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Tak
science forum beginner

Joined: 07 Mar 2005
Posts: 5

Posted: Thu Jun 29, 2006 10:29 pm    Post subject: Wave impedance and loss in conductive plastic

Have been working on the captioned subject for a couple of
days, but cannot find my error. Please can gurus here help me.
There must be an error or two in my math somewhere as the result,
including following two equations, is different from well known
numbers.

Are those two equations correct?

Assume that conductive plastic sheet has
dielectric constant=e,
permiability=m, (=4*pi*1e-7)
conductivity=S, and
thickness=t (t << wavelength), at
angle freq=w.

Q1. wave impedance in the sheet(Zm):
Zm = sqrt[ abs{ (m-j0)/(e-jS/w) } ]
Is this right?
sqrt means square root, and abs means absulute value
of the complex number, and j is sqrt(-1).

Q2. E field strength after passing thurogh this sheet
and just before exit of the sheet(E):
skindepth(d) = sqrt{ 2 / (w*m*S) }
E = exp (- t/d) * (strength_just_after_entry)
Is this correct?
exp means exponent.

Thanks in advance for any help.
Tak
noshellswill
science forum beginner

Joined: 15 Apr 2006
Posts: 12

Posted: Fri Jun 30, 2006 2:53 am    Post subject: Re: Wave impedance and loss in conductive plastic

On Thu, 29 Jun 2006 15:29:58 -0700, Tak wrote:

 Quote: Asked this in other forum, but had no response. Have been working on the captioned subject for a couple of days, but cannot find my error. Please can gurus here help me. There must be an error or two in my math somewhere as the result, including following two equations, is different from well known numbers. Are those two equations correct? Assume that conductive plastic sheet has dielectric constant=e, permiability=m, (=4*pi*1e-7) conductivity=S, and thickness=t (t << wavelength), at angle freq=w. Q1. wave impedance in the sheet(Zm): Zm = sqrt[ abs{ (m-j0)/(e-jS/w) } ] Is this right? sqrt means square root, and abs means absulute value of the complex number, and j is sqrt(-1). Q2. E field strength after passing thurogh this sheet and just before exit of the sheet(E): skindepth(d) = sqrt{ 2 / (w*m*S) } E = exp (- t/d) * (strength_just_after_entry) Is this correct? exp means exponent. Thanks in advance for any help. Tak

BigT:

Depends .............

IF you are "counting" wave behavior from a point just IN-FRONT-OF the
lossy dielectric, and measuring just AFTER the wave leaves the lossy
dielectric then you have lots more work to do.

Simply stated ( but not simply done ) reflection coefficients at the
two boundaries force you to sum field magnitudes and phases everywhere ...
even for two boundaries it's a real PITA.

Smith charts help ...

nss
*********
j.alexander.hawkins@gmail
science forum beginner

Joined: 28 Jun 2006
Posts: 5

Posted: Fri Jun 30, 2006 3:24 am    Post subject: Re: Wave impedance and loss in conductive plastic

Tak wrote:
 Quote: Asked this in other forum, but had no response. Have been working on the captioned subject for a couple of days, but cannot find my error. Please can gurus here help me. There must be an error or two in my math somewhere as the result, including following two equations, is different from well known numbers. Are those two equations correct? Assume that conductive plastic sheet has dielectric constant=e, permiability=m, (=4*pi*1e-7) conductivity=S, and thickness=t (t << wavelength), at angle freq=w. Q1. wave impedance in the sheet(Zm): Zm = sqrt[ abs{ (m-j0)/(e-jS/w) } ] Is this right? sqrt means square root, and abs means absulute value of the complex number, and j is sqrt(-1).

no. where to you get 0 from? also, calm down with the abs. the wave
impedance
is in general complex. its real only when youre medium is not lossy.
interpetation being E,H are out of phase in a partialy coductive
medium.

 Quote: Q2. E field strength after passing thurogh this sheet and just before exit of the sheet(E): skindepth(d) = sqrt{ 2 / (w*m*S) } correct. E = exp (- t/d) * (strength_just_after_entry) you mean before entry... kind of right. you seem to be talking about a

plane wave normaly incident on a lossy medium. youve got more
complicated problem. i.e. you have reflection coeficients and
transmission coefficients at the boundrys of the surface. i.e. some of
the E will bounce back, some will pass through, attenuated and shifted
or delayed in phase. you then have another boundary condition you have
to worry about when you leave the conductive medum. if your really
interested, go to the library and get Microwave Engineering by Pozar if
you want to know more about the problem youre describing. your errors
are more from interpetation then the math.
 Quote: Is this correct? exp means exponent. Thanks in advance for any help. Tak
Tak
science forum beginner

Joined: 07 Mar 2005
Posts: 5

Posted: Fri Jun 30, 2006 5:46 am    Post subject: Re: Wave impedance and loss in conductive plastic

Thanks for replies, both of you.
What I was doing is to get absoption loss within the material.
I think I have equation of the reflection part. (Zm-Z0)/(Zm+Z0) for
entry reflection and 2*Zm/(Zm+Z0) for crossing. But I do not have
confidence in this Zm,,, that is the Q1.

It is a lossy sheet (conductive with S). I think imaginary part, or
to 1000 times larger than the real part of e.

 Quote: where to you get 0 from? I have no idea about this imaginary portion of the numerartor

(m-j0),,,, that is Q2. What
should I put in this part (currently 0)?

 Quote: you mean before entry I mean just_AFTER_entry and before_exit. In other words, absorption

loss in the
material, after 2*Zm/(Zm+Z0) and befor exit. I thought exp(-t/d) is
the absorption loss.
BTW, I will sum up the multiple reflections within the material later.

 Quote: your errors are more from interpetation than the math. Probably yes. That is the ditch I am in, needing help.

Tak
Tak
science forum beginner

Joined: 07 Mar 2005
Posts: 5

Posted: Fri Jun 30, 2006 8:22 am    Post subject: Re: Wave impedance and loss in conductive plastic

 Quote: calm down with the abs. the wave impedance is in general complex.

BINGO!
Thank you. The "abs" was wrong. I must calculate in complex format.

Tak
j.alexander.hawkins@gmail
science forum beginner

Joined: 28 Jun 2006
Posts: 5

Posted: Fri Jun 30, 2006 11:23 am    Post subject: Re: Wave impedance and loss in conductive plastic

Tak wrote:
 Quote: calm down with the abs. the wave impedance is in general complex. BINGO! Thank you. The "abs" was wrong. I must calculate in complex format. (Please ignore my previous append.) Tak

tak
your doing very well i think. (if your doing this with so few
references call me impressed) but i may have spoke too soon on the
other post. the attenuation was based on the assumption the conductor
is good..... i.e. (by your notation)
S>>we or S/we>>1... i got worried about that after i read the
conductive plastic... otherwise, the skin depth, (attenuation), and the
wave impedance is the sqrare root of a complex number... just make sure
you check.

take care,

john
Tak
science forum beginner

Joined: 07 Mar 2005
Posts: 5

Posted: Sun Jul 02, 2006 1:26 am    Post subject: Re: Wave impedance and loss in conductive plastic

john,
 Quote: S>>we or S/we>>1... i got worried about that after i read the conductive plastic... otherwise, the skin depth, (attenuation), and the wave impedance is the sqrare root of a complex number

Yes, thanks for the note.
Am starting all math in complex format.
Tak

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