Bode Plots

Wednesday, 10 July 2019

5:35 PM

𝐴﷐𝑗𝜔﷯=﷐﷐𝐴﷮𝑜﷯﷐1+﷐𝑗𝜔﷮﷐ω﷮𝑧1﷯﷯﷯﷐1+﷐𝑗𝜔﷮﷐ω﷮𝑧2﷯﷯﷯…﷮﷐1+﷐𝑗𝜔﷮﷐ω﷮𝑝1﷯﷯﷯﷐1+﷐𝑗𝜔﷮﷐ω﷮𝑝2﷯﷯﷯… ﷯ Zeros at ﷐𝜔﷮𝑧1﷯, ﷐ω﷮𝑧2﷯, .… ﷐ω﷮𝑧𝑛﷯ Poles at ﷐𝜔﷮𝑝1﷯, ﷐ω﷮𝑝2﷯, .… ﷐ω﷮𝑝𝑛﷯ 20﷐log﷮|𝐴﷐𝑗𝜔﷯|﷯ Drawing Amplitude Superimpose each zero and pole Identify the poles and zero, then draw each contribution and add together Zeroes cause an increase of 20dB / decade (Zero for frequencies less than the pole) Poles cause a decrease of 20dB / decade (Zero for frequencies less than the pole) Also add the constant (20𝑙𝑜𝑔(﷐𝐴﷮𝑜﷯)) For zeros/poles at the origin, locate 𝜔=1 and add/subtract 20dB / decade Untitled picture.png Machine generated alternative text: Phase Sum the inverse tan of the zeros and subtract the sum of the inverse tan of the poles ﷐﷐tan﷮−1﷯﷮﷐𝜔﷮﷐ω﷮𝑧1﷯﷯﷯+﷐﷐tan﷮−1﷯﷮﷐𝜔﷮﷐ω﷮𝑧2﷯﷯﷯+…+﷐﷐tan﷮−1﷯﷮﷐ω﷮﷐ω﷮𝑧𝑛﷯﷯﷯−﷐﷐﷐tan﷮−1﷯﷮﷐ω﷮﷐𝜔﷮𝑝1﷯﷯﷯+﷐﷐tan﷮−1﷯﷮﷐ω﷮﷐ω﷮𝑝2﷯﷯﷯+…+﷐﷐tan﷮−1﷯﷮﷐ω﷮﷐ω﷮𝑝𝑛﷯﷯﷯﷯ 𝜔<0.1﷐ω﷮𝑧𝑛﷯ 0° 𝜔=﷐ω﷮𝑧𝑛﷯ 45° ω>10﷐𝜔﷮𝑧𝑛﷯ 90° Untitled picture.png Machine generated alternative text:

 

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