4.5 Small-Signal Parameters

Chapter 4.5 Small-Signal Parameters

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

  • 4.5 Small-Signal Parameters 79ure 4.1) is shown at the center. The series resistances to the base, emitter and col-lector are shown respectively by rb, rE, and rc. Also, between each pair of terminals there is some finite capacitance shown as Cbc, Cce, Cbe. This circuit can be simplified by noting that of the extrinsic resistors, rb is the largest and as a result, rE and rc are often omitted along with the capacitances Cbc, Cce, Cbe. Resistor rE is low due to high doping of the emitter while rc is reduced by a buried layer in the n-collec-tor. The base resistance rb is the source of several problems. First, it forms an input voltage divider between rb, rp, and Cp, which reduces the input signal amplitude and deteriorates high-frequency response. It also directly adds to thermal noise. The resulting simplified small-signal models are shown as a pi-model in Figure 4.7(a) and as a T-model as in Figure 4.7(b). While rp is associated with the pi-model and re is associated with the T-model, it can be easily verified, for example with SPICE simulations, that both models have identical terminal impedances and identical frequency responses for all values of driving or load impedances. Note that at low frequencies, rp has base current flowing through it while re has emitter current flow-ing through it, hence for vp to be the same in both models, re is smaller than rp by a factor of (b + 1). We note that with either model, we may use re as an estimate of resistance seen looking into the emitter (the estimate is exact at low frequencies if rb is small and the base is grounded). We also note that re is approximately equal to the inverse of gm and this will be used extensively in various parts of the book.4.5  Small-Signal ParametersNow that the small-signal model has been presented, some simple formulas will be presented to help determine what model parameter values should be at different operating points.First, the short-circuit current gain b is given by ��large-signalsmall-signalcCbBiIiIβ (4.3)noting that currents can be related by: cbeiii+ = (4.4)Figure 4.7  Simplified small-signal models for bipolar transistor: (a) pi-model and (b) T-model.