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Extra resources for Analog Electronics: Circuits, Systems and Signal Processing
V2 V3 V4 , . 48) Signals and signal processing 37 However, the overall gain could be found as the sum of the individual gains if a logarithmic measure were used. Recall that If xxy =z then l o g x 4 - l o g j = logz Clearly, it is much easier to work with sums than with products. Such a logarithmic measure is the bel (named after Alexander Graham Bell known for his work in the development of telephony) and the better known decibel (abbreviated as dB). The bel is defined as a power ratio. It is important to remember that it is a ratio and not an absolute measure such as the volt, the ampere and others.
69) Note that the condition that the exponent t/RC is a dimensionless number is satisfied. 30. It can be shown that the inifial slopes of the graphs (dvR/dt and dvc/dt at / = 0) are -V/x and -\-V/T respectively. 30. The Hnes are of course tangential to the curves at / = 0 since the slopes are the same at that point. 27 from A to B has the result of setting the generator (supply) voltage from Kto 0. 368 \ / + 0 r t Fig. -Ccircuit showing the time constant t. 1) provides /7? 75) and the voltages are VR = /i?
Signals and signal processing 43 phase shift/deg i\ 90 4J\ 80 \ \ \ s \ \ \\ NS. 70 N 60 '. 1 fo 4 2 6 — 8 2 \ jL \ >JS 4 TT^"^* 6 8 4 2 6 8 10Ofo lO^o fo 2 4 6 8 frequency Fig. 26 The phase-frequency (Bode) plot for a high-pass circuit. Note that only first-order circuits are considered here. The order of more advanced filter circuits is discussed in Chapter 10. Bode plots are also easy to use to examine the response of cascaded circuits or of systems which have several high- or low-pass time constants associated with them.