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: john@rfic.co.uk 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 + = + = t t The resulting multiplied signal will be: () ( 2 2 1 1 t . sin . t . ABsin a.b ) + + = 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 + = + = + = ) ( ) ( ) ( ) ( ) ( 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 - + + + = + + + + + = ) 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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Sheet 2 of 20 () 3(dB) Fm Fm Fm than less 3dB or half is Fm s other word in 2 LC Fm To T ie re, temperatu room At To T 1 2 LC 1 Fm Therefore, 2 LC LC , DSB For K) (273 re temperatu room To mixer, of re temperatu T Where To T 1) - (LC 1 Fm (SSB) (DSB) (SSB) (DSB) (DSB) (DSB) = = = + = = ° = = + = SSB SSB SSB DSB (3) Isolation: These parameters define how much signal leakage will occur between pairs of ports. ie RF to LO,LO to IF and RF to IF. So if for example RF to IF isolation was specified at 35dB this means that the RF at the IF port will be 35dB lower than the RF applied to RF port.
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MOS_Gilbert_Cell_Mixer - Sheet 1 of 20 Gilbert Cell Mixer...

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