RC Time constant question

[Nora]

Hello-
I have an RC low-pass single order filter.
R = 40k
C = 10uF

The 3db point I'm filtering at is 1/2*pi*R*C = 0.4 Hz
The RC time constant is R*C = 0.4
Does this mean that there will be a 0.4 second delay between my input signal and output signal?

Thank you,
N_N

 

[pstuckey]

If you apply a step voltage to your RC, then after one time constant the capacitor will be 63% of the step voltage. After four time constants it will basically be there (99%).

 

[WimRFP]

Hello,

No, you don't get a delayed signal as the delay is frequency dependent. So if you put in a step from U0 to zero, you will get exponential decay ( U0*e^(-t/tau) ). tau = RC, e = 2.718... (natural log base). The decaying signal doesn't look like the original signal. When you go from 0 to U0, you will get (U0(1-e^(-t/tau) ).

Assuming that the input signal is digital signal (for example a square wave) and you feed the output from the low pass RC filter to a comparator, then the RC filter + comparator may behave as delay for the digital signal.

 

[baby_1]

hello wimRFP
Thanks for your explanation.but i don't find the answer.for sin or cos or modulate signal we have a delay at output?
or for a impedance matching?

 

[WimRFP]

Are you familiar with complex calculus?

If so, calculate the transfer function (H(jw) ). Arg( H(jw) ) gives you the phase.

The time delay introduced by the low pass filter for a steady state sinusoidal signal is Tphase

Tphase = phi/w, w = 2*pi*f, phi = phase shift in radians.

When using degrees: Tphase = phi/(360*f), phi in degrees.

To find the delay for the information on a modulated signal, you need differentiation:

Tgroup = d(phi)/d(w). phi in radians.

For an impedance matching network, the steps are the same (so determine transfer function), but the math is more elaborate.

The more narrow band a matching section, the longer Tgroup. Tgroup = const/BW. BW is bandwidth (Hz) and the constant depends on the number of resonators used. A certain filter at 10 GHz with BW = 1 MHz has same group delay as filter with BW = 1 MHz at 100 MHz (assuming same filter shape).