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3 Physical causes of nonlinearity Operation under finite power-supply voltages Essential non-linear characteristics of electronic active components (transistors, diodes, etc.) Mismatch of input signal levels to a design Mismatch of number of input signals to a design All rights reserved 3

5 Problems caused by nonlinear distortions Reception Spurii ( signals show up, even if nonexistent at input) Reduce dynamic range Reduce sensitivity (desensitization) Blocking of desired signals All rights reserved 5

Blocking (De-Sensing) The presence of an adjacent

10 1 db compression point Definition The 1 db compression point specifies the output power of an amplifier at which the output signal lags behind the nominal output power by 1 db. All rights reserved 10

15 Models of nonlinear blocks and their characterization P out [dbm] Amplitude Response Linear Block Φ[deg.] Phase 0 P out [dbm] P in [dbm] Φ[deg.] Non-Linear Block P in [dbm] AM-AM Saturation 0 P in [dbm] P in [dbm] All rights reserved 15

Nonlinearities An ideal amplifier The connection to the input and output voltage is as

17 Nonlinearities In practice where v out (t) voltage at output of two-port v in (t) voltage at input of two port a 0 DC component a 1 gain G a n coefficients of the nonlinear element of the voltage gain All rights reserved 17

22 Single-tone driving Harmonics The levels of harmonics increase over proportionally with their order as the input level increases, i.e. Changing the input level by A db Changes the n th harmonic level by n A db Note: This assumes the memory-less modelling applies. All rights reserved 22

23 Two-tone driving Intermodulation Two-tone driving applies a signal v(t) into the input of the two-port block. This signal consists of the sum of two sinusoidal harmonic tones. All rights reserved 23

31 Slope of OIP2 and OIP3 vs. Pin [dbm] The log-log power plot of IM 2 is of slope 2dB/dB The log-log power plot of IM 3 is of slope 3dB/dB The log-log power plot of IM N is of slope NdB/dB All rights reserved 31

35 3rd Order Intermodulation Equations OIP 3 [dbm]=iip 3 [dbm]+g[db] P in dbm = P 3 dbc + Pout 3 dbm G[dB] P 3 dbc = P out1 [dbm]-p out3 [dbm]= =2(OIP 3 [dbm]-p out1 [dbm])= = 2 3 (OIP 3[dBm]-P out3 [dbm]) All rights reserved 35

37 Spurious Free Dynamic Range Definition Maximal to minimal input signal power ratio in db Maximal signal such that the 2-Tone IM products are at the output noise power level Minimal signal equals the sensitivity with a prescribed SNR out. Assume here SNR out =1 (0dB). All rights reserved 37

38 Spurious Free Dynamic Range (cont d) P 3 dbc = 2 3 (OIP 3[dBm]-P out3 [dbm]) For 3 rd order IM Products at the noise level: 2 DR [ OIP3 10log( ktinbfr G )][ db ] 3 If SNR out 0dB in the sensitivity definition, then: 2 S DR [ OIP3 10log( kt inbfrg ( ) out )] [ db ] 3 N All rights reserved 38

39 Cascade Intercept Point Assuming incoherent combining of IM products it is possible to show that: 2 nd Order IM s: OIP G G OIP G G OIP G OIP OIP sys (1) (2) ( N 1) ( N ) 2 2 N 2 3 N 2 N rd Order IM s: ( OIP ) ( G G OIP ) ( G G OIP ) ( G OIP ) ( OIP ) sys 2 (1) 2 (2) 2 ( N 1) 2 ( N ) N 3 3 N 3 N 3 3 All rights reserved 39

40 Cascade Intercept Point Another Form Assuming incoherent combining of IM products it is possible to show that: 2 nd Order IM s: 1 G G G... OIP G OIP G G OIP G OIP T T T sys (1) (2) ( N ) T 2 3 rd Order IM s: G G G... ( OIP ) ( G OIP ) ( G G OIP ) ( G OIP ) T T T sys 2 (1) 2 (2) 2 ( N ) T 3 All rights reserved 40

41 Measuring Nonlinear Behavior Most common measurements: Second level using a network analyzer and power sweeps gain compression AM to PM conversion using a spectrum analyzer + source(s) harmonics, particularly second and third intermodulation products resulting from two or more RF carriers All rights reserved 41

43 Third order Spurious Free Dynamic Range, SFRD-3 Spurious Free Dynamic Range Definition Maximal to minimal input signal power ratio in db Maximal signal such that the 2-Tone IM products are at the output noise power level Minimal signal equals the sensitivity with a prescribed SNR out. Assume here (or if not specified otherwise) SNR out =1 (0dB). All rights reserved 43

44 Design Tradeoffs between linearity and Sensitivity Optimization Sensitivity Optimization First stage with high gain First stage with low NF Linearity Optimization Limit the gain of the first stages Last stage with high IP All rights reserved 44

ELEN 701 RF & Microwave Systems Engineering. Lecture 8 November 8, 2006 Dr. Michael Thorburn Santa Clara University

ELEN 701 RF & Microwave Systems Engineering Lecture 8 November 8, 2006 Dr. Michael Thorburn Santa Clara University System Noise Figure Signal S1 Noise N1 GAIN = G Signal G x S1 Noise G x (N1+No) Self Noise