EECS 242 Mixer Noise and Design UC Berkeley EECS 242 Copyright Prof Ali M Niknejad and Dr Osama Shana a SSB vs DSB NF definition Ideal noiseless mixer LO image noise Ni Gmix Ni S Ni image noise Gmix IF IF Because of the image problem a receive mixer down converts both desired and the image bands to IF frequency This means folding the noise at the image frequency on top of the desired band at IF Therefore the total noise at IF is as follows 1 The noise at desired RF band down converted to IF 2 the noise at image RF band down converted to IF 3 The noise added by the mixer noisy circuit itself UC Berkeley EECS 242 Copyright Prof Ali M Niknejad and Dr Osama Shana a Single side band SSB NF The single side band NF definition assumes that there is no signal at the image frequency except the source noise This definition is useful in finite IF architectures where the image signal is suppressed by an image filter before reaching the mixer The NF is the degradation of S N at mixer output Therefore one can write UC Berkeley EECS 242 Copyright Prof Ali M Niknejad and Dr Osama Shana a IEEE Noise Definition As seen from the SSB noise figure equation if the mixer is noiseless Nmix 0 the mixer SSB NF is 3dB because of the image noise folding It is important to know that this definition is the one used by microwave mixer designers for years It is also the definition used in SpectreRF simulator The IEEE definition of Single Side band SSB NF The IEEE has a slightly different definition for SSB NF It argues that the mixer should not be penalized by the image source noise folding The only image noise folding that is allowed to count towards calculating the mixer SSB NF is that which is due to the mixer circuitry itself The input image noise should not be counted Therefore the IEEE SSB NF assumes there is a sharp bandpass filter that passes the desired band with the source noise and knocks down the image noise to the negligible level As a result one can write UC Berkeley EECS 242 Copyright Prof Ali M Niknejad and Dr Osama Shana a IEEE Noise Def cont Image noise filter LO Noiseless mixer image noise Nd Gmix Nd IF Sd Nd IF As seen from the IEEE SSB equation if the mixer is noiseless the mixer SSB NF is actually 0dB the spirit behind the new definition UC Berkeley EECS 242 Copyright Prof Ali M Niknejad and Dr Osama Shana a Double Side band DSB NF LO Noiseless mixer image Nd Gmix d image noise Nd IF Sd Nd Nim Gmix im IF The double side band NF definition assumes that the image band contains both noise and an image signal identical to the desired band signal This definition is useful in direct conversion receiver where the image is the signal itself Therefore one can write UC Berkeley EECS 242 Copyright Prof Ali M Niknejad and Dr Osama Shana a DSB NF cont Therefore It can be seen that the difference between the SSB NF and DSB NF is exactly 3dB However with the SSB IEEE the difference is not exactly 3dB In fact the difference between the SSB IEEE and the SSB NF approaches 3dB as the mixer NF is very high The SSB IEEE noise factor can be related to that of the DSB as UC Berkeley EECS 242 Copyright Prof Ali M Niknejad and Dr Osama Shana a Periodically Time Varying Systems Suppose the AC signal at output is given by Let X f be the spectrum of is Y f be the spectrum of Io1 If we fix the output frequency at fIF then we see energy from multiple bands folding into output spectrum 0 UC Berkeley EECS 242 IF LO IF LO LO IF 2LO IF 2LO 2LO IF Copyright Prof Ali M Niknejad and Dr Osama Shana a Mixer Conversion Gain n 1 fLO fIF n 1 fLO fIF n 2 2fLO fIF The coefficient P1 k then represents the conversion gain from frequency k fLO fIF to fIF If we assume hard switching then P1 t is a square wave and the coefficients are UC Berkeley EECS 242 Copyright Prof Ali M Niknejad and Dr Osama Shana a Single and Double Bal Mixer Io Io1 Io2 I1 I2 I5 I4 Io1 Io1 I1 I2 I1 I2 M1 Io2 M2 I1 I2 M1 VLO I4 M2 M4 I5 M5 VLO I3 IB is Vin M3 I3 IB is Vin I6 IB is M3 M6 2IB UC Berkeley EECS 242 Copyright Prof Ali M Niknejad and Dr Osama Shana a Core Noise Model VLO t Io1 I1 I2 Vo Vx I1 Vx p0 t IB IB t I2 TM1 LO Io1 I1 I2 M2 I1 VLO I2 M1 M2 VLO t I3 IB is p1 t 1 1 Vin M3 a UC Berkeley EECS 242 I3 IB is t b Copyright Prof Ali M Niknejad and Dr Osama Shana a Noise from Gm Stage WSS PSD A cyclostationary process is a random process whose statistics are periodic functions of time The PSD of a cyclostationary process is given by S f t If we measure a cyclostationary process over a bandwidth 1 period we observe a stationary process Example White noise deter periodic func UC Berkeley EECS 242 Copyright Prof Ali M Niknejad and Dr Osama Shana a Gm Stage Noise cont If Sn3 t Nn3 white then For a square wave p1 t 1 1 For first sidebands fLO fIF this noise accounts for of noise UC Berkeley EECS 242 Copyright Prof Ali M Niknejad and Dr Osama Shana a Gm Stage Noise cont accounts for The remaining harmonics account for the rest 10 Assume p1 t is a straight line during period when both devices on vo vx vx vo UC Berkeley EECS 242 1 Copyright Prof Ali M Niknejad and Dr Osama Shana a Single Balanced Mixer Noise Noise due to M3 transconductor Input referred noise voltage for M3 with degeneration Time variance of problem Gilbert Cell Thermal noise of switching pair When we switch hard the noise is due to M3 only transconductor neglecting capcitance and output impedance of M3 UC Berkeley EECS 242 Copyright Prof Ali M Niknejad and Dr Osama Shana a Noise of Switching Pair Hard switching is good for low noise output When both M1 M2 on during the switching period then the noise PSD at output is UC Berkeley EECS 242 I1 LO HIGH RF M1 M2 M3 LO LOW output impedance Copyright Prof Ali M Niknejad and Dr Osama Shana a Noise of Switching Pair cont 4X power Total transconductance of diff pair for LO port to differential output current UC Berkeley EECS 242 Copyright Prof Ali M Niknejad and Dr Osama Shana a Noise of Switching Pair cont LO amplitude UC Berkeley EECS 242 Copyright Prof Ali M Niknejad and Dr Osama Shana a Noise from LO Port 2 switching pairs Swtiching pairs UC Berkeley EECS 242 LO Copyright Prof Ali M Niknejad …