An example with pole and zero

Figures 2-5 added allegorize architecture of Bode plots. This archetype with both a pole and a aught shows how to use superposition. To begin, the apparatus are presented separately.

Figure 2 shows the Bode consequence artifice for a aught and a low-pass pole, and compares the two with the Bode beeline band plots. The straight-line plots are accumbent up to the pole (zero) area and afresh bead (rise) at 20 dB/decade. The additional Figure 3 does the aforementioned for the phase. The appearance plots are accumbent up to a abundance agency of ten beneath the pole (zero) area and afresh bead (rise) at 45°/decade until the abundance is ten times college than the pole (zero) location. The plots afresh are afresh accumbent at college frequencies at a final, absolute appearance change of 90°.

Figure 4 and Figure 5 appearance how superposition (simple addition) of a pole and aught artifice is done. The Bode beeline band plots afresh are compared with the exact plots. The aught has been confused to college abundance than the pole to accomplish a added absorbing example. Notice in Figure 4 that the 20 dB/decade bead of the pole is arrested by the 20 dB/decade acceleration of the aught consistent in a accumbent consequence artifice for frequencies aloft the aught location. Notice in Figure 5 in the appearance artifice that the straight-line approximation is appealing almost in the arena area both pole and aught affect the phase. Notice aswell in Figure 5 that the ambit of frequencies area the appearance changes in the beeline band artifice is bound to frequencies a agency of ten aloft and beneath the pole (zero) location. Area the appearance of the pole and the aught both are present, the straight-line appearance artifice is accumbent because the 45°/decade bead of the pole is arrested by the overlapping 45°/decade acceleration of the aught in the bound ambit of frequencies area both are alive contributors to the phase.

Example with pole and zero

Figure 2: Bode consequence artifice for aught and low-pass pole; curves labeled "Bode" are the straight-line Bode plots

Figure 3: Bode appearance artifice for aught and low-pass pole; curves labeled "Bode" are the straight-line Bode plots

Figure 4: Bode consequence artifice for pole-zero combination; the area of the aught is ten times college than in Figures 2&3; curves labeled "Bode" are the straight-line Bode plots

Figure 5: Bode appearance artifice for pole-zero combination; the area of the aught is ten times college than in Figures 2&3; curves labeled "Bode" are the straight-line Bode plots