4.6.1 fT as a Function of Current

Chapter 4.6.1 fT as a Function of Current

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

  • 82 A Brief Review of TechnologyUsing this result, the Miller multiplication of Cm results in 311222cvCCkCCCCCCCCvCππππµπµπµππµæöæö=+-=++=++»ç÷ç÷èøèø (4.18)Because the output is matched, it is assumed that half the current flows into the output impedance and half the current flows into the load and thus the real power into the load is i2R/4. Then, with the help of (4.14) and (4.16), the output power Po is: 2202 2 2{ }44mcbobg vizPrk C Cπ µωÂ== (4.19) 2 24omibPgPrk C Cπ µω= (4.20)If this is set equal to 1, one can solve for fmax. 0max222112448mTbbbbgffrr k C Cr k Ck C Cπ µµπ µβπππ=== (4.21)where rbb is the total base resistance given by bbbrr rπ=. Note that fmax can be related to the geometric mean of fT and the corner frequency defined by rb and Cm.4.6.1  fT as a Function of CurrentfT is heavily bias dependent, therefore only when properly biased at a current of IoptfT will the transistor have its maximum fT as shown in Figure 4.8. As seen in (4.10), fT is dependent on Cp and gm. The capacitor Cp is often described as being a combination of the base-emitter junction capacitance Cje and the diffusion ca-pacitance Cd. The junction capacitance is voltage dependent, where the capacitance decreases at higher voltage. The diffusion capacitance is current dependent and increases with increasing current. However, for current levels below the current for peak fT, gm increases faster with increasing current; hence, fT is increasing in this region. At high currents, fT drops due to current crowding and conductivity modu-lation effects in the base region [1].Note that in many processes, fT is nearly independent of size for the same cur-rent density in the emitter (but always a strong function of current). Some fT curves that could be for a typical modern 50-GHz SiGe process are shown in Figure 4.9.Example 4.1: fT and fmax CalculationsFrom the data in Table 4.1 for a typical 50-GHz bipolar process, calculate zo, fT, and fmax for the 15´ transistor. Use this to verify some of the approximations made in the above derivation for fmax.Solution: At 7.9 mA, gm is equal to 316 mA/V and if b = 100, then rp = 316.5W and fT is calculated to be 71.8 GHz. It can be noted that a simulation of the complete model