Archived from groups: rec.audio.tech,sci.electronics.design (

More info?)

"Fred Bartoli" <fred._canxxxel_this_bartoli@RemoveThatAlso_free.fr_AndThisToo> writes:

> "Randy Yates" <yates@ieee.org> a écrit dans le message news:

> ekpc8qz2.fsf@ieee.org...

> > John Popelish <jpopelish@rica.net> writes:

> >

> > > Steve Hill wrote:

> > >>

> > >> Can anyone tell me how I should be calculating Parasitic Inductance,

> > >> Resistance and Capacitance? Any equations would be helpful. I am

> > >> revising for a telecommunications module and can't seem to find

> > >> anything anywhere and with no answers to work with, I am confused

> > >> whether I am doing it right.

> > >>

> > >> Typical question:

> > >> A 10.1nH inductor at 1GHz is purely resistive. The measured value of

> > >> resistance is 127ohms. Calculate the parasitic capacitance. [2 Marks]

> > >

> > > If an inductance (assumed to be a lumped inductance) looks resistive,

> > > then it is being resonated (canceled) at that frequency by an equal

> > > magnitude capacitive impedance. Magnitude of inductive impedance is

> > > 2*pi*f*L. Magnitude of capacitive impedance is 1/(2*pi*f*C). Set

> > > them equal and solve for C.

> >

> > The resistance would be irrelevent for this problem, then, but

> > represents the series resistance of the device.

>

>

> Nope, it's the equivalent parallel resistace of the tank, i.e. Rs*Q^2 (when

> Q is high enough).

> Here, estimating Q ~ Rp/L*w0 = 127/(10.1*2*pi) = 2 is clearly not enough for

> the approximation to hold so you have to do the exact maths.

Thanks for the correction, Fred.

So you model the circuit as a capacitor in parallel with the inductor and

a series resistor, in which case we have a parallel resonant circuit instead

of a series resonant circuit? Yup, that makes more sense.

The problem can then be solved exactly as follows:

1. First calculate the series resistance R. One equation for the

total impedance of the circuit is [1]

Z_T = (R^2 + X_L^2) / R

You know Z_T and X_L so you can rearrange this equation in the form

of a quadratic equation and solve for R.

2. Now plug this value of R into the relationship

X_C = (R^2 + X_L^2) / X_L

Note that I used my trusty old book [2] from DeVry, which is now

almost 30 years old.

Man, I would've flunked this question myself without doing some

serious review. I've had my head in the digital stuff way too

long.

--Randy

[1] I am using the somewhat arcane TeX typesetting system syntax here

in which a "_" is used for subscript and a "^" is used for a

superscript.

[2] "Introductory Circuit Analysis," Robert L. Boylestad (2nd edition)

--

Randy Yates

Sony Ericsson Mobile Communications

Research Triangle Park, NC, USA

randy.yates@sonyericsson.com, 919-472-1124