Question

Problem 1 Consider the following asymptotic Bode plots. Note that the frequencies are in Hz. For each frequency response shown in (a)-(d), do the following: 1. Determine the transfer function H(s). 2. Synthesize H(s) using the RC circuits shown in Tables 3.4, 4.2 and 4.3 of the handout. Use as few opamps, resistors and capacitors as possible to simplify your design. Note: If you prefer, you can down-scale (by a frequency scaling factor ky) the original frequency response to work with smaller corner frequency values to simplify circuit synthesis. After the circuit is synthesized, you can up-scale the circuit by ky to the original frequency range. For an example of this method, please see steps 1 and 2 in Homework #2 Solutions fron Spring 2012. 3. Now use magnitude scaling (with appropriate values for km) to achieve practical component values 4. Use a circuit simulator to verify that the frequency response of your km-scaled circuit matches H(s). Whenever possible, you should choose the kin values to make the final resistor values be in the 1-100kΩ range. Don't worry if you end up a bit higher or lower than this range.

Answer 1

Asymptotic Bode plot: The given plot has 4 corner frequency m c_1 = 1000 rad/sec m c_2 = 4000 rad/sec m c_3 = 10,000 rad/sec m c_4 = 80,000 rad/sec At low frequency and, the dB magnetic = 6 dB Implies 20 log (k) = 6 dB Implies log (k) = 6.3 Implies k = 1.99 almostequalto 2 At, w = w c_1, the slope change is -20 Therefore pole is Added with Implies (1 + s/1000) At w = w c_2, A slope change is 0 dB/d A zero is Added Implies (1 + s/4000) \r\n At w = w c_3, A pole is Added Since, Slope change is -20 dB/ Implies 1/(1 + s/10,000) At w = w c_1, A slope change in 0 dB/de, A zero is added Implies (1 + s/80,000) Therefore overall function H(s) = k (1 + s/4000) (1 + s/80,000) /(1 + s/1000) (1 + s/10,000) H(s) + 2 (s + 4000) (s + 80,000)/4000 times 80,000/(s + 1000) (s + 10,000)