Rc time constant, low pass filter?

[ppp1262]

Hello,

For a first order RC low pass filter we have (wikipedia)
ω=1/τ , τ=R*C, 3db cutoff

we also have Z=1/(ωC) for any capacitor

giving Z=R at cutoff

However if Z=R then Vout=Vin*0.50, which is not 3db

What am I doing wrong?

 

[FvM]

However if Z=R then Vout=Vin*0.50

This is wrong, you didn't consider AC network properties. Actually, you have Vc² + Vr² = Vin², because of the 90° phase shift between Vc and Vr.


See Chapter 4

 

[ppp1262]

Hello,

But all I have done is used Ohm's Law, how can it be wrong?

 

[FvM]

Read the suggested literature. Ohms law doesn't apply for AC networks.

 

[Audioguru]

Since the capacitor causes a 90 degrees phase shift at the cutoff frequency then the power is half, not the voltage. The voltage is -3db (0.707 times) when the power is half.

 

[LvW]

Read the suggested literature. Ohms law doesn't apply for AC networks.

So is U(jω)=I(jω)•jωL wrong?

 

[FvM]

So is U(jω)=I(jω)•jωL wrong?

To answer the question clearly (of course you know the answer), you need an unequivocal definition of involved formula
entities, if they are are scalars or vectors? It's not clear from your notation in my opinion.

Generally, you can apply the usual calculus for DC networks to AC, if you change to complex respectively vectorial entities. But the connotation of "ohm" (e.g. "ohmic resistance") is contraditing the usage of the term "ohms law" in this regard, I think.

 

[LvW]

Of course, I agree, a simple formula like the one I gave in my response requires some explanation - in case the reader does not know anything about electronics basics and the rules to manipulate with imaginary figures.

However, don´t you think also the simple statement "Ohm´s law does not apply for ac networks" deserves some explanation? Otherwise PPP1262 could believe that the voltage-to-current ratio wouldn´t be constant in ac circuits (if the frequency remains constant).

 

[FvM]

However, don´t you think also the simple statement "Ohm´s law does not apply for ac networks" deserves some explanation?

Yes, of course. I gave the explanation before and also suggested literature.
But PPP1262 asked, without refering to it, how ohms law can be wrong.

 

[LvW]

Hello,
But all I have done is used Ohm's Law, how can it be wrong?

Hi PPP1262:

For your information, here are two excerpts from
Horowitz/Hill "The art of electronics":

1.) "As we will see, it is possible to generalize Ohm´s law, replacing the word "resistance" with "impedance", in order to describe any circuit containing linear passive devices (resistors, capacitors, inductors)."

2.) "...we can apply complex Ohm´s law to circuits containing capacitors and inductors, just as for resistors, once we know the reactance of a capacitor or inductor".

Your error was, that you didn´t consider the complex nature of these reactances and the rules to manipulate them mathematically.