RC LOW-PASS FILTER VS FREQUENCY

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This simple RC filter is a great entry into creating an Excel Design Tool. We'll use the awesome Formula capabilities and Built-In Functions to create a freq range and then calculate the filter's Magnitude and Phase.

Excel Functions
- SQRT(), LOG10(), ATAN()
Excel File
- RC_LP_Freq1.xlsx

NOTE: This topic shows one approach using Excel. Other ways may be better suited for your learning or designing. Copy the file and play in the sandbox of other possibilities.

RC FILTER

Cuttoff Frequency (-3dB)

fc = 1 / ( 2 * pi * R* C)

General transfer function in the s-domain

H(s) = s / ( s + a)

a = 1 / (R*C)

Magnitude and Phase in the frequency domain.

w = 2*pi*f

|H(s)| = a / sqrt( w² + a² )

Phase = -atan( w / a )

EXCEL STRATEGY

Create frequency points at logrithmic intervals.

ENTER

fstart = 1
Npoints (per decade) = 10

CALC

f = fstart*10^(N/Npoints)
w = 2*PI()*f

Calculate the Magnitude and Phase.

CALC

|H(f)| = a / SQRT(w^2+a^2)
|Hf|dB = 20*LOG10( |H(f)| )
Phase = -ATAN(w/a)*180/PI()

CHECK RESULTS

Plot the results using a Scatter plot.
Set frequency (x axis) to log scale.
At what f does the magnitude drop -3dB?
Where soes the phase hit -45 deg?

TRY IT!

Change R or C by x2 or x1/2 (possibly x10 or x1/10)
Predict the results, see what happens!
Adjust fstart and Npoints for a better view of the results.