Bode Plots

Wednesday, 24 April 2019

5:24 PM

Bode plots are plots of the magnitude response in decibels (dB),
and phase response (degrees) as a function of frequency (rad/s) on a logarithmic scale

﷐𝐻﷐𝑗𝑤﷯﷯=20﷐﷐log﷮10﷯﷮|𝐻﷐𝑗𝑤﷯|﷯ A rational transfer function, the general form is 𝐻﷐𝑗𝑤﷯=﷐𝐾﷐﷐𝑗𝑤﷯﷮±1﷯﷐1+﷐𝑗𝑤﷮﷐𝑧﷮1﷯﷯﷯﷐1+﷐𝑗𝑤﷮﷐𝑧﷮2﷯﷯﷯…﷐1+2𝑗﷐𝜁﷮1﷯﷐𝜔﷮﷐ω﷮𝑘﷯﷯+﷐﷐﷐𝑗ω﷮﷐ω﷮𝑘﷯﷯﷯﷮2﷯﷯…﷮﷐1+﷐𝑗𝜔﷮﷐𝑝﷮1﷯﷯﷯﷐1+﷐𝑗𝜔﷮﷐𝑝﷮2﷯﷯﷯…﷐1+2𝑗﷐𝜁﷮2﷯﷐𝜔﷮﷐ω﷮𝑛﷯﷯+﷐﷐﷐𝑗ω﷮﷐ω﷮𝑛﷯﷯﷯﷮2﷯﷯…﷯ Note that: ﷐﷐log﷮10﷯﷮|𝐻﷐𝑗𝑤﷯|﷯=﷐﷐log﷮10﷯﷮|𝐾|﷯±﷐﷐log﷮10﷯﷮𝜔﷯+﷐﷐log﷮10﷯﷮﷐1+﷐𝑗ω﷮﷐𝑧﷮1﷯﷯﷯﷯+﷐﷐log﷮10﷯﷮﷐1+﷐𝑗ω﷮﷐𝑧﷮2﷯﷯﷯﷯+…+﷐﷐log﷮10﷯﷮﷐1+2𝑗﷐𝜁﷮1﷯﷐𝜔﷮﷐ω﷮𝑘﷯﷯+﷐﷐﷐𝑗ω﷮﷐ω﷮𝑘﷯﷯﷯﷮2﷯﷯﷯+…−﷐﷐log﷮10﷯﷮﷐1+﷐𝑗𝜔﷮﷐𝑝﷮1﷯﷯﷯﷯−…−﷐﷐log﷮10﷯﷮﷐1+2﷐𝜁﷮2﷯﷐𝜔﷮﷐ω﷮𝑛﷯﷯+﷐﷐﷐𝑗ω﷮﷐ω﷮𝑛﷯﷯﷯﷮2﷯﷯﷯−… ∠𝐻﷐𝑗𝜔﷯=∠𝐾+∠﷐﷐𝑗ω﷯﷮±1﷯+∠﷐1+﷐𝑗ω﷮﷐𝑧﷮2﷯﷯﷯+…+∠﷐1+2𝑗﷐𝜁﷮1﷯﷐𝜔﷮﷐ω﷮𝑘﷯﷯+﷐﷐﷐𝑗ω﷮﷐ω﷮𝑘﷯﷯﷯﷮2﷯﷯+…−∠﷐1+﷐𝑗𝜔﷮﷐𝑝﷮1﷯﷯﷯−…−…………… This means we can sketch each factor separately and add them graphically Constant term Zero or pole at origin (ie 𝑗𝜔 or ﷐1﷮𝑗𝜔﷯) - magnitude is 20﷐﷐log﷮10﷯﷮𝜔﷯ (zero), or −20﷐﷐log﷮10﷯﷮𝜔﷯ (pole) - phase is 90° (zero), or −90° (pole) Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings        Ink Drawings Ink Drawings Ink Drawings Ink Drawings
Single zero or pole 1+﷐𝑗ω﷮﷐𝑧﷮1﷯﷯ (zero) ﷐1﷮1+﷐𝑗ω﷮﷐𝑝﷮1﷯﷯﷯ (pole) 20﷐﷐log﷮10﷯﷮﷐1+﷐𝑗ω﷮﷐𝑧﷮1﷯﷯﷯﷯ →20﷐﷐log﷮10﷯﷮1﷯=0 as 𝜔→0 →20﷐﷐log﷮10﷯﷮﷐ω﷮﷐﷐𝑧﷮1﷯﷯﷯﷯ as 𝜔→∞ =20﷐﷐log﷮10﷯﷮𝜔﷯−20﷐﷐log﷮10﷯﷮|﷐𝑧﷮1﷯﷯| Ink Drawings Ink Drawings Ink Drawings   
Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings                

 

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