Introduction to Frequency Analysis of Amplifiers
Frequency independent analysis that is used so far in this book provides fast and relatively simple way to analyse and design amplifiers and other electronic circuits. This method is based on a simple assumption that the circuit is capable to accept and p
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Introduction to Frequency Analysis of Amplifiers
Frequency independent analysis that is used so far in this book provides fast and relatively simple way to analyse and design amplifiers and other electronic circuits. This method is based on a simple assumption that the circuit is capable to accept and process signals whose frequency spectrum includes all frequencies, from minus infinity to plus infinity. Nonetheless, we already know that elements capable to store energy need a finite amount of time to change their internal states. For slow changes this time delay is negligible, thus “low-frequency” approximation produces acceptable results. However, as the signal frequency increases, the impedances of frequency dependent components drastically change. In this chapter we review basic techniques of “frequency analysis” that is appropriate for low to medium frequencies.
7.1
Amplifier Bandwidth
A simple first-order RC (or RL) network shows frequency profile that corresponds to either HPF or LPF, see Chap. 3 and they are simplest frequency dependent circuit models (LC network comprises two energy storage elements, thus it is a second-order network). In principle, to the first approximation any circuit could be reduced and approximated by its equivalent RC or RL network. In other words, practical technique to determine frequency domain response of an amplifier involves a sequence of circuit reductions until a simple RC or RL network is achieved and analysed. Complex components (i.e. C or L) are in effect frequency controlled resistances that create voltage/current dividers whose gains are also frequency dependent. At the same time, realistic communication systems are based on processing of multi-tone signals (see Sect. 9.1.2) such as square and other modulated waveforms, not only a single sinusoidal forms. For this reason, it is important to determine “frequency bandwidth”, that is, the range of acceptable frequencies (or, frequency spectrum of the I/O signal), of amplifiers intended for RF applications. A typical electronic circuit shows the frequency characteristics as in Fig. 7.1, where three distinct regions are clearly visible: 1. LF band: this region is characteristic for DC frequency component being completely blocked by infinite resistance of HPF path (see Sects. 3.2 and 3.3). On decibel scale, DC gain limits to negative infinity (i.e. DC means ω = 0, thus log(0) = −∞). Very low-frequency tones close to DC experience HPF attenuation of +20dB/dec from very low frequency until ωL . This boundary © Springer Nature Switzerland AG 2021 R. Sobot, Wireless Communication Electronics, https://doi.org/10.1007/978-3-030-48630-3_7
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7 Frequency Analysis
Fig. 7.1 A typical frequency bandwidth profile and its definitions
AV (mid) −3dB
LF
HF
+90
midband
0
phase (deg)
AV (dB)
+45
−45
BW
−90 wL
Frequency (w )
wH
frequency is set at the point of −3dB attenuation relative to the maximal amplitude as measured in decibels. This region is consequence of large capacitive/inductive components in the circuit
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