3.8 Problems

Chapter 3.8 Problems

Physics Lecture Notes – Phys 395 Electronics Book
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Physics Lecture Notes – Phys 395 Electronics Book

  • CHAPTER 3. FILTER CIRCUITS613.8Problems1. In the following circuit, the input signal is v = v0 exp(jωt), and the components havebeen chosen such that L = R/ω and C =3/(ωR). The output is at the terminals AB.RCLv(t)BASG(a) What is the transfer function H(jω)?(b) Find the current in the circuit.(c) What is the voltage drop across each element of the circuit?(d) Show algebraically that at any instant the potential difference around the circuitis zero.(e) At time t = Nπ/ω, where N =0, 2, 4, ... make a sketch showing the voltage acrosseach element in the complex plane and show that the vector sum of the voltagedrops is equal to the voltage supplied.(f) Write an expression for|H(jω)|.(g) What is the limit of|H(jω)| as ω goes to zero?(h) What is the limit of|H(jω)| as ω goes to infinity?(i) What is the corner frequency?(j) What is|H(jω)| at the corner frequency?(k) Make a sketch showing the characteristics of|H(jω)| on a log-log plot. Label theslope of the curve where possible, the corner frequency, and the value of|H(jω)|at the corner frequency.(l) Describe the high and low frequency behavior in dB/octave.2.(a) Draw a passive LCR low-pass filter and write down the transfer function of yourfour-terminal network.(b) Determine approximations to the transfer function and filter corner frequency(s).(c) Write the resonance frequency, ωr =1/√LC, in terms of the corner frequency(s).3. Write down the transfer function, H(jω), for the network shown below, and from itfind: