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yes this was clear since the beginning of this thread (see first posting).
i think i've found the answer concerning the laplace-fourier-relationship of the cos transform:
http://en.wikipedia.org/wiki/Laplace_transform#Inverse_Laplace_transform (section 4.3.2)
and
**broken link removed** (slide...
thanks for your quick answer.
i will give it a try:
laplace transform of cos(w0*t) =
s / ( s^2 + w0^2 )
-> substitution of s = "sigma + jw" with sigma=0 leads to
jw / ( -w^2 + w0^2 )
= ?
i don't see the way how to get to the fourier transform of cos "1/2 * (delta(f-f0) + delta(f+f0))" after...
hmm, the question is still open: starting with the laplace transform of cos "s/(s^2+w0^2)" and substituting "s=j*w" i'm stuck in the last step mentionned in the first posting.
how to proceed there (explicite steps) to get to the fourier transform of cos?
ok, but this is what i already said in the first posting. the actual question was:
how to use this fact to find the relationship between the "fourier transform of cosinus" and the "laplace transform of cosinus"?
Hello,
I often hear "the Fourier transfer function is equal to the Laplace transfer function with the Laplace variable s replaced by j*w: H(j*w) = H(s)".
Can anyone explain how this applies to cos(w0*t)?
The Fourier transform of cos(w0*t) is "1/2 * ( delta(f-f0) + delta(f+f0) )" (where...
definition of "resistance looking into"
Hello,
in the book "Microelectronic Circuits" (Sedra Smith, 5th Edition, page 446) the emitter resistance is defined as "... the small-signal resistance between base and emitter, looking into the emitter...".
The same formulation is...
Thank you for your quick reply.
So for transfer functions like
s / ( s - w )
and
s / ( s + w )
the pole frequency will always be mentioned as positive number
fp = wp / ( 2 * pi )
independent of the fact that the mathematically correct pole would be -wp or +wp ...(?)
Hello,
in textbooks (for example Sedra Smith, Microelectronic Circuits, Fifth Edition, page 334) one sometimes encounters a formula like:
Vo/Vi = ... * s / ( s + w )
where s is the Laplace variable (s = a + j*b) and w corresponds to the 3-db frequency of the high-pass filter.
Mathematically...
The knot in my head was solved by a lecturer:
gm*Vin equals 0 (since the output impedance Rds (approximation) is infinity and there is no way for the current to flow)
Hence the last equation in the picture leads to Vin=Vx
Hello Ratch,
thank you for your quick response.
I'm interested in finding out more about this "General Immittance Theorem". Do you know where I can find its proof? (I could'nt find any in the web - maybe it's name is different)
Nevertheless for this case I'd like to use Thevenin's theorem...
Hello,
I have a question concerning the derivation of the thevenin equivalent circuit shown on page 16 (upper part) in
https://www-soc.lip6.fr/~hassan/lec3_single_stage.pdf
I know that the small signal equivalent of a diode connected transistor corresponds to a 1/gmb resitor.
It is also clear...
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