How Do You Calculate and Graph Impedance in RC Filters?

[Monsu]

You are given a low pass filter of 50nF and a resistor of 100 KOhm.
a) Draw the circuit diagram;
b) Calculate the 3dB frequency;
c) Calculate the impedance of the series circuit of R and C and draw it in the complex plane at
about 2 decades around the 3dB point and at the 3dB point.
d) Draw the circuit diagram for a high pass filter with same components.


I am asked to calculate the 3db freq, right? is this the right formula f = 1 / (2piRC) ?
and afterwards calc the impedance z = R + jXc where Xc = 1 / (2pifC) ?
and then getting the decades, say our freq was 31.8Hz , 2 decades below would b 0.318? 2 decades above would b 3180?
then we should use those values of f to determine the Xc at those frequencies, and then find z at each of these frequencies?
then we plot a graph showing all the z's?


pls smne help me coz I'm totally confused!
thanks in advance!

 

[member 553083]

Yes, the formula you mentioned above is correct for calculating the 3dB frequency. You can use it to calculate the impedance of the series circuit at different frequencies. You should plot a graph showing the impedance at each frequency. For a high pass filter, the circuit diagram will be similar to the low pass filter with the capacitor in series and the resistor in parallel.

 

[wais]

a) The circuit diagram for a low pass filter with a 50nF capacitor and a 100 KOhm resistor would look like this:

[Image: Low Pass Filter Diagram]

b) To calculate the 3dB frequency, we can use the formula f = 1 / (2piRC). Plugging in the values of 50nF for C and 100 KOhm for R, we get:

f = 1 / (2 * pi * 100000 * 0.00000005) = 318.3 Hz

c) The impedance of the series circuit of R and C can be calculated using the formula z = R + jXc, where Xc = 1 / (2pi*f*C). At the 3dB frequency of 318.3 Hz, the impedance would be:

z = 100000 + j * (1 / (2 * pi * 318.3 * 0.00000005)) = 100000 + j * 99.4 Ohms

To plot the impedance in the complex plane, we can use the values of f calculated in part (b) to determine the Xc at 2 decades below and above the 3dB point. This would give us the following values:

At 0.318 Hz: Xc = 1 / (2 * pi * 0.318 * 0.00000005) = 3.16 MOhms
At 3180 Hz: Xc = 1 / (2 * pi * 3180 * 0.00000005) = 3.16 KOhms

Plotting these values on the complex plane, we get the following graph:

[Image: Impedance Graph]

d) To create a high pass filter with the same components, we can simply switch the positions of the capacitor and resistor in the circuit. The circuit diagram would look like this:

[Image: High Pass Filter Diagram]

The 3dB frequency and impedance calculations for the high pass filter would be the same as the low pass filter, except the roles of R and C would be reversed.