EECS 242 RF Mixers UC Berkeley EECS 242 Copyright Prof Ali M Niknejad Mixers The Mixer is a critical component in communication circuits It translates information content to a new frequency Information PSD UC Berkeley EECS 242 Mixer Copyright Prof Ali M Niknejad Why use a mixer transmit side 1 Translate information to a frequency appropriate for transmission Example Antennas smaller and more efficient at high frequencies 2 Spectrum sharing Move information into separate channels in order to share spectrum and allow simultaneous use 3 Interference resiliance 1 2 Geographic map of cell sites 3 4 1 2 UC Berkeley EECS 242 Copyright Prof Ali M Niknejad Why use mixer in the receiver RF band Q of filter Desired channel Bandpass filter at o requires a high Q for narrowband signals Ch 1 2 3 4 5 f 200 kHz GSM High Q UC Berkeley EECS 242 Copyright Prof Ali M Niknejad Mixers in Receivers cont High Q Insertion Loss Filter center frequency must change to select a given channel tunable filter difficult to implement Mixing has big advantage Translate information down to a fixed intermediate frequency or IF 1 GHz 10 MHz 100x decrease in Q required Don t need a tunable filter High Q channel filter IF Issue Mixer has high noise factor Superheterodyne receiver architecture UC Berkeley EECS 242 Copyright Prof Ali M Niknejad Mixers Specifications Conversion Gain Ratio of voltage power at output frequency to input voltage power at input frequency Noise Figure DSB versus SSB Linearity Image Rejection LO Feedthrough Downconversion RF power IF power Up conversion IF power RF power Input Output RF Feedthrough UC Berkeley EECS 242 Copyright Prof Ali M Niknejad Mixer Implementation We know that any non linear circuit acts like a mixer Two tones 1 2 UC Berkeley EECS 242 f x Non linear 2nd order IM Copyright Prof Ali M Niknejad Squarer Example x x2 DC second harmonic y Desired mixing Product component What we would prefer LO IF RF A true quadrant multiplier with good dynamic range is difficult to fabricate UC Berkeley EECS 242 Copyright Prof Ali M Niknejad LTV Mixer LTI LTV No new frequencies New tones in output Example Suppose the resistance of an element is modulated harmonically UC Berkeley EECS 242 Copyright Prof Ali M Niknejad Time Varying Systems In general any periodically time varying system can achieve frequency translation consider n 1 plus n 1 UC Berkeley EECS 242 Copyright Prof Ali M Niknejad Desired Mixing Product Output contains desired signal plus a lot of other signals filter out undesired components UC Berkeley EECS 242 Copyright Prof Ali M Niknejad Convolution in Frequency Ideal multiplier mixer periodic input input p t y t x t UC Berkeley EECS 242 Copyright Prof Ali M Niknejad Convolution in Frequency cont X f X f peaks at fRF f fRF Translated spectrum peaks Y f n 1 n 2 n 3 f Input spectrum is translated into multiple sidebands or image frequencies Also the output at a particular frequency originates from multiple input frequency bands UC Berkeley EECS 242 Copyright Prof Ali M Niknejad How Low can you LO Take the simplest mixer output IF x t IF LO1 RF LO2 Low side injection High side injection Side note Which LO frequency to pick LO1 or LO2 Channel spacing No of channels Tuning range range UC Berkeley EECS 242 fLO larger implies smaller tuning Copyright Prof Ali M Niknejad Image Problem Back to the original problem RF LO IMAGE RF LO IMAGE Question Why filter before mixer in spectrum analyzer Image reject filter Channel selection Answer Image rejection IF Image reject filter LNA LO Receiver architecture is getting complicated UC Berkeley EECS 242 Copyright Prof Ali M Niknejad Origin of Image Problem If we could multiply by a complex exponential then image problem goes away IF frequency High side injection Low side injection Image Freq UC Berkeley EECS 242 Copyright Prof Ali M Niknejad Review of Linear Systems and PSD Average response of LTI system UC Berkeley EECS 242 Copyright Prof Ali M Niknejad Average Value Property DC gain UC Berkeley EECS 242 Copyright Prof Ali M Niknejad Output RMS Statistics Recall the definition for the autocorrelation function UC Berkeley EECS 242 Copyright Prof Ali M Niknejad Autocorrelation Function is a real and even function of since UC Berkeley EECS 242 is a real and even function of Copyright Prof Ali M Niknejad Autocorrelation Function 2 UC Berkeley EECS 242 Copyright Prof Ali M Niknejad Average Power in X t Consider x t as a voltage waveform with total average power Let s measure the power in x t in the band 0 1 Ideal LPF The average power in the frequency range 0 1 is now W radian W Hz UC Berkeley EECS 242 Copyright Prof Ali M Niknejad Average Power in X t 2 Generalize To measure the power in any frequency range apply an ideal bandpass filter with passband 1 2 The interpretation of xx as the power spectral density PSD is clear UC Berkeley EECS 242 Copyright Prof Ali M Niknejad Spectrum Analyzer A spectrum analyzer measures the PSD of a signal Poor man s spectrum analyzer Wide dynamic range mixer Sharp filter vertical Phase noise Sweep VCO Linear wide tuning range UC Berkeley EECS 242 generation CRT horiz Copyright Prof Ali M Niknejad EECS 242 Current Commutating Active Mixers UC Berkeley EECS 242 Copyright Prof Ali M Niknejad Balanced Mixer An unbalanced mixer has a transfer function which contains both RF LO and IF For a single balanced mixer the LO signal is balanced bipolar so we have Has DC Has DC No DC As a result the output contacts LO but no RF component For a double balanced mixer the LO and RF are balanced so there is no LO or RF leakage UC Berkeley EECS 242 Copyright Prof Ali M Niknejad Noise in an Ideal Mixers Consider the simplest ideal multiplying mixer RF IF LO Noise IF RF LO IM What s the noise figure for the conversion process Input noise power due to source is kTB where B is the bandwidth of the input signal Input signal has power Ps at either the lower or upper sideband UC Berkeley EECS 242 Copyright Prof Ali M Niknejad Noise in Ideal Mixers At the IF frequency we have the down converted signal G Ps and down converted noise from two sidebands LO IF and LO IF For ideal mixer G G G IF RF LO For a real mixer noise from multiple sidebands can fold into IF frequency degrade NF UC Berkeley EECS 242 Copyright Prof Ali M Niknejad Noise in CMOS Current Commutating Mixer After Terrovitis JSSC I1 M1 I2 M2 LO RF Assume is is small relative to IB and perform Taylor series expansion M3 vx vx 1 All current through M1 UC Berkeley EECS 242 M2 Both on