RadioBanter - View Single Post - phase angle and impedance of resonant circuits

August 31st 05, 12:59 AM

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