RF, Microwave & Wireless. All rights reserved

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

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

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

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

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

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

OIP3 and OIM3 Linear Scale At IP : 2 2 2 1 2 3 a3 2 A 2 1 thus. aa 9 A 2 4 2 a 2 3 a IP 3 2 a P OIP. 3 1 out1 IP 3 3 3a3 3 2 9 2 3 3 3 out3 3 in 3 in Also IM a P a P 4 2 2 3 a 1 a P G P 2 a OIP 3 3 6 3 3 3 3 1 in 2 in 1 3 All rights reserved 34

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

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

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

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

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 ) 2 1 2 1 2 2 T 2 3 rd Order IM s: 2 2 2 1 G G G... ( OIP ) ( G OIP ) ( G G OIP ) ( G OIP ) T T T sys 2 (1) 2 (2) 2 ( N ) 2 3 1 3 1 2 3 T 3 All rights reserved 40

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

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

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