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Each capacitor in a circuit is important at only one end of the frequency spectrum. For this reason, for this reason, we can develop specific equivalent circuits that apply to the lowfrequency range, to midband, and to the high-frequency range.
The equivalent circuits used for calculations in the midband range are the same as those considered up to this point in the text. As already mentioned, the couplings and bypass capacitors in this region are treated as short circuits. The stray and transistor capacitances are treated as open circuits. In this frequency range, there are no capacitances in the equivalent circuit. These circuits are referred to as midband equivalent circuits.
In this frequency range, we use a low-frequency equivalent circuit. In this region, couplings and bypasscapacitors must be included in the equivalent circuit and in the amplification factor equations.The stray and transistor capacitances are treated as open circuits. The mathematical expressions obtained forthe amplification factor in this frequency range must approach the midband results as f approaches the midband frequency range, since in this limit the capacitors approach short-circuit conditions.
In this frequency range, we use a high-frequency equivalent circuit.In this region, couplings and bypasscapacitorsare treated as short circuits. The transistor andany parasitic or load capacitances must be taken as into account in this equivalent circuit. The mathematical expressions obtained forthe amplification factor in this frequency range must approach the midband results as f approaches the midband frequency range, since in this limit the capacitors approach open-circuit conditions.
Frequency Response Analysis
Using the three equivalent circuits just considered rather than complete circuit is an approximation technique that produces useful hand-analysis results while avoiding complex transfer functions. This technique is valid if there is a large separation between fL, and fH, that is fH_fl. This condition is satisfied in many electronic circuits that we will consider.
Computer simulations, such as PSpice, can take into account all capacitances and can produce frequency response curves that are more accurate that the handanalysis results. However, the computer results do not provide any physical insight into a particular result and hence do not provide any suggestions as to design changes that can be made to improve a particular frequency response. A hand analysis can provide insight into the «whys and wherefores» of a particular response. This basic understanding can then lead to a better circuit design.
In the next section, we introduce two simple circuits to begin our frequency analysis study. We initially derive the mathematical expressions relating output voltage to input voltage (transfer function) as a function of signal frequency. From these functions, we can develop the response curves. The two frequency response curves give the magnitude of the transfer function versus frequency and the phase of the transfer functionversus frequency. The phase response relates the phase of the output signal to the phase of the inputsignal.
We will then develop a technique by which we can easily sketch the frequency response curves without resorting to a full analysis of the transfer function. This simplified approach will lead to a general understanding of the frequency response of electronic circuit. We will then rely on a computer simulation to provide more detailed calculations when required.
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