LC low-pass filter issue

[talking]

I have designed LC low-pass filter. The following code analyzes mag/phase bode plot of the filter.

You would see the phase curve shows from 0 to -180 deg from the results (see the attached.) of the following code. But it doesn't make sense, because ...

phase is defined as -arctan(w/wc), where w is frequency and wc is cut-off frequency. Whatever we have instead of w/wc, phase should not have the value lower than -90 deg.

But Matlab Bode function does as follows. Please help to understand this or correct my code for this issue.

Actually, it might be Matlab question, but I'm posting it here, since it can be solved by someone who has a background of LC filter design.

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L = 15e-9; C = 24*1e-12; R = 50;

figure(1); num1 = [0 0 1]; den1 = [L*C L/R 1]; sys1 = tf(num1, den1);

[mag1, phase1, W1] = bode(sys1); mag_dB1 = 20*log10(mag1));

subplot(211); semilogx(W1/(2*pi), mag_dB1); title('Bode Diagram'); ylabel('Magnitude (dB)'); grid on;

subplot(212); semilogx(W1/(2*pi), phase1)); xlabel('Frequency (Hz)'); ylabel('Phase (deg)'); grid on;

 

[LvW]

Hi talking,

A second-order lowpass - as in your case - always has a phase response as shown (between 0 and -180 deg). What is your problem?

 

[FvM]

phase is defined as -arctan(w/wc), where w is frequency and wc is cut-off frequency. Whatever we have instead of w/wc, phase should not have the value lower than -90 deg.

Would be true only for a first order low-pass.

 

[talking]

Thanks for answers, FvM and LvW.
I think I was confused with the phase equation for the 2nd order LPF.
As you know better, the phase equation of the first-order LPF is -arctan(W/Wc).
then what is the equation for the second-order LPF?

 

[FvM]

what is the equation for the second-order LPF?

Different, depending on the pole Q. But always spanning 0 to -180 degeree.