign a polarity to X in order to maintain relative
phase angles. Capacitive reactance is assigned a negative value
while inductive reactance is assigned a positive value.

For admittance Y (such as with a parallel-resonant circuit), the
magnitude (|Y|) is the same square-root of the sums of the
squares (and thus always positive), but the inductive susceptance
is negative and the capacitive susceptance is positive in value.

Doing "vector plotting" is generally NOT a good short-cut way
to get acquainted with either Y or Z...UNLESS you ALWAYS keep
in mind the relative phase of inductance and the relative
phase of capacitance...and forget the small frequency differences
where reactance/susceptance of L is bigger/smaller than reactance/
susceptance of C. AT RESONANCE the angles are EQUAL in magnitude
but opposed in phase; they equate to zero.

The rules of arithmetic of the "rectangular form" of complex
quantities is well-known and mentioned in all sorts of texts,
including the mathematics handbooks. Going through numbers with
rectangular form is no more harder/easier than trying to plot
vectors with polar form representation.

Assignment to the student: Learn the rectangular-form arithmentic
rules for complex quantities. ANY text that has anything to say
about complex quantities will have those rules.

A hint to keep from re-inventing the wheel. The HP 32S and 33
scientific pocket calculators have both forms' arithmentic rules
preprogrammed...AND they do both the real and imaginary part
calculations and answer displays like right now. The HP 33
costs about $50 new.

Actually I lent my handbook for a few weeks out to an 11-year old boy
who was was selling magazines door to door for his school, he thought
my lab was "neat" and I told him about the hobby.

"When you get finished,
the distance from the origin to the tip of the last vector is the
magnitude of the admittance (1/|Z|) and the angle from the real axis is
the angle of the admittance. This is the negative of the angle of the
impedance."

Do you mean that the angle the admittance is in the opposite quadrant
of the impedance?

wrote:
"When you get finished,
the distance from the origin to the tip of the last vector is the
magnitude of the admittance (1/|Z|) and the angle from the real axis is
the angle of the admittance. This is the negative of the angle of the
impedance."

Do you mean that the angle the admittance is in the opposite quadrant
of the impedance?

If the angle of the admittance is 20 degrees, the angle of the impedance
is -20 degrees. Draw a set of axes. Draw a vector at an angle of 20
degrees from the real (horizontal) axis (20 degrees counterclockwise
from the axis). Now draw another vector at an angle of -20 degrees from
that axis (20 degrees clockwise from the axis). Are they in opposite
quadrants?

Roy Lewallen, W7EL

THANKS for explaining it so simply.

From the Advanced part I already knew:
1) P = I I R, P = EI
2) ELI the ICE man
These came in handy since the Extra restates some Advanced questions.

I've taken the EHAM practice tests for extra and passed them 3 times in
a row by memorizing:

1) Tip to tail reactances for magniture and angle for series resonant
circuit
2) Tip to tail reciprocal reactances parallel resonant circuit, take
reciprocal back and opposite angle for answer.
2) BW = F/Q (sorry for the mnemonic: f**k over you, you rhymes with
Q)
3) reactance = 2 pi F value, reciprocal for capacitors

And now I am getting 77% to 85%, which is enough, I think. There's
sections of the exam which are not relevant to my use of the hobby,
just as there are other sections not relevant to other people's use.

I am beginning to understand that what the Extra written test is
purported to measure is exposure to a number of facets of amateur radio
actively pursued over a number of years. Essentially, if you practice
at least 3 to 5 seperate parts of amateur radio for at least a few
years, you'll already know the bulk of the exam.

That's what got me 55% - 66% of the way already. All I needed to do
was practice a little to extend what I already knew about circuits from
building.

I'll keep practicing till VEC time.

Thanks a million, folks!

The Eternal Squire

Nope, they are not. I found that out the hard way when working the
exam questions tonight.

Oops, one other thing I forgot to mention:

Q = XL / XR

The Eternal Squire