3 Filter Circuits

Chapter 3 Filter Circuits

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

  • Chapter 3Filter CircuitsLets now apply our knowledge of AC circuits to some practical applications. We will firstlook at some simple passive filters (skipping active filters) and then an amplifier model.Again we will rely on complex variables.3.1Filters and AmplifiersSimplistically, filters and amplifiers can be considered as four-terminal networks describedby a transfer function as follows:vout(jω)= H(jω)vin(jω).(3.1)Figure 3.1 shows some ideal transfer functions. If H(jω)= H≡ A is a real constantthen we call the network an ideal amplifier. If H(jω)=Θ(j(ω− ω0)) is a heavyside stepfunction we refer to the circuit as an ideal low-pass filter, and if H(jω)=1− Θ(j(ω− ω0))an ideal high-pass filter.3.2Log-Log Plots and DecibelsA log-log plot of a circuit’s transfer function can be a useful qualitative tool to allow us tounderstand most of the important features of filter and amplifier circuits. The commonlyused decibel unit will be defined. Although unappealing to the physicist this unit is still inwide spread use in electronics. Lets start.If P1 and P2 are two powers, we define the decibel asdB≡ 10 logP2P1=10 logV22V 21=20 logV2V1.(3.2)where we have used P∝ V2.The decibel is a property of the network and not the signals.Hence we can makeuse of any convenient signals in defining decibel. If two constant equal amplitude sources,|vin(jω1)| =|vin(jω2)|, are applied to a four-terminal network we may write44