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1 5. SOURCES OF ERRORS. 5.4. Low-noise design: noise matching. 5.4.1. Optimum source resistance 5.4. Low-noise design: noise matching The. 5.4.1. Optimum.

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Presentation on theme: "1 5. SOURCES OF ERRORS. 5.4. Low-noise design: noise matching. 5.4.1. Optimum source resistance 5.4. Low-noise design: noise matching The. 5.4.1. Optimum."— Presentation transcript:

1 1 5. SOURCES OF ERRORS. 5.4. Low-noise design: noise matching. 5.4.1. Optimum source resistance 5.4. Low-noise design: noise matching The. 5.4.1. Optimum source resistance

2 2 1 10 100 0.1 10 1 10 2 10 3 10 4 10 0 v n in rms, nV/Hz 0.5 e n = 2 nV/Hz 0.5, i n = 20 pA /Hz 0.5 enen  4kTR s B i n R s R s for minimum F 0.2 0.4 0.6 0.8 1 R s,  10 1 10 2 10 3 10 4 10 0 F 0.5 0 SNR 0.5 5 10 15 20 0 V in = e n ·1 Hz 0.5 R s for maximum SNR v n in rms = [4kTR s + e n rms 2 + (i n rms R s ) 2 ] 0.5 Example: Noise factor and SNR as a function of R s 5. SOURCES OF ERRORS. 5.4. Low-noise design: noise matching. 5.4.1. Optimum source resistance

3 3 A. Transformer matching with an 1 : n turns ratio RsRs Measurement object V msr 1: n n 2 R s nV in V in RLRL VoVo inin Measurement system enen 5. SOURCES OF ERRORS. 5.4. Low-noise design: noise matching. 5.4.1. Optimum source resistance Measurement objectMeasurement system n2Rsn2Rs nV in RLRL VoVo inin V msr enen AVAV AVAV

4 4 V in n = n e n ·1 Hz 0.5 2 4 6 8 10 R s n 2,  10 1 10 2 10 3 10 4 10 0 SNR 0.5 F 0.5 Example: Optimum source resistance 1 10 100 0.1 10 1 10 2 10 3 10 4 10 0 v n in rms, nV/Hz 0.5 R s =1 , e n = 2 nV/Hz 0.5, i n = 20 pA /Hz 0.5 enen  4kTR s B i n R s Thermal noise in R s R s n 2 V in n RsRs V in 1: n 5. SOURCES OF ERRORS. 5.4. Low-noise design: noise matching. 5.4.1. Optimum source resistance

5 5 n : 1n : 1 RsRs Measurement object V msr R s /n 2 V in /n V in RLRL VoVo inin AVAV Measurement system R s /n 2 Measurement object V in /n RLRL VoVo inin AVAV Measurement system V msr enen enen B. Transformer coupling with an n : 1 turns ratio 5. SOURCES OF ERRORS. 5.4. Low-noise design: noise matching. 5.4.1. Optimum source resistance

6 6 Home exercise: Optimize noise factor and SNR 1 10 100 0.1 10 1 10 2 10 3 10 4 10 0 v n in rms, nV/Hz 0.5 R s =200 , e n = 2 nV/Hz 0.5, i n = 20 pA /Hz 0.5 enen  4kTR s B n 2 R s,  i n R s Thermal noise in R s R s /n 2,  10 1 10 2 10 3 10 4 10 0 SNR 0.5 F 0.5 R s / n 2 V in / n RsRs V in n : 1n : 1 ? 5. SOURCES OF ERRORS. 5.4. Low-noise design: noise matching. 5.4.1. Optimum source resistance

7 7 C. Parallel connection of input stages 5. SOURCES OF ERRORS. 5.4. Low-noise design: noise matching. 5.4.1. Optimum source resistance

8 8 Next lecture Next lecture:

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