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### Network # Help in a passive low pass filter

#### ra585ed

Dec 15, 2011
1
Hi everyone..
Good morning/evening..
I hope you all fine..
I need your help..

I have this RC CIRCUIT
: Assume the following:
: I need to find V(out) (magnitude only), in the Phasor domain, in terms of the frequency ω and I need to show that the cutoff frequency of this circuit is 1/RC.

Can any body help me with that..? I will be Grateful.

#### Laplace

Apr 4, 2010
1,252
In order to solve this problem you need to use phasor algebra. Phasor algebra has the advantage that it reduces steady-state sinusoidal circuits to the form of pure resistance circuits. Once the problem has been converted to the frequency domain it is essentially a resistive problem. The only difference is that the real-number algebra used for resistive circuits becomes complex-number algebra for frequency-domain circuits. I will presume you are proficient in doing simple arithmetic (add, subtract, multiply, divide) with complex numbers.

The circuit is a simple voltage divider in the frequency domain; therefore, structure the solution as a resistor voltage divider but then use impedance instead of resistance. For cutoff frequency I would assume that means the half-power point. Since power is proportional to the square of the voltage, (Vout/Vin)^2=1/2, what is the frequency where Vo/Vi=0.707?

#### Harald Kapp

##### Moderator
Moderator
Nov 17, 2011
12,615
Note that the formulae in "assume the following" give the cutoff angular frequency omega . If you want the cutoff frequency in terms of cyclic frequency, you'll have to factor in 2*Pi.

Harald

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