52 System Level Architecture and Design Considerations==-Þ=-=´=´=230.6(1)(1)442.76 0.9 nV 2.49 nV / HznVGAVGAnVGAsssvNFkTvFkTRkTRRIf the same noise current is now fed into 5W||5 kW instead of 50W||5 kW, the noise voltage will be approximately 1/10 since in either case the 5 kW resistor can be ignored. So using VnVGA = 0.249 nV results in:´=+=+=+==´22224 (0.249 nV)2.512.51 0.03 2.54 4.05 dB(0.9 nV)10nVGARFs vRFvF FkTR GSo the VGA has nearly no effect on noise, but a real VGA would have both current and voltage noise, leading to somewhat higher noise. Also, noise due to an extra buffer is low due to the GRF preceding it. Note that GRF is power gain and GvRF is voltage gain. So in this case we see that even though the block looks like it fails the spec, it actually only adds a small fraction of the noise allowed by the original specification. However, because 15 dB is more than the 10 dB specified, this now results in pressure on the VGA designer by the system designer possibly resulting in wrongful termination and a series of lawsuits. If only the systems designer had used (3.14), life would have been so much better for all involved! 3.2.2 The Linearity of Components in SeriesLinearity can also be computed for components in series. Starting with two ampli-fiers in series that have unique nonlinear transfer functions of: =++=++23o112323o21 o12 o13 o1aiaiaibbbvk vk vk vvk vk vk v (3.15)Each block will have an IIP3 of: 1IIP3_131IIP3_ 2323 ||23 ||aabbkvkkvk== (3.16)From (3.15) vo2 can be expanded to give an overall transfer function of: =++++++ …2233o21 11 112132123 1()(2)abiababibabaabaivk k vk kk k vk kk k kk kv (3.17)Note that this equation is truncated after the third-order terms and it is assumed that higher order terms are less important.