10 Issues in RFIC Design: Noise, Linearity, and SignalsThus, we can now also formally define signal-to-noise ratio. If the signal has a power of S then the SNR is: SNRNoise FloorS= (2.10)Thus, if the electronics added no noise and if the detector required a signal-to-noise ratio (SNR) of 0 dB, then a signal at -121 dBm could just be detected. The minimum detectable signal in a receiver is also referred to as the receiver sensitivity. However, the SNR required to detect bits reliably, (e.g., BER = 10-3) is typically not 0 dB. The actual required SNR depends on a variety of factors, such as bit rate, energy per bit, IF filter bandwidth, detection method (e.g., synchronous or not), interference levels, and so forth. Such calculations are the topics of a digital com-munications course [6, 7] and will also be discussed in Section 2.4.1. Typical results for a bit error rate of 10-3 is about 7 dB for QPSK, about 12 dB for 16 QAM, and about 17 dB for 64 QAM, though often higher numbers are quoted to leave a safety margin. It should be noted that for data transmission, lower BER is often required (e.g., 10-6 resulting in an SNR requirement of 11 dB or more for QPSK). Thus, the input signal level must be above the noise floor level by at least this amount. Conse-quently, the minimum detectable signal level in a 200-kHz bandwidth is more like -114 to -110 dBm (assuming no noise is added by the electronics).2.2.4 The Concept of Noise FigureNoise added by electronics will directly add to the noise from the input. Thus, for reliable detection, the previously calculated minimum detectable signal level must be modified to include the noise from the active circuitry. Noise from the electronics is described by noise factor F, which is a measure of how much the signal-to-noise ratio is degraded through the system. By noting that: oiSG S= × (2.11)where Si is the input signal power, So is the output signal power, and G is the power gain So/Si. We derive the following for noise factor: (source)(total)(total)(total)(source)/SNR/SNR/()/iioiiiooooiS NNS NFS NS G NG N====×× (2.12)where No(total) is the total noise at the output, No(source) is the noise at the output originating from the source, and No(added) is the noise at the output added by the electronic circuitry. Noting that: (total)(source)(added)oooNNN=+ (2.13)noise factor can be written in several useful alternative forms: +==== +×(total)(total)(source)(added)(added)(source)(source)(source)(source)1oooooioooNNNNNFG NNNN (2.14)