Bode plot - transition between low and high freq...

[powersys]

Consider a single real zero in the left half of the s-plane. This will have the form (s/z+1) ==> (jw/z+1) in time constant form. At low frequencies (w near 0), the magnitude of this term is approximately 1 ==> 0 db. At high frequencies (w/z >> 1), the magnitude of this term is approximately |w/z| ==> 20*log_10(|w/z|) db. At frequency w=w1, the magnitude is |w1/z|, and at frequency w=10*w1, the magnitude is 10*|w1/z|. In decibels, this is an increase by 20*log_10(10) which is 20 db. Therefore, at high frequencies, the magnitude curve for this simple zero will increase by 20 db every time the frequency increases by a factor of 10. When frequency is plotted on a log scale, the curve will be a straight line with a slope of +20 db/decade (decade of frequency = change of frequency by a factor of 10). At low frequencies, the magnitude will be approximately 0 db. The transition between low and high frequencies is at w=z r/s.

I don't understand why w=z is said to the 'transition point' between low and high frequencies. Why not w=0.9z or w=1.1z? Pls advise. Thanks.

 

[v_c]

I think the transition point corresponds to the 3dB point of the log magnitude.
This is where the gain drops to \[1/\sqrt{2}\] of the flat band value.
This is also known as the half-power bandwidth.

Take for example a lowpass filter with transfer function
\[\frac{1}{1+s/z}\] with the transition point
is at \[\omega=z\]. At low frequencies the gain is 1 (0dB) and at
frequencies above \[\omega=z\], the gain will fall at -20dB/decade.
At the transition frequency the gain will be -3.01dB (-3dB).
Half of the spectral power content will be contained at frequencies below \[\omega=z\].
By the way, in constructing asymptotic Bode plots (straight lines) the term "break frequency" sometimes gets used to describe this frequency. The term "corner frequency" is also used. Many names for the same thing.

I hope that this helps you out.

Best regards,
v_c