Bode phase can be lower than -90 deg ???

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 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.

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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;

Answer 1

[Wayne King]

Hi, the phase in bode() is computed using atan2(). If you look at the help for atan2(), you'll see that it returns an angle in the range -pi<theta<=pi. That is why you see the phase response in degrees going from -180 to 180.