1. Equipment Noise Characterization P s (W) N TH (W) = kTB B Desired Signal Thermal Noise G1G1 GNGN Ideal Components Contained within bandwidth “B”

2. Noise Ratio G1G1 N 1 (mW) P S1 (mW) + N TH (mW)G 1 (P S1 (mW) + N TH (mW) + N 1 (mW)) T 0 is ALWAYS 290 K for Noise Ratio Computations If NR is given, then we can compute Definition: A measure of how much a system degrades SNR. Ratio of noise added to thermal noise (KT 0 B) +

3. Equipment Noise Characterization P S0 (dBm) N TH (dBm) = 10 log 10 (kT 0 B) + 30 dB B Desired Signal Thermal Noise G1G1 Practical Components L 1 (dB) Noise spectral density out of any device can never be less than kT. N 1 (dBm) Shot noise contribution of first amp. We model the noise contribution as being added at the amp input, and amplified by the amp’s gain. Since noise power is being added, we must use mW, NOT dBm. Because kTB is in Watts! +

4. Cascade Noise Ratio G 1, NR 1 N1N1 G 2, NR 2 N2N2 G 1 (P S1 + kT 0 B+ N 1 )G 2 (G 1 (P S1 + kT 0 B + N 1 )+N 2 ) Which can be Generalized to N Stages: Friis’ Formula +

5. Noise Ratio with Preceding Insertion Loss B G 1, NR 1 L 1 (dB) N 1 (dBm)  1 P S1 + kT 0 B G 1 (  1 P S1 + kT 0 B + N 1 ) Since the effects of preceding loss are multiplicative w.r.t. both noise ratio and gain, it makes sense to deal with losses using dB units... +

6. Noise Figure (dB) Noise Figure, NF(dB), is Noise Ratio expressed in dB: Noise characteristics for devices are usually published/specified by Noise Figure (dB). When a device with specified Gain and Noise Figure (G I, NF I ; both in dB) is preceded by one or more passive devices with specified total insertion loss (L I in dB), they can be combined into a single stage having G C (dB) = G I (dB) – L I (dB) and NF C (dB) = NF I (dB) + L I (dB) G I, NF I LILI G C, NF C

7. System Noise Figure The overall noise figure for a system containing both active gain stages and passive loss stages is computed as follows: 1.Combine all passive losses with their succeeding gain stages using G C,I (dB) = G I (dB) – L I (dB) and NF C,I (dB) = NF I (dB) + L I (dB) 2.The sum of the resulting combined gains (in dB) is total system gain, G SYS (dB) 2.Convert all combined gains and noise figures to their ratio metric (non-dB) values 3.Apply Friis’ formula using the resulting combined Gains and Noise Ratios to obtain overall Noise Ratio for the system. 4.Convert overall Noise Ratio back into dB’s : NF SYS (dB)

8. System Noise Temperature Concepts of Noise Figure and Noise Ratio were developed when virtually all communications system were terrestrially based, hence the implicit use of T 0 = 290 K (the mean blackbody temperature of the earth). No one ever aimed an antenna up at the sky and expected to receive anything meaningful. With the advent of space communication and radio astronomy, an equivalent concept of noise temperature was developed which seemed to make more sense in that context: If we subtract one from each side of Friis’ formula and then multiply both sides by T 0, we have: Substituting the definition of equivalent noise temperature from above,

9. Discussion Consider Friis’ Formula: The Noise Ratio contributions of all but the first stage are reduced by the gains of preceding stages. 1.The gain of the first stage should be high, to reduce the contributions of succeeding stages. 2.The Noise Ratio of the first stage should be as low as possible, since it contributes directly to the system noise ratio. 3.Any passive losses prior to the first gain stage should be minimized, as it detracts from 1 and 2 above.

10. Example G 1 = 15 dB NF 1 = 6 dB L 1 = 2 dB G 3 = 25 dB NF 3 = 16 dB L 2 = 5 dB G 2 = 10 dB NF 2 = 12 dB G 4 = 18 dB NF 4 = 12 dB Step 1: Combine all passive losses with succeeding gain stages. G 2 = 10 dB NF 2 = 12 dB G 4 = 18 dB NF 4 = 12 dB G 3 = 20 dB NF 3 = 21 dB G 1 = 13 dB NF 1 = 8 dB Step 2: Convert Gains and Noise Figures ratio-metric Forms G 2 = 10 NR 2 = 16 G 4 = 64 NR 4 = 16 G 3 = 100 NR 3 = 128 G 1 = 20 NR 1 = 6.4 Step 3: Combine Gains and Noise Ratios Using Friis’ FormulaStep 4: Convert overall Gain and Noise Ratio Back to dB