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Sheet 1 of 20 Gilbert Cell Mixer Design Tutorial J P Silver E-mail: [email protected]1ABSTRACT Frequency translation in a system, is performed by a non-linear device known as a mixer. There are vari-ous topographies from simple single ended, single balanced mixers to more complicated double & triple balanced mixers that provide better isolation from the Local Oscillator (LO) and spurious. The most popular double-balanced mixer used in RFIC designs is the Gilbert Cell mixer. The design of this mixer is the subject of this paper. 2INTRODUCTION Mixers are non-linear devices used in systems to trans-late (multiply) one frequency to another. All mixer types work on the principle that a large Local Oscillator (LO) RF drive will cause switching/modulating the incoming Radio Frequency (RF) to the Intermediate Frequency (IF). The multiplication process begins by inputting two sig-nals: )Bsin(bsignaland)Asin(a2211φωφω+=+=ttThe resulting multiplied signal will be: ()(2211t.sin.t.ABsina.b)φωφω++=This can be multiplied out thus: ()(()()2211t.Bandt.A WhereB-AcosBAcos21-sinAsinB..identity trigthisUsingφωφω+=+=−+=)()()()()(())()()()()(()2111212122112211tcostcos2AB-t.t.cost.t.cos2AB-φφφωφφωωφωφωφωφω−−−−+++=+−+−+++=)3MIXER DEFINITIONS (1) Conversion Gain: This is the ratio (in dB) between the IF signal (usually the difference frequency between the RF and LO signals) and the RF signal. (2) Noise Figure: Noise figure is defined as the ratio of SNR at the IF port to the SNR of the RF port. (i) Single sideband (SSB): This assumes the only noise from the signal ω1and not the image frequency ω1-1, this would be the case if a band-pass filter was added in front of the mixer eg. RF = 1694 MHz, LO = 1557MHz to give an IF of 137MHz. Also an image IF will add to 137MHz from an RF of 1420MHz ie 1557MHz-1420MHz = 137MHz (ii) Double sideband (DSB): In DSB both side-bands are available thus it has twice as much power available at the IF port compared to the SSB signal. As a result, it’s conversion loss is 3dB less than that of an SSB signal, as shown: ()()()()2LCLCratioslossofin termsor )(3LCLCbygiven islossconversionandP2PSSB(IF)DSB(IF)SSBDSBSSBDSBdB=−==(iii) DSB to SSB Noise Figure conversion Sum frequency (re-moved by filtering) Difference frequency ie I.F
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