MOS_Gilbert_Cell_Mixer

MOS_Gilbert_Cell_Mixer - Sheet 1 of 20 Gilbert Cell Mixer...

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Sheet 1 of 20 Gilbert Cell Mixer Design Tutorial J P Silver E-mail: [email protected] 1 ABSTRACT 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. 2 INTRODUCTION 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( b signal and ) Asin( a 2 2 1 1 φ ω φ ω + = + = t t The resulting multiplied signal will be: ( ) ( 2 2 1 1 t . sin . t . ABsin a.b ) φ ω φ ω + + = This can be multiplied out thus: ( ) ( [ ] ( ) ( ) 2 2 1 1 t . B and t . A Where B - A cos B A cos 2 1 - sinAsinB .. identity trig this Using φ ω φ ω + = + = + = ) ( ) ( ) ( ) ( ) ( ( ) [ ] ) ( ) ( ) ( ) ( ) ( ( ) [ ] 2 1 1 1 2 1 2 1 2 2 1 1 2 2 1 1 t cos t cos 2 AB - t . t . cos t . t . cos 2 AB - φ φ φ ω φ φ ω ω φ ω φ ω φ ω φ ω + + + = + + + + + = ) 3 MIXER 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 ω 1 and not the image frequency ω 1 -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: ( ) ( ) ( ) ( ) 2 LC LC ratios loss of in terms or ) ( 3 LC LC by given is loss conversion and P 2 P SSB (IF) DSB (IF) SSB DSB SSB DSB dB = = = (iii) DSB to SSB Noise Figure conversion Sum frequency (re- moved by filtering) Difference frequency ie I.F
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