Asymptotic approximation on Bode diagrams

These are conventional first-order systems where the phase of the output lags behind the phase of the input. 

Low frequency (LF) asymptote When lu 0, G(juj) K. Hence the LF asymptote is a horizontal line at K dB. 

High frequency (HF) asymptote When uj 3 1/T, equation (6.18) approximates to 

As can be seen from equation (6.34), each time the frequency doubles (an increase of one octave) the modulus halves, or falls by 6dB. Or alternatively, each time the frequency increases by a factor of 10 (decade), the modulus falls by 10, or 20 dB. Hence the HF asymptote for a first-order system has a slope which can be expressed as —6 dB per octave, or —20 dB per decade. 

From equation (6.34), when lu = l/T, the HF asymptote has a value of K. Flenee the asymptotes interseet at tu = l/Trad/s. Also at this frequeney, from equation (6.18) the exaet modulus has a value 

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