3/7/2005 Mixers.doc 1/6 Jim Stiles The Univ. of Kansas Dept. of EECS Mixers A mixer is a three-port, non-linear microwave device. The three ports of a mixer are distinct and unique, and are typically referred to as: 1) The RF (Radio Frequency) port 2) The IF (Intermediate Frequency) port 3) The LO (Local Oscillator) port Q: So just what does a mixer do?? A: A clue is in its symbol: ⊗ Æ A mixer is a multiplier (×) !! RF port IF port LO port The Mixer3/7/2005 Mixers.doc 2/6 Jim Stiles The Univ. of Kansas Dept. of EECS Say there is a signal ()RFvt at the RF mixer port, and a signal ()LOvt at the LO mixer port. An ideal mixer would then produce at the IF port, a signal ()IFvt, where: () ()()RF LO IFvtv t v t= (an ideal mixer) To see why this might be useful, consider a case where: ()()RF RFRF LOvtcostvtcostωω== Multiplying these signals, we get: () ()()()()()()1122IF RF LORF LORF LO RF LOvtvtvtcos t cos tcos t cos tωωωω ωω===−++ At the IF port we have created two signals with new frequencies! One new signal has a frequency that is the difference of the LO and RF signal frequencies: ()12RF LOcos tωω−3/7/2005 Mixers.doc 3/6 Jim Stiles The Univ. of Kansas Dept. of EECS While the other new signal has a frequency that is the sum of the LO and RF signal frequencies: ()12RF LOcos tωω+ But alas, mixers are not ideal! A more accurate model of the (non-ideal) relationship between ()RFvt, ()LOvt, and ()IFvt is: () ()()() () () ()() () ()() () ()223263729541823RF RF LORF RF LIF RF LORF LO LOLOOav t av tv t av tvtavtavtav t av tv tav tv t av t=+++ ++++++" where the values an are real-valued constants. ω()Vω RF LOωω− RF LOωω+ RFω LOω3/7/2005 Mixers.doc 4/6 Jim Stiles The Univ. of Kansas Dept. of EECS Just as with an amplifier, a mixer will produce 1st-order, 2nd-order, 3rd-order, and even higher order terms! As a result, there will be many signals created at the IF port. If we did all the trigonometry, we would find that the signal frequencies created from these terms (in relation to RFω and LOω) are: 1st order: RF LO,ωω 2nd order: 22RF LO RF LO RF LO,,,ωωωωωω−+ 3rd order: 22332 2RF LO LO RF RFLO RF LO RF LO,,,,,ωω ωω ωωωωω ω−−++ examples of higher orders: 4257827 134RF LO RFLO RF LO,,,ωωωωωω−+ Note that the ideal mixer (multiplier) occurs when all constants an are zero, except for the constant a4. The result in this case being: () ()()4RIF FLOavvtv tt= (ideal mixer response) and thus the only signals created are the 2nd order terms and RF LO RF LO−+ωωωω.3/7/2005 Mixers.doc 5/6 Jim Stiles The Univ. of Kansas Dept. of EECS Of course for a “real” mixer, all the constants an are non-zero, although for good mixers all but a4 are relatively small. Thus, for good mixers, most of the signals created at the IF output will be of relatively low power, with exception of the signal at frequencies and RF LO RF LO−+ωωωω. All other signals (meaning other than and RF LO RF LO−+ωωωω) at the IF are known as spurious signals—or in the vernacular of radio engineers, “spurs”. Q: How are mixers constructed? A: Multiplication is a decidedly non-linear operation. As such, it requires non-linear devices to implement. Typically, these non-linear devices are diodes, but sometimes transistors are used. For example, as those of you who aced EECS 312 know, the junction diode equation is: ()1vDnVTsDiIe=− This non-linear function can be expanded using a Taylor series as: ()231231vDnVTsDDDDiIe bvbvbv=−=+++" DiDv+−3/7/2005 Mixers.doc 6/6 Jim Stiles The Univ. of Kansas Dept. of EECS And if, for example: ()()()RF LODvtvtvt=+ we find that the diode will create high-order terms, including () ()RF LOvtv t: () ()()() () () ()()222222RF LO RF LORF LObv t v t bv t vvtv tt+= + + Basically, generating high-order terms with any non-linear device is not at all difficult (just try and keep it from happening!). The trick is to generate only the 2nd order term () ()RF LOvtv t, while somehow suppressing the rest. Thus, mixer design is as much art as it is science! Popular designs include the balanced mixer (with 2 junction diodes), and the double balanced mixer (with 4 junction diodes). A Double-Balanced
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