4.6 High-Frequency Effects

Chapter 4.6 High-Frequency Effects

Radio Frequency Integrated Circuit Design Second Edition Book
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Radio Frequency Integrated Circuit Design Second Edition Book

  • 80 A Brief Review of TechnologyTransconductance gm is given by: cCcmTiII qgvvkTπ=== (4.5)where IC is the dc collector current. Note that the small-signal value of gm in (4.5) is related to the large-signal behavior of (4.1) by differentiation. At a low frequency where the transistor input impedance is resistive, ic and ib can be related by: cbmm biig vg i rππβ=== (4.6)(neglecting current through ro) which means that: mg rπβ = (4.7)As well, the output resistance can be determined in terms of the early voltage VA: AoCVrI= (4.8)4.6  High-Frequency EffectsThere are two typical figures of merit fT and fmax used to describe how fast a transis-tor will operate. fT is the frequency at which the short-circuit current gain b is equal to 1. fmax is the frequency at which the maximum available power gain GA,max is equal to 1.Referring to Figure 4.7, an expression can be found for the corner frequency fb, beyond which the current gain b decreases: 112()2fr CCr Cβππµπ πππ=»+ (4.9)Since this is a first-order roll-off, fT is b times higher than fb. 02 ()22mmCTTggIffCCCC vβπµππβπππ==»=+ (4.10)The maximum frequency for which power gain can be achieved is called fmax, while GA,max is the maximum achievable gain at a particular frequency. fmax and GA,max are measured by conjugately matching the source and the load to the transistor.fmax can be determined by noting that at fmax the impedance of Cp is very low, and the presence of Cm and the Miller effect makes the impedance even lower. As a result, rp can be ignored and the input impedance is approximately equal to rb (the